tag:blogger.com,1999:blog-3927035823662886342024-03-10T06:18:12.884+03:30 Executive Methods for Problem SolutionThis blog is about new ideas which give us new methods and new theorems as the tools to break complex problems in all fields such as Strategic Management, Engineering, Financial Management and so on and finally to solve these problems in the real world in which there is the balance of the cost and the time.Gholamreza Soleimanihttp://www.blogger.com/profile/03273527405719420253noreply@blogger.comBlogger135125tag:blogger.com,1999:blog-392703582366288634.post-43475260508603812192024-02-25T19:03:00.000+03:302024-02-25T19:03:28.434+03:30Your goal is to become a data analytics professional. How can you make a profession out of your present skills?<p> </p><p></p><p class="MsoNormal"><span style="font-family: "Times New Roman", "serif";">The first step is to identify the most
pressing issues, which are prevalent in many small and medium-sized businesses.
For the greatest data analysis, financial control, and other features, they all
require a system that processes raw entry data automatically.<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-family: "Times New Roman","serif"; mso-ascii-theme-font: major-bidi; mso-bidi-language: FA; mso-bidi-theme-font: major-bidi; mso-hansi-theme-font: major-bidi;">To solve many problems even when designing the
system mentioned above, you need to create a bearing or support. As a matter of
fact, your best creativity to solve a problem is to construct a support such as
the Brooklyn Bridge, a hybrid cable-stayed suspension bridge in New York City.
You can review other examples at the below links:<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-family: "Times New Roman","serif"; mso-ascii-theme-font: major-bidi; mso-bidi-language: FA; mso-bidi-theme-font: major-bidi; mso-hansi-theme-font: major-bidi;">Point (J) in article of “</span><span style="font-family: "Times New Roman","serif"; mso-ascii-theme-font: major-bidi; mso-bidi-font-family: Arial; mso-bidi-language: FA; mso-bidi-theme-font: minor-bidi; mso-hansi-theme-font: major-bidi;"><a href="https://emfps.blogspot.com/2010/10/executive-methods-for-solving-of.html">Executivemethods for solving of the problems (part 1)</a></span><span style="font-family: "Times New Roman","serif"; mso-ascii-theme-font: major-bidi; mso-bidi-font-family: Arial; mso-bidi-language: FA; mso-bidi-theme-font: minor-bidi; mso-hansi-theme-font: major-bidi;">”<o:p></o:p></span></p><p class="MsoNormal"><span class="MsoHyperlink"><span style="font-family: "Times New Roman","serif"; mso-ascii-theme-font: major-bidi; mso-bidi-language: FA; mso-bidi-theme-font: major-bidi; mso-hansi-theme-font: major-bidi;">And</span></span><span class="MsoHyperlink"><span style="color: windowtext; font-family: "Times New Roman", "serif";"> </span></span><span class="MsoHyperlink"><span style="font-family: "Times New Roman","serif"; mso-ascii-theme-font: major-bidi; mso-bidi-language: FA; mso-bidi-theme-font: major-bidi; mso-hansi-theme-font: major-bidi;">article of “</span></span><span style="font-family: "Times New Roman","serif"; mso-ascii-theme-font: major-bidi; mso-bidi-font-family: Arial; mso-bidi-language: FA; mso-bidi-theme-font: minor-bidi; mso-hansi-theme-font: major-bidi;"><a href="https://emfps.blogspot.com/2011/01/supporter-systems-sleepers-in-nature.html">TheSupporter Systems (sleepers) in the Nature for Tunneling</a></span><span style="font-family: "Times New Roman","serif"; mso-ascii-theme-font: major-bidi; mso-bidi-font-family: Arial; mso-bidi-language: FA; mso-bidi-theme-font: minor-bidi; mso-hansi-theme-font: major-bidi;">”<o:p></o:p></span></p><p class="MsoNormal"><span style="font-family: "Times New Roman", "serif";">The most important support for designing a
system is a trustworthy database. The next step is to create independent
supports by going to empty space outside of the system. For instance, in
Microsoft Excel, you can add new columns between raw entry data and use nested
IF statements, ideally forming your raw data.<b><o:p></o:p></b></span></p><p class="MsoNormal"><span style="font-family: "Times New Roman","serif"; mso-ascii-theme-font: major-bidi; mso-bidi-font-family: Arial; mso-bidi-language: FA; mso-bidi-theme-font: minor-bidi; mso-hansi-theme-font: major-bidi;"><br /></span></p><p class="MsoNormal"><span style="font-family: "Times New Roman","serif"; mso-ascii-theme-font: major-bidi; mso-bidi-font-family: Arial; mso-bidi-language: FA; mso-bidi-theme-font: minor-bidi; mso-hansi-theme-font: major-bidi;"><br /></span></p><br /><p></p>Gholamreza Soleimanihttp://www.blogger.com/profile/03273527405719420253noreply@blogger.com0tag:blogger.com,1999:blog-392703582366288634.post-12556281696821683532023-11-22T21:33:00.000+03:302023-11-22T21:33:01.623+03:30مدل آنالیز طراحی شده با اکسل : راس گیری فاکتور وچک همزمان برای تا 200 مشتری<p class="MsoNormal" dir="rtl" style="text-align: right; unicode-bidi: embed;"></p><p class="MsoNormal" dir="rtl" style="text-align: right; unicode-bidi: embed;"><span lang="FA" style="font-family: "B Nazanin"; font-size: 12.0pt; line-height: 115%; mso-bidi-language: FA;">در زنجیره تامین</span><span dir="LTR"></span><span dir="LTR"></span><span dir="LTR" style="font-size: 12.0pt; line-height: 115%; mso-bidi-font-family: "B Nazanin"; mso-bidi-language: FA;"><span dir="LTR"></span><span dir="LTR"></span>,</span><span dir="RTL"></span><span dir="RTL"></span><span lang="FA" style="font-family: "B Nazanin"; font-size: 12.0pt; line-height: 115%; mso-bidi-language: FA;"><span dir="RTL"></span><span dir="RTL"></span> خصوصا شرکت های پخش و هلدینگ ها همراه با زیر مجموعه هایی شامل
تولید </span><span lang="FA" style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%; mso-bidi-language: FA;">–</span><span lang="FA" style="font-family: "B Nazanin"; font-size: 12.0pt; line-height: 115%; mso-bidi-language: FA;"> بازرگانی- توزیع و همچنین شرکت های تولیدی که محصول نهایی آنها بعنوان بخشی
از مواد اولیه شرکت های تولیدی دیگر استفاده میگردد</span><span dir="LTR"></span><span dir="LTR"></span><span dir="LTR" style="font-size: 12.0pt; line-height: 115%; mso-bidi-font-family: "B Nazanin"; mso-bidi-language: FA;"><span dir="LTR"></span><span dir="LTR"></span>,</span><span dir="RTL"></span><span dir="RTL"></span><span style="font-family: "B Nazanin"; font-size: 12.0pt; line-height: 115%; mso-bidi-language: FA;"><span dir="RTL"></span><span dir="RTL"></span> <span lang="FA">معمولا دارای
مشتریان زیاد (تامین کننده و خریدار) از صنایع گوناگون میباشند. از طرفی با توجه
به گردش مالی بسیار بالا</span></span><span dir="LTR"></span><span dir="LTR"></span><span dir="LTR" style="font-size: 12.0pt; line-height: 115%; mso-bidi-font-family: "B Nazanin"; mso-bidi-language: FA;"><span dir="LTR"></span><span dir="LTR"></span>,</span><span dir="RTL"></span><span dir="RTL"></span><span lang="FA" style="font-family: "B Nazanin"; font-size: 12.0pt; line-height: 115%; mso-bidi-language: FA;"><span dir="RTL"></span><span dir="RTL"></span> مجبور به دریافت و پرداخت های اسنادی و موعدی هستند. یکی از
مهمترین راههای سنجش رفتار مالی مشتریانی که جهت بدهی خود چک (اسناد پرداختنی
موعدی) تحویل میدهند</span><span dir="LTR"></span><span dir="LTR"></span><span dir="LTR" style="font-size: 12.0pt; line-height: 115%; mso-bidi-font-family: "B Nazanin"; mso-bidi-language: FA;"><span dir="LTR"></span><span dir="LTR"></span> ,</span><span lang="FA" style="font-family: "B Nazanin"; font-size: 12.0pt; line-height: 115%; mso-bidi-language: FA;">استفاده از راس گیری فاکتور و چک میباشد. <o:p></o:p></span></p>
<p class="MsoNormal" dir="rtl" style="text-align: right; unicode-bidi: embed;"><span lang="FA" style="font-family: "B Nazanin"; font-size: 12.0pt; line-height: 115%; mso-bidi-language: FA;">این مدل آنالیز</span><span dir="LTR"></span><span dir="LTR"></span><span dir="LTR" style="font-size: 12.0pt; line-height: 115%; mso-bidi-font-family: "B Nazanin"; mso-bidi-language: FA;"><span dir="LTR"></span><span dir="LTR"></span>,</span><span dir="RTL"></span><span dir="RTL"></span><span lang="FA" style="font-family: "B Nazanin"; font-size: 12.0pt; line-height: 115%; mso-bidi-language: FA;"><span dir="RTL"></span><span dir="RTL"></span> فرصتی را برای مدیران و تصمیم گیران شرکتها ایجاد میکند تا بطور
همزمان بتوانند راس محاسبه شده برای فاکتورها و چک ها را تا 200 مشتری و برای
حداکثر یک دوره سه ماهه فقط روی یک صفحه اکسل (یا در فرمت </span><span dir="LTR"></span><span dir="LTR"></span><span dir="LTR" style="font-size: 12.0pt; line-height: 115%; mso-bidi-font-family: "B Nazanin"; mso-bidi-language: FA;"><span dir="LTR"></span><span dir="LTR"></span><span style="mso-spacerun: yes;"> </span>pdf</span><span lang="FA" style="font-family: "B Nazanin"; font-size: 12.0pt; line-height: 115%; mso-bidi-language: FA;">و قابل پرینت) بصورت داشبورد مدیریتی مشاهده و کنترل نمایند. <o:p></o:p></span></p>
<p class="MsoNormal" dir="rtl" style="text-align: right; unicode-bidi: embed;"><span lang="FA" style="font-family: "B Nazanin"; font-size: 12.0pt; line-height: 115%; mso-bidi-language: FA;">ضمنا در این مدل مشکل جمع و تفریق تاریخ های شمسی کاملا
مرتفع شده بطوریکه بدون استفاده از کدهای </span><span dir="LTR" style="font-size: 12.0pt; line-height: 115%; mso-bidi-font-family: "B Nazanin"; mso-bidi-language: FA;">VBA</span><span dir="RTL"></span><span dir="RTL"></span><span lang="FA" style="font-family: "B Nazanin"; font-size: 12.0pt; line-height: 115%; mso-bidi-language: FA;"><span dir="RTL"></span><span dir="RTL"></span> و تعریف ماژول های جدید</span><span dir="LTR"></span><span dir="LTR"></span><span dir="LTR" style="font-size: 12.0pt; line-height: 115%; mso-bidi-font-family: "B Nazanin"; mso-bidi-language: FA;"><span dir="LTR"></span><span dir="LTR"></span>,</span><span dir="RTL"></span><span dir="RTL"></span><span style="font-family: "B Nazanin"; font-size: 12.0pt; line-height: 115%; mso-bidi-language: FA;"><span dir="RTL"></span><span dir="RTL"></span> <span lang="FA">شما قادر خواهید
بود هر دو عملیات جمع و تقریق را دقیقا مشابه تقویم میلادی دراکسل محاسبه نمایید. <o:p></o:p></span></span></p>
<p class="MsoNormal" dir="rtl" style="text-align: right; unicode-bidi: embed;"><b><span lang="FA" style="font-family: "B Nazanin"; font-size: 12.0pt; line-height: 115%; mso-bidi-language: FA;">راس گیری فاکتور وچک <o:p></o:p></span></b></p>
<p class="MsoNormal" dir="rtl" style="text-align: right; unicode-bidi: embed;"><span lang="FA" style="font-family: "B Nazanin"; font-size: 12.0pt; line-height: 115%; mso-bidi-language: FA;">راس گیری چک</span><span dir="LTR"></span><span dir="LTR"></span><span dir="LTR" style="font-size: 12.0pt; line-height: 115%; mso-bidi-font-family: "B Nazanin"; mso-bidi-language: FA;"><span dir="LTR"></span><span dir="LTR"></span>,</span><span dir="RTL"></span><span dir="RTL"></span><span style="font-family: "B Nazanin"; font-size: 12.0pt; line-height: 115%; mso-bidi-language: FA;"><span dir="RTL"></span><span dir="RTL"></span> <span lang="FA">محاسبه میانگین وزنی برای رسیدن به یک زمان واحد
وصول از میان تعدادی چک صادر شده در زمان های مختلف میباشد.<o:p></o:p></span></span></p>
<p class="MsoNormal" dir="rtl" style="text-align: right; unicode-bidi: embed;"><span lang="FA" style="font-family: "B Nazanin"; font-size: 12.0pt; line-height: 115%; mso-bidi-language: FA;"><span style="mso-spacerun: yes;"> </span>اما گاهی اوقات
مشتری برای چندین فاکتور صادر شده در زمانهای مختلف</span><span dir="LTR"></span><span dir="LTR"></span><span dir="LTR" style="font-size: 12.0pt; line-height: 115%; mso-bidi-font-family: "B Nazanin"; mso-bidi-language: FA;"><span dir="LTR"></span><span dir="LTR"></span>,</span><span dir="RTL"></span><span dir="RTL"></span><span lang="FA" style="font-family: "B Nazanin"; font-size: 12.0pt; line-height: 115%; mso-bidi-language: FA;"><span dir="RTL"></span><span dir="RTL"></span> چندین فقره چک با تاریخهای وصول
متفاوت تحویل میدهد. در این حالت ما نیاز داریم اول راس فاکتور ها را محاسبه نموده
بطوریکه این زمان راس بعنوان مبدا زمانی محاسبه راس چکها در نظر گرفته خواهد شد.
سپس راس زمانی چکها را محاسبه نماییم. <o:p></o:p></span></p><p class="MsoNormal" dir="rtl" style="text-align: right; unicode-bidi: embed;"><span lang="FA" style="font-family: "B Nazanin"; font-size: 12.0pt; line-height: 115%; mso-bidi-language: FA;">بعنوان مثال: فرض کنیم مشتری </span><span dir="LTR" style="font-size: 12.0pt; line-height: 115%; mso-bidi-font-family: "B Nazanin"; mso-bidi-language: FA;">X</span><span dir="RTL"></span><span dir="RTL"></span><span lang="FA" style="font-family: "B Nazanin"; font-size: 12.0pt; line-height: 115%; mso-bidi-language: FA;"><span dir="RTL"></span><span dir="RTL"></span> در زمانهای
مختلف از ما خرید نموده و شش فاکتور برای او بشرح زیر صادر شده است:<o:p></o:p></span></p><div dir="rtl" style="text-align: right;"><br /></div><p dir="rtl" style="text-align: right;"></p><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhy50XWH50Kv7uZB5YnQJ7KFIT4EzG2iKo_pjVCsYD-vC9LPve7N-N9zg9V0wPbHAAO4S8BKS0XbCLLxL-uLzGpmY4yIIh-U8BDUgS7RJ9pJ_b1e1f5ys_1qIqUL5rIQsLFXK_BP1IYfdiFlDo8hiZZpCGwbwhNrFk7vLaF8JLjsyRx7uVxBSEgfVBL_-c/s672/1_1.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="251" data-original-width="672" height="120" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhy50XWH50Kv7uZB5YnQJ7KFIT4EzG2iKo_pjVCsYD-vC9LPve7N-N9zg9V0wPbHAAO4S8BKS0XbCLLxL-uLzGpmY4yIIh-U8BDUgS7RJ9pJ_b1e1f5ys_1qIqUL5rIQsLFXK_BP1IYfdiFlDo8hiZZpCGwbwhNrFk7vLaF8JLjsyRx7uVxBSEgfVBL_-c/s320/1_1.png" width="320" /></a></div><br /><div class="separator" style="clear: both; text-align: center;"><br /></div><br /><div class="separator" dir="rtl" style="clear: both; text-align: right;"><br /></div><div dir="rtl" style="text-align: right;"><p class="MsoNormal" style="text-align: right; unicode-bidi: embed;"><span lang="FA" style="font-family: "B Nazanin"; font-size: 12pt; line-height: 115%;">همانطور که مشاهده می کنید</span><span dir="LTR"></span><span dir="LTR"></span><span dir="LTR" style="font-size: 12pt; line-height: 115%;"><span dir="LTR"></span><span dir="LTR"></span>,</span><span dir="RTL"></span><span dir="RTL"></span><span lang="FA" style="font-family: "B Nazanin"; font-size: 12pt; line-height: 115%;"><span dir="RTL"></span><span dir="RTL"></span> مبدا زمانی کلیه فاکتورها تاریخ
03/02/1400 میباشد. حالا باید فاصله زمانی هر فاکتور را از این مبدا بدست آورده و
در مبلغ فاکتور (بستانکاری) ضرب نماییم:</span></p></div><div dir="rtl" style="text-align: right;"><p class="MsoNormal" dir="RTL" style="direction: rtl; unicode-bidi: embed;"></p><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjj6NzBNKJXZTEQ8Zc6REKiu1n-FgzIkhj2gS6lnZUKlyLzjveVP9SD-A4jAkgmQC5kgMFx9Rg-EVol86JVJ9z2Tt8yWx_vUtO7FsoY8vPVgN3B2kiS84ncoygvg3K8xBRtOUnah1ykdXJPJBl6aEIRff8Vourj4VMULXsv91VAzKhapC6gjMVZei-pNDo/s494/1_1_1.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="422" data-original-width="494" height="273" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjj6NzBNKJXZTEQ8Zc6REKiu1n-FgzIkhj2gS6lnZUKlyLzjveVP9SD-A4jAkgmQC5kgMFx9Rg-EVol86JVJ9z2Tt8yWx_vUtO7FsoY8vPVgN3B2kiS84ncoygvg3K8xBRtOUnah1ykdXJPJBl6aEIRff8Vourj4VMULXsv91VAzKhapC6gjMVZei-pNDo/s320/1_1_1.png" width="320" /></a></div><br /><span lang="FA" style="font-family: "B Nazanin"; font-size: 12.0pt; line-height: 115%; mso-bidi-language: FA;"></span><p></p><p class="MsoNormal" dir="RTL" style="direction: rtl; unicode-bidi: embed;"><span lang="FA" style="font-family: "B Nazanin"; font-size: 12.0pt; line-height: 115%; mso-bidi-language: FA;">در این مرحله نتایج را با هم جمع می کنیم:<o:p></o:p></span></p><p class="MsoNormal" dir="RTL" style="direction: rtl; unicode-bidi: embed;"></p><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjw3Ap7stgH3Jmnn4J0O6xW6wIi3FjaqRtCyRkaoMuwckyZueAzPD1HDTKNwTXjlkbp1V_1I6-uO3b-LNZiunFCFW5mz5lkbMacoiz3LvLLX8IM0BgkFs8eAAZownb1r2dtbaIIoiVUwNKWW5YDSZJP8UZAHZctUkUtKpTs5-nmVjp1H08Q81YZeOOpHlM/s1089/1_1_2.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="66" data-original-width="1089" height="19" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjw3Ap7stgH3Jmnn4J0O6xW6wIi3FjaqRtCyRkaoMuwckyZueAzPD1HDTKNwTXjlkbp1V_1I6-uO3b-LNZiunFCFW5mz5lkbMacoiz3LvLLX8IM0BgkFs8eAAZownb1r2dtbaIIoiVUwNKWW5YDSZJP8UZAHZctUkUtKpTs5-nmVjp1H08Q81YZeOOpHlM/s320/1_1_2.png" width="320" /></a></div><br /><span lang="FA" style="font-family: "B Nazanin"; font-size: 12.0pt; line-height: 115%; mso-bidi-language: FA;"><span dir="RTL" lang="FA" style="font-size: 12pt; line-height: 115%;">سپس
جمع حاصل را بر جمع کل مبلغ فاکتور ها تقسیم می کنیم:</span></span><p></p><p class="MsoNormal" dir="RTL" style="direction: rtl; unicode-bidi: embed;"><span lang="FA" style="font-family: "B Nazanin"; font-size: 12.0pt; line-height: 115%; mso-bidi-language: FA;"></span></p><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEi3n-uhthUyPP7um_Bo3Yo1lV_JsZJAnu5AQVRnm4yCmDgDANMUHHlPIxG7wWaGkg9Z_aM4MMN7RJYJ6napo91Cr2nc0uPfVcadCv8mGBNQqs7Kt0N7X8b_JWHOOoBi2254MStqu1ZMWH_OZ3VKaTNm6zos-Pnah_6WaGSBgOZag6PPD3tBpAL6AMufBWk/s474/1_1_3.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="100" data-original-width="474" height="68" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEi3n-uhthUyPP7um_Bo3Yo1lV_JsZJAnu5AQVRnm4yCmDgDANMUHHlPIxG7wWaGkg9Z_aM4MMN7RJYJ6napo91Cr2nc0uPfVcadCv8mGBNQqs7Kt0N7X8b_JWHOOoBi2254MStqu1ZMWH_OZ3VKaTNm6zos-Pnah_6WaGSBgOZag6PPD3tBpAL6AMufBWk/s320/1_1_3.png" width="320" /></a></div><p></p><p class="MsoNormal" dir="RTL" style="direction: rtl; unicode-bidi: embed;"><span lang="FA" style="font-family: "B Nazanin"; font-size: 12.0pt; line-height: 115%; mso-bidi-language: FA;">در نتیجه راس زمانی فاکتور ها برابر 27 روز است که اگر به
مبدا زمان اضافه نماییم</span><span dir="LTR"></span><span dir="LTR"></span><span dir="LTR" style="font-size: 12.0pt; line-height: 115%; mso-bidi-font-family: "B Nazanin"; mso-bidi-language: FA;"><span dir="LTR"></span><span dir="LTR"></span>,</span><span dir="RTL"></span><span dir="RTL"></span><span lang="FA" style="font-family: "B Nazanin"; font-size: 12.0pt; line-height: 115%; mso-bidi-language: FA;"><span dir="RTL"></span><span dir="RTL"></span> تاریخ مبدا برای محاسبه راس چکها معادل 30/02//1400 خواهد بود.<o:p></o:p></span></p><p class="MsoNormal" dir="RTL" style="direction: rtl; unicode-bidi: embed;"><span lang="FA" style="font-family: "B Nazanin"; font-size: 12.0pt; line-height: 115%; mso-bidi-language: FA;">این تاریخ راس فاکتورها بعنوان مبدا زمانی جهت محاسبه راس
چکها در نظر گرفته میشود.<o:p></o:p></span></p><p class="MsoNormal" dir="RTL" style="direction: rtl; unicode-bidi: embed;"><span lang="FA" style="font-family: "B Nazanin"; font-size: 12.0pt; line-height: 115%; mso-bidi-language: FA;"><span dir="RTL" lang="FA" style="font-size: 12pt; line-height: 115%;">
<span dir="RTL" lang="FA" style="font-size: 12pt; line-height: 115%;">حالا فرض کنیم مشتری </span><span style="font-family: "Calibri","sans-serif"; font-size: 12.0pt; line-height: 115%; mso-ansi-language: EN-US; mso-ascii-theme-font: minor-latin; mso-bidi-font-family: "B Nazanin"; mso-bidi-language: FA; mso-fareast-font-family: Calibri; mso-fareast-language: EN-US; mso-fareast-theme-font: minor-latin; mso-hansi-theme-font: minor-latin;">X</span><span dir="RTL"></span><span dir="RTL"></span><span dir="RTL" lang="FA" style="font-size: 12pt; line-height: 115%;"><span dir="RTL"></span><span dir="RTL"></span> جهت تسویه فاکتورها</span><span dir="LTR"></span><span dir="LTR"></span><span style="font-family: "Calibri","sans-serif"; font-size: 12.0pt; line-height: 115%; mso-ansi-language: EN-US; mso-ascii-theme-font: minor-latin; mso-bidi-font-family: "B Nazanin"; mso-bidi-language: FA; mso-fareast-font-family: Calibri; mso-fareast-language: EN-US; mso-fareast-theme-font: minor-latin; mso-hansi-theme-font: minor-latin;"><span dir="LTR"></span><span dir="LTR"></span>,</span><span dir="RTL"></span><span dir="RTL"></span><span dir="RTL" style="font-size: 12pt; line-height: 115%;"><span dir="RTL"></span><span dir="RTL"></span> <span lang="FA">تعداد 5 فقره چک بشرح زیر تحویل میدهد:</span></span></span></span></p><p class="MsoNormal" dir="RTL" style="direction: rtl; unicode-bidi: embed;"><span lang="FA" style="font-family: "B Nazanin"; font-size: 12.0pt; line-height: 115%; mso-bidi-language: FA;"><span dir="RTL" lang="FA" style="font-size: 12pt; line-height: 115%;"><span dir="RTL" style="font-size: 12pt; line-height: 115%;"></span></span></span></p><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgBqqVbOo-JQKnMrpcAoSRb5oNWwOLaWnJQJnbgnEk53bH7g4l6TlWvkUXlvEunvdox2Tbq6uAgefdwwWlx2KNDZ-rgvGDVj8GQrbE4PVV_XGV_qZdS2OvzuQMSlM0dRtdhcCijnGAyeJ2OmmWEzJ-Y8bZ8gh0BpMrrFKOXtTfcQSXsg5u3HqCfkSHTsac/s498/1_2.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="220" data-original-width="498" height="141" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgBqqVbOo-JQKnMrpcAoSRb5oNWwOLaWnJQJnbgnEk53bH7g4l6TlWvkUXlvEunvdox2Tbq6uAgefdwwWlx2KNDZ-rgvGDVj8GQrbE4PVV_XGV_qZdS2OvzuQMSlM0dRtdhcCijnGAyeJ2OmmWEzJ-Y8bZ8gh0BpMrrFKOXtTfcQSXsg5u3HqCfkSHTsac/s320/1_2.png" width="320" /></a></div><br /><span lang="FA"></span><p></p><p class="MsoNormal" dir="RTL" style="direction: rtl; unicode-bidi: embed;"><span lang="FA" style="font-family: "B Nazanin"; font-size: 12.0pt; line-height: 115%; mso-bidi-language: FA;">دقیقا شبیه به محاسبه راس فاکتورها</span><span dir="LTR"></span><span dir="LTR"></span><span dir="LTR" style="font-size: 12.0pt; line-height: 115%; mso-bidi-font-family: "B Nazanin"; mso-bidi-language: FA;"><span dir="LTR"></span><span dir="LTR"></span>,</span><span dir="RTL"></span><span dir="RTL"></span><span lang="FA" style="font-family: "B Nazanin"; font-size: 12.0pt; line-height: 115%; mso-bidi-language: FA;"><span dir="RTL"></span><span dir="RTL"></span> فاصله زمانی چکها را از تاریخ
مبدا (تاریخ راس فاکتورها) محاسبه نموده و در مبلغ چکها ضرب می کنیم:<o:p></o:p></span></p><p class="MsoNormal" dir="RTL" style="direction: rtl; unicode-bidi: embed;"></p><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEj2mSeV2QZuL4-WgPZSAtHCimDCTiT2DT-W1EbBzb5ZeAdtwFYx2HNKF5mwkJDHKqKSz5bTbJSKPYpQbIRQOjAKZhzKMVfA5GaEJTiFLZyCmu6Yts99pybx8IsOK4ZV4fRZhzBEMr42OpukmjHJ2-eaVy0Q2-umDeXno8CMxVBhshj2GJgDDAX1UbhT3W8/s595/1_2_1.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="410" data-original-width="595" height="221" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEj2mSeV2QZuL4-WgPZSAtHCimDCTiT2DT-W1EbBzb5ZeAdtwFYx2HNKF5mwkJDHKqKSz5bTbJSKPYpQbIRQOjAKZhzKMVfA5GaEJTiFLZyCmu6Yts99pybx8IsOK4ZV4fRZhzBEMr42OpukmjHJ2-eaVy0Q2-umDeXno8CMxVBhshj2GJgDDAX1UbhT3W8/s320/1_2_1.png" width="320" /></a></div><span dir="RTL" lang="FA" style="font-family: "B Nazanin"; font-size: 12.0pt; line-height: 115%; mso-ansi-language: EN-US; mso-ascii-font-family: Calibri; mso-ascii-theme-font: minor-latin; mso-bidi-language: FA; mso-fareast-font-family: Calibri; mso-fareast-language: EN-US; mso-fareast-theme-font: minor-latin; mso-hansi-font-family: Calibri; mso-hansi-theme-font: minor-latin;">سپس
نتایج بدست امده را جمع می کنیم:</span><p></p><p class="MsoNormal" dir="RTL" style="direction: rtl; unicode-bidi: embed;"></p><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEieb3dImJyUXc4bLC0Cr3-Ixa20rGGzyugeZNBcNOpJP-zKjTWBSRz0foZRdDT38RVcaQ0cZOjiI8OMJYsGlFd28j4pxaKg4rq6l0mPHw6NE7zwP6b-2ewh8_mmuD4w0d88xnPBUr_Ly1b5IWYndFs6-rlW1p7FVaBzwRHZ5s5UmRtQf6OHQn6OY-EuB1E/s1008/1_2_2.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="59" data-original-width="1008" height="19" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEieb3dImJyUXc4bLC0Cr3-Ixa20rGGzyugeZNBcNOpJP-zKjTWBSRz0foZRdDT38RVcaQ0cZOjiI8OMJYsGlFd28j4pxaKg4rq6l0mPHw6NE7zwP6b-2ewh8_mmuD4w0d88xnPBUr_Ly1b5IWYndFs6-rlW1p7FVaBzwRHZ5s5UmRtQf6OHQn6OY-EuB1E/s320/1_2_2.png" width="320" /></a></div><p></p><p class="MsoNormal" dir="RTL" style="direction: rtl; unicode-bidi: embed;"><span lang="FA" style="font-family: "B Nazanin"; font-size: 12.0pt; line-height: 115%; mso-bidi-language: FA;">و عدد حاصله را
بر جمع کل مبلغ چکها تقسیم می نماییم:<o:p></o:p></span></p><p class="MsoNormal" dir="RTL" style="direction: rtl; unicode-bidi: embed;"></p><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEi08ogrs5ntAmuoLW8TK4B0MHlSIlNU8AMygDo-9yNorySFumTsO1SkXsHsqk6tomAJh9IMBiKbOdiiodlrAVI2P7juazMhtGh6RN1XHwY4vOE7P_9YFU0KYzSv36xpczMmQdxyNG6wtyhGFqGTpd7r8IONAjfE1L-W5Y1v0Uiqv5t2llri5XstT1FF7SE/s391/1_2_3.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="84" data-original-width="391" height="69" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEi08ogrs5ntAmuoLW8TK4B0MHlSIlNU8AMygDo-9yNorySFumTsO1SkXsHsqk6tomAJh9IMBiKbOdiiodlrAVI2P7juazMhtGh6RN1XHwY4vOE7P_9YFU0KYzSv36xpczMmQdxyNG6wtyhGFqGTpd7r8IONAjfE1L-W5Y1v0Uiqv5t2llri5XstT1FF7SE/s320/1_2_3.png" width="320" /></a></div><p class="MsoNormal" dir="RTL" style="direction: rtl; unicode-bidi: embed;"><span lang="FA" style="font-family: "B Nazanin"; font-size: 12.0pt; line-height: 115%; mso-bidi-language: FA;">در نتیجه راس چکها
برابر 209 روز است که اگر به مبدا زمان اضافه نماییم</span><span dir="LTR"></span><span dir="LTR"></span><span dir="LTR" style="font-size: 12.0pt; line-height: 115%; mso-bidi-font-family: "B Nazanin"; mso-bidi-language: FA;"><span dir="LTR"></span><span dir="LTR"></span>,</span><span dir="RTL"></span><span dir="RTL"></span><span lang="FA" style="font-family: "B Nazanin"; font-size: 12.0pt; line-height: 115%; mso-bidi-language: FA;"><span dir="RTL"></span><span dir="RTL"></span> تاریخ راس چکها برابر 24/09//1400
خواهد بود.<o:p></o:p></span></p>
<p class="MsoNormal" dir="RTL" style="direction: rtl; unicode-bidi: embed;"><span lang="FA" style="font-family: "B Nazanin"; font-size: 12.0pt; line-height: 115%; mso-bidi-language: FA;">حال فرض کنیم نرخ
بهره سالیانه مورد توافق طرقین معادل 36 در صد باشد</span><span dir="LTR"></span><span dir="LTR"></span><span dir="LTR" style="font-size: 12.0pt; line-height: 115%; mso-bidi-font-family: "B Nazanin"; mso-bidi-language: FA;"><span dir="LTR"></span><span dir="LTR"></span>,</span><span dir="RTL"></span><span dir="RTL"></span><span lang="FA" style="font-family: "B Nazanin"; font-size: 12.0pt; line-height: 115%; mso-bidi-language: FA;"><span dir="RTL"></span><span dir="RTL"></span> میزان سودی که مشتری </span><span dir="LTR" style="font-size: 12.0pt; line-height: 115%; mso-bidi-font-family: "B Nazanin"; mso-bidi-language: FA;">X</span><span dir="RTL"></span><span dir="RTL"></span><span lang="FA" style="font-family: "B Nazanin"; font-size: 12.0pt; line-height: 115%; mso-bidi-language: FA;"><span dir="RTL"></span><span dir="RTL"></span> خواهد پرداخت
بشرح زیر محاسبه میگردد:<o:p></o:p></span></p><p class="MsoNormal" dir="RTL" style="direction: rtl; unicode-bidi: embed;"></p><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEigcT0gAxyiSLa_p6Skhu600l7sNhFHucIVX3laUCeImHdbQgiv5HkF0CUFkQLx5hedRF5CVk2Tv5SmQAplfymqmW40F1P2QG_eSyCl2-SI6uHbTRmy5dgRYaCfUIy8cgx3h_CpL6n7j9T_PVcafIcAZ1n2J7A1qibTYx8-ytHgZC_fJh8cKcoSdKboa_I/s893/1_2_4.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="96" data-original-width="893" height="34" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEigcT0gAxyiSLa_p6Skhu600l7sNhFHucIVX3laUCeImHdbQgiv5HkF0CUFkQLx5hedRF5CVk2Tv5SmQAplfymqmW40F1P2QG_eSyCl2-SI6uHbTRmy5dgRYaCfUIy8cgx3h_CpL6n7j9T_PVcafIcAZ1n2J7A1qibTYx8-ytHgZC_fJh8cKcoSdKboa_I/s320/1_2_4.png" width="320" /></a></div><br /><span lang="FA" style="font-family: "B Nazanin"; font-size: 12.0pt; line-height: 115%; mso-bidi-language: FA;"></span><p></p><p class="MsoNormal" dir="RTL" style="direction: rtl; unicode-bidi: embed;"><span lang="FA" style="font-family: "B Nazanin"; font-size: 12.0pt; line-height: 115%; mso-bidi-language: FA;">در نتیجه کل مبلغ
پرداختی مشتری </span><span dir="LTR" style="font-size: 12.0pt; line-height: 115%; mso-bidi-font-family: "B Nazanin"; mso-bidi-language: FA;">X</span><span dir="RTL"></span><span dir="RTL"></span><span lang="FA" style="font-family: "B Nazanin"; font-size: 12.0pt; line-height: 115%; mso-bidi-language: FA;"><span dir="RTL"></span><span dir="RTL"></span> برابر خواهد شد با:<o:p></o:p></span></p><p class="MsoNormal" dir="RTL" style="direction: rtl; unicode-bidi: embed;"></p><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjrIY_n9fdM0pINP7YV28PHuE0qMCmHl7BEmTnGEF63Rn_8OZ7bfkAW7STXLN7rT9ma7rvfGfSHFTb1nN1L8LX8giCQ74zXMJpIJ3qLD5D7V_ZOY1mV13eocDDhpgeTq_lfJgBt7VPDqP-z5FSKcFNDeWDzQ_ehpE2v9rMWeVU2RUXlgQTJbO6kxxKvM8I/s685/1_2_5.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="87" data-original-width="685" height="41" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjrIY_n9fdM0pINP7YV28PHuE0qMCmHl7BEmTnGEF63Rn_8OZ7bfkAW7STXLN7rT9ma7rvfGfSHFTb1nN1L8LX8giCQ74zXMJpIJ3qLD5D7V_ZOY1mV13eocDDhpgeTq_lfJgBt7VPDqP-z5FSKcFNDeWDzQ_ehpE2v9rMWeVU2RUXlgQTJbO6kxxKvM8I/s320/1_2_5.png" width="320" /></a></div><p></p><p class="MsoNormal" dir="RTL" style="direction: rtl; unicode-bidi: embed;"><b><span lang="FA" style="font-family: "B Nazanin"; font-size: 12.0pt; line-height: 115%; mso-bidi-language: FA;">راس گیری فاکتور وچک همزمان
برای تا 200 مشتری<o:p></o:p></span></b></p><p class="MsoNormal" dir="RTL" style="direction: rtl; unicode-bidi: embed;"><span lang="FA" style="font-family: "B Nazanin"; font-size: 12.0pt; line-height: 115%; mso-bidi-language: FA;">در این مدل آنالیز طراحی شده با
اکسل</span><span dir="LTR"></span><span dir="LTR"></span><span dir="LTR" style="font-size: 12.0pt; line-height: 115%; mso-bidi-font-family: "B Nazanin"; mso-bidi-language: FA;"><span dir="LTR"></span><span dir="LTR"></span>,</span><span dir="RTL"></span><span dir="RTL"></span><span lang="FA" style="font-family: "B Nazanin"; font-size: 12.0pt; line-height: 115%; mso-bidi-language: FA;"><span dir="RTL"></span><span dir="RTL"></span> شما قادر خواهید بود تا همزمان برای 200 مشتری در طول یک دوره سه
ماهه راس چک برای همه مشتریان را روی یک صفحه اکسل بصورت یک داشبورد مدیریتی بررسی
و کنترل نمایید.<o:p></o:p></span></p><p class="MsoNormal" dir="RTL" style="direction: rtl; unicode-bidi: embed;"><b><span lang="FA" style="font-family: "B Nazanin"; font-size: 12.0pt; line-height: 115%; mso-bidi-language: FA;">روش استفاده از این مدل گام
به گام و بترتیب در ادامه می آید:<o:p></o:p></span></b></p><p class="MsoNormal" dir="RTL" style="direction: rtl; unicode-bidi: embed;"><span lang="FA" style="font-family: "B Nazanin"; font-size: 12.0pt; line-height: 115%; mso-bidi-language: FA;">1. از نرم افزار حسابداری</span><span dir="LTR"></span><span dir="LTR"></span><span dir="LTR" style="font-size: 12.0pt; line-height: 115%; mso-bidi-font-family: "B Nazanin"; mso-bidi-language: FA;"><span dir="LTR"></span><span dir="LTR"></span>,</span><span dir="RTL"></span><span dir="RTL"></span><span lang="FA" style="font-family: "B Nazanin"; font-size: 12.0pt; line-height: 115%; mso-bidi-language: FA;"><span dir="RTL"></span><span dir="RTL"></span> لیست نام کلیه
مشتریان را روی اکسل خروجی گرفته و در شیت </span><span dir="LTR" style="font-size: 12.0pt; line-height: 115%; mso-bidi-font-family: "B Nazanin"; mso-bidi-language: FA;">Data Base</span><span dir="RTL"></span><span dir="RTL"></span><span lang="FA" style="font-family: "B Nazanin"; font-size: 12.0pt; line-height: 115%; mso-bidi-language: FA;"><span dir="RTL"></span><span dir="RTL"></span> این مدل وارد می کنیم<o:p></o:p></span></p><p class="MsoNormal" dir="RTL" style="direction: rtl; unicode-bidi: embed;"></p><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh-IS5ZQVW5h08AQzRpjKTaVJgPb7kpmh5i2iLiAWmDnc9fZ6AOaQqegA9HvOGj3wLgEtsGUUcpRbJH9gMOIxcw5T1oUwspdVnjvvIEZQIu0wJ3fJ2Hm9soLY53rwgknjkjTSRMtqNPhoOuJAV0NFk0psPNpvtkKx1LxajKJ1T7-WEG26L15oBo4qMtUMk/s527/1_3.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="527" data-original-width="458" height="320" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh-IS5ZQVW5h08AQzRpjKTaVJgPb7kpmh5i2iLiAWmDnc9fZ6AOaQqegA9HvOGj3wLgEtsGUUcpRbJH9gMOIxcw5T1oUwspdVnjvvIEZQIu0wJ3fJ2Hm9soLY53rwgknjkjTSRMtqNPhoOuJAV0NFk0psPNpvtkKx1LxajKJ1T7-WEG26L15oBo4qMtUMk/s320/1_3.png" width="278" /></a></div><br /><p></p><p class="MsoNormal" dir="RTL" style="direction: rtl; unicode-bidi: embed;"><span dir="RTL"></span><span dir="RTL"></span><b><span lang="FA" style="font-family: "B Nazanin"; font-size: 12.0pt; line-height: 115%; mso-bidi-language: FA;"><span dir="RTL"></span><span dir="RTL"></span>2. ورود اطلاعات
مربوط به بستانکاری:<o:p></o:p></span></b></p><p class="MsoNormal" dir="RTL" style="direction: rtl; unicode-bidi: embed;"><span lang="FA" style="font-family: "B Nazanin"; font-size: 12.0pt; line-height: 115%; mso-bidi-language: FA;"> اگر از نرم افزار حسابداری استفاده میکنید
بطورمثال: نرم افزار سپیدار</span><span dir="LTR"></span><span dir="LTR"></span><span dir="LTR" style="font-size: 12.0pt; line-height: 115%; mso-bidi-font-family: "B Nazanin"; mso-bidi-language: FA;"><span dir="LTR"></span><span dir="LTR"></span>,</span><span dir="RTL"></span><span dir="RTL"></span><span style="font-family: "B Nazanin"; font-size: 12.0pt; line-height: 115%; mso-bidi-language: FA;"><span dir="RTL"></span><span dir="RTL"></span> <span lang="FA">شما میتوانید از منوی "شرکت" وارد قسمت "فهرست"
شوید سپس فرم "گزارش ساز" را انتخاب نموده و در صفحه باز شده تیک علامت "</span></span><span dir="LTR"></span><span dir="LTR"></span><span dir="LTR" style="font-size: 12.0pt; line-height: 115%; mso-bidi-font-family: "B Nazanin"; mso-bidi-language: FA;"><span dir="LTR"></span><span dir="LTR"></span>(<b>+</b>)</span><span dir="RTL"></span><span dir="RTL"></span><span style="font-family: "B Nazanin"; font-size: 12.0pt; line-height: 115%; mso-bidi-language: FA;"><span dir="RTL"></span><span dir="RTL"></span> <span lang="FA">مشتریان
و فروش" را زده </span></span><span lang="AR-SA" style="font-family: "B Nazanin"; font-size: 12.0pt; line-height: 115%;">و از “صورتحساب مشتریان” </span><span lang="FA" style="font-family: "B Nazanin"; font-size: 12.0pt; line-height: 115%; mso-bidi-language: FA;">بعد از تایید فرم کوچکی که باز میشود</span><span dir="LTR"></span><span dir="LTR"></span><span dir="LTR" style="font-size: 12.0pt; line-height: 115%; mso-bidi-font-family: "B Nazanin"; mso-bidi-language: FA;"><span dir="LTR"></span><span dir="LTR"></span>,</span><span lang="FA" style="font-family: "B Nazanin"; font-size: 12.0pt; line-height: 115%; mso-bidi-language: FA;">تنها از مشتریانی که مانده حساب صفر
دارند</span><span dir="LTR"></span><span dir="LTR"></span><span dir="LTR" style="font-size: 12.0pt; line-height: 115%; mso-bidi-font-family: "B Nazanin"; mso-bidi-language: FA;"><span dir="LTR"></span><span dir="LTR"></span>,</span><span lang="AR-SA" style="font-family: "B Nazanin"; font-size: 12.0pt; line-height: 115%;">گزارش
خروجی اکسل صادرنمایید.<o:p></o:p></span></p><p class="MsoNormal" dir="RTL" style="direction: rtl; unicode-bidi: embed;"><span lang="AR-SA" style="font-family: "B Nazanin"; font-size: 12.0pt; line-height: 115%;"> حالامجددا وارد
"سیستم مشتریان و فروش" شده و از قسمت عملیات “مرور فروش” را انتخاب
نمایید. سپس بازه تاریخی مورد نظر را وارد نمایید</span><span dir="LTR"></span><span dir="LTR"></span><span dir="LTR" style="font-size: 12.0pt; line-height: 115%; mso-bidi-font-family: "B Nazanin";"><span dir="LTR"></span><span dir="LTR"></span>.</span><span dir="RTL"></span><span dir="RTL"></span><span lang="AR-SA" style="font-family: "B Nazanin"; font-size: 12.0pt; line-height: 115%;"><span dir="RTL"></span><span dir="RTL"></span>
و از تب "اسناد فروش" و یا گزينه "فاكتور فروش"</span><span dir="LTR"></span><span dir="LTR"></span><span dir="LTR" style="font-size: 12.0pt; line-height: 115%; mso-bidi-font-family: "B Nazanin";"><span dir="LTR"></span><span dir="LTR"></span>,</span><span dir="RTL"></span><span dir="RTL"></span><span lang="FA" style="font-family: "B Nazanin"; font-size: 12.0pt; line-height: 115%; mso-bidi-language: FA;"><span dir="RTL"></span><span dir="RTL"></span> از کلیه صفحات مربوط به فاکتور
های فروش خروجی اکسل تهیه کنید. دراین مرحله در گزارش اکسل</span><span dir="LTR"></span><span dir="LTR"></span><span dir="LTR" style="font-size: 12.0pt; line-height: 115%; mso-bidi-font-family: "B Nazanin"; mso-bidi-language: FA;"><span dir="LTR"></span><span dir="LTR"></span>,</span><span dir="RTL"></span><span dir="RTL"></span><span style="font-family: "B Nazanin"; font-size: 12.0pt; line-height: 115%; mso-bidi-language: FA;"><span dir="RTL"></span><span dir="RTL"></span> <span lang="FA">فاکتورهای برگشتی
(مرجوعی) را فیلتر نموده و همه آنها را از گزارش حذف نمایید.<o:p></o:p></span></span></p><p class="MsoNormal" dir="RTL" style="direction: rtl; unicode-bidi: embed;"><span lang="FA" style="font-family: "B Nazanin"; font-size: 12.0pt; line-height: 115%; mso-bidi-language: FA;">در این مرحله گزارش اکسل فاکتور
های فروش باید با گزارش اکسل صورت حساب مشتریان همسان سازی شود و مغایرت ها
حذف گردد. شما میتوانید برای این عملیات همسان
سازی</span><span dir="LTR"></span><span dir="LTR"></span><span dir="LTR" style="font-size: 12.0pt; line-height: 115%; mso-bidi-font-family: "B Nazanin"; mso-bidi-language: FA;"><span dir="LTR"></span><span dir="LTR"></span>,</span><span dir="RTL"></span><span dir="RTL"></span><span lang="FA" style="font-family: "B Nazanin"; font-size: 12.0pt; line-height: 115%; mso-bidi-language: FA;"><span dir="RTL"></span><span dir="RTL"></span> از <b><i><a href="https://emfps.blogspot.com/2023/06/discrepancy-analysis-1-model-made-by.html" target="_blank">مدل آنالیز مغایرت گیری (1 )</a></i></b> استفاده نمایید. <o:p></o:p></span></p><p class="MsoNormal" dir="RTL" style="direction: rtl; unicode-bidi: embed;"><span lang="FA" style="font-family: "B Nazanin"; font-size: 12.0pt; line-height: 115%; mso-bidi-language: FA;">حالا گزارش کامل فروش شما آماده
هست و میتوانید آن را وارد شیت بستانکار مدل آنالیز راس گیری وارد نمایید.<o:p></o:p></span></p><p class="MsoNormal" dir="RTL" style="direction: rtl; unicode-bidi: embed;"><span lang="FA" style="font-family: "B Nazanin"; font-size: 12.0pt; line-height: 115%; mso-bidi-language: FA;">
</span></p><p class="MsoNormal" dir="RTL" style="direction: rtl; unicode-bidi: embed;"><span lang="FA" style="font-family: "B Nazanin"; font-size: 12.0pt; line-height: 115%; mso-bidi-language: FA;">یک نمونه مثال بشرح زیر میباشد:<o:p></o:p></span></p><p class="MsoNormal" dir="RTL" style="direction: rtl; unicode-bidi: embed;">
</p><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEja9BWTw7h4F1o1iOslOS4azBDeg210NWs_OSmZfxtN4BX-Bp9t4nPcQJcJ3zrn7csi7D7FtIPr9G-qdK2Qd5tL1LQ6EfRWu6cwbvDSjIbLc9MTx3tzigi9vrWMhdNA0NHIp2_hwPkF-huCeSXOpb2xBscGIMNGWMbpyxrxzddd7mj3pxE3YZu2XNrBrjg/s1250/2.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="536" data-original-width="1250" height="137" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEja9BWTw7h4F1o1iOslOS4azBDeg210NWs_OSmZfxtN4BX-Bp9t4nPcQJcJ3zrn7csi7D7FtIPr9G-qdK2Qd5tL1LQ6EfRWu6cwbvDSjIbLc9MTx3tzigi9vrWMhdNA0NHIp2_hwPkF-huCeSXOpb2xBscGIMNGWMbpyxrxzddd7mj3pxE3YZu2XNrBrjg/s320/2.png" width="320" /></a></div><br /><span lang="FA" style="font-family: "B Nazanin"; font-size: 12.0pt; line-height: 115%; mso-bidi-language: FA;"></span><p></p><p class="MsoNormal" dir="RTL" style="direction: rtl; unicode-bidi: embed;"><span lang="FA" style="font-family: "B Nazanin"; font-size: 12.0pt; line-height: 115%; mso-bidi-language: FA;">نکته بسیار مهم صحت سنجی این گزارش
است. با توجه به اینکه اکثر شرکت ها اسناد حسابداری را بصورت دستی وارد می کنند</span><span dir="LTR"></span><span dir="LTR"></span><span dir="LTR" style="font-size: 12.0pt; line-height: 115%; mso-bidi-font-family: "B Nazanin"; mso-bidi-language: FA;"><span dir="LTR"></span><span dir="LTR"></span>,</span><span dir="RTL"></span><span dir="RTL"></span><span style="font-family: "B Nazanin"; font-size: 12.0pt; line-height: 115%; mso-bidi-language: FA;"><span dir="RTL"></span><span dir="RTL"></span> <span lang="FA">شما میتوانید گزارش
نهایی فروش فوق را مستقیما از </span></span><span lang="FA" style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%; mso-ascii-font-family: Calibri; mso-ascii-theme-font: minor-latin; mso-bidi-language: FA; mso-hansi-font-family: Calibri; mso-hansi-theme-font: minor-latin;">"</span><span lang="FA" style="font-family: "B Nazanin"; font-size: 12.0pt; line-height: 115%; mso-bidi-language: FA;">دفتر معین ویا تفضیلی</span><span lang="FA" style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%; mso-ascii-font-family: Calibri; mso-ascii-theme-font: minor-latin; mso-bidi-language: FA; mso-hansi-font-family: Calibri; mso-hansi-theme-font: minor-latin;">" -
"بدهی های جاری"</span><span lang="FA" style="font-family: "B Nazanin"; font-size: 12.0pt; line-height: 115%; mso-bidi-language: FA;"> از </span><span lang="FA" style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%; mso-ascii-font-family: Calibri; mso-ascii-theme-font: minor-latin; mso-bidi-language: FA; mso-hansi-font-family: Calibri; mso-hansi-theme-font: minor-latin;">"</span><span lang="FA" style="font-family: "B Nazanin"; font-size: 12.0pt; line-height: 115%; mso-bidi-language: FA;">حساب درآمد و فروش</span><span lang="FA" style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%; mso-ascii-font-family: Calibri; mso-ascii-theme-font: minor-latin; mso-bidi-language: FA; mso-hansi-font-family: Calibri; mso-hansi-theme-font: minor-latin;">"</span><span lang="FA" style="font-family: "B Nazanin"; font-size: 12.0pt; line-height: 115%; mso-bidi-language: FA;"> تهیه نمایید.</span></p><p class="MsoNormal" dir="RTL" style="direction: rtl; unicode-bidi: embed;"><span lang="FA" style="font-family: "B Nazanin"; font-size: 12.0pt; line-height: 115%; mso-bidi-language: FA;"> <o:p></o:p></span><span lang="AR-SA" style="font-family: "B Nazanin"; font-size: 12pt; line-height: 115%;">پس از ورود به سیستم</span><span dir="LTR"></span><span dir="LTR"></span><span dir="LTR" style="font-size: 12pt; line-height: 115%;"><span dir="LTR"></span><span dir="LTR"></span> </span><span lang="AR-SA" style="font-family: "B Nazanin"; font-size: 12pt; line-height: 115%;">سپیدار</span><span dir="LTR"></span><span dir="LTR"></span><span dir="LTR" style="font-size: 12pt; line-height: 115%;"><span dir="LTR"></span><span dir="LTR"></span> </span><span lang="AR-SA" style="font-family: "B Nazanin"; font-size: 12pt; line-height: 115%;">در منوی سمت راست ، وارد قسمت حسابداری
شده و در قسمت عملیات روی گزینه “مرور حسابها” كلیك كنید . فرمی كه در اختیار شما
قرار می گیرد، می توانید اعمال فیلتر نموده و</span><span dir="LTR"></span><span dir="LTR"></span><span dir="LTR" style="font-size: 12pt; line-height: 115%;"><span dir="LTR"></span><span dir="LTR"></span> </span><span lang="FA" style="font-family: "B Nazanin"; font-size: 12pt; line-height: 115%;">از</span><span lang="AR-SA" style="font-family: "B Nazanin"; font-size: 12pt; line-height: 115%;">گزارش مربوط
به </span><span lang="FA" style="font-family: "B Nazanin"; font-size: 12pt; line-height: 115%;">"حساب درآمد و فروش"خروجی اکسل</span><span lang="AR-SA" style="font-family: "B Nazanin"; font-size: 12pt; line-height: 115%;">
تهیه نمایید.</span></p>
<p class="MsoNormal" dir="RTL" style="direction: rtl; unicode-bidi: embed;"><span lang="FA" style="font-family: "B Nazanin"; font-size: 12.0pt; line-height: 115%; mso-bidi-language: FA;">جهت صحت سنجی و کنترل فاکتور های
فروش</span><span dir="LTR"></span><span dir="LTR"></span><span dir="LTR" style="font-size: 12.0pt; line-height: 115%; mso-bidi-font-family: "B Nazanin"; mso-bidi-language: FA;"><span dir="LTR"></span><span dir="LTR"></span>,</span><span dir="RTL"></span><span dir="RTL"></span><span lang="FA" style="font-family: "B Nazanin"; font-size: 12.0pt; line-height: 115%; mso-bidi-language: FA;"><span dir="RTL"></span><span dir="RTL"></span> می توانید اطلاعات گزارش کامل فروش (اکسل اول) را بهمراه اطلاعات مربوط
به </span><span lang="AR-SA" style="font-family: "B Nazanin"; font-size: 12.0pt; line-height: 115%;">گزارش </span><span lang="FA" style="font-family: "B Nazanin"; font-size: 12.0pt; line-height: 115%; mso-bidi-language: FA;">"حساب درآمد و فروش"
(اکسل دوم) وارد <b><i><a href="https://emfps.blogspot.com/2023/06/discrepancy-analysis-1-model-made-by.html" target="_blank">مدل آنالیز مغایرت گیری (1 )</a> </i></b>نمایید و سیستم بطور
خودکار مغایرت ها را به شما نشان میدهد. <o:p></o:p></span></p>
<p class="MsoNormal" dir="RTL" style="direction: rtl; unicode-bidi: embed;"><b><span lang="FA" style="font-family: "B Nazanin"; font-size: 12.0pt; line-height: 115%; mso-bidi-language: FA;">3. ورود اطلاعات مربوط به بدهکاری:<o:p></o:p></span></b></p>
<p class="MsoNormal" dir="RTL" style="direction: rtl; unicode-bidi: embed;"><span lang="FA" style="font-family: "B Nazanin"; font-size: 12.0pt; line-height: 115%; mso-bidi-language: FA;">مشابه قسمت قبل (ورود اطلاعات
مربوط به بستانکاری)</span><span dir="LTR"></span><span dir="LTR"></span><span dir="LTR" style="font-size: 12.0pt; line-height: 115%; mso-bidi-font-family: "B Nazanin"; mso-bidi-language: FA;"><span dir="LTR"></span><span dir="LTR"></span>,</span><span dir="RTL"></span><span dir="RTL"></span><span lang="FA" style="font-family: "B Nazanin"; font-size: 12.0pt; line-height: 115%; mso-bidi-language: FA;"><span dir="RTL"></span><span dir="RTL"></span> از سیستم </span><span lang="AR-SA" style="font-family: "B Nazanin"; font-size: 12.0pt; line-height: 115%;">“صورتحساب مشتریان” اما این بار از
کلیه مبالغ پرداخت شده (نقد وچک) توسط مشتریانی که مانده حساب آنها صفر است</span><span dir="LTR"></span><span dir="LTR"></span><span dir="LTR" style="font-size: 12.0pt; line-height: 115%; mso-bidi-font-family: "B Nazanin";"><span dir="LTR"></span><span dir="LTR"></span>,</span><span dir="RTL"></span><span dir="RTL"></span><span lang="FA" style="font-family: "B Nazanin"; font-size: 12.0pt; line-height: 115%; mso-bidi-language: FA;"><span dir="RTL"></span><span dir="RTL"></span> گزارش اکسل تهیه نمایید.<o:p></o:p></span></p>
<p class="MsoNormal" dir="RTL" style="direction: rtl; unicode-bidi: embed;"><span lang="FA" style="font-family: "B Nazanin"; font-size: 12.0pt; line-height: 115%; mso-bidi-language: FA;"> سپس از </span><span lang="AR-SA" style="font-family: "B Nazanin"; font-size: 12.0pt; line-height: 115%;">سیستم
"اسناد فروش"</span><span dir="LTR"></span><span dir="LTR"></span><span dir="LTR" style="font-size: 12.0pt; line-height: 115%; mso-bidi-font-family: "B Nazanin";"><span dir="LTR"></span><span dir="LTR"></span>,</span><span dir="RTL"></span><span dir="RTL"></span><span lang="FA" style="font-family: "B Nazanin"; font-size: 12.0pt; line-height: 115%; mso-bidi-language: FA;"><span dir="RTL"></span><span dir="RTL"></span> فقط از فاکتورهای
برگشتی (مرجوعی) گزارش اکسل بگیرید. نهایتا اطلاعات هر دو اکسل را در یک ستون
ترکیب نمایید. حالا گزارش کامل بدهی شما آماده هست.<o:p></o:p></span></p>
<p class="MsoNormal" dir="RTL" style="direction: rtl; unicode-bidi: embed;"><span lang="FA" style="font-family: "B Nazanin"; font-size: 12.0pt; line-height: 115%; mso-bidi-language: FA;">جهت صحت سنجی</span><span dir="LTR"></span><span dir="LTR"></span><span dir="LTR" style="font-size: 12.0pt; line-height: 115%; mso-bidi-font-family: "B Nazanin"; mso-bidi-language: FA;"><span dir="LTR"></span><span dir="LTR"></span>,</span><span dir="RTL"></span><span dir="RTL"></span><span style="font-family: "B Nazanin"; font-size: 12.0pt; line-height: 115%; mso-bidi-language: FA;"><span dir="RTL"></span><span dir="RTL"></span> <span lang="FA">شما میتوانید گزارش
نهایی بدهی فوق را مستقیما از سیستم حسابداری و "دفتر معین ویا تفضیلی" -
"دارایی های جاری" و از "حساب صندوق " </span></span><span dir="LTR"></span><span dir="LTR"></span><span dir="LTR" style="font-size: 12.0pt; line-height: 115%; mso-bidi-font-family: "B Nazanin"; mso-bidi-language: FA;"><span dir="LTR"></span><span dir="LTR"></span>,</span><span dir="RTL"></span><span dir="RTL"></span><span lang="FA" style="font-family: "B Nazanin"; font-size: 12.0pt; line-height: 115%; mso-bidi-language: FA;"><span dir="RTL"></span><span dir="RTL"></span>"حساب بانک
" </span><span dir="LTR"></span><span dir="LTR"></span><span dir="LTR" style="font-size: 12.0pt; line-height: 115%; mso-bidi-font-family: "B Nazanin"; mso-bidi-language: FA;"><span dir="LTR"></span><span dir="LTR"></span>,</span><span dir="RTL"></span><span dir="RTL"></span><span style="font-family: "B Nazanin"; font-size: 12.0pt; line-height: 115%; mso-bidi-language: FA;"><span dir="RTL"></span><span dir="RTL"></span> </span><span lang="FA" style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%; mso-ascii-font-family: Calibri; mso-ascii-theme-font: minor-latin; mso-bidi-language: FA; mso-hansi-font-family: Calibri; mso-hansi-theme-font: minor-latin;">"حساب اسناد دریافتنی" و نهایتا " حساب
هزینه ها (مربوط به فاکتورهای برگشتی)" گزارش اکسل صادر نمایید. سپس با
استفاده از<a href="https://emfps.blogspot.com/2023/06/discrepancy-analysis-1-model-made-by.html" target="_blank"> </a></span><b><i><span lang="FA" style="font-family: "B Nazanin"; font-size: 12.0pt; line-height: 115%; mso-bidi-language: FA;"><a href="https://emfps.blogspot.com/2023/06/discrepancy-analysis-1-model-made-by.html" target="_blank">مدل آنالیز مغایرت گیری (1 )</a> </span></i></b><span lang="FA" style="font-family: "B Nazanin"; font-size: 12.0pt; line-height: 115%; mso-bidi-language: FA;">هر دو گزارش فوق را مقایسه و کنترل کنید. <o:p></o:p></span></p>
<p class="MsoNormal" dir="RTL" style="direction: rtl; unicode-bidi: embed;"><span lang="FA" style="font-family: "B Nazanin"; font-size: 12.0pt; line-height: 115%; mso-bidi-language: FA;">یک نمونه مثال بشرح زیر میباشد:<o:p></o:p></span></p><p class="MsoNormal" dir="RTL" style="direction: rtl; unicode-bidi: embed;"></p><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhsbcU4Zli9HC6PRRgxCQPI8Q-8fShpnLJ2JvGu-5I9T5SEGbEyhr_sQrMtliMHuhzGeHJWKXPvTvIprdax20qF-2qqUCGJDmp50FtqvZjca6uAk37vccXkxu7JuDjc6_7nEhVGXab63DNg5g0_NUzw6Tnp1qQaIv-3jQrcfanFqGvBLCEtGuxZt8CtRQM/s1252/3.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="528" data-original-width="1252" height="135" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhsbcU4Zli9HC6PRRgxCQPI8Q-8fShpnLJ2JvGu-5I9T5SEGbEyhr_sQrMtliMHuhzGeHJWKXPvTvIprdax20qF-2qqUCGJDmp50FtqvZjca6uAk37vccXkxu7JuDjc6_7nEhVGXab63DNg5g0_NUzw6Tnp1qQaIv-3jQrcfanFqGvBLCEtGuxZt8CtRQM/s320/3.png" width="320" /></a></div><br /><p></p><p class="MsoNormal" dir="RTL" style="direction: rtl; unicode-bidi: embed;"><span dir="RTL"></span><span dir="RTL"></span><b><span lang="FA" style="font-family: "B Nazanin"; font-size: 12.0pt; line-height: 115%; mso-bidi-language: FA;"><span dir="RTL"></span><span dir="RTL"></span>4. راس گیری
چکها برای همه مشتریان<o:p></o:p></span></b></p><p class="MsoNormal" dir="RTL" style="direction: rtl; unicode-bidi: embed;"><span lang="FA" style="font-family: "B Nazanin"; font-size: 12.0pt; line-height: 115%; mso-bidi-language: FA;">
</span></p><p class="MsoNormal" dir="RTL" style="direction: rtl; unicode-bidi: embed;"><span lang="FA" style="font-family: "B Nazanin"; font-size: 12.0pt; line-height: 115%; mso-bidi-language: FA;">در نتیجه نهایتا پس از ورود
اطلاعات بستانکاری و بدهکاری سیستم بصورت خودکار</span><span dir="LTR"></span><span dir="LTR"></span><span dir="LTR" style="font-size: 12.0pt; line-height: 115%; mso-bidi-font-family: "B Nazanin"; mso-bidi-language: FA;"><span dir="LTR"></span><span dir="LTR"></span>,</span><span dir="RTL"></span><span dir="RTL"></span><span lang="FA" style="font-family: "B Nazanin"; font-size: 12.0pt; line-height: 115%; mso-bidi-language: FA;"><span dir="RTL"></span><span dir="RTL"></span> راس چک ها را برای کلیه مشتریان
همراه با سود توافقی محاسبه و اعلام می کند:<o:p></o:p></span></p><p class="MsoNormal" dir="RTL" style="direction: rtl; unicode-bidi: embed;"></p><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhFwiWtEz8BUkD3En1OzPA3Z9gaATPWeDu2hTv66prk05xtL9b8mH0ICBO6uIys56KJgW1c_w8ncrDQqkPAJL2w4F_YRc8XmGPnlJ5yuCwiGgRET8lya0NLDjnDgpedri_JTxiCjmfbaCK6oJgsLQ6a-r_qgdU441ZrHmG6J4RgBog-_UGyF_-lK26k32Y/s689/4.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="534" data-original-width="689" height="248" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhFwiWtEz8BUkD3En1OzPA3Z9gaATPWeDu2hTv66prk05xtL9b8mH0ICBO6uIys56KJgW1c_w8ncrDQqkPAJL2w4F_YRc8XmGPnlJ5yuCwiGgRET8lya0NLDjnDgpedri_JTxiCjmfbaCK6oJgsLQ6a-r_qgdU441ZrHmG6J4RgBog-_UGyF_-lK26k32Y/s320/4.png" width="320" /></a></div><br /><span lang="FA" style="font-family: "B Nazanin"; font-size: 12.0pt; line-height: 115%; mso-bidi-language: FA;"></span><p></p><p class="MsoNormal" dir="RTL" style="direction: rtl; unicode-bidi: embed;"><span lang="FA" style="font-family: "B Nazanin"; font-size: 12.0pt; line-height: 115%; mso-bidi-language: FA;">ویدیو کلیپ زیر مربوط به روش کار
این مدل می باشد:<o:p></o:p></span></p><p class="MsoNormal" dir="RTL" style="direction: rtl; unicode-bidi: embed;"></p><div class="separator" style="clear: both; text-align: center;"><iframe allowfullscreen='allowfullscreen' webkitallowfullscreen='webkitallowfullscreen' mozallowfullscreen='mozallowfullscreen' width='320' height='266' src='https://www.blogger.com/video.g?token=AD6v5dzjdufuuMI857A6rpJYNBFXLJ8bZcperhE1MnazjG_nU7r4_0uE83pmTFh0nZXEGIvUL273hPlbTHr4ijKeGw' class='b-hbp-video b-uploaded' frameborder='0'></iframe></div><br /><span lang="FA" style="font-family: "B Nazanin"; font-size: 12.0pt; line-height: 115%; mso-bidi-language: FA;"><br /></span><p></p><span lang="FA" style="font-family: "B Nazanin"; font-size: 12.0pt; line-height: 115%; mso-bidi-language: FA;"><br /></span><p></p><p class="MsoNormal" dir="RTL" style="direction: rtl; unicode-bidi: embed;"><span lang="FA" style="font-family: "B Nazanin"; font-size: 12.0pt; line-height: 115%; mso-bidi-language: FA;"><br /></span></p></div><div dir="rtl" style="text-align: right;"><br /></div>Gholamreza Soleimanihttp://www.blogger.com/profile/03273527405719420253noreply@blogger.com0tag:blogger.com,1999:blog-392703582366288634.post-16075032158361344252023-09-15T17:16:00.000+03:302023-09-15T17:16:22.838+03:30Income statement simulation model<p> </p><p></p><p class="MsoNormal"><b><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%; mso-ascii-theme-font: major-bidi; mso-bidi-theme-font: major-bidi; mso-fareast-font-family: Calibri; mso-hansi-theme-font: major-bidi;">ABSTRACT<o:p></o:p></span></b></p>
<p class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0mm; mso-layout-grid-align: none; text-autospace: none;"><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; mso-ascii-theme-font: major-bidi; mso-bidi-theme-font: major-bidi; mso-font-kerning: 12.0pt; mso-hansi-theme-font: major-bidi;"><o:p> </o:p></span></p>
<p class="MsoNormal"><span style="font-family: "Times New Roman","serif"; mso-ascii-theme-font: major-bidi; mso-bidi-theme-font: major-bidi; mso-fareast-font-family: Calibri; mso-hansi-theme-font: major-bidi;">By using “Sensitivity Analysis” in
Microsoft Excel, we will be able to analyze an algorithm with a maximum of two
independent variables (two-way data table). The purpose of this project is to
present an analytic model made by Microsoft Excel where this model allows
us to analyze an algorithm with up to four independent variables. An
example of an “Income Statement Simulation Model” to obtain a maximum of 10
scenarios has been presented in which this model shows us how the independent
variables of Sales growth rate, COGS growth rate, Operating expenses growth
rate, and Interest growth rate should be combined to reach a target net income
based on the data of previous year. </span><b><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%; mso-ascii-theme-font: major-bidi; mso-bidi-theme-font: major-bidi; mso-font-kerning: 12.0pt; mso-hansi-theme-font: major-bidi;"><o:p></o:p></span></b></p>
<p class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0mm; mso-layout-grid-align: none; text-autospace: none;"><b><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; mso-ascii-theme-font: major-bidi; mso-bidi-theme-font: major-bidi; mso-font-kerning: 12.0pt; mso-hansi-theme-font: major-bidi;">Introduction<o:p></o:p></span></b></p>
<p class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0mm; mso-layout-grid-align: none; text-autospace: none;"><b><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; mso-ascii-theme-font: major-bidi; mso-bidi-theme-font: major-bidi; mso-font-kerning: 12.0pt; mso-hansi-theme-font: major-bidi;"><o:p> </o:p></span></b><span style="font-family: "Times New Roman", "serif"; font-size: 12pt;">As you know, there are three important </span><a href="https://www.investopedia.com/terms/f/financial-statements.asp"><span style="color: windowtext; font-family: "Times New Roman", "serif"; font-size: 12pt; text-decoration-line: none;">financial statements</span></a><span style="font-family: "Times New Roman", "serif"; font-size: 12pt;"> to
show the financial performance of a company in a specific period of the time
which are as follows:</span></p>
<p class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0mm; mso-layout-grid-align: none; text-autospace: none;"><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; mso-ascii-theme-font: major-bidi; mso-bidi-theme-font: major-bidi; mso-font-kerning: 12.0pt; mso-hansi-theme-font: major-bidi;">- Income Statement<o:p></o:p></span></p>
<p class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0mm; mso-layout-grid-align: none; text-autospace: none;"><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; mso-ascii-theme-font: major-bidi; mso-bidi-theme-font: major-bidi; mso-font-kerning: 12.0pt; mso-hansi-theme-font: major-bidi;">- Balance sheet <o:p></o:p></span></p>
<p class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0mm; mso-layout-grid-align: none; text-autospace: none;"><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; mso-ascii-theme-font: major-bidi; mso-bidi-theme-font: major-bidi; mso-font-kerning: 12.0pt; mso-hansi-theme-font: major-bidi;">- Cash flow statement<o:p></o:p></span></p>
<p class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0mm; mso-layout-grid-align: none; text-autospace: none;"><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; mso-ascii-theme-font: major-bidi; mso-bidi-theme-font: major-bidi; mso-font-kerning: 12.0pt; mso-hansi-theme-font: major-bidi;"><o:p> </o:p></span><span style="font-family: "Times New Roman", "serif"; font-size: 12pt;">An income statement which sometimes is referred to</span><span style="background: white; color: #121316; font-family: Arial, "sans-serif";"> </span><span style="font-family: "Times New Roman", "serif"; font-size: 12pt;">as a “profit and loss statement (P&L)” is included
some independent variables such as revenue, Cost of Goods Sold, expenses, gains,
and losses where an algorithm is establishing a logical relationship among them
to reach a net income. This document can help to business owners make decision
about the company’s strategies how the combination of increase or decrease on
the growth rate of these independent variables will lead the company to earn
more profit.</span></p>
<p class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0mm; mso-layout-grid-align: none; text-autospace: none;"><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; mso-ascii-theme-font: major-bidi; mso-bidi-theme-font: major-bidi; mso-font-kerning: 12.0pt; mso-hansi-theme-font: major-bidi;"><br />
</span><b><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; mso-ascii-theme-font: major-bidi; mso-bidi-theme-font: major-bidi; mso-fareast-font-family: Calibri; mso-hansi-theme-font: major-bidi;">Income Statement Simulation Model</span></b><b><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; mso-ascii-theme-font: major-bidi; mso-bidi-theme-font: major-bidi; mso-font-kerning: 12.0pt; mso-hansi-theme-font: major-bidi;"><o:p></o:p></span></b></p>
<p class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0mm; mso-layout-grid-align: none; text-autospace: none;"><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; mso-ascii-theme-font: major-bidi; mso-bidi-theme-font: major-bidi; mso-font-kerning: 12.0pt; mso-hansi-theme-font: major-bidi;"><o:p> </o:p></span><span style="font-family: "Times New Roman", "serif"; font-size: 12pt;">Suppose we need to know that if we want to reach a growth rate of ”X”
on previous year of net income our company in the next year, how the
independent variables of “Sales growth rate”, “Cost of Goods Sold growth rate”
, “Operating expenses growth rate” and “Interest growth rate” will move.
Definitely the speed of this analysis is very important because every time we
have to change and compare these variables with the conditions of macroeconomic
indicators such as Inflation, GDP, Interest, Unemployment, CPI, and so on.</span></p><p class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0mm; mso-layout-grid-align: none; text-autospace: none;"><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; mso-ascii-theme-font: major-bidi; mso-bidi-theme-font: major-bidi; mso-font-kerning: 12.0pt; mso-hansi-theme-font: major-bidi;">Basically, we will determine a target net income in accordance with a
growth rate of ”X” for the next year and
we will examine many scenarios combined with above four independent
variables to reach our target net income. This Income Statement Simulation model
can help us to increase the acceleration of our analysis with the least error
to find out the best optimized solutions. <o:p></o:p></span></p><p></p><p class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0mm; mso-layout-grid-align: none; text-autospace: none;"><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; mso-ascii-theme-font: major-bidi; mso-bidi-theme-font: major-bidi; mso-font-kerning: 12.0pt; mso-hansi-theme-font: major-bidi;"> </span><b><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; mso-ascii-theme-font: major-bidi; mso-bidi-theme-font: major-bidi; mso-font-kerning: 12.0pt; mso-hansi-theme-font: major-bidi;">How does this model work?</span></b></p><p class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0mm; mso-layout-grid-align: none; text-autospace: none;"><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; mso-ascii-theme-font: major-bidi; mso-bidi-theme-font: major-bidi; mso-font-kerning: 12.0pt; mso-hansi-theme-font: major-bidi;"> </span><span style="font-family: "Times New Roman", "serif"; font-size: 12pt;">First of all, we need to import four levels of the
data, such as the INPUTS, into the cells of this model as follows:</span></p><p class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0mm; mso-layout-grid-align: none; text-autospace: none;"><span style="font-family: "Times New Roman", "serif"; font-size: 12pt;"><br /></span></p><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEja4IJZHaq3UQFoBc8waePKg70HXmZUeL-EB7CMTZw0xX_UzjhGdoXv2YYqB22v9PoqJsmv98IxE7WXrBXzFJSi6hl8xHzecSRNc2sKDw8xcKqrV3KnBiubw53pUwTEikkeg-4iQn7g_bgusML7dT0MWJ35KzYTHshlTkbqvIYVaFJ4nKI_rNtJ3teUsZ0/s1261/1.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="460" data-original-width="1261" height="117" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEja4IJZHaq3UQFoBc8waePKg70HXmZUeL-EB7CMTZw0xX_UzjhGdoXv2YYqB22v9PoqJsmv98IxE7WXrBXzFJSi6hl8xHzecSRNc2sKDw8xcKqrV3KnBiubw53pUwTEikkeg-4iQn7g_bgusML7dT0MWJ35KzYTHshlTkbqvIYVaFJ4nKI_rNtJ3teUsZ0/s320/1.png" width="320" /></a></div><div class="separator" style="clear: both; text-align: center;"><br /></div><p>
</p><p class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0mm; mso-layout-grid-align: none; text-autospace: none;"><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; mso-ascii-theme-font: major-bidi; mso-bidi-theme-font: major-bidi; mso-font-kerning: 12.0pt; mso-hansi-theme-font: major-bidi;">1. The data from the income statement of your company related to the
previous year. <o:p></o:p></span></p>
<p class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0mm; mso-layout-grid-align: none; text-autospace: none;"><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; mso-ascii-theme-font: major-bidi; mso-bidi-theme-font: major-bidi; mso-font-kerning: 12.0pt; mso-hansi-theme-font: major-bidi;">2. To enter the range for all four independent variables (Min &
Max)<o:p></o:p></span></p>
<p class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0mm; mso-layout-grid-align: none; text-autospace: none;"><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; mso-ascii-theme-font: major-bidi; mso-bidi-theme-font: major-bidi; mso-font-kerning: 12.0pt; mso-hansi-theme-font: major-bidi;">3. To choose a minimum for the error<o:p></o:p></span></p>
<p class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0mm; mso-layout-grid-align: none; text-autospace: none;"><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; mso-ascii-theme-font: major-bidi; mso-bidi-theme-font: major-bidi; mso-font-kerning: 12.0pt; mso-hansi-theme-font: major-bidi;">4. To determine the growth rate for the target net income <o:p></o:p></span></p>
<p class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0mm; mso-layout-grid-align: none; text-autospace: none;"><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; mso-ascii-theme-font: major-bidi; mso-bidi-theme-font: major-bidi; mso-font-kerning: 12.0pt; mso-hansi-theme-font: major-bidi;"><o:p> </o:p></span><span style="font-family: "Times New Roman", "serif"; font-size: 12pt;">Now, we have a maximum of 10 scenarios (OUTPUTS) for a combination of
four independent variables, including “sales growth rate”, “Cost of Goods Sold
growth rate”, “Operating expenses growth rate” and “, Interest growth rate”,
where the impact of these variables will be approximately equal to our target
net income and also the OUTPUTS are included amounts of minimum, average, and
maximum for these valuables. For comparing the average results of this model
and defined target net income based on the percentage of error, we are referred
to the cells of “A16:B18”.</span></p>
<p class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0mm; mso-layout-grid-align: none; text-autospace: none;"><span style="font-family: "Times New Roman", "serif"; font-size: 12pt;">Please see the below video:</span></p><p class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0mm; mso-layout-grid-align: none; text-autospace: none;"><span style="font-family: "Times New Roman", "serif"; font-size: 12pt;"><br /></span></p><p class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0mm; mso-layout-grid-align: none; text-autospace: none;"></p><div class="separator" style="clear: both; text-align: center;"><iframe allowfullscreen='allowfullscreen' webkitallowfullscreen='webkitallowfullscreen' mozallowfullscreen='mozallowfullscreen' width='320' height='266' src='https://www.blogger.com/video.g?token=AD6v5dwnFnM0K1OMjnpo9bLXPg0L7aCVjjzxDwsnK4TPtbRGEBBR5wH41_iN-SQYSizWQPLDHpvKsSvOGQMEDh1G8g' class='b-hbp-video b-uploaded' frameborder='0'></iframe></div><br /><span style="font-family: "Times New Roman", "serif"; font-size: 12pt;"><br /></span><p></p><p class="MsoNormal"><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%; mso-ascii-theme-font: major-bidi; mso-bidi-theme-font: major-bidi; mso-hansi-theme-font: major-bidi;">When we start our analysis with this
model, for 10 combinations of these variables, we will also obtain 10 scenarios
for income statement as follows:<o:p></o:p></span></p><br /><p></p><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh-iq9L50T9zosmrAuVHkY9xus_6IM7eu2FOOLdB18fufZ_e8dN1g6Gz4fXeePMnSHZXZPkjjo6T6HMK2CCDfphYrsBgWxQdJYbPdWQtRPCjJnEvvog0ABaH1H6jjHYmMic566dMt92vyixkF6q1k1U8BR1fReldo445OGndAeCHgB_qeVaUI3zZlPcyCo/s1155/2.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="362" data-original-width="1155" height="100" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh-iq9L50T9zosmrAuVHkY9xus_6IM7eu2FOOLdB18fufZ_e8dN1g6Gz4fXeePMnSHZXZPkjjo6T6HMK2CCDfphYrsBgWxQdJYbPdWQtRPCjJnEvvog0ABaH1H6jjHYmMic566dMt92vyixkF6q1k1U8BR1fReldo445OGndAeCHgB_qeVaUI3zZlPcyCo/s320/2.png" width="320" /></a></div><br /><div><br /></div><div><p class="MsoNormal"><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%; mso-ascii-theme-font: major-bidi; mso-bidi-theme-font: major-bidi; mso-hansi-theme-font: major-bidi;">Please see the below video:<o:p></o:p></span></p><br /></div><div class="separator" style="clear: both; text-align: center;"><iframe allowfullscreen='allowfullscreen' webkitallowfullscreen='webkitallowfullscreen' mozallowfullscreen='mozallowfullscreen' width='320' height='266' src='https://www.blogger.com/video.g?token=AD6v5dznKYvzpvOB3VfF2nk7G3yEqFKXJzyYSfFiK30C33VIuAH3l_Ww56AeGl99Ugm6h0I9reWmctJt0IbLOSWVeg' class='b-hbp-video b-uploaded' frameborder='0'></iframe></div><br /><div><br /></div><div><p class="MsoNormal"><b><i><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%; mso-ascii-theme-font: major-bidi; mso-bidi-theme-font: major-bidi; mso-hansi-theme-font: major-bidi;">If you have any
questions, please do not hesitate to send them to my email address: </span></i></b><a href="mailto:Soleimani_gh@hotmail.com"><b><i><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%; mso-ascii-theme-font: major-bidi; mso-bidi-theme-font: major-bidi; mso-hansi-theme-font: major-bidi;">Soleimani_gh@hotmail.com</span></i></b></a><b><i><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%; mso-ascii-theme-font: major-bidi; mso-bidi-theme-font: major-bidi; mso-hansi-theme-font: major-bidi;"><o:p></o:p></span></i></b></p><i><b>WhatsApp: +98 9109250225</b></i></div>Gholamreza Soleimanihttp://www.blogger.com/profile/03273527405719420253noreply@blogger.com0tag:blogger.com,1999:blog-392703582366288634.post-79335880525798752082023-09-05T17:17:00.001+03:302023-09-05T17:25:40.774+03:30A Predictive Model to Discover the Relationship among Stocks, Forex, and Commodities: Application of DEMATEL Method<p> </p><p></p><p class="MsoNormal"><b><i><span style="font-family: "Times New Roman","serif"; font-size: 14pt; line-height: 115%; mso-ascii-theme-font: major-bidi; mso-bidi-theme-font: major-bidi; mso-hansi-theme-font: major-bidi;">“Search,
follow, and focus everywhere that there is very high daily frequency, high Beta
and high market cap then take your analysis to organize your own portfolio”<o:p></o:p></span></i></b></p><br /><p></p><p></p><p class="MsoNormal"><b><span style="font-family: "Times New Roman","serif"; font-size: 12pt; line-height: 115%; mso-ascii-theme-font: major-bidi; mso-bidi-theme-font: major-bidi; mso-hansi-theme-font: major-bidi;">ABSTRACT<o:p></o:p></span></b></p>
<p class="MsoNormal"><span style="font-family: "Times New Roman","serif"; font-size: 12pt; line-height: 115%; mso-ascii-theme-font: major-bidi; mso-bidi-theme-font: major-bidi; mso-hansi-theme-font: major-bidi;"><o:p> </o:p></span><span style="font-family: "Times New Roman", "serif"; font-size: 12pt;">To determine the relationship
between stocks, forex, and commodities, a prediction model utilizing Microsoft
Excel has been created. Three variables are measured to determine the
relationship: the distance between points, the growth curve, and the direction
of the motion. A portfolio of 20 assets has been chosen, comprising stocks,
forex, and commodities. The daily return rate (change %) calculation is the
only criterion to find the association. The DEMATEL method of decision-making
has been used to determine the importance of the influence assets collectively
as well as the high and low influencers, where the criterion is the direction
of the motion and the possibilities are 20 assets because the direction of the
motion is the most crucial characteristic to quantify the relationship. The
priority of the influence assets as a whole as well as the influential
relationships has been established for future study using the DEMATEL
technique.</span></p><p></p><p class="MsoNormal"><b><span style="font-family: "Times New Roman","serif"; font-size: 12pt; line-height: 115%; mso-ascii-theme-font: major-bidi; mso-bidi-theme-font: major-bidi; mso-hansi-theme-font: major-bidi;">Introduction <o:p></o:p></span></b></p><p class="MsoNormal"><b><span style="font-family: "Times New Roman","serif"; font-size: 12pt; line-height: 115%; mso-ascii-theme-font: major-bidi; mso-bidi-theme-font: major-bidi; mso-hansi-theme-font: major-bidi;"> </span></b><span style="font-family: "Times New Roman", "serif"; font-size: 12pt; line-height: 115%;">One of the simplest statistical
calculations you can carry out in Excel is correlation. Even though it is
simple, it is a huge aid in understanding the relationships between two or more
variables. It's crucial to understand that correlation simply reveals how
closely two variables are related to one another. However, a correlation does
not always predicate causation. It implies that the statement that altering one
variable will alter another is not always valid. Therefore, we have to use
different techniques to detect a causal relationship such as the nonlinear
regression, Structural Equation Modeling (SEM), </span><a href="https://www.statisticssolutions.com/free-resources/directory-of-statistical-analyses/factor-analysis/"><span color="windowtext" style="font-family: "Times New Roman", "serif"; font-size: 12pt; line-height: 115%; text-decoration-line: none;">factor
analysis</span></a><span style="font-family: "Times New Roman", "serif"; font-size: 12pt; line-height: 115%;">, </span><a href="https://www.statisticssolutions.com/data-analysis-plan-multiple-linear-regression/"><span color="windowtext" style="font-family: "Times New Roman", "serif"; font-size: 12pt; line-height: 115%; text-decoration-line: none;">multiple
regression analysis</span></a><span style="font-family: "Times New Roman", "serif"; font-size: 12pt; line-height: 115%;">, path analysis,
and so on. Python, R, or SCALA are the most common programming languages to
learn for predictive modeling that is based on machine learning.</span></p><p class="MsoNormal"><span style="font-family: "Times New Roman","serif"; font-size: 12pt; line-height: 115%; mso-ascii-theme-font: major-bidi; mso-bidi-theme-font: major-bidi; mso-hansi-theme-font: major-bidi;">In this project, a predictive model using
Microsoft Excel has been designed to extract the influential relationships
among the assets. <o:p></o:p></span></p><p class="MsoNormal"><span style="font-family: "Times New Roman","serif"; font-size: 12pt; line-height: 115%; mso-ascii-theme-font: major-bidi; mso-bidi-theme-font: major-bidi; mso-hansi-theme-font: major-bidi;"> </span><b><span style="font-family: "Times New Roman","serif"; font-size: 12pt; line-height: 115%; mso-ascii-theme-font: major-bidi; mso-bidi-theme-font: major-bidi; mso-hansi-theme-font: major-bidi;">Predictive
Model</span></b></p><p>
<span style="font-family: "Times New Roman","serif"; font-size: 12pt; line-height: 115%; mso-ansi-language: EN-US; mso-ascii-theme-font: major-bidi; mso-bidi-language: AR-SA; mso-bidi-theme-font: major-bidi; mso-fareast-font-family: Calibri; mso-fareast-language: EN-US; mso-fareast-theme-font: minor-latin; mso-hansi-theme-font: major-bidi;">A
predictive model is a type of data analysis that projects activity, behavior,
and trends using both recent and historical data. Of course, when it comes to the fundamentals
of prediction, we resort to traditional and fuzzy logic and state, "If p,
then q." Everything begins with the relationship between these two
hypotheses, "p" and "q," and is then continued and evolved
by the world's cause-and-effect chain. Since there is no such thing as absolute
zero in the cosmos, this network of networks will never come to an end. When I
first heard about classical logic in high school, I remember wondering why the
English letters "p" and "q" were used. A few years later,
after learning about fuzzy logic, I speculated that these two letters might act
as an "eyeglass" to help us see and understand our surroundings more
clearly.</span></p><p></p><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgBc2x1GxOx8iKZkxtixpzKicxTDfInoLudJQnRXV9WKWjAD7WLH-KmGdA19ckyT0-B4e9G-y2z2F79Xq1909EMIZsoZxYRGnyWqhRg7AlN9b4NX_kTCFOIW-v69wTLQ_gZ__wWLnlWtLN69j3P8SJD8s18apkslnqjsUXTizUgRjAfIIoN8ePJAQwLi0I/s642/1.png" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="385" data-original-width="642" height="192" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgBc2x1GxOx8iKZkxtixpzKicxTDfInoLudJQnRXV9WKWjAD7WLH-KmGdA19ckyT0-B4e9G-y2z2F79Xq1909EMIZsoZxYRGnyWqhRg7AlN9b4NX_kTCFOIW-v69wTLQ_gZ__wWLnlWtLN69j3P8SJD8s18apkslnqjsUXTizUgRjAfIIoN8ePJAQwLi0I/s320/1.png" width="320" /></a></div><br /><span style="font-family: "Times New Roman","serif"; font-size: 12pt; line-height: 115%; mso-ansi-language: EN-US; mso-ascii-theme-font: major-bidi; mso-bidi-language: AR-SA; mso-bidi-theme-font: major-bidi; mso-fareast-font-family: Calibri; mso-fareast-language: EN-US; mso-fareast-theme-font: minor-latin; mso-hansi-theme-font: major-bidi;"><p class="MsoNormal"><span style="font-family: "Times New Roman","serif"; font-size: 12pt; line-height: 115%; mso-ascii-theme-font: major-bidi; mso-bidi-theme-font: major-bidi; mso-hansi-theme-font: major-bidi;">In this project, a predictive model
has been designed using Microsoft Excel.<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-family: "Times New Roman","serif"; font-size: 12pt; line-height: 115%; mso-ascii-theme-font: major-bidi; mso-bidi-theme-font: major-bidi; mso-hansi-theme-font: major-bidi;">How is the data processed by this
model?<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-family: "Times New Roman","serif"; font-size: 12pt; line-height: 115%; mso-ascii-theme-font: major-bidi; mso-bidi-theme-font: major-bidi; mso-hansi-theme-font: major-bidi;">There are four fields for data entry
in Step 1: "Date" and "Price" for each asset. Excel
requires four columns since we wish to compare two assets.<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-family: "Times New Roman","serif"; font-size: 12pt; line-height: 115%; mso-ascii-theme-font: major-bidi; mso-bidi-theme-font: major-bidi; mso-hansi-theme-font: major-bidi;">Step 2: Because there are typically
certain gaps between the dates of two assets, the system automatically matches
the dates of both assets into one column when we enter historical data for any
asset (date and price). This acts as a kind of timing index.<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-family: "Times New Roman","serif"; font-size: 12pt; line-height: 115%; mso-ascii-theme-font: major-bidi; mso-bidi-theme-font: major-bidi; mso-hansi-theme-font: major-bidi;">Step 3: In front of the index date
column, the price of each asset will be split into one column.<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-family: "Times New Roman","serif"; font-size: 12pt; line-height: 115%; mso-ascii-theme-font: major-bidi; mso-bidi-theme-font: major-bidi; mso-hansi-theme-font: major-bidi;">Step 4: The rate of return will be
calculated for each asset’s price <o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-family: "Times New Roman","serif"; font-size: 12pt; line-height: 115%; mso-ascii-theme-font: major-bidi; mso-bidi-theme-font: major-bidi; mso-hansi-theme-font: major-bidi;">Step 5: According to the return
rate, the direction of motion for both assets and two consecutive days is
evaluated; if the assets are moving in the same way, the result will be
"1," otherwise "0." The total rows of return rate will then
be divided by the total number of "1"s. The outcome will be regarded
as the direction's likelihood.</span><span dir="RTL" lang="FA" style="font-family: "Times New Roman","serif"; font-size: 12pt; line-height: 115%; mso-ascii-theme-font: major-bidi; mso-bidi-language: FA; mso-bidi-theme-font: major-bidi; mso-hansi-theme-font: major-bidi;"><o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-family: "Times New Roman","serif"; font-size: 12pt; line-height: 115%; mso-ascii-theme-font: major-bidi; mso-bidi-theme-font: major-bidi; mso-hansi-theme-font: major-bidi;">Step 6: When calculating the return
rate for both assets in a single day, the distance between the points will be
taken into account. If the difference between the two points is less than the
distance change, the result will be "1," otherwise "0." The
total rows of return rate will then be divided by the total number of
"1"s. The outcome will be regarded as the distance's probability.<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-family: "Times New Roman","serif"; font-size: 12pt; line-height: 115%; mso-ascii-theme-font: major-bidi; mso-bidi-theme-font: major-bidi; mso-hansi-theme-font: major-bidi;">Step 7: The growth curve between two
assets will be measured, where if the difference return rate between two assets
in one day and the difference return rate between two assets in the next day is
less than the growth rate, it will be "1" otherwise "0".
Then total numbers of ‘1" will be divided by total rows of return rate.
The result will be considered as the probability for the growth curve.<o:p></o:p></span></p>
<p class="MsoNormal"><b><i><span style="font-family: "Times New Roman","serif"; font-size: 12pt; line-height: 115%; mso-ascii-theme-font: major-bidi; mso-bidi-theme-font: major-bidi; mso-hansi-theme-font: major-bidi;">Remark: It
appears that steps 6 and 7 are equivalent. Even though there is a significant
difference in the return rates of two assets, it is still feasible that their
growth curves are similar. As a result, I must separate the growth curve and
the distance appropriately. (Please view the video below.)</span></i></b><span style="font-family: "Times New Roman","serif"; font-size: 12pt; line-height: 115%; mso-ascii-theme-font: major-bidi; mso-bidi-theme-font: major-bidi; mso-hansi-theme-font: major-bidi;"><o:p></o:p></span></p><br /></span><p></p><p></p><div class="separator" style="clear: both; text-align: center;"><iframe allowfullscreen='allowfullscreen' webkitallowfullscreen='webkitallowfullscreen' mozallowfullscreen='mozallowfullscreen' width='320' height='266' src='https://www.blogger.com/video.g?token=AD6v5dzgvTrqYVnCve7m_ygAAjMOItjFAdW48KAtghBUIouWyhq4828iM-KEYPnV-5-zz54F_zohAGP2SKcqoEpiOQ' class='b-hbp-video b-uploaded' frameborder='0'></iframe></div><br /><div class="separator" style="clear: both; text-align: center;"><br /></div><br /><span style="font-family: "Times New Roman","serif"; font-size: 12pt; line-height: 115%; mso-ansi-language: EN-US; mso-ascii-theme-font: major-bidi; mso-bidi-language: AR-SA; mso-bidi-theme-font: major-bidi; mso-fareast-font-family: Calibri; mso-fareast-language: EN-US; mso-fareast-theme-font: minor-latin; mso-hansi-theme-font: major-bidi;"><p class="MsoNormal"><span style="font-family: "Times New Roman","serif"; font-size: 12pt; line-height: 115%; mso-ascii-theme-font: major-bidi; mso-bidi-theme-font: major-bidi; mso-hansi-theme-font: major-bidi;">Step 8: </span><span style="mso-ascii-font-family: Calibri; mso-bidi-font-family: Arial; mso-fareast-font-family: Calibri; mso-hansi-font-family: Calibri;">The measurement of
the correlation using Microsoft Excel for the time series of return rates for
both assets<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-family: "Times New Roman","serif"; font-size: 12pt; line-height: 115%; mso-ascii-theme-font: major-bidi; mso-bidi-theme-font: major-bidi; mso-hansi-theme-font: major-bidi;">Step 9: Using the sensitivity
analysis in Microsoft Excel to reach the distance and growth rate with more
than 95% probability<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-family: "Times New Roman","serif"; font-size: 12pt; line-height: 115%; mso-ascii-theme-font: major-bidi; mso-bidi-theme-font: major-bidi; mso-hansi-theme-font: major-bidi;">Step 10: The aforementioned
processes (5), (6), (7), and (8) are once more computed to forecast a one-day
delay between two assets, where we say: "If asset X is high, then asset Y
will be high in the next day" and vice versa. Each of the three variables'
probabilities will be taken into account.<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-family: "Times New Roman","serif"; font-size: 12pt; line-height: 115%; mso-ascii-theme-font: major-bidi; mso-bidi-theme-font: major-bidi; mso-hansi-theme-font: major-bidi;">The figure below illustrates each of
the aforementioned steps:</span><b><span style="font-family: "Times New Roman","serif"; font-size: 8pt; line-height: 115%; mso-ascii-theme-font: major-bidi; mso-bidi-theme-font: major-bidi; mso-hansi-theme-font: major-bidi; mso-no-proof: yes;"> <o:p></o:p></span></b></p><p class="MsoNormal"><span style="font-family: "Times New Roman","serif"; font-size: 12pt; line-height: 115%; mso-ascii-theme-font: major-bidi; mso-bidi-theme-font: major-bidi; mso-hansi-theme-font: major-bidi;"><br /></span></p><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhC6_Ao_PeXNspCwjjTch9ye6GJD55gJtn7NSqOnTy8vvBstXRnOOgXe6k3nqRnGXPnnGjKy3vWocarvSVqkgPkq8wxT4m2veOeF8nQF3X_VVaOck3BlHg8OeNXCs7bKlkOZ3EQVdWZus7UoDDxK4YRwz9gkOLmAXbeIx37mfg4WYa1dkNjw7Kl_VEMCPE/s1255/3.png" style="font-family: "Times New Roman"; font-size: medium; margin-left: 1em; margin-right: 1em; text-align: center;"><img border="0" data-original-height="580" data-original-width="1255" height="148" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhC6_Ao_PeXNspCwjjTch9ye6GJD55gJtn7NSqOnTy8vvBstXRnOOgXe6k3nqRnGXPnnGjKy3vWocarvSVqkgPkq8wxT4m2veOeF8nQF3X_VVaOck3BlHg8OeNXCs7bKlkOZ3EQVdWZus7UoDDxK4YRwz9gkOLmAXbeIx37mfg4WYa1dkNjw7Kl_VEMCPE/s320/3.png" width="320" /></a></span><p></p><p class="MsoNormal"><b><span style="font-family: "Times New Roman","serif"; font-size: 12pt; line-height: 115%; mso-ascii-theme-font: major-bidi; mso-bidi-theme-font: major-bidi; mso-hansi-theme-font: major-bidi;">Finding<o:p></o:p></span></b></p><p class="MsoNormal"><span style="font-family: "Times New Roman","serif"; font-size: 12pt; line-height: 115%; mso-ascii-theme-font: major-bidi; mso-bidi-theme-font: major-bidi; mso-hansi-theme-font: major-bidi;">Comparing the currencies
"EUR/HKD" and "EUR/AED" is one of the better examples that
have been discovered.<o:p></o:p></span></p><p class="MsoNormal"><span style="font-family: "Times New Roman","serif"; font-size: 12pt; line-height: 115%; mso-ascii-theme-font: major-bidi; mso-bidi-theme-font: major-bidi; mso-hansi-theme-font: major-bidi;">We can observe that this model and
the prior 10-year historical data have a strong relationship; therefore, we may
use them as the index for future investigations. <o:p></o:p></span></p><p>
</p><p class="MsoNormal"><span style="font-family: "Times New Roman","serif"; font-size: 12pt; line-height: 115%; mso-ascii-theme-font: major-bidi; mso-bidi-theme-font: major-bidi; mso-hansi-theme-font: major-bidi;">Please see below video:<o:p></o:p></span></p><p class="MsoNormal"><span style="font-family: "Times New Roman","serif"; font-size: 12pt; line-height: 115%; mso-ascii-theme-font: major-bidi; mso-bidi-theme-font: major-bidi; mso-hansi-theme-font: major-bidi;"><br /></span></p><p class="MsoNormal"></p><div class="separator" style="clear: both; text-align: center;"><iframe allowfullscreen='allowfullscreen' webkitallowfullscreen='webkitallowfullscreen' mozallowfullscreen='mozallowfullscreen' width='320' height='266' src='https://www.blogger.com/video.g?token=AD6v5dwiCChoGShrnPgQUEf5HMnJ88IqnEc5dDyRcBw57nbEcUvaW_honXWeuaXTmTqzgHpby28bWI03iRirQXmb-Q' class='b-hbp-video b-uploaded' frameborder='0'></iframe></div><br /><span style="font-family: "Times New Roman","serif"; font-size: 12pt; line-height: 115%; mso-ascii-theme-font: major-bidi; mso-bidi-theme-font: major-bidi; mso-hansi-theme-font: major-bidi;"></span><p></p><p class="MsoNormal"><span style="font-family: "Times New Roman","serif"; font-size: 12pt; line-height: 115%; mso-ascii-theme-font: major-bidi; mso-bidi-theme-font: major-bidi; mso-hansi-theme-font: major-bidi;">Let me verify the information above
using the following historical diagram that I have taken from the Yahoo Finance
website:<o:p></o:p></span></p><p class="MsoNormal"><span style="font-family: "Times New Roman","serif"; font-size: 12pt; line-height: 115%; mso-ascii-theme-font: major-bidi; mso-bidi-theme-font: major-bidi; mso-hansi-theme-font: major-bidi;"><br /></span></p><p class="MsoNormal"></p><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjKZ4di6yyDaLwmS8XsWdSsl2BAizix0k0XTq98yfll_NpjTcC9bsHKsVgKXkhyDfCmxlx3aEATdUGA37VrNHEenW_RLYpghHJ_lWofXw--pMAqooFS4K8eCbQiFOUGCQANJUSjVrw4mHr8qo26615_N9b7g2Y-o79IFoz9inJfkkTeFdBiAhpHefba0Lg/s1027/hkd.png" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="465" data-original-width="1027" height="145" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjKZ4di6yyDaLwmS8XsWdSsl2BAizix0k0XTq98yfll_NpjTcC9bsHKsVgKXkhyDfCmxlx3aEATdUGA37VrNHEenW_RLYpghHJ_lWofXw--pMAqooFS4K8eCbQiFOUGCQANJUSjVrw4mHr8qo26615_N9b7g2Y-o79IFoz9inJfkkTeFdBiAhpHefba0Lg/s320/hkd.png" width="320" /></a></div><br /><span style="font-family: Times New Roman, serif;">Historical data of EUR/HKD (more than 10 years) </span><p></p><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjJEpRGUqAlD9J1aE8glAhDf5Sqwbvoxy7pueFb5ivrrYu8PQRYbNySidChg91OSqg_1l3EjLrOKatRBbht-x0RLK8Ipm-3EF6tU5vpTa3g5g0bdViDiLvzsws4URCIYq-7H6R_T4Cwi6YOLSPVZis6dl0GntDKS0_qy9dHJWyFxYkBVT6cj7PeBEuoCZA/s1028/aed.png" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="455" data-original-width="1028" height="142" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjJEpRGUqAlD9J1aE8glAhDf5Sqwbvoxy7pueFb5ivrrYu8PQRYbNySidChg91OSqg_1l3EjLrOKatRBbht-x0RLK8Ipm-3EF6tU5vpTa3g5g0bdViDiLvzsws4URCIYq-7H6R_T4Cwi6YOLSPVZis6dl0GntDKS0_qy9dHJWyFxYkBVT6cj7PeBEuoCZA/s320/aed.png" width="320" /></a></div><p><span style="font-family: "Times New Roman", serif;">Historical data of EUR/AED (more than 10 years) </span></p><p><span style="font-family: "Times New Roman", serif;"><br /></span></p><p></p><p class="MsoNormal"><span style="font-family: "Times New Roman","serif"; font-size: 12pt; line-height: 115%; mso-fareast-font-family: Calibri;">As you can see, all
three variables have a good relationship with each other, so we can say that
for a relationship rate greater than 80%, there are the following connections:<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-family: "Times New Roman","serif"; font-size: 12pt; line-height: 115%; mso-fareast-font-family: Calibri;">If
"EUR/HKD" is high or low, then "EUR/AED" is high or low.<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-family: "Times New Roman","serif"; font-size: 12pt; line-height: 115%; mso-fareast-font-family: Calibri;">And <o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-family: "Times New Roman","serif"; font-size: 12pt; line-height: 115%; mso-fareast-font-family: Calibri;">If
"EUR/AED" is high or low, "EUR/HKD" is high or low.<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-family: "Times New Roman","serif"; font-size: 12pt; line-height: 115%; mso-fareast-font-family: Calibri;"><span style="mso-spacerun: yes;"> </span>Or: <o:p></o:p></span></p><p class="MsoNormal"></p><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjrxO872MqDzPKuIZJtBSHe4O4cAJEBSp9ZaNYT6Lo8HvBGc1X_3iB6F74LA0idAqsRJN5ANDa_LGZfh1CexDhINESAzXSps5_V6RNQuUTYjJ2PJRylIZdtEsb-z_nb2lgZiDGlsENNHGRCg5BPqN9RqOrNl5XUmbxX5iRUKWvLoMjUDYFnrylLMuFEWeE/s386/4.png" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="104" data-original-width="386" height="86" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjrxO872MqDzPKuIZJtBSHe4O4cAJEBSp9ZaNYT6Lo8HvBGc1X_3iB6F74LA0idAqsRJN5ANDa_LGZfh1CexDhINESAzXSps5_V6RNQuUTYjJ2PJRylIZdtEsb-z_nb2lgZiDGlsENNHGRCg5BPqN9RqOrNl5XUmbxX5iRUKWvLoMjUDYFnrylLMuFEWeE/s320/4.png" width="320" /></a></div><br /><p></p><p class="MsoNormal"><span style="font-family: "Times New Roman","serif"; font-size: 12pt; line-height: 115%; mso-ascii-theme-font: major-bidi; mso-bidi-theme-font: major-bidi; mso-fareast-font-family: Calibri; mso-hansi-theme-font: major-bidi;">Of
course, if a one-day delay is predicted, the proportion will drop
significantly.<o:p></o:p></span></p><p class="MsoNormal"><span style="font-family: "Times New Roman","serif"; font-size: 12pt; line-height: 115%; mso-ascii-theme-font: major-bidi; mso-bidi-theme-font: major-bidi; mso-fareast-font-family: Calibri; mso-hansi-theme-font: major-bidi;"><br /></span></p><span style="font-family: "Times New Roman", serif;"></span><p></p><p class="MsoNormal"><b><span style="font-family: "Times New Roman","serif"; font-size: 12pt; line-height: 115%; mso-ascii-theme-font: major-bidi; mso-bidi-theme-font: major-bidi; mso-fareast-font-family: Calibri; mso-hansi-theme-font: major-bidi;"> </span></b><b><span style="font-family: "Times New Roman","serif"; font-size: 12pt; line-height: 115%; mso-ascii-theme-font: major-bidi; mso-bidi-theme-font: major-bidi; mso-fareast-font-family: Calibri; mso-hansi-theme-font: major-bidi;">DEMATEL Method</span></b></p><p class="MsoNormal"><span style="font-family: "Times New Roman","serif"; font-size: 12pt; line-height: 115%; mso-fareast-font-family: Calibri;">
</span></p><p class="MsoNormal"><span style="font-family: "Times New Roman","serif"; font-size: 12pt; line-height: 115%; mso-ascii-theme-font: major-bidi; mso-bidi-theme-font: major-bidi; mso-fareast-font-family: Calibri; mso-hansi-theme-font: major-bidi;">This
project's goal is to use the DEMATEL technique, where a portfolio of assets has
only been evaluated using one criterion, the return rate. This method aids in
depicting the ad hoc relationship between the alternative assets as well as
prioritizing them.<o:p></o:p></span></p><p class="MsoNormal"><span style="font-family: "Times New Roman","serif"; font-size: 12pt; line-height: 115%; mso-ascii-theme-font: major-bidi; mso-bidi-theme-font: major-bidi; mso-fareast-font-family: Calibri; mso-hansi-theme-font: major-bidi;"></span></p><p class="MsoNormal"><span style="font-family: "Times New Roman","serif"; font-size: 12pt; line-height: 115%; mso-ascii-theme-font: major-bidi; mso-bidi-theme-font: major-bidi; mso-fareast-font-family: Calibri; mso-hansi-theme-font: major-bidi;">The
Battelle Memorial Institute's Geneva Research Center launched the Decision
Making Trial and Evaluation Laboratory (DEMATEL). DEMATEL plots a causal link
map and offers visual answers to issues, making it possible to separate many
criteria into a cause-and-effect diagram.<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-family: "Times New Roman","serif"; font-size: 12pt; line-height: 115%; mso-ascii-theme-font: major-bidi; mso-bidi-theme-font: major-bidi; mso-fareast-font-family: Calibri; mso-hansi-theme-font: major-bidi;">The
procedure of the DEMATEL technique is composed of five steps, as follows:<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-family: "Times New Roman","serif"; font-size: 12pt; line-height: 115%; mso-ascii-theme-font: major-bidi; mso-bidi-theme-font: major-bidi; mso-fareast-font-family: Calibri; mso-hansi-theme-font: major-bidi;">Step 1:
Obtain the pair-wise comparison matrix and establish a measurement scale, such
as a Likert scale.<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-family: "Times New Roman","serif"; font-size: 12pt; line-height: 115%; mso-ascii-theme-font: major-bidi; mso-bidi-theme-font: major-bidi; mso-fareast-font-family: Calibri; mso-hansi-theme-font: major-bidi;">Step 2:
Extract the direct relationship matrix of influential factors.<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-family: "Times New Roman","serif"; font-size: 12pt; line-height: 115%; mso-ascii-theme-font: major-bidi; mso-bidi-theme-font: major-bidi; mso-fareast-font-family: Calibri; mso-hansi-theme-font: major-bidi;">Step 3:
Calculate the normalized direction-relation matrix.<o:p></o:p></span></p><br /><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh-puI9gmkCl95aajcFSPfzIB0slNbYbK4ilHDZAssyTAuMgvKuOSZENhhnF2oFvicv86EgUL1GYVOnL4GLZbiWQ2lxHM1GiEWJglfnSetOR5qM6hn_buakUhRq3RepVVS2qEL1bqZLsxFzwOc8V11C5s9cTQ2Nnm5LKVERnxgOJyodISoCORouHG8iIPw/s485/5.png" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="189" data-original-width="485" height="125" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh-puI9gmkCl95aajcFSPfzIB0slNbYbK4ilHDZAssyTAuMgvKuOSZENhhnF2oFvicv86EgUL1GYVOnL4GLZbiWQ2lxHM1GiEWJglfnSetOR5qM6hn_buakUhRq3RepVVS2qEL1bqZLsxFzwOc8V11C5s9cTQ2Nnm5LKVERnxgOJyodISoCORouHG8iIPw/s320/5.png" width="320" /></a></div><p class="MsoNormal"><span style="font-family: "Times New Roman","serif"; font-size: 12pt; line-height: 115%; mso-ascii-theme-font: major-bidi; mso-bidi-theme-font: major-bidi; mso-fareast-font-family: Calibri; mso-hansi-theme-font: major-bidi;">Where: <o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-family: "Times New Roman","serif"; font-size: 12pt; line-height: 115%; mso-ascii-theme-font: major-bidi; mso-bidi-theme-font: major-bidi; mso-fareast-font-family: Calibri; mso-hansi-theme-font: major-bidi;">N = Normalized
Direction-Relation Matrix<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-family: "Times New Roman","serif"; font-size: 12pt; line-height: 115%; mso-ascii-theme-font: major-bidi; mso-bidi-theme-font: major-bidi; mso-fareast-font-family: Calibri; mso-hansi-theme-font: major-bidi;">D = Direct
Relation Matrix<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-family: "Times New Roman","serif"; font-size: 12pt; line-height: 115%; mso-ascii-theme-font: major-bidi; mso-bidi-theme-font: major-bidi; mso-fareast-font-family: Calibri; mso-hansi-theme-font: major-bidi;">d<sub>ij</sub>
= a member of Direct Relation Matrix<o:p></o:p></span></p><p class="MsoNormal"><span style="font-family: "Times New Roman","serif"; font-size: 12pt; line-height: 115%; mso-ascii-theme-font: major-bidi; mso-bidi-theme-font: major-bidi; mso-fareast-font-family: Calibri; mso-hansi-theme-font: major-bidi;"><br /></span></p><p class="MsoNormal"><span style="font-family: "Times New Roman","serif"; font-size: 12pt; line-height: 115%; mso-ascii-theme-font: major-bidi; mso-bidi-theme-font: major-bidi; mso-fareast-font-family: Calibri; mso-hansi-theme-font: major-bidi;">Step 4:
Compute the Total Relation Matrix from below function:<o:p></o:p></span></p><br /><p></p><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEg1A_aAbeMap10I6fCCXG2ypuh4gGbDQ6B-xMQUVHgxu93Qj0CWdAg2FlTRViGk5kdtizv_JpQgoBDxeZmTijgUJAhQZ9K1hjtJji5UwEGRdkt1ogfMTc6HuJ-66KqLlJFMS_p-tzGZmPaXcdCKwPkC-si1cohNtJNaI0ulnlCsryfO30sLpZZkvEKR6HA/s787/6.png" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="105" data-original-width="787" height="43" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEg1A_aAbeMap10I6fCCXG2ypuh4gGbDQ6B-xMQUVHgxu93Qj0CWdAg2FlTRViGk5kdtizv_JpQgoBDxeZmTijgUJAhQZ9K1hjtJji5UwEGRdkt1ogfMTc6HuJ-66KqLlJFMS_p-tzGZmPaXcdCKwPkC-si1cohNtJNaI0ulnlCsryfO30sLpZZkvEKR6HA/s320/6.png" width="320" /></a></div><p class="MsoNormal"><span style="font-family: "Times New Roman","serif"; font-size: 12pt; line-height: 115%; mso-ascii-theme-font: major-bidi; mso-bidi-theme-font: major-bidi; mso-fareast-font-family: Calibri; mso-hansi-theme-font: major-bidi;">Where:<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-family: "Times New Roman","serif"; font-size: 12pt; line-height: 115%; mso-ascii-theme-font: major-bidi; mso-bidi-theme-font: major-bidi; mso-fareast-font-family: Calibri; mso-hansi-theme-font: major-bidi;"><span style="mso-spacerun: yes;"> </span>I = the identity matrix<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-family: "Times New Roman","serif"; font-size: 12pt; line-height: 115%; mso-ascii-theme-font: major-bidi; mso-bidi-theme-font: major-bidi; mso-fareast-font-family: Calibri; mso-hansi-theme-font: major-bidi;">N = Normalized
Direction-Relation Matrix<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-family: "Times New Roman","serif"; font-size: 12pt; line-height: 115%; mso-ascii-theme-font: major-bidi; mso-bidi-theme-font: major-bidi; mso-fareast-font-family: Calibri; mso-hansi-theme-font: major-bidi;">T = Total
Relation Matrix<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-family: "Times New Roman","serif"; font-size: 12pt; line-height: 115%; mso-ascii-theme-font: major-bidi; mso-bidi-theme-font: major-bidi; mso-fareast-font-family: Calibri; mso-hansi-theme-font: major-bidi;"><o:p> </o:p></span></p>
<p class="MsoNormal"><span style="font-family: "Times New Roman","serif"; font-size: 12pt; line-height: 115%; mso-ascii-theme-font: major-bidi; mso-bidi-theme-font: major-bidi; mso-fareast-font-family: Calibri; mso-hansi-theme-font: major-bidi;">Step 5:
Obtain the causal relationship.<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-family: "Times New Roman","serif"; font-size: 12pt; line-height: 115%; mso-ascii-theme-font: major-bidi; mso-bidi-theme-font: major-bidi; mso-fareast-font-family: Calibri; mso-hansi-theme-font: major-bidi;">The i<sup>th</sup>
row and j<sup>th</sup> column of the complete relationship matrix T should be
designated as R<sub>i</sub> and C<sub>j</sub>. The sum (R<sub>i</sub> + C<sub>j</sub>)
indicates the degree of significance that element i (i = j) has within the
entire system. But (R<sub>i</sub> - C<sub>j</sub>) shows the net impact of
element i with (i = j). The net cause is revealed when the difference is
positive, and the net effect is shown when the difference is negative. The
values of (R<sub>i</sub> + C<sub>j</sub>) are plotted along the x axis, while
(R<sub>i</sub> - C<sub>j</sub>) are plotted along the y axis.<o:p></o:p></span></p>
<p class="MsoNormal"><b><span style="font-family: "Times New Roman","serif"; font-size: 12pt; line-height: 115%; mso-ascii-theme-font: major-bidi; mso-bidi-theme-font: major-bidi; mso-fareast-font-family: Calibri; mso-hansi-theme-font: major-bidi;">Application of DEMATEL to evaluate the relationships among the
assets<o:p></o:p></span></b></p>
<p class="MsoNormal"><span style="font-family: "Times New Roman","serif"; font-size: 12pt; line-height: 115%; mso-ascii-theme-font: major-bidi; mso-bidi-theme-font: major-bidi; mso-fareast-font-family: Calibri; mso-hansi-theme-font: major-bidi;">The
DEMATEL method's general steps have been used as follows:<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-family: "Times New Roman","serif"; font-size: 12pt; line-height: 115%; mso-ascii-theme-font: major-bidi; mso-bidi-theme-font: major-bidi; mso-fareast-font-family: Calibri; mso-hansi-theme-font: major-bidi;">Prior
to beginning step 1, we must choose our portfolio of assets, which should
include the company's stocks, currency pairings, cryptocurrencies, and
commodities. Since there are only a few widely used currencies and commodities,
picking them up doesn't need to take too much time, but choosing stocks does
require a plan for research and analysis.<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-family: "Times New Roman","serif"; font-size: 12pt; line-height: 115%; mso-ascii-theme-font: major-bidi; mso-bidi-theme-font: major-bidi; mso-fareast-font-family: Calibri; mso-hansi-theme-font: major-bidi;">Typically,
we order the stocks based on the six factors listed below:<o:p></o:p></span></p>
<ol start="1" style="margin-top: 0mm;" type="1">
<li class="MsoNormal" style="mso-list: l0 level1 lfo1; tab-stops: list 36.0pt;"><span style="font-family: "Times New Roman","serif"; font-size: 12pt; line-height: 115%; mso-ascii-theme-font: major-bidi; mso-bidi-theme-font: major-bidi; mso-fareast-font-family: Calibri; mso-hansi-theme-font: major-bidi;">High
market capitalization (high market cap)<o:p></o:p></span></li>
<li class="MsoNormal" style="mso-list: l0 level1 lfo1; tab-stops: list 36.0pt;"><span style="font-family: "Times New Roman","serif"; font-size: 12pt; line-height: 115%; mso-ascii-theme-font: major-bidi; mso-bidi-theme-font: major-bidi; mso-fareast-font-family: Calibri; mso-hansi-theme-font: major-bidi;">High beta
(beta > 1.1)<o:p></o:p></span></li>
<li class="MsoNormal" style="mso-list: l0 level1 lfo1; tab-stops: list 36.0pt;"><span style="font-family: "Times New Roman","serif"; font-size: 12pt; line-height: 115%; mso-ascii-theme-font: major-bidi; mso-bidi-theme-font: major-bidi; mso-fareast-font-family: Calibri; mso-hansi-theme-font: major-bidi;">Very high
daily frequency on the daily prices</span></li><li class="MsoNormal" style="mso-list: l0 level1 lfo1; tab-stops: list 36.0pt;"><span style="font-family: "Times New Roman","serif"; font-size: 12pt; line-height: 115%; mso-ascii-theme-font: major-bidi; mso-bidi-theme-font: major-bidi; mso-fareast-font-family: Calibri; mso-hansi-theme-font: major-bidi;">Very large
range of changes (return rate) per day during a period of historical data<o:p></o:p></span></li>
<li class="MsoNormal" style="mso-list: l0 level1 lfo1; tab-stops: list 36.0pt;"><span style="font-family: "Times New Roman","serif"; font-size: 12pt; line-height: 115%; mso-ascii-theme-font: major-bidi; mso-bidi-theme-font: major-bidi; mso-fareast-font-family: Calibri; mso-hansi-theme-font: major-bidi;">To track
the change in volume per day during a period of historical data<o:p></o:p></span></li>
<li class="MsoNormal" style="mso-list: l0 level1 lfo1; tab-stops: list 36.0pt;"><span style="font-family: "Times New Roman","serif"; font-size: 12pt; line-height: 115%; mso-ascii-theme-font: major-bidi; mso-bidi-theme-font: major-bidi; mso-fareast-font-family: Calibri; mso-hansi-theme-font: major-bidi;">Price-to-Earnings
Ratio (PE ratio)<o:p></o:p></span></li>
</ol>
<p class="MsoNormal"><span style="font-family: "Times New Roman","serif"; font-size: 12pt; line-height: 115%; mso-ascii-theme-font: major-bidi; mso-bidi-theme-font: major-bidi; mso-fareast-font-family: Calibri; mso-hansi-theme-font: major-bidi;">The top
four factors are more crucial than the rest.<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-family: "Times New Roman","serif"; font-size: 12pt; line-height: 115%; mso-ascii-theme-font: major-bidi; mso-bidi-theme-font: major-bidi; mso-fareast-font-family: Calibri; mso-hansi-theme-font: major-bidi;">I have
chosen 20 assets for this project to create an initial matrix, and they are as
follows:<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-family: "Times New Roman","serif"; font-size: 12pt; line-height: 115%; mso-ascii-theme-font: major-bidi; mso-bidi-theme-font: major-bidi; mso-fareast-font-family: Calibri; mso-hansi-theme-font: major-bidi;">A ={X<sub>1,
</sub>X<sub>2, </sub>X<sub>3 …</sub>X<sub>20</sub>}<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-family: "Times New Roman","serif"; font-size: 12pt; line-height: 115%; mso-ascii-theme-font: major-bidi; mso-bidi-theme-font: major-bidi; mso-fareast-font-family: Calibri; mso-hansi-theme-font: major-bidi;">The
following are two different initial matrix types that have been created:<o:p></o:p></span></p>
<p class="MsoNormal"><b><span style="font-family: "Times New Roman","serif"; font-size: 12pt; line-height: 115%; mso-ascii-theme-font: major-bidi; mso-bidi-theme-font: major-bidi; mso-fareast-font-family: Calibri; mso-hansi-theme-font: major-bidi;">- DEMATEL approach on asset return rates with no delay<o:p></o:p></span></b></p>
<p class="MsoNormal"><b><span style="font-family: "Times New Roman","serif"; font-size: 12pt; line-height: 115%; mso-ascii-theme-font: major-bidi; mso-bidi-theme-font: major-bidi; mso-fareast-font-family: Calibri; mso-hansi-theme-font: major-bidi;">- One-day delay in the return rates of two assets using the DEMATEL
approach<o:p></o:p></span></b></p>
<p class="MsoNormal"><span style="font-family: "Times New Roman","serif"; font-size: 12pt; line-height: 115%; mso-ascii-theme-font: major-bidi; mso-bidi-theme-font: major-bidi; mso-fareast-font-family: Calibri; mso-hansi-theme-font: major-bidi;">Both
types of assets are examined for their direction of motion during two
successive days, and the likelihood that a relationship will exist between the
two is computed in order to create the initial matrix. It is obvious that
future studies will delve into detail and depth using the variables of distance
between the points and growth curve.<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-family: "Times New Roman","serif"; font-size: 12pt; line-height: 115%; mso-ascii-theme-font: major-bidi; mso-bidi-theme-font: major-bidi; mso-fareast-font-family: Calibri; mso-hansi-theme-font: major-bidi;">For
both categories, a Likert scale has been taken into consideration as follows:<o:p></o:p></span></p><br /><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhFhypQUzf5eRizTi91SdYl5TvIMnGaNVF3V4FxXDJBxWPzyXkZX8XPrkHBW5mJUUybiCi38HapNtqiAkdWBBCjTNvn5DGuklYpucKfmDesyjtMN5CMu9Zg8ot9j-qtsvaORjopJTNfPbSPeVOpxBcawzySMXx1CY18kP6yotHGUHTe7IQ1d_pvuTViStc/s539/7.png" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="262" data-original-width="539" height="156" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhFhypQUzf5eRizTi91SdYl5TvIMnGaNVF3V4FxXDJBxWPzyXkZX8XPrkHBW5mJUUybiCi38HapNtqiAkdWBBCjTNvn5DGuklYpucKfmDesyjtMN5CMu9Zg8ot9j-qtsvaORjopJTNfPbSPeVOpxBcawzySMXx1CY18kP6yotHGUHTe7IQ1d_pvuTViStc/s320/7.png" width="320" /></a></div><p class="MsoNormal"><b><span style="font-family: "Times New Roman","serif"; font-size: 12pt; line-height: 115%; mso-ascii-theme-font: major-bidi; mso-bidi-theme-font: major-bidi; mso-fareast-font-family: Calibri; mso-hansi-theme-font: major-bidi;">DEMATEL approach on asset return rates with no delay<o:p></o:p></span></b></p>
<p class="MsoNormal"><span style="font-family: "Times New Roman","serif"; font-size: 12pt; line-height: 115%; mso-ascii-theme-font: major-bidi; mso-bidi-theme-font: major-bidi; mso-fareast-font-family: Calibri; mso-hansi-theme-font: major-bidi;">Because
the probability results represent a biconditional logical connective among the
asset return rates in this procedure, the pair-wise comparison matrix is
symmetric. As a result, step (1) is as follows:<o:p></o:p></span></p><br /><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEi_E6GYVOZkJfxZ4FAGrCjak6syG7x0CTfPVYmDf6V2GIcH-yPJy8yLxWskn-OS_ZrhoENkc8rKhjt-I9mEtOPtujMsnikv_6AvHKqlrVyZxqbSvtQxM-II6wfO1JdWPRnrGrBpXDpiP7J5BNUQZi8XhPnO2YJJvFJCg3IZ5LrnqA4MAIrQHNR1PWcD5Bo/s841/8.png" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="500" data-original-width="841" height="190" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEi_E6GYVOZkJfxZ4FAGrCjak6syG7x0CTfPVYmDf6V2GIcH-yPJy8yLxWskn-OS_ZrhoENkc8rKhjt-I9mEtOPtujMsnikv_6AvHKqlrVyZxqbSvtQxM-II6wfO1JdWPRnrGrBpXDpiP7J5BNUQZi8XhPnO2YJJvFJCg3IZ5LrnqA4MAIrQHNR1PWcD5Bo/s320/8.png" width="320" /></a></div><p class="MsoNormal"><span style="font-family: "Times New Roman","serif"; font-size: 12pt; line-height: 115%; mso-ascii-theme-font: major-bidi; mso-bidi-theme-font: major-bidi; mso-fareast-font-family: Calibri; mso-hansi-theme-font: major-bidi;">Step 2:
By establishing the measurement scale, we will have the below Direct Relation
Matrix:<o:p></o:p></span></p><br /><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgiQV4Ug8Nvi0y_BXr9FjpeVBLEeqMVN--3hxG4bbndMnWLI_TZp3nhWkM-rhOr8pj5SrSRiBF_x5d4SEshN8VHaf1CZSQqaDp8CRNyvUD71a34gr9rML2r1MPXevK2UuUzvMfvD18G2KroctQ3kwDY8Jc4XT28x-tiZcq6GFjOmNTShekQLk0PNXpCM_A/s671/9.png" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="470" data-original-width="671" height="224" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgiQV4Ug8Nvi0y_BXr9FjpeVBLEeqMVN--3hxG4bbndMnWLI_TZp3nhWkM-rhOr8pj5SrSRiBF_x5d4SEshN8VHaf1CZSQqaDp8CRNyvUD71a34gr9rML2r1MPXevK2UuUzvMfvD18G2KroctQ3kwDY8Jc4XT28x-tiZcq6GFjOmNTShekQLk0PNXpCM_A/s320/9.png" width="320" /></a></div><p class="MsoNormal"><span style="font-family: "Times New Roman","serif"; font-size: 12pt; line-height: 115%; mso-ascii-theme-font: major-bidi; mso-bidi-theme-font: major-bidi; mso-fareast-font-family: Calibri; mso-hansi-theme-font: major-bidi;">Step 3:
Normalized Direction-Relation Matrix<o:p></o:p></span></p><br /><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhaCW-iSZKUzrf7Cs-BPLKvZSH_AN7ysU8-YsCVPB-Mr6WR2tZDo7JVxBVbojwbOGs9c03vlELn1-EcvEhWxAf0f6tUSynB_l5Tsx-RhUpU35xcrdmJWifa4wqnKaYiwBQlUIKLIVPcFfCiIeD23gnXlCI-Ji21ss9jlCuq8NpKf_BbaYQsZFfS4MbN6ew/s941/10.png" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="451" data-original-width="941" height="153" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhaCW-iSZKUzrf7Cs-BPLKvZSH_AN7ysU8-YsCVPB-Mr6WR2tZDo7JVxBVbojwbOGs9c03vlELn1-EcvEhWxAf0f6tUSynB_l5Tsx-RhUpU35xcrdmJWifa4wqnKaYiwBQlUIKLIVPcFfCiIeD23gnXlCI-Ji21ss9jlCuq8NpKf_BbaYQsZFfS4MbN6ew/s320/10.png" width="320" /></a></div><p class="MsoNormal"><span style="font-family: "Times New Roman","serif"; font-size: 12pt; line-height: 115%; mso-ascii-theme-font: major-bidi; mso-bidi-theme-font: major-bidi; mso-fareast-font-family: Calibri; mso-hansi-theme-font: major-bidi;">Step 4:
Total Relation Matrix<o:p></o:p></span></p><br /><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhRyWXIph05_1IbrYstZXGAZ30_wroc26AJkOeKIW82mNRTUZ2gHcSL5O_l3hvF04aEiu2Q0xH8RDAQMRgS2RM2Mck_88BDDAyC7pIwcelfRaZUSSaKAk2gB6JNtOCPu5J5_bNyfmsygdVVnFhYTg-tfXhbk2q4NIoWGftxZ5Jxk7GJwH2txFQwrHB1qKE/s980/11.png" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="467" data-original-width="980" height="152" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhRyWXIph05_1IbrYstZXGAZ30_wroc26AJkOeKIW82mNRTUZ2gHcSL5O_l3hvF04aEiu2Q0xH8RDAQMRgS2RM2Mck_88BDDAyC7pIwcelfRaZUSSaKAk2gB6JNtOCPu5J5_bNyfmsygdVVnFhYTg-tfXhbk2q4NIoWGftxZ5Jxk7GJwH2txFQwrHB1qKE/s320/11.png" width="320" /></a></div><p class="MsoNormal"><span style="font-family: "Times New Roman","serif"; font-size: 12pt; line-height: 115%; mso-ascii-theme-font: major-bidi; mso-bidi-theme-font: major-bidi; mso-fareast-font-family: Calibri; mso-hansi-theme-font: major-bidi;">Step 5:
Obtain the causal relation<o:p></o:p></span></p><br /><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEg-tjcb5YlrGS66NhEpCYNdFHWYUoxfpm-OJfb643ae2HcCKU2fh6Y9CtPtYI9mRerRmVmQHlsY7sdZM-nEIygKGztuQaAchh3-fdbCdtDRBQU7qMhh6UaoFOjTOMuLAWPBm7OiLYfJi83RmKiUHvwyvpk3u8WmP0IHCV0oSewr-xHm3aGrpBNs1kI4X18/s493/12.png" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="493" data-original-width="452" height="320" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEg-tjcb5YlrGS66NhEpCYNdFHWYUoxfpm-OJfb643ae2HcCKU2fh6Y9CtPtYI9mRerRmVmQHlsY7sdZM-nEIygKGztuQaAchh3-fdbCdtDRBQU7qMhh6UaoFOjTOMuLAWPBm7OiLYfJi83RmKiUHvwyvpk3u8WmP0IHCV0oSewr-xHm3aGrpBNs1kI4X18/s320/12.png" width="293" /></a></div><p class="MsoNormal"><span style="font-family: "Times New Roman","serif"; font-size: 12pt; line-height: 115%; mso-ascii-theme-font: major-bidi; mso-bidi-theme-font: major-bidi; mso-fareast-font-family: Calibri; mso-hansi-theme-font: major-bidi;">As you
can see, the most important asset in this portfolio has been denoted by <b>“X<sub>5</sub>”</b>.<o:p></o:p></span></p>
<p class="MsoNormal"><b><span style="font-family: "Times New Roman","serif"; font-size: 12pt; line-height: 115%; mso-ascii-theme-font: major-bidi; mso-bidi-theme-font: major-bidi; mso-fareast-font-family: Calibri; mso-hansi-theme-font: major-bidi;">One-day delay in the return rates of two assets using the DEMATEL
approach<o:p></o:p></span></b></p>
<p class="MsoNormal"><span style="font-family: "Times New Roman","serif"; font-size: 12pt; line-height: 115%; mso-ascii-theme-font: major-bidi; mso-bidi-theme-font: major-bidi; mso-fareast-font-family: Calibri; mso-hansi-theme-font: major-bidi;">In this
instance, the return rate between two assets with a one-day delay is analyzed
in both directions. As a result, we can predict the return rate of an item by a
probability percentage using the return rate of another asset recorded the day
prior.</span></p><p class="MsoNormal"><span style="font-family: "Times New Roman", "serif"; font-size: 12pt;">Step 1:
To develop the initial matrix</span></p><br /><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjBpboKe6z-JU8VQtVcVKMOWPdxw8H6uOtkgLS-4TyaTi1arRUNbhMJdLw_ztoHliMebJR3j_e6nbGSlydWfUzgI-iwokX64bq5vOYiMgBFo4iDCZgJAR4dTxCaK1TqUpmfPpFWF4A6PsnP7joDD2mP41j9NpBRnZz4uuq6_y3eKR-7EhMlYDowKy_kVts/s900/14.png" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="462" data-original-width="900" height="164" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjBpboKe6z-JU8VQtVcVKMOWPdxw8H6uOtkgLS-4TyaTi1arRUNbhMJdLw_ztoHliMebJR3j_e6nbGSlydWfUzgI-iwokX64bq5vOYiMgBFo4iDCZgJAR4dTxCaK1TqUpmfPpFWF4A6PsnP7joDD2mP41j9NpBRnZz4uuq6_y3eKR-7EhMlYDowKy_kVts/s320/14.png" width="320" /></a></div><p class="MsoNormal"><span style="font-family: "Times New Roman","serif"; font-size: 12pt; line-height: 115%; mso-ascii-theme-font: major-bidi; mso-bidi-theme-font: major-bidi; mso-fareast-font-family: Calibri; mso-hansi-theme-font: major-bidi;">For
example, we can say that if the return rate of X<sub>1 </sub>is low or high,
then the return rate of X<sub>13</sub> will be low or high in the next day by a
likelihood of 63.2%, and if the return rate of X<sub>13 </sub>is low or high,
then the return rate of X<sub>1</sub> will be low or high in the next day by a
likelihood of 45.7%".<o:p></o:p></span></p>
<span style="font-family: "Times New Roman","serif"; font-size: 12pt; line-height: 115%; mso-ansi-language: EN-US; mso-ascii-theme-font: major-bidi; mso-bidi-language: AR-SA; mso-bidi-theme-font: major-bidi; mso-fareast-font-family: Calibri; mso-fareast-language: EN-US; mso-hansi-theme-font: major-bidi;">Step 2: Obtain Direct Relation Matrix</span><div><span style="font-family: "Times New Roman","serif"; font-size: 12pt; line-height: 115%; mso-ansi-language: EN-US; mso-ascii-theme-font: major-bidi; mso-bidi-language: AR-SA; mso-bidi-theme-font: major-bidi; mso-fareast-font-family: Calibri; mso-fareast-language: EN-US; mso-hansi-theme-font: major-bidi;"><br /></span></div><div><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgJ8ye7FfsGEMf_SPH4itDYkhgM3yLsHRNu5SbJOY8j3t8Hs4b_zGRYP2lg-gakuw1E3gtZ8GPQ4k0BCSur6azzqISKYAYz8Rsns0J8BXeOXWGoNI-8E63ZgAxsIG10nviV2BzHQKLzdH4qSuHezj9uVoHrwhHhWYXma_9A8pRVwJkZgdY0zKRZFnVG__c/s971/15.png" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="468" data-original-width="971" height="154" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgJ8ye7FfsGEMf_SPH4itDYkhgM3yLsHRNu5SbJOY8j3t8Hs4b_zGRYP2lg-gakuw1E3gtZ8GPQ4k0BCSur6azzqISKYAYz8Rsns0J8BXeOXWGoNI-8E63ZgAxsIG10nviV2BzHQKLzdH4qSuHezj9uVoHrwhHhWYXma_9A8pRVwJkZgdY0zKRZFnVG__c/s320/15.png" width="320" /></a></div><div class="separator" style="clear: both; text-align: center;"><br /></div><span style="font-family: "Times New Roman","serif"; font-size: 12pt; line-height: 115%; mso-ansi-language: EN-US; mso-ascii-theme-font: major-bidi; mso-bidi-language: AR-SA; mso-bidi-theme-font: major-bidi; mso-fareast-font-family: Calibri; mso-fareast-language: EN-US; mso-hansi-theme-font: major-bidi;"><p class="MsoNormal"><span style="font-family: "Times New Roman","serif"; font-size: 12pt; line-height: 115%; mso-ascii-theme-font: major-bidi; mso-bidi-theme-font: major-bidi; mso-hansi-theme-font: major-bidi;">Step 3: Normalized
Direction-Relation Matrix<o:p></o:p></span></p><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjYseX2loXM0doYgfNNAN4ykyd2jPQjxbBHSXGn1BzijvaSUa8nUdOPnIz4Ok82JR4DuE5ecNad5pnUdOiCiMWpRvROpLiGVCM1y0sTUFzxUAZPzK6DZXWiN_Q8SLR5ioMCCrl08MzRxq_OIGnBhVfvAjpT0tBragTOx2oQzMb-Rjd8cRK7r3RiwVTKC8k/s941/16.png" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="453" data-original-width="941" height="154" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjYseX2loXM0doYgfNNAN4ykyd2jPQjxbBHSXGn1BzijvaSUa8nUdOPnIz4Ok82JR4DuE5ecNad5pnUdOiCiMWpRvROpLiGVCM1y0sTUFzxUAZPzK6DZXWiN_Q8SLR5ioMCCrl08MzRxq_OIGnBhVfvAjpT0tBragTOx2oQzMb-Rjd8cRK7r3RiwVTKC8k/s320/16.png" width="320" /></a></div></span></div><div><p class="MsoNormal"><span style="font-family: "Times New Roman","serif"; font-size: 12pt; line-height: 115%; mso-ascii-theme-font: major-bidi; mso-bidi-theme-font: major-bidi; mso-hansi-theme-font: major-bidi;">Step 4: </span><span style="font-family: "Times New Roman","serif"; font-size: 12pt; line-height: 115%; mso-ascii-theme-font: major-bidi; mso-bidi-theme-font: major-bidi; mso-fareast-font-family: Calibri; mso-hansi-theme-font: major-bidi;">Total Relation Matrix<o:p></o:p></span></p><br /></div><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjnhVz4QaKODbhAEUp7kKbhBfRHr0WMUXRH3E58qpXmM1U-Xyz6hP4_6OotlN_j9DC_T_b7DD30_TXMOEFTcrnu8a5nyKs2G0yzA--QFDduJA1E0sP1nUU6PNYNpKZQ65OOdOP-5AGHVxjsK2b0S3wH6veoGApWZy9uIxooQwDC_b4OiNdCuKXwsvVeMos/s975/17.png" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="471" data-original-width="975" height="155" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjnhVz4QaKODbhAEUp7kKbhBfRHr0WMUXRH3E58qpXmM1U-Xyz6hP4_6OotlN_j9DC_T_b7DD30_TXMOEFTcrnu8a5nyKs2G0yzA--QFDduJA1E0sP1nUU6PNYNpKZQ65OOdOP-5AGHVxjsK2b0S3wH6veoGApWZy9uIxooQwDC_b4OiNdCuKXwsvVeMos/s320/17.png" width="320" /></a></div><p class="MsoNormal"><span style="font-family: "Times New Roman","serif"; font-size: 12pt; line-height: 115%; mso-ascii-theme-font: major-bidi; mso-bidi-theme-font: major-bidi; mso-hansi-theme-font: major-bidi;">Step 5: Obtain the causal relation<o:p></o:p></span></p><br /><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhYIJixBKmg2N3nBDkIRbxINUE7DbF8eT65rE_8-7mfs_dMoaUdDp9WBfbXOwJx59SRkO9yfeqQiy452iV9N_SSd9dxbfqFGazsVYNpIOM8qd4g1_3TxuEqart08MQo5aBSUC4WPItpI2btr_ODVj2BveKF6uFgRaVkP4IKLXJehkgFq59cOfYY8bzPEGg/s532/18.png" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="454" data-original-width="532" height="273" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhYIJixBKmg2N3nBDkIRbxINUE7DbF8eT65rE_8-7mfs_dMoaUdDp9WBfbXOwJx59SRkO9yfeqQiy452iV9N_SSd9dxbfqFGazsVYNpIOM8qd4g1_3TxuEqart08MQo5aBSUC4WPItpI2btr_ODVj2BveKF6uFgRaVkP4IKLXJehkgFq59cOfYY8bzPEGg/s320/18.png" width="320" /></a></div><p class="MsoNormal"><span style="font-family: "Times New Roman","serif"; font-size: 12pt; line-height: 115%; mso-ascii-theme-font: major-bidi; mso-bidi-theme-font: major-bidi; mso-hansi-theme-font: major-bidi;">Finally, the causal relationship can
be plotted as follows:<o:p></o:p></span></p><br /><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgXPeeBTV7i1kNDV_G5gR_Ss64Goetb9z4vQtG0fQzqaa8RWBVzH9FHk56IOa2xjqdp9md24colCKX-kYr-LpYW2_-8P4v_3nhlUv2JNduz7HvnQ-Baa_sYssCeG_a2-38Q_JhXXq0W83LJ0ZvXcMLaledAAe03OIPHrR5AyXwQsqfR_5Ay97uACY8Tvzo/s909/19.png" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="474" data-original-width="909" height="167" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgXPeeBTV7i1kNDV_G5gR_Ss64Goetb9z4vQtG0fQzqaa8RWBVzH9FHk56IOa2xjqdp9md24colCKX-kYr-LpYW2_-8P4v_3nhlUv2JNduz7HvnQ-Baa_sYssCeG_a2-38Q_JhXXq0W83LJ0ZvXcMLaledAAe03OIPHrR5AyXwQsqfR_5Ay97uACY8Tvzo/s320/19.png" width="320" /></a></div><p class="MsoNormal"><b><span style="font-family: "Times New Roman","serif"; font-size: 12pt; line-height: 115%; mso-ascii-theme-font: major-bidi; mso-bidi-theme-font: major-bidi; mso-hansi-theme-font: major-bidi;">Conclusion<o:p></o:p></span></b></p>
<p class="MsoNormal"><span style="font-family: "Times New Roman","serif"; font-size: 12pt; line-height: 115%; mso-ascii-theme-font: major-bidi; mso-bidi-theme-font: major-bidi; mso-hansi-theme-font: major-bidi;">What, in fact, is X<sub>12</sub> or
X<sub>7</sub>? Undoubtedly, it relies on the way I select my portfolio. In
order to arrive at a logical conclusion, we actually need to further
investigate, analysis, and compare a large number of different portfolios.<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-family: "Times New Roman","serif"; font-size: 12pt; line-height: 115%; mso-ascii-theme-font: major-bidi; mso-bidi-theme-font: major-bidi; mso-hansi-theme-font: major-bidi;"><span style="mso-spacerun: yes;"> </span>The strategy for future research can be summed
up as follows:<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-family: "Times New Roman","serif"; font-size: 12pt; line-height: 115%; mso-ascii-theme-font: major-bidi; mso-bidi-theme-font: major-bidi; mso-hansi-theme-font: major-bidi;">- Going to details by defining a
threshold limited to select a new portfolio and examine the distance point to
point and growth curve<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-family: "Times New Roman","serif"; font-size: 12pt; line-height: 115%; mso-ascii-theme-font: major-bidi; mso-bidi-theme-font: major-bidi; mso-hansi-theme-font: major-bidi;">- Select numerous additional
portfolios and contrast them to verify the earlier findings.<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-family: "Times New Roman","serif"; font-size: 12pt; line-height: 115%; mso-ascii-theme-font: major-bidi; mso-bidi-theme-font: major-bidi; mso-hansi-theme-font: major-bidi;">- Pick the time period for the
historical data. To determine whether or not the outcomes are the same, we must
choose different time windows (what are the start time and finish time?).<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-family: "Times New Roman","serif"; font-size: 12pt; line-height: 115%; mso-ascii-theme-font: major-bidi; mso-bidi-theme-font: major-bidi; mso-hansi-theme-font: major-bidi;">- To forecast a delay of two days,
one week, or even one month as opposed to one.<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-family: "Times New Roman","serif"; font-size: 12pt; line-height: 115%; mso-ascii-theme-font: major-bidi; mso-bidi-theme-font: major-bidi; mso-hansi-theme-font: major-bidi;">Finally, a plan for future study
should be developed to evaluate particular cause-and-effect assets like X<b><sub>12</sub></b>
and X<b><sub>7</sub></b>. This plan should include reviewing annual reports, 10-K
and 10-Q reports, income statements, balance sheets, and other documents as
well as using tools such as DCF and MC methods for further analysis.<o:p></o:p></span></p><br />Gholamreza Soleimanihttp://www.blogger.com/profile/03273527405719420253noreply@blogger.com0tag:blogger.com,1999:blog-392703582366288634.post-56306727943027815382023-08-27T23:45:00.002+03:302023-08-28T00:17:14.558+03:30Accounting Software for Dealers, Traders, and Brokers<p> </p><p></p><p class="MsoNormal" style="line-height: 150%; margin-bottom: 0mm; mso-layout-grid-align: none; text-autospace: none;"><b><span style="font-family: "Times New Roman","serif"; font-size: 14pt; line-height: 150%; mso-ascii-theme-font: major-bidi; mso-bidi-theme-font: major-bidi; mso-font-kerning: 12.0pt; mso-hansi-theme-font: major-bidi;">Introduction<o:p></o:p></span></b></p>
<p class="MsoNormal" style="line-height: 150%; margin-bottom: 0mm; mso-layout-grid-align: none; text-autospace: none;"><b><span style="font-family: "Times New Roman","serif"; font-size: 14pt; line-height: 150%; mso-ascii-theme-font: major-bidi; mso-bidi-theme-font: major-bidi; mso-font-kerning: 12.0pt; mso-hansi-theme-font: major-bidi;"><o:p> </o:p></span></b><span style="font-family: "Times New Roman", "serif"; font-size: 14pt;">When we are speaking about accounting software, it is
expected to manage, record, and report the day-to-day financial transactions of
a firm. Of course, there are many types of accounting software for the specific
needs of an industry or business. This accounting software can be used for </span><b style="font-family: "Times New Roman", "serif"; font-size: 14pt;"><i>multi-currency
transaction recording.</i></b></p>
<p class="MsoNormal" style="line-height: 150%; margin-bottom: 0mm; mso-layout-grid-align: none; text-autospace: none;"><span style="font-family: "Times New Roman","serif"; font-size: 14pt; line-height: 150%; mso-ascii-theme-font: major-bidi; mso-bidi-theme-font: major-bidi; mso-font-kerning: 12.0pt; mso-hansi-theme-font: major-bidi;">The purpose of this project is to control and record
daily financial transactions and business deals in multi-currency for reporting
daily customer's account balances by using accounting software based on
Microsoft Excel.</span></p>
<p class="MsoNormal" style="line-height: 150%; margin-bottom: 0mm; mso-layout-grid-align: none; text-autospace: none;"><b><span style="font-family: "Times New Roman","serif"; font-size: 14pt; line-height: 150%; mso-ascii-theme-font: major-bidi; mso-bidi-theme-font: major-bidi; mso-font-kerning: 12.0pt; mso-hansi-theme-font: major-bidi;">How does this software wotk?</span></b></p><p class="MsoNormal" style="line-height: 150%; margin-bottom: 0mm; mso-layout-grid-align: none; text-autospace: none;"><span style="font-family: "Times New Roman","serif"; font-size: 14pt; line-height: 150%; mso-ascii-theme-font: major-bidi; mso-bidi-theme-font: major-bidi; mso-font-kerning: 12.0pt; mso-hansi-theme-font: major-bidi;">The most powerful and distinguishing feature of this
accounting software is its ability to manage and record business deals, and by
recording the appropriate format of any deal, the system automatically
calculates the complicated tasks.<o:p></o:p></span></p>
<p class="MsoNormal" style="line-height: 150%; margin-bottom: 0mm; mso-layout-grid-align: none; text-autospace: none;"><span style="font-family: "Times New Roman", "serif"; font-size: 14pt;">Let me start with some examples:</span></p>
<p class="MsoNormal" style="line-height: 150%; margin-bottom: 0mm; mso-layout-grid-align: none; text-autospace: none;"><span style="font-family: "Times New Roman", "serif"; font-size: 14pt;">Suppose you are managing a network of customers,
deals, and financial transactions just like the one cited below:</span></p>
<p class="MsoNormal" style="line-height: 150%; margin-bottom: 0mm; mso-layout-grid-align: none; text-autospace: none;"><span style="font-family: "Times New Roman","serif"; font-size: 14pt; line-height: 150%; mso-ascii-theme-font: major-bidi; mso-bidi-theme-font: major-bidi; mso-font-kerning: 12.0pt; mso-hansi-theme-font: major-bidi;"> </span><span style="font-family: "Times New Roman", "serif"; font-size: 14pt;">You agreed with your customer (X), who will transfer
EUR 480,000 on behalf of you due to your Performa Invoice (Buying some
industrial machinery), while you will pay him Dirham (AED). Your deal is as
follows:</span></p>
<p class="MsoNormal" style="line-height: 150%; margin-bottom: 0mm; mso-layout-grid-align: none; text-autospace: none;"><span style="font-family: "Times New Roman","serif"; font-size: 14pt; line-height: 150%; mso-ascii-theme-font: major-bidi; mso-bidi-theme-font: major-bidi; mso-font-kerning: 12.0pt; mso-hansi-theme-font: major-bidi;"> </span><span style="font-family: "Times New Roman", "serif"; font-size: 14pt;">Company "X" will charge you a fee of 0.4%
for your EUR remittance (1- 0.004 = 0.996), and this company will also consider
the ask-bid spread of 35 pips on the rate of EUR / AED = 4.0856.</span></p>
<p class="MsoNormal" style="line-height: 150%; margin-bottom: 0mm; mso-layout-grid-align: none; text-autospace: none;"><span style="font-family: "Times New Roman","serif"; font-size: 14pt; line-height: 150%; mso-ascii-theme-font: major-bidi; mso-bidi-theme-font: major-bidi; mso-font-kerning: 12.0pt; mso-hansi-theme-font: major-bidi;"> </span><span style="font-family: "Times New Roman", "serif"; font-size: 14pt;">How can you calculate the cost of this business deal,
which is your loss?</span></p>
<p class="MsoNormal" style="line-height: 150%; margin-bottom: 0mm; mso-layout-grid-align: none; text-autospace: none;"><span style="font-family: "Times New Roman","serif"; font-size: 14pt; line-height: 150%; mso-ascii-theme-font: major-bidi; mso-bidi-theme-font: major-bidi; mso-font-kerning: 12.0pt; mso-hansi-theme-font: major-bidi;"><o:p> </o:p></span><span style="font-family: "Times New Roman", "serif"; font-size: 14pt;">Solution:</span></p><br /><p></p><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjDUML8eb2SBvEQ_xp51q7F3dyJJVzcspr_2YfBjwHTuHiiqKAFDkEDZO2XjmiJ5uOjYkNCPumH2QjYTXuFzlGtT7oSXvlIMyoNYyIWf67IwBy8koWRGLzbAbyZJYFwy4OpDzoTQOc5XSVqiAHM3Sxm7M8LN2vWmWbdRHiTPen1sS-KddnmY_ZNdQ_x5U4/s510/A1.png" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="510" data-original-width="333" height="377" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjDUML8eb2SBvEQ_xp51q7F3dyJJVzcspr_2YfBjwHTuHiiqKAFDkEDZO2XjmiJ5uOjYkNCPumH2QjYTXuFzlGtT7oSXvlIMyoNYyIWf67IwBy8koWRGLzbAbyZJYFwy4OpDzoTQOc5XSVqiAHM3Sxm7M8LN2vWmWbdRHiTPen1sS-KddnmY_ZNdQ_x5U4/w319-h377/A1.png" width="319" /></a></div><br /><p class="MsoNormal" style="line-height: normal; margin-bottom: 0mm; mso-layout-grid-align: none; text-autospace: none;"><span style="font-family: "Times New Roman","serif"; font-size: 14pt; mso-ascii-theme-font: major-bidi; mso-bidi-theme-font: major-bidi; mso-font-kerning: 12.0pt; mso-hansi-theme-font: major-bidi;">Let me record this deal in a cell of Excel as follows:<o:p></o:p></span></p><p class="MsoNormal" style="line-height: normal; margin-bottom: 0mm; mso-layout-grid-align: none; text-autospace: none;"><span style="font-family: "Times New Roman", "serif"; font-size: 14pt;"><b><i>Purchase 480,000*1.004 EUR @ 4.0856+0.0035 AED</i></b></span></p><p class="MsoNormal" style="line-height: normal; margin-bottom: 0mm; mso-layout-grid-align: none; text-autospace: none;"><span style="font-family: "Times New Roman","serif"; font-size: 14pt; mso-ascii-theme-font: major-bidi; mso-bidi-theme-font: major-bidi; mso-font-kerning: 12.0pt; mso-hansi-theme-font: major-bidi;"> </span><span style="font-family: "Times New Roman", "serif"; font-size: 14pt;">Or</span></p><p class="MsoNormal" style="line-height: normal; margin-bottom: 0mm; mso-layout-grid-align: none; text-autospace: none;"><span style="font-family: "Times New Roman", "serif"; font-size: 14pt;"><b><i>Purchase 480,000/0.996 EUR @ 4.0856+0.0035 AED</i></b></span></p><p class="MsoNormal" style="line-height: normal; margin-bottom: 0mm; mso-layout-grid-align: none; text-autospace: none;"><span style="font-family: "Times New Roman","serif"; font-size: 14pt; mso-ascii-theme-font: major-bidi; mso-bidi-theme-font: major-bidi; mso-font-kerning: 12.0pt; mso-hansi-theme-font: major-bidi;"> </span><span style="font-family: "Times New Roman", "serif"; font-size: 14pt;">Please see the below video:</span></p><div class="separator" style="clear: both; text-align: center;"><br /></div><br /><p></p><div class="separator" style="clear: both; text-align: center;"><iframe allowfullscreen="" class="BLOG_video_class" height="266" src="https://www.youtube.com/embed/zisIaIGESHc" width="320" youtube-src-id="zisIaIGESHc"></iframe></div><br /><div class="separator" style="clear: both; text-align: center;"><br /></div><p class="MsoNormal" style="line-height: 150%; margin-bottom: .0001pt; margin-bottom: 0mm; mso-layout-grid-align: none; text-autospace: none;"><span style="font-family: "Times New Roman","serif"; font-size: 14.0pt; line-height: 150%; mso-ascii-theme-font: major-bidi; mso-bidi-theme-font: major-bidi; mso-font-kerning: 12.0pt; mso-hansi-theme-font: major-bidi;">As you can see, this software automatically calculates
the amounts of sale, purchase, and Profit or Loss where we have:</span></p><p class="MsoNormal" style="line-height: 150%; margin-bottom: .0001pt; margin-bottom: 0mm; mso-layout-grid-align: none; text-autospace: none;"><span style="font-family: "Times New Roman", "serif"; font-size: 14pt;">Your purchase (Received) of EUR = EUR 481,920</span></p>
<p class="MsoNormal" style="line-height: 150%; margin-bottom: 0mm; mso-layout-grid-align: none; text-autospace: none;"><span style="font-family: "Times New Roman","serif"; font-size: 14pt; line-height: 150%; mso-ascii-theme-font: major-bidi; mso-bidi-theme-font: major-bidi; mso-font-kerning: 12.0pt; mso-hansi-theme-font: major-bidi;"><o:p> </o:p></span><span style="font-family: "Times New Roman", "serif"; font-size: 14pt;">Your sale (Paid) of AED = AED 1,970,619</span></p>
<p class="MsoNormal" style="line-height: 150%; margin-bottom: 0mm; mso-layout-grid-align: none; text-autospace: none;"><span style="font-family: "Times New Roman","serif"; font-size: 14pt; line-height: 150%; mso-ascii-theme-font: major-bidi; mso-bidi-theme-font: major-bidi; mso-font-kerning: 12.0pt; mso-hansi-theme-font: major-bidi;"><o:p> </o:p></span><span style="font-family: "Times New Roman", "serif"; font-size: 14pt;">Your loss = AED (9,531)</span></p><p class="MsoNormal" style="line-height: 150%; margin-bottom: 0mm; mso-layout-grid-align: none; text-autospace: none;"><span style="font-family: "Times New Roman","serif"; font-size: 14pt; line-height: 150%; mso-ascii-theme-font: major-bidi; mso-bidi-theme-font: major-bidi; mso-font-kerning: 12.0pt; mso-hansi-theme-font: major-bidi;">In the next business deal, you will sell this
industrial machinery to company "Y" for 2% profit plus an ask-bid
spread of 45 pips, and you will receive Russian rubles (RUB) from company "Y."<o:p></o:p></span></p><p class="MsoNormal" style="line-height: 150%; margin-bottom: 0mm; mso-layout-grid-align: none; text-autospace: none;">
</p><p class="MsoNormal" style="line-height: 150%; margin-bottom: 0mm; mso-layout-grid-align: none; text-autospace: none;"><span style="font-family: "Times New Roman","serif"; font-size: 14pt; line-height: 150%; mso-ascii-theme-font: major-bidi; mso-bidi-theme-font: major-bidi; mso-font-kerning: 12.0pt; mso-hansi-theme-font: major-bidi;">We can calculate your profit due to this deal as
follows:<o:p></o:p></span></p><p class="MsoNormal" style="line-height: 150%; margin-bottom: 0mm; mso-layout-grid-align: none; text-autospace: none;"></p><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgSukaubkni_yscp-S5t0GyhGiuVbt8tCrLaHxiNrzMXb5lrlU7phUMZAu4VrCCLgvxVaJEmIbMQp4w770EQjWt2Dqyv6kKozlGbhNK8t1ipr7IIVfd1eZ52gOXPf9u7tQ8RuQwDnfs4EOGi3IYfL3d045dn6pRC4_lIdULx4sItadI647TDnJnCgjdlI0/s477/A2.png" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="477" data-original-width="444" height="320" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgSukaubkni_yscp-S5t0GyhGiuVbt8tCrLaHxiNrzMXb5lrlU7phUMZAu4VrCCLgvxVaJEmIbMQp4w770EQjWt2Dqyv6kKozlGbhNK8t1ipr7IIVfd1eZ52gOXPf9u7tQ8RuQwDnfs4EOGi3IYfL3d045dn6pRC4_lIdULx4sItadI647TDnJnCgjdlI0/s320/A2.png" width="298" /></a></div><br /><p></p><p class="MsoNormal" style="line-height: normal; margin-bottom: 0mm; mso-layout-grid-align: none; text-autospace: none;"><span style="font-family: "Times New Roman","serif"; font-size: 14pt; mso-ascii-theme-font: major-bidi; mso-bidi-theme-font: major-bidi; mso-font-kerning: 12.0pt; mso-hansi-theme-font: major-bidi;">The deal will be:<o:p></o:p></span></p><p class="MsoNormal" style="line-height: normal; margin-bottom: 0mm; mso-layout-grid-align: none; text-autospace: none;"><span style="font-family: "Times New Roman","serif"; font-size: 14pt; mso-ascii-theme-font: major-bidi; mso-bidi-theme-font: major-bidi; mso-font-kerning: 12.0pt; mso-hansi-theme-font: major-bidi;"> </span><span style="font-family: "Times New Roman", "serif"; font-size: 14pt;"><i><b>Sell 480,000*1.02 EUR @ 101.2297+0.0045
RUB</b></i></span></p><p class="MsoNormal" style="line-height: normal; margin-bottom: 0mm; mso-layout-grid-align: none; text-autospace: none;"><span lang="DE" style="font-family: "Times New Roman","serif"; font-size: 14pt; mso-ansi-language: DE; mso-ascii-theme-font: major-bidi; mso-bidi-theme-font: major-bidi; mso-font-kerning: 12.0pt; mso-hansi-theme-font: major-bidi;"> </span><span style="font-family: "Times New Roman", "serif"; font-size: 14pt;">See below video:</span></p><p class="MsoNormal" style="line-height: normal; margin-bottom: 0mm; mso-layout-grid-align: none; text-autospace: none;"></p><div class="separator" style="clear: both; text-align: center;"><iframe allowfullscreen="" class="BLOG_video_class" height="266" src="https://www.youtube.com/embed/szVhfOb_6WA" width="320" youtube-src-id="szVhfOb_6WA"></iframe></div><br /><span style="font-family: "Times New Roman", "serif"; font-size: 14pt;"><br /></span><p></p><div class="separator" style="clear: both; text-align: center;"><br /></div><br /><p class="MsoNormal" style="line-height: 150%; margin-bottom: 0mm; mso-layout-grid-align: none; text-autospace: none;"><span style="font-family: "Times New Roman","serif"; font-size: 14pt; line-height: 150%; mso-ascii-theme-font: major-bidi; mso-bidi-theme-font: major-bidi; mso-font-kerning: 12.0pt; mso-hansi-theme-font: major-bidi;">Then, Mr. "Z" will pay you CAD for all
amounts of your RUB by 0.135% less than the rate of CAD/RUB = 68.6724.<o:p></o:p></span></p><p class="MsoNormal" style="line-height: normal; margin-bottom: 0mm; mso-layout-grid-align: none; text-autospace: none;">
</p><p class="MsoNormal" style="line-height: 150%; margin-bottom: 0mm; mso-layout-grid-align: none; text-autospace: none;"><span style="font-family: "Times New Roman","serif"; font-size: 14pt; line-height: 150%; mso-ascii-theme-font: major-bidi; mso-bidi-theme-font: major-bidi; mso-font-kerning: 12.0pt; mso-hansi-theme-font: major-bidi;">Definitely, you will gain from this deal as follows:<o:p></o:p></span></p><p class="MsoNormal" style="line-height: 150%; margin-bottom: 0mm; mso-layout-grid-align: none; text-autospace: none;"></p><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjl2AUghv-4ALlzO_Hs2HIubGrWKpPeql9rNKV-f9jCScafDmi5KF4cwq1Yd4vcbqXFa6v22NO2giAftvhmuRXuQSiFV2XyNC3SFUKProZD1SJLL8wJelzi49Jst3lmesxuM1Qpz2EohIj_iB-FvoxMLM1D1sTt4rO_rSO9I9ldqYgc6dyd5bBqMh7tkf4/s447/A3.png" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="447" data-original-width="358" height="320" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjl2AUghv-4ALlzO_Hs2HIubGrWKpPeql9rNKV-f9jCScafDmi5KF4cwq1Yd4vcbqXFa6v22NO2giAftvhmuRXuQSiFV2XyNC3SFUKProZD1SJLL8wJelzi49Jst3lmesxuM1Qpz2EohIj_iB-FvoxMLM1D1sTt4rO_rSO9I9ldqYgc6dyd5bBqMh7tkf4/s320/A3.png" width="256" /></a></div><br /><p></p><p class="MsoNormal" style="line-height: normal; margin-bottom: 0mm; mso-layout-grid-align: none; text-autospace: none;"><span style="font-family: "Times New Roman","serif"; font-size: 14pt; mso-ascii-theme-font: major-bidi; mso-bidi-theme-font: major-bidi; mso-font-kerning: 12.0pt; mso-hansi-theme-font: major-bidi;">This deal will be:<o:p></o:p></span></p><p class="MsoNormal" style="line-height: normal; margin-bottom: 0mm; mso-layout-grid-align: none; text-autospace: none;"><b><i><span style="font-family: "Times New Roman","serif"; font-size: 14pt; mso-ascii-theme-font: major-bidi; mso-bidi-theme-font: major-bidi; mso-font-kerning: 12.0pt; mso-hansi-theme-font: major-bidi;"> </span><span style="font-family: "Times New Roman", "serif"; font-size: 14pt;">Sell 49,564,264 RUB @ 68.6724/1.00135 CAD</span></i></b></p><p class="MsoNormal" style="line-height: normal; margin-bottom: 0mm; mso-layout-grid-align: none; text-autospace: none;"><span style="font-family: "Times New Roman","serif"; font-size: 14pt; mso-ascii-theme-font: major-bidi; mso-bidi-theme-font: major-bidi; mso-font-kerning: 12.0pt; mso-hansi-theme-font: major-bidi;"> </span><span style="font-family: "Times New Roman", "serif"; font-size: 14pt;">See below video:</span></p><p class="MsoNormal" style="line-height: normal; margin-bottom: 0mm; mso-layout-grid-align: none; text-autospace: none;"><span style="font-family: "Times New Roman", "serif"; font-size: 14pt;"><br /></span></p><p class="MsoNormal" style="line-height: normal; margin-bottom: 0mm; mso-layout-grid-align: none; text-autospace: none;"></p><div class="separator" style="clear: both; text-align: center;"><iframe allowfullscreen="" class="BLOG_video_class" height="266" src="https://www.youtube.com/embed/TEZs2GcMll0" width="320" youtube-src-id="TEZs2GcMll0"></iframe></div><br /><span style="font-family: "Times New Roman", "serif"; font-size: 14pt;"><br /></span><p></p><div class="separator" style="clear: both; text-align: center;"><span style="font-family: "Times New Roman", "serif"; font-size: 14pt; text-align: left;">Finally, the time is over, and you should pay your
debt to company "X.". In this case, you have to sell to Mr.
"W" the amounts of CAD to receive Dirham. He will charge you a
remittance fee of 0.3% and an ask-bid spread of minus 30 pips on the rate of
CAD/AAED = 2.7778 as follows:</span></div><p class="MsoNormal" style="line-height: 150%; margin-bottom: 0mm; mso-layout-grid-align: none; text-autospace: none;"></p><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiduIxbS4Qf0kTlvoWbzh4menJpIqXyi5ST-Mn6c2B2QaaSEiEIybrmqP4988NY7OoRjM6OSzJ714M9JBgK9wsZcYu4srWrto1f0oEIJ5d1PJNhLCwV2w8S0jQOYgcCMPz6DWUoKijMs3-iVjzNBVznLbrtr0PADq99Uy-mOHdIj5x3db5pSUIxx1PE-Rk/s471/A4_REC.png" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="471" data-original-width="320" height="320" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiduIxbS4Qf0kTlvoWbzh4menJpIqXyi5ST-Mn6c2B2QaaSEiEIybrmqP4988NY7OoRjM6OSzJ714M9JBgK9wsZcYu4srWrto1f0oEIJ5d1PJNhLCwV2w8S0jQOYgcCMPz6DWUoKijMs3-iVjzNBVznLbrtr0PADq99Uy-mOHdIj5x3db5pSUIxx1PE-Rk/s320/A4_REC.png" width="217" /></a></div><p></p><p class="MsoNormal" style="line-height: 150%; margin-bottom: 0mm; mso-layout-grid-align: none; text-autospace: none;"><span style="font-family: "Times New Roman","serif"; font-size: 14pt; line-height: 150%; mso-ascii-theme-font: major-bidi; mso-bidi-theme-font: major-bidi; mso-font-kerning: 12.0pt; mso-hansi-theme-font: major-bidi;">We can record this deal just like the one cited below:<o:p></o:p></span></p><p class="MsoNormal" style="line-height: 150%; margin-bottom: 0mm; mso-layout-grid-align: none; text-autospace: none;"><span style="font-family: "Times New Roman", "serif"; font-size: 14pt;"><b><i>Purchase 1,970,619*1.003 AED @ 2.7778-0.003 CAD</i></b></span></p><p class="MsoNormal" style="line-height: 150%; margin-bottom: 0mm; mso-layout-grid-align: none; text-autospace: none;"><span style="font-family: "Times New Roman","serif"; font-size: 14pt; line-height: 150%; mso-ascii-theme-font: major-bidi; mso-bidi-theme-font: major-bidi; mso-font-kerning: 12.0pt; mso-hansi-theme-font: major-bidi;"> </span><span style="font-family: "Times New Roman", "serif"; font-size: 14pt;">I will also record this business deal into accounting
software, and then we can glance at the final account balance as follows:</span></p><p class="MsoNormal" style="line-height: 150%; margin-bottom: 0mm; mso-layout-grid-align: none; text-autospace: none;"><span style="font-family: "Times New Roman", "serif"; font-size: 14pt;"><br /></span></p><p class="MsoNormal" style="line-height: 150%; margin-bottom: 0mm; mso-layout-grid-align: none; text-autospace: none;"></p><div class="separator" style="clear: both; text-align: center;"><iframe allowfullscreen="" class="BLOG_video_class" height="266" src="https://www.youtube.com/embed/SK0KAo-k0ek" width="320" youtube-src-id="SK0KAo-k0ek"></iframe></div><p></p><div class="separator" style="clear: both; text-align: center;"><br /></div><div class="separator" style="clear: both; text-align: left;"><br /></div><div class="separator" style="clear: both; text-align: left;"><span style="font-family: "Times New Roman", "serif"; font-size: 18.6667px;">Here is a screenshot from account balance:</span></div><div class="separator" style="clear: both; text-align: center;"><br /></div><div class="separator" style="clear: both; text-align: center;"><br /></div><p class="MsoNormal" style="line-height: normal; margin-bottom: 0mm; mso-layout-grid-align: none; text-autospace: none;"></p><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjPaKHX6XQkByypOdxxNFSJwbFEPxX5i86FSy6s0WCMPyFTBy500HWO5emgpeCNDoILbzwjs6e2nwYj39k5SMxGhDUKOc15poCqfk7MBrfJQ3RmAxynb6ELc3DJc3J0CEzzP89Sso4GGc0FjpIKy8eg8eJugPGSVI6SunG_JdBZsvi3HV8xcYs9mD0Ad9M/s1046/A5.png" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="211" data-original-width="1046" height="105" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjPaKHX6XQkByypOdxxNFSJwbFEPxX5i86FSy6s0WCMPyFTBy500HWO5emgpeCNDoILbzwjs6e2nwYj39k5SMxGhDUKOc15poCqfk7MBrfJQ3RmAxynb6ELc3DJc3J0CEzzP89Sso4GGc0FjpIKy8eg8eJugPGSVI6SunG_JdBZsvi3HV8xcYs9mD0Ad9M/w474-h105/A5.png" width="474" /></a></div><br /><p></p><p class="MsoNormal" style="line-height: 150%; margin-bottom: 0mm; mso-layout-grid-align: none; text-autospace: none;"></p><p class="MsoNormal" style="line-height: 150%; margin-bottom: 0mm; mso-layout-grid-align: none; text-autospace: none;"><span style="font-family: "Times New Roman","serif"; font-size: 14pt; line-height: 150%; mso-ascii-theme-font: major-bidi; mso-bidi-theme-font: major-bidi; mso-font-kerning: 12.0pt; mso-hansi-theme-font: major-bidi;">According to the above balance account:<o:p></o:p></span></p>
<p class="MsoNormal" style="line-height: 150%; margin-bottom: 0mm; mso-layout-grid-align: none; text-autospace: none;"><span style="font-family: "Times New Roman","serif"; font-size: 14pt; line-height: 150%; mso-ascii-theme-font: major-bidi; mso-bidi-theme-font: major-bidi; mso-font-kerning: 12.0pt; mso-hansi-theme-font: major-bidi;"> </span><span style="font-family: "Times New Roman", "serif"; font-size: 14pt;">You have a debt to company "X" equal to AED
1,970,619</span></p>
<p class="MsoNormal" style="line-height: 150%; margin-bottom: 0mm; mso-layout-grid-align: none; text-autospace: none;"><span style="font-family: "Times New Roman","serif"; font-size: 14pt; line-height: 150%; mso-ascii-theme-font: major-bidi; mso-bidi-theme-font: major-bidi; mso-font-kerning: 12.0pt; mso-hansi-theme-font: major-bidi;">When you receive the industrial machinery from company
"X" and deliver it to company "Y", the amounts of EUR
481,920 and EUR 489,600 will automatically be cleared.<o:p></o:p></span></p>
<p class="MsoNormal" style="line-height: 150%; margin-bottom: 0mm; mso-layout-grid-align: none; text-autospace: none;"><span style="font-family: "Times New Roman","serif"; font-size: 14pt; line-height: 150%; mso-ascii-theme-font: major-bidi; mso-bidi-theme-font: major-bidi; mso-font-kerning: 12.0pt; mso-hansi-theme-font: major-bidi;">You should receive the amount of RUB 49,564,264 from
company "Y" due to the delivery of the industrial machinery.<o:p></o:p></span></p>
<p class="MsoNormal" style="line-height: 150%; margin-bottom: 0mm; mso-layout-grid-align: none; text-autospace: none;"><span style="font-family: "Times New Roman","serif"; font-size: 14pt; line-height: 150%; mso-ascii-theme-font: major-bidi; mso-bidi-theme-font: major-bidi; mso-font-kerning: 12.0pt; mso-hansi-theme-font: major-bidi;">In exchange for receiving CAD 722,724, you are
expected to pay the amount of RUB 49,564,264 to Mr. Z.<o:p></o:p></span></p>
<p class="MsoNormal" style="line-height: 150%; margin-bottom: 0mm; mso-layout-grid-align: none; text-autospace: none;"><span style="font-family: "Times New Roman","serif"; font-size: 14pt; line-height: 150%; mso-ascii-theme-font: major-bidi; mso-bidi-theme-font: major-bidi; mso-font-kerning: 12.0pt; mso-hansi-theme-font: major-bidi;">Your debt to Mr. W is equal to CAD 712,315 and your
credit is equal to AED 1,976,531.<o:p></o:p></span></p>
<p class="MsoNormal" style="line-height: 150%; margin-bottom: 0mm; mso-layout-grid-align: none; text-autospace: none;"><span lang="DE" style="font-family: "Times New Roman","serif"; font-size: 14pt; line-height: 150%; mso-ansi-language: DE; mso-ascii-theme-font: major-bidi; mso-bidi-theme-font: major-bidi; mso-font-kerning: 12.0pt; mso-hansi-theme-font: major-bidi;"><o:p> </o:p></span><span style="font-family: "Times New Roman", "serif"; font-size: 14pt;">You only need to record the deals in the mentioned
format into a cell, and then you will automatically have all account balances
on a sheet of Excel. I have named this model Artificial Intelligence by
Microsoft Excel.</span></p>
<p class="MsoNormal" style="line-height: 150%; margin-bottom: 0mm; mso-layout-grid-align: none; text-autospace: none;"><span style="font-family: "Times New Roman", "serif"; font-size: 14pt;">The next step is to keep track of the accounts that
your customers have paid and received in order to update the balances.</span></p><p class="MsoNormal" style="line-height: 150%; margin-bottom: 0mm; mso-layout-grid-align: none; text-autospace: none;"><span style="font-family: "Times New Roman","serif"; font-size: 14pt; line-height: 150%; mso-ascii-theme-font: major-bidi; mso-bidi-theme-font: major-bidi; mso-font-kerning: 12.0pt; mso-hansi-theme-font: major-bidi;">For clearing accounts, Mr. "W" will transfer
the amount of AED 1,970,619 on behalf of you to the banking account of company
"X.".<o:p></o:p></span></p>
<p class="MsoNormal" style="line-height: 150%; margin-bottom: 0mm; mso-layout-grid-align: none; text-autospace: none;"><span style="font-family: "Times New Roman","serif"; font-size: 14pt; line-height: 150%; mso-ascii-theme-font: major-bidi; mso-bidi-theme-font: major-bidi; mso-font-kerning: 12.0pt; mso-hansi-theme-font: major-bidi;">When you deliver the machinery to company
"Y", the amounts of EUR 481,920 and EUR 489,600 will be settled.<o:p></o:p></span></p>
<p class="MsoNormal" style="line-height: 150%; margin-bottom: 0mm; mso-layout-grid-align: none; text-autospace: none;"><span style="font-family: "Times New Roman", "serif"; font-size: 14pt;">The company "y" will pay the amount of RUB
49,564,264 to Mr. Z," and he will pay the amount of CAD 712,315 to Mr. W
on behalf of you.</span></p>
<p class="MsoNormal" style="line-height: 150%; margin-bottom: 0mm; mso-layout-grid-align: none; text-autospace: none;"><span style="font-family: "Times New Roman","serif"; font-size: 14pt; line-height: 150%; mso-ascii-theme-font: major-bidi; mso-bidi-theme-font: major-bidi; mso-font-kerning: 12.0pt; mso-hansi-theme-font: major-bidi;">The difference between the amounts of AED 1,970,619
and AED 1,976,531 will be equal to the fee charged for the business deal with
Mr. W," which should be cleared.<o:p></o:p></span></p>
<p class="MsoNormal" style="line-height: 150%; margin-bottom: 0mm; mso-layout-grid-align: none; text-autospace: none;"><span style="font-family: "Times New Roman", "serif"; font-size: 14pt;">Now, you will have the updated balances for all your
customers.</span></p>
<p class="MsoNormal" style="line-height: 150%;"><span style="font-family: "Times New Roman","serif"; font-size: 14pt; line-height: 150%; mso-ascii-theme-font: major-bidi; mso-bidi-theme-font: major-bidi; mso-hansi-theme-font: major-bidi;">As a
result, your total profit will be equal to CAD 10,409.<o:p></o:p></span></p>
<p class="MsoNormal" style="line-height: 150%;"><span style="font-family: "Times New Roman","serif"; font-size: 14pt; line-height: 150%; mso-ascii-theme-font: major-bidi; mso-bidi-theme-font: major-bidi; mso-hansi-theme-font: major-bidi;">Please
see the below video:<o:p></o:p></span></p><br /><p></p><div class="separator" style="clear: both; text-align: center;"><iframe allowfullscreen="" class="BLOG_video_class" height="266" src="https://www.youtube.com/embed/MacIxrJ5jJQ" width="320" youtube-src-id="MacIxrJ5jJQ"></iframe></div><br /><div class="separator" style="clear: both; text-align: center;"><br /></div><br /><div><br /></div><div><p class="MsoNormal"><span style="font-family: "Times New Roman","serif"; font-size: 14pt; line-height: 115%; mso-ascii-theme-font: major-bidi; mso-bidi-theme-font: major-bidi; mso-hansi-theme-font: major-bidi;"><b><i>If you have any questions, do not
hesitate to send your request to my email:<o:p></o:p></i></b></span></p>
<p class="MsoNormal"><span style="font-family: "Times New Roman","serif"; font-size: 14pt; line-height: 115%; mso-ascii-theme-font: major-bidi; mso-bidi-theme-font: major-bidi; mso-hansi-theme-font: major-bidi;"><b><i>soleimani_gh@hotmail.com</i></b><o:p></o:p></span></p><br /></div><div class="separator" style="clear: both; text-align: center;"><br /></div><br /><div class="separator" style="clear: both; text-align: center;"><br /></div><br /><div class="separator" style="clear: both; text-align: center;"><br /></div><br />Gholamreza Soleimanihttp://www.blogger.com/profile/03273527405719420253noreply@blogger.com0tag:blogger.com,1999:blog-392703582366288634.post-25709381808095471932023-06-25T17:27:00.003+03:302023-11-13T19:27:32.738+03:30Discrepancy Analysis (2): A Model Made by Microsoft Excel<p> </p><p></p><p class="MsoNormal" style="line-height: normal; margin-bottom: 0mm; mso-layout-grid-align: none; text-autospace: none;"><span style="font-family: "Times New Roman","serif"; font-size: 12pt; mso-ascii-theme-font: major-bidi; mso-bidi-theme-font: major-bidi; mso-font-kerning: 12.0pt; mso-hansi-theme-font: major-bidi;">Sometimes finding the discrepancies between the accounts is easy, but
that can be very complicated as a real case in which to extract the area of
discrepancies would be impossible.<o:p></o:p></span></p>
<p class="MsoNormal" style="line-height: normal; margin-bottom: 0mm; mso-layout-grid-align: none; text-autospace: none;"><span style="font-family: "Times New Roman","serif"; font-size: 12pt; mso-ascii-theme-font: major-bidi; mso-bidi-theme-font: major-bidi; mso-font-kerning: 12.0pt; mso-hansi-theme-font: major-bidi;">For instance, suppose your customer settles the sales invoice in
partial payments during a period of time. On the other hand, it is possible; the
partial payments made by your customer are not exactly equal to the total sum
mentioned in the credit section of your bank account.<o:p></o:p></span></p>
<p class="MsoNormal" style="line-height: normal; margin-bottom: 0mm; mso-layout-grid-align: none; text-autospace: none;"><span style="font-family: "Times New Roman","serif"; font-size: 12pt; mso-ascii-theme-font: major-bidi; mso-bidi-theme-font: major-bidi; mso-font-kerning: 12.0pt; mso-hansi-theme-font: major-bidi;">In fact, here we have two big problems with auditing the accounts:<o:p></o:p></span></p>
<p class="MsoNormal" style="line-height: normal; margin-bottom: 0mm; mso-layout-grid-align: none; text-autospace: none;"><span style="font-family: "Times New Roman","serif"; font-size: 12pt; mso-ascii-theme-font: major-bidi; mso-bidi-theme-font: major-bidi; mso-font-kerning: 12.0pt; mso-hansi-theme-font: major-bidi;"><o:p> </o:p></span><span style="font-family: "Times New Roman", "serif"; font-size: 12pt;">1.</span><span style="font-family: "Times New Roman", "serif"; font-size: 12pt;"> </span><span style="font-family: "Times New Roman", "serif"; font-size: 12pt;">In the credit section of a
bank account, we have the total sum which has been divided into many partial
payments on the debit section of a bank account.</span></p>
<p class="MsoNormal" style="line-height: normal; margin-bottom: 0mm; mso-layout-grid-align: none; text-autospace: none;"><span style="font-family: "Times New Roman","serif"; font-size: 12pt; mso-ascii-theme-font: major-bidi; mso-bidi-theme-font: major-bidi; mso-font-kerning: 12.0pt; mso-hansi-theme-font: major-bidi;"><o:p> </o:p></span><span style="font-family: "Times New Roman", "serif"; font-size: 12pt;">2. The above total sum is not exactly equal to the partial payments.</span></p>
<p class="MsoNormal" style="line-height: normal; margin-bottom: 0mm; margin-left: 36.0pt; margin-right: 0mm; margin-top: 0mm; margin: 0mm 0mm 0mm 36pt; mso-layout-grid-align: none; text-autospace: none;"><span style="font-family: "Times New Roman","serif"; font-size: 12pt; mso-ascii-theme-font: major-bidi; mso-bidi-theme-font: major-bidi; mso-font-kerning: 12.0pt; mso-hansi-theme-font: major-bidi;"><o:p> </o:p></span></p>
<p class="MsoNormal"><span style="font-family: "Times New Roman","serif"; font-size: 12pt; line-height: 115%; mso-ascii-theme-font: major-bidi; mso-bidi-theme-font: major-bidi; mso-font-kerning: 12.0pt; mso-hansi-theme-font: major-bidi;">Following to
the article of <a href="https://emfps.blogspot.com/2023/06/discrepancy-analysis-1-model-made-by.html" target="_blank">Discrepancy Analysis (1): A Model Made by Microsoft Excel</a> </span><span style="font-family: "Times New Roman","serif"; font-size: 12pt; line-height: 115%; mso-ascii-theme-font: major-bidi; mso-bidi-theme-font: major-bidi; mso-font-kerning: 12.0pt; mso-hansi-theme-font: major-bidi;">, here is a new analytic model that it can help us
to fix these two problems.<o:p></o:p></span></p>
<p class="MsoNormal" style="line-height: normal; margin-bottom: 0mm; mso-layout-grid-align: none; text-autospace: none;"><span style="font-family: "Times New Roman","serif"; font-size: 12pt; mso-ascii-theme-font: major-bidi; mso-bidi-theme-font: major-bidi; mso-font-kerning: 12.0pt; mso-hansi-theme-font: major-bidi;"><o:p> </o:p></span></p>
<p class="MsoNormal" style="line-height: normal; margin-bottom: 0mm; mso-layout-grid-align: none; text-autospace: none;"><b><span style="font-family: "Times New Roman","serif"; font-size: 12pt; mso-ascii-theme-font: major-bidi; mso-bidi-theme-font: major-bidi; mso-font-kerning: 12.0pt; mso-hansi-theme-font: major-bidi;">How does this model process the data?<o:p></o:p></span></b></p>
<p class="MsoNormal" style="line-height: normal; margin-bottom: 0mm; mso-layout-grid-align: none; text-autospace: none;"><span style="font-family: "Times New Roman","serif"; font-size: 12pt; mso-ascii-theme-font: major-bidi; mso-bidi-theme-font: major-bidi; mso-font-kerning: 12.0pt; mso-hansi-theme-font: major-bidi;"><o:p> </o:p></span></p>
<p class="MsoNormal" style="line-height: normal; margin-bottom: 0mm; mso-layout-grid-align: none; text-autospace: none;"><span style="font-family: "Times New Roman","serif"; font-size: 12pt; mso-ascii-theme-font: major-bidi; mso-bidi-theme-font: major-bidi; mso-font-kerning: 12.0pt; mso-hansi-theme-font: major-bidi;">The process of data will be accomplished into three phases:<o:p></o:p></span></p>
<p class="MsoNormal" style="line-height: normal; margin-bottom: 0mm; mso-layout-grid-align: none; text-autospace: none;"><span style="font-family: "Times New Roman","serif"; font-size: 12pt; mso-ascii-theme-font: major-bidi; mso-bidi-theme-font: major-bidi; mso-font-kerning: 12.0pt; mso-hansi-theme-font: major-bidi;"><o:p> </o:p></span></p>
<p class="MsoNormal" style="line-height: normal; margin-bottom: 0mm; mso-layout-grid-align: none; text-autospace: none;"><span style="font-family: "Times New Roman","serif"; font-size: 12pt; mso-ascii-theme-font: major-bidi; mso-bidi-theme-font: major-bidi; mso-font-kerning: 12.0pt; mso-hansi-theme-font: major-bidi;">1. To accumulate the data of Debit and Credit (Contraction)<o:p></o:p></span></p>
<p class="MsoNormal" style="line-height: normal; margin-bottom: 0mm; mso-layout-grid-align: none; text-autospace: none;"><span style="font-family: "Times New Roman","serif"; font-size: 12pt; mso-ascii-theme-font: major-bidi; mso-bidi-theme-font: major-bidi; mso-font-kerning: 12.0pt; mso-hansi-theme-font: major-bidi;"><o:p> </o:p></span></p>
<p class="MsoNormal" style="line-height: normal; margin-bottom: 0mm; mso-layout-grid-align: none; text-autospace: none;"><span style="font-family: "Times New Roman","serif"; font-size: 12pt; mso-ascii-theme-font: major-bidi; mso-bidi-theme-font: major-bidi; mso-font-kerning: 12.0pt; mso-hansi-theme-font: major-bidi;">2. To solve many equations simultaneously<o:p></o:p></span></p>
<p class="MsoNormal" style="line-height: normal; margin-bottom: 0mm; mso-layout-grid-align: none; text-autospace: none;"><span style="font-family: "Times New Roman","serif"; font-size: 12pt; mso-ascii-theme-font: major-bidi; mso-bidi-theme-font: major-bidi; mso-font-kerning: 12.0pt; mso-hansi-theme-font: major-bidi;"><o:p> </o:p></span></p>
<p class="MsoNormal" style="line-height: normal; margin-bottom: 0mm; mso-layout-grid-align: none; text-autospace: none;"><span style="font-family: "Times New Roman","serif"; font-size: 12pt; mso-ascii-theme-font: major-bidi; mso-bidi-theme-font: major-bidi; mso-font-kerning: 12.0pt; mso-hansi-theme-font: major-bidi;">3. To extend the data of Debit and Credit (Expansion)<o:p></o:p></span></p>
<p class="MsoNormal" style="line-height: normal; margin-bottom: 0mm; mso-layout-grid-align: none; text-autospace: none;"><span style="font-family: "Times New Roman","serif"; font-size: 12pt; mso-ascii-theme-font: major-bidi; mso-bidi-theme-font: major-bidi; mso-font-kerning: 12.0pt; mso-hansi-theme-font: major-bidi;"><o:p> </o:p></span></p>
<p class="MsoNormal" style="line-height: normal; margin-bottom: 0mm; mso-layout-grid-align: none; text-autospace: none;"><b><span style="font-family: "Times New Roman","serif"; font-size: 12pt; mso-ascii-theme-font: major-bidi; mso-bidi-theme-font: major-bidi; mso-font-kerning: 12.0pt; mso-hansi-theme-font: major-bidi;">Phase (1)</span></b><span style="font-family: "Times New Roman","serif"; font-size: 12pt; mso-ascii-theme-font: major-bidi; mso-bidi-theme-font: major-bidi; mso-font-kerning: 12.0pt; mso-hansi-theme-font: major-bidi;"> when you enter data into the appropriate columns, the system
automatically sums all amounts related to each day. Then, depending on your
choice, this model accumulates the amounts the rows of debit and credit. For
instance, suppose you have 400 rows of data for debit and 460 rows of data for
credit. You are willing to get only 10 rows for debit and credit. When you
enter your order of 10, the system automatically accumulates all 400 and 460
rows into 10 rows. <o:p></o:p></span></p>
<p class="MsoNormal" style="line-height: normal; margin-bottom: 0mm; mso-layout-grid-align: none; text-autospace: none;"><span style="font-family: "Times New Roman","serif"; font-size: 12pt; mso-ascii-theme-font: major-bidi; mso-bidi-theme-font: major-bidi; mso-font-kerning: 12.0pt; mso-hansi-theme-font: major-bidi;"><o:p> </o:p></span></p>
<p class="MsoNormal" style="line-height: normal; margin-bottom: 0mm; mso-layout-grid-align: none; text-autospace: none;"><b><span style="font-family: "Times New Roman","serif"; font-size: 12pt; mso-ascii-theme-font: major-bidi; mso-bidi-theme-font: major-bidi; mso-font-kerning: 12.0pt; mso-hansi-theme-font: major-bidi;">Phase (2)</span></b><span style="font-family: "Times New Roman","serif"; font-size: 12pt; mso-ascii-theme-font: major-bidi; mso-bidi-theme-font: major-bidi; mso-font-kerning: 12.0pt; mso-hansi-theme-font: major-bidi;"> the data of phase (1) is transferred into two columns of “Debit” and
“Credit” but maximum 10 rows. The chosen number of rows depends on the capacity
of system (Type of processor, RAM and so on).<o:p></o:p></span></p>
<p class="MsoNormal" style="line-height: normal; margin-bottom: 0mm; mso-layout-grid-align: none; text-autospace: none;"><span style="font-family: "Times New Roman","serif"; font-size: 12pt; mso-ascii-theme-font: major-bidi; mso-bidi-theme-font: major-bidi; mso-font-kerning: 12.0pt; mso-hansi-theme-font: major-bidi;">Here, we have 1024 equations that should be solved simultaneously.</span></p>
<p class="MsoNormal" style="line-height: normal; margin-bottom: 0mm; mso-layout-grid-align: none; text-autospace: none;"><span style="font-family: "Times New Roman","serif"; font-size: 12pt; mso-ascii-theme-font: major-bidi; mso-bidi-theme-font: major-bidi; mso-font-kerning: 12.0pt; mso-hansi-theme-font: major-bidi;">Suppose there are below data on two columns:<o:p></o:p></span></p><p class="MsoNormal" style="line-height: normal; margin-bottom: 0mm; mso-layout-grid-align: none; text-autospace: none;"><span style="font-family: "Times New Roman","serif"; font-size: 12pt; mso-ascii-theme-font: major-bidi; mso-bidi-theme-font: major-bidi; mso-font-kerning: 12.0pt; mso-hansi-theme-font: major-bidi;"><br /></span></p><p class="MsoNormal" style="line-height: normal; margin-bottom: 0mm; mso-layout-grid-align: none; text-autospace: none;"></p><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEij1Bgqc95gh8FoXec-YQMnYg3n-kEv3TwFwqARCxb_H-8II50Iysw4MQ5F3CoBcQKg5V24I5T6SoPx5p9BZIlRLr9x4bZHed2_GFVbM9qDcgAuP_YEY8oVZ5z5Khw92g_le8LgSj_RHibu9B6lUwvncE7pOBm2LtZD6l132xU0zDX8ldetcJqll6fUmis/s915/Data.png" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="80" data-original-width="915" height="28" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEij1Bgqc95gh8FoXec-YQMnYg3n-kEv3TwFwqARCxb_H-8II50Iysw4MQ5F3CoBcQKg5V24I5T6SoPx5p9BZIlRLr9x4bZHed2_GFVbM9qDcgAuP_YEY8oVZ5z5Khw92g_le8LgSj_RHibu9B6lUwvncE7pOBm2LtZD6l132xU0zDX8ldetcJqll6fUmis/s320/Data.png" width="320" /></a></div><div class="separator" style="clear: both; text-align: center;"><br /></div><div class="separator" style="clear: both; text-align: center;"><br /></div><p></p><p class="MsoNormal" style="line-height: normal; margin-bottom: 0mm; mso-layout-grid-align: none; text-autospace: none;"><span style="font-family: "Times New Roman","serif"; font-size: 12pt; mso-ascii-theme-font: major-bidi; mso-bidi-theme-font: major-bidi; mso-font-kerning: 12.0pt; mso-hansi-theme-font: major-bidi;">The general format of equations can be as follows:<o:p></o:p></span></p><p class="MsoNormal" style="line-height: normal; margin-bottom: 0mm; mso-layout-grid-align: none; text-autospace: none;"><span style="font-family: "Times New Roman","serif"; font-size: 12pt; mso-ascii-theme-font: major-bidi; mso-bidi-theme-font: major-bidi; mso-font-kerning: 12.0pt; mso-hansi-theme-font: major-bidi;"><br /></span></p><p class="MsoNormal" style="line-height: normal; margin-bottom: 0mm; mso-layout-grid-align: none; text-autospace: none;"></p><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjkSS8XIVjrpfvN2KJQ8pm3_Q_0jc_Rcu_aJ0cVZg6nbe9JscJLHYbeMkyu4xDwTDIUnODoLQRnz_pTOPTrkeX6dNIX6oug33WqvumQP22jjSmGcEcF9yIB0yzql93vtBgse1NNYNuN6exzUkMAmFHMLAXW_Wyv3iAEbed8LQL2-tns5mK7bDTAkTjhrwI/s398/Equations.png" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="359" data-original-width="398" height="289" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjkSS8XIVjrpfvN2KJQ8pm3_Q_0jc_Rcu_aJ0cVZg6nbe9JscJLHYbeMkyu4xDwTDIUnODoLQRnz_pTOPTrkeX6dNIX6oug33WqvumQP22jjSmGcEcF9yIB0yzql93vtBgse1NNYNuN6exzUkMAmFHMLAXW_Wyv3iAEbed8LQL2-tns5mK7bDTAkTjhrwI/s320/Equations.png" width="320" /></a></div><br /><span style="font-family: "Times New Roman","serif"; font-size: 12pt; mso-ascii-theme-font: major-bidi; mso-bidi-theme-font: major-bidi; mso-font-kerning: 12.0pt; mso-hansi-theme-font: major-bidi;"><br /></span><p></p><p></p><p class="MsoNormal" style="line-height: normal; margin-bottom: 0mm; mso-layout-grid-align: none; text-autospace: none;"><span style="font-family: "Times New Roman","serif"; font-size: 12pt; mso-ascii-theme-font: major-bidi; mso-bidi-theme-font: major-bidi; mso-font-kerning: 12.0pt; mso-hansi-theme-font: major-bidi;">Phase (3) the result of phase (2) will give us some scenarios which are
the solved equations but accumulated .Therefore, we will choose a scenario and
transfer it into a model of phase (3) to extend the data (Expansion).<o:p></o:p></span></p><p class="MsoNormal" style="line-height: normal; margin-bottom: 0mm; mso-layout-grid-align: none; text-autospace: none;"><span style="font-family: "Times New Roman","serif"; font-size: 12pt; mso-ascii-theme-font: major-bidi; mso-bidi-theme-font: major-bidi; mso-font-kerning: 12.0pt; mso-hansi-theme-font: major-bidi;"> </span><span style="font-family: "Times New Roman", "serif"; font-size: 12pt;">By doing each three phases, we will finish a step. We have to repeat
several steps to find out the date and the location where the discrepancies
occurred.</span></p><p class="MsoNormal" style="line-height: normal; margin-bottom: 0mm; mso-layout-grid-align: none; text-autospace: none;"><span style="font-family: "Times New Roman","serif"; font-size: 12pt; mso-ascii-theme-font: major-bidi; mso-bidi-theme-font: major-bidi; mso-font-kerning: 12.0pt; mso-hansi-theme-font: major-bidi;"> </span><b><span style="font-family: "Times New Roman","serif"; font-size: 12pt; mso-ascii-theme-font: major-bidi; mso-bidi-theme-font: major-bidi; mso-font-kerning: 12.0pt; mso-hansi-theme-font: major-bidi;">How does this model work?</span></b></p><p class="MsoNormal" style="line-height: normal; margin-bottom: 0mm; mso-layout-grid-align: none; text-autospace: none;"><b><span style="font-family: "Times New Roman","serif"; font-size: 12pt; mso-ascii-theme-font: major-bidi; mso-bidi-theme-font: major-bidi; mso-font-kerning: 12.0pt; mso-hansi-theme-font: major-bidi;"> </span></b><span style="font-family: "Times New Roman", "serif"; font-size: 12pt;">Firstly, we should enter the data of Debit and Credit into two columns.
Secondly, we need to change two independent variables of “</span><b style="font-family: "Times New Roman", "serif"; font-size: 12pt;"><i>error”</i></b><span style="font-family: "Times New Roman", "serif"; font-size: 12pt;">
and “</span><b style="font-family: "Times New Roman", "serif"; font-size: 12pt;"><i>milestone”</i></b><span style="font-family: "Times New Roman", "serif"; font-size: 12pt;"> to achieve the best scenario.</span></p><p class="MsoNormal" style="line-height: normal; margin-bottom: 0mm; mso-layout-grid-align: none; text-autospace: none;"><span style="font-family: "Times New Roman","serif"; font-size: 12pt; mso-ascii-theme-font: major-bidi; mso-bidi-theme-font: major-bidi; mso-font-kerning: 12.0pt; mso-hansi-theme-font: major-bidi;"> </span></p><p class="MsoNormal" style="line-height: normal; margin-bottom: 0mm; mso-layout-grid-align: none; text-autospace: none;"><span style="font-family: "Times New Roman","serif"; font-size: 12pt; mso-ascii-theme-font: major-bidi; mso-bidi-theme-font: major-bidi; mso-font-kerning: 12.0pt; mso-hansi-theme-font: major-bidi;">What are the variables of “<b><i>error”</i></b> and “<b><i>milestone”</i></b>?<o:p></o:p></span></p><p class="MsoNormal" style="line-height: normal; margin-bottom: 0mm; mso-layout-grid-align: none; text-autospace: none;">
</p><p class="MsoNormal" style="line-height: normal; margin-bottom: 0mm; mso-layout-grid-align: none; text-autospace: none;"><span style="font-family: "Times New Roman","serif"; font-size: 12pt; mso-ascii-theme-font: major-bidi; mso-bidi-theme-font: major-bidi; mso-font-kerning: 12.0pt; mso-hansi-theme-font: major-bidi;"> </span><span style="font-family: "Times New Roman", "serif"; font-size: 12pt;">“</span><b style="font-family: "Times New Roman", "serif"; font-size: 12pt;"><i>error</i></b><span style="font-family: "Times New Roman", "serif"; font-size: 12pt;">” is following below formula:</span></p><p class="MsoNormal" style="line-height: normal; margin-bottom: 0mm; mso-layout-grid-align: none; text-autospace: none;"><span style="font-family: "Times New Roman","serif"; font-size: 12pt; mso-ascii-theme-font: major-bidi; mso-bidi-theme-font: major-bidi; mso-font-kerning: 12.0pt; mso-hansi-theme-font: major-bidi;"><o:p></o:p></span></p><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEi2PAmaO6hOYbXkF2z9kKuTmZGumIcmwlsaOP6u9FfvOLQbTVJWCz0_1V7hXB2oh0dqOIFok35JzvfoHfR98bpfJgKzgr-onPe60wc_sU7xE_2dTj5lGMchyT_e5uIFpxzml8mzpO3eaynzh3p6TlvKdUJC2oj6spBHcAl7_AB7CZsa1_BU0XCR1b1MHHw/s464/error.png" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="348" data-original-width="464" height="240" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEi2PAmaO6hOYbXkF2z9kKuTmZGumIcmwlsaOP6u9FfvOLQbTVJWCz0_1V7hXB2oh0dqOIFok35JzvfoHfR98bpfJgKzgr-onPe60wc_sU7xE_2dTj5lGMchyT_e5uIFpxzml8mzpO3eaynzh3p6TlvKdUJC2oj6spBHcAl7_AB7CZsa1_BU0XCR1b1MHHw/s320/error.png" width="320" /></a></div><br /><p></p><p class="MsoNormal" style="line-height: normal; margin-bottom: 0mm; mso-layout-grid-align: none; text-autospace: none;"><span style="font-family: "Times New Roman","serif"; font-size: 12pt; mso-ascii-theme-font: major-bidi; mso-bidi-theme-font: major-bidi; mso-font-kerning: 12.0pt; mso-hansi-theme-font: major-bidi;">By changing “<b><i>milestone”</i></b>, we are able to obtain the
desired accumulated data in ideal row numbers. The final step is to copy and
paste the results into the model of expansion and to repeat previous steps.<o:p></o:p></span></p>
<p class="MsoNormal" style="line-height: normal; margin-bottom: 0mm; mso-layout-grid-align: none; text-autospace: none;"><b><span style="font-family: "Times New Roman","serif"; font-size: 12pt; mso-ascii-theme-font: major-bidi; mso-bidi-theme-font: major-bidi; mso-font-kerning: 12.0pt; mso-hansi-theme-font: major-bidi;">Let me take some examples:</span></b></p>
<p class="MsoNormal" style="line-height: normal; margin-bottom: 0mm; mso-layout-grid-align: none; text-autospace: none;"><span style="font-family: "Times New Roman","serif"; font-size: 12pt; mso-ascii-theme-font: major-bidi; mso-bidi-theme-font: major-bidi; mso-font-kerning: 12.0pt; mso-hansi-theme-font: major-bidi;"><o:p> </o:p></span><span style="font-family: "Times New Roman", "serif"; font-size: 12pt;">1. I will fill out the data in column Debit and also the same data in
column Credit. Therefore, we do not have any discrepancy in the first step.</span></p>
<p class="MsoNormal" style="line-height: normal; margin-bottom: 0mm; mso-layout-grid-align: none; text-autospace: none;"><span style="font-family: "Times New Roman","serif"; font-size: 12pt; mso-ascii-theme-font: major-bidi; mso-bidi-theme-font: major-bidi; mso-font-kerning: 12.0pt; mso-hansi-theme-font: major-bidi;"><o:p> </o:p></span><span style="font-family: "Times New Roman", "serif"; font-size: 12pt;">2. Suppose the operator of accounting software took a mistake to record
$ 10,000 instead of $ 1000 (Yellow highlighted). We have to change Milestone
until we achieve a fixed date. Here is the location of the discrepancy.</span></p>
<p class="MsoNormal" style="line-height: normal; margin-bottom: 0mm; mso-layout-grid-align: none; text-autospace: none;"><span style="font-family: "Times New Roman","serif"; font-size: 12pt; mso-ascii-theme-font: major-bidi; mso-bidi-theme-font: major-bidi; mso-font-kerning: 12.0pt; mso-hansi-theme-font: major-bidi;"><o:p> </o:p></span><span style="font-family: "Times New Roman", "serif"; font-size: 12pt;">Please see the video below:</span></p><div><br /></div><br /><p></p><div class="separator" style="clear: both; text-align: center;"><iframe allowfullscreen="" class="BLOG_video_class" height="266" src="https://www.youtube.com/embed/s8PANc4eJYI" width="320" youtube-src-id="s8PANc4eJYI"></iframe></div><br /><div class="separator" style="clear: both; text-align: center;"><br /></div><div class="separator" style="clear: both; text-align: center;"><br /></div><br /><p></p><p class="MsoNormal" style="line-height: normal; margin-bottom: 0mm; mso-layout-grid-align: none; text-autospace: none;"><span style="font-family: "Times New Roman","serif"; font-size: 12pt; mso-ascii-theme-font: major-bidi; mso-bidi-theme-font: major-bidi; mso-font-kerning: 12.0pt; mso-hansi-theme-font: major-bidi;">3. Now, I change $ 5000 to $50,000 in row 1540 and column Credit. By
the same try, we will find the area of the discrepancy.<o:p></o:p></span></p>
<p class="MsoNormal" style="line-height: normal; margin-bottom: 0mm; mso-layout-grid-align: none; text-autospace: none;"><span style="font-family: "Times New Roman","serif"; font-size: 12pt; mso-ascii-theme-font: major-bidi; mso-bidi-theme-font: major-bidi; mso-font-kerning: 12.0pt; mso-hansi-theme-font: major-bidi;"><o:p> </o:p></span></p>
<p class="MsoNormal" style="line-height: normal; margin-bottom: 0mm; mso-layout-grid-align: none; text-autospace: none;"><span style="font-family: "Times New Roman","serif"; font-size: 12pt; mso-ascii-theme-font: major-bidi; mso-bidi-theme-font: major-bidi; mso-font-kerning: 12.0pt; mso-hansi-theme-font: major-bidi;">Please see the video below:<o:p></o:p></span></p><p class="MsoNormal" style="line-height: normal; margin-bottom: 0mm; mso-layout-grid-align: none; text-autospace: none;"><span style="font-family: "Times New Roman","serif"; font-size: 12pt; mso-ascii-theme-font: major-bidi; mso-bidi-theme-font: major-bidi; mso-font-kerning: 12.0pt; mso-hansi-theme-font: major-bidi;"><br /></span></p><br /><p></p><div class="separator" style="clear: both; text-align: center;"><iframe allowfullscreen="" class="BLOG_video_class" height="266" src="https://www.youtube.com/embed/7bWGu3tVmtA" width="320" youtube-src-id="7bWGu3tVmtA"></iframe></div><br /><div class="separator" style="clear: both; text-align: center;"><br /></div><p></p><p class="MsoNormal" style="line-height: normal; margin-bottom: 0mm; mso-layout-grid-align: none; text-autospace: none;"><span style="font-family: "Times New Roman","serif"; font-size: 12pt; mso-ascii-theme-font: major-bidi; mso-bidi-theme-font: major-bidi; mso-font-kerning: 12.0pt; mso-hansi-theme-font: major-bidi;">As you can see, we do not need to go to phase (3).<o:p></o:p></span></p>
<p class="MsoNormal" style="line-height: normal; margin-bottom: 0mm; mso-layout-grid-align: none; text-autospace: none;"><span style="font-family: "Times New Roman","serif"; font-size: 12pt; mso-ascii-theme-font: major-bidi; mso-bidi-theme-font: major-bidi; mso-font-kerning: 12.0pt; mso-hansi-theme-font: major-bidi;"><o:p> </o:p></span><span style="font-family: "Times New Roman", "serif"; font-size: 12pt;">4. In this example, suppose you have received a total amount for three
invoices sent to the customer while there is the discrepancy between the total
receiving and three invoices.</span></p>
<p class="MsoNormal" style="line-height: normal; margin-bottom: 0mm; mso-layout-grid-align: none; text-autospace: none;"><span style="font-family: "Times New Roman","serif"; font-size: 12pt; mso-ascii-theme-font: major-bidi; mso-bidi-theme-font: major-bidi; mso-font-kerning: 12.0pt; mso-hansi-theme-font: major-bidi;">On column credit and row 1545, I add $2,500,000 but on column debit and
rows<o:p></o:p></span></p>
<p class="MsoNormal" style="line-height: normal; margin-bottom: 0mm; mso-layout-grid-align: none; text-autospace: none;"><span style="font-family: "Times New Roman","serif"; font-size: 12pt; mso-ascii-theme-font: major-bidi; mso-bidi-theme-font: major-bidi; mso-font-kerning: 12.0pt; mso-hansi-theme-font: major-bidi;">1545, 1546 and 1547, I add $ 1,500,000, $ 500,000 and $488,905. Here,
when I change the error by more than $9000, I can access to a focus area,
otherwise I receive three locations that show three areas of the discrepancies.<o:p></o:p></span></p>
<p class="MsoNormal" style="line-height: normal; margin-bottom: 0mm; mso-layout-grid-align: none; text-autospace: none;"><span style="font-family: "Times New Roman","serif"; font-size: 12pt; mso-ascii-theme-font: major-bidi; mso-bidi-theme-font: major-bidi; mso-font-kerning: 12.0pt; mso-hansi-theme-font: major-bidi;"><o:p> </o:p></span><span style="font-family: "Times New Roman", "serif"; font-size: 12pt;">Please see the video below:</span></p><p class="MsoNormal" style="line-height: normal; margin-bottom: 0mm; mso-layout-grid-align: none; text-autospace: none;"></p><div class="separator" style="clear: both; text-align: center;"><br /></div><br /><span style="font-family: "Times New Roman", "serif"; font-size: 12pt;"><br /></span><p></p>
<p class="MsoNormal" style="line-height: normal; margin-bottom: 0mm; mso-layout-grid-align: none; text-autospace: none;"><span style="font-family: "Times New Roman","serif"; font-size: 12pt; mso-ascii-theme-font: major-bidi; mso-bidi-theme-font: major-bidi; mso-font-kerning: 12.0pt; mso-hansi-theme-font: major-bidi;"><o:p> </o:p></span></p><div class="separator" style="clear: both; text-align: center;"><span style="font-family: "Times New Roman","serif"; font-size: 12pt; mso-ascii-theme-font: major-bidi; mso-bidi-theme-font: major-bidi; mso-font-kerning: 12.0pt; mso-hansi-theme-font: major-bidi;"><iframe allowfullscreen="" class="BLOG_video_class" height="266" src="https://www.youtube.com/embed/evLBvAYl46A" width="320" youtube-src-id="evLBvAYl46A"></iframe></span></div><span style="font-family: "Times New Roman","serif"; font-size: 12pt; mso-ascii-theme-font: major-bidi; mso-bidi-theme-font: major-bidi; mso-font-kerning: 12.0pt; mso-hansi-theme-font: major-bidi;"><br /></span><p></p><p class="MsoNormal" style="line-height: normal; margin-bottom: 0mm; mso-layout-grid-align: none; text-autospace: none;"><b><i><span style="font-family: "Times New Roman","serif"; font-size: 12pt; mso-ascii-theme-font: major-bidi; mso-bidi-theme-font: major-bidi; mso-font-kerning: 12.0pt; mso-hansi-theme-font: major-bidi;">NOTE:<o:p></o:p></span></i></b></p>
<p class="MsoNormal" style="line-height: normal; margin-bottom: 0mm; mso-layout-grid-align: none; text-autospace: none;"><b><i><span style="font-family: "Times New Roman","serif"; font-size: 12pt; mso-ascii-theme-font: major-bidi; mso-bidi-theme-font: major-bidi; mso-font-kerning: 12.0pt; mso-hansi-theme-font: major-bidi;">Since this model is under test, interested people who
have real<o:p></o:p></span></i></b></p>
<p class="MsoNormal" style="line-height: normal; margin-bottom: 0mm; mso-layout-grid-align: none; text-autospace: none;"><b><i><span style="font-family: "Times New Roman","serif"; font-size: 12pt; mso-ascii-theme-font: major-bidi; mso-bidi-theme-font: major-bidi; mso-font-kerning: 12.0pt; mso-hansi-theme-font: major-bidi;">cases, do not hesitate to send their data to my email:<o:p></o:p></span></i></b></p>
<p class="MsoNormal" style="line-height: normal; margin-bottom: 0mm; mso-layout-grid-align: none; text-autospace: none;"><b><i><u><span style="font-family: "Times New Roman","serif"; font-size: 12pt; mso-ascii-theme-font: major-bidi; mso-bidi-theme-font: major-bidi; mso-font-kerning: 12.0pt; mso-hansi-theme-font: major-bidi;">soleimani_gh@hotmail.com</span></u></i></b><b><i><span style="font-family: "Times New Roman","serif"; font-size: 12pt; mso-ascii-theme-font: major-bidi; mso-bidi-theme-font: major-bidi; mso-font-kerning: 12.0pt; mso-hansi-theme-font: major-bidi;"><o:p></o:p></span></i></b></p>
<p class="MsoNormal" style="line-height: normal; margin-bottom: 0mm; mso-layout-grid-align: none; text-autospace: none;"><b><i><span style="font-family: "Times New Roman","serif"; font-size: 12pt; mso-ascii-theme-font: major-bidi; mso-bidi-theme-font: major-bidi; mso-font-kerning: 12.0pt; mso-hansi-theme-font: major-bidi;">Do not worry about the security of your data, because
you can multiply or divide all the data of columns debit and credit by a
positive real number such as 0.058, 3.7, 6, and so on, and then send it to me.<o:p></o:p></span></i></b></p>
<p class="MsoNormal" style="line-height: normal; margin-bottom: 0mm; mso-layout-grid-align: none; text-autospace: none;"><b><i><span style="font-family: "Times New Roman","serif"; font-size: 12pt; mso-ascii-theme-font: major-bidi; mso-bidi-theme-font: major-bidi; mso-font-kerning: 12.0pt; mso-hansi-theme-font: major-bidi;"><o:p> </o:p></span></i></b></p><br /><p></p><div class="separator" style="clear: both; text-align: center;"><br /></div><br />Gholamreza Soleimanihttp://www.blogger.com/profile/03273527405719420253noreply@blogger.com0tag:blogger.com,1999:blog-392703582366288634.post-78185263484439090652023-06-21T23:28:00.002+03:302023-12-20T19:20:47.415+03:30Discrepancy Analysis (1): A Model Made by Microsoft Excel<p> </p><p></p><p class="MsoNormal"><span style="font-family: "Times New Roman","serif"; font-size: 12pt; line-height: 115%; mso-ascii-theme-font: major-bidi; mso-bidi-theme-font: major-bidi; mso-font-kerning: 12.0pt; mso-hansi-theme-font: major-bidi;">Suppose you
are expected to control the balance of the accounts between the sales of the
store network and the accounts receivable in the banking network as follows:<o:p></o:p></span></p><br /><p></p><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEj44ar5VYxZmrQXuwnh8be3UN__tC9nuVdtV9fOv4C5HZopoh2UH34bEKjp3nkqiLrT-rVxXSuMMmjHGliGRwqFL2z9EbCqIbWHNFV_GO1D6IfoiN7uNR1Er7Z_X86ikegOOMO_K0ON3MMryYAXFGqjPNmb6KTuRUi1guGE7RlLgc1MdWj50396yeGLgeQ/s973/Flowchart.png" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="668" data-original-width="973" height="220" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEj44ar5VYxZmrQXuwnh8be3UN__tC9nuVdtV9fOv4C5HZopoh2UH34bEKjp3nkqiLrT-rVxXSuMMmjHGliGRwqFL2z9EbCqIbWHNFV_GO1D6IfoiN7uNR1Er7Z_X86ikegOOMO_K0ON3MMryYAXFGqjPNmb6KTuRUi1guGE7RlLgc1MdWj50396yeGLgeQ/s320/Flowchart.png" width="320" /></a></div><div class="separator" style="clear: both; text-align: center;"><br /></div><div class="separator" style="clear: both; text-align: center;"><br /></div><p class="MsoNormal"><span style="font-family: "Times New Roman","serif"; font-size: 12pt; line-height: 115%; mso-ascii-theme-font: major-bidi; mso-bidi-language: FA; mso-bidi-theme-font: major-bidi; mso-font-kerning: 12.0pt; mso-hansi-theme-font: major-bidi;">The above flowchart says to us, you should release the customer’s order to
conform to the invoice when you receive the bank receipt sent by the customer. <o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-family: "Times New Roman","serif"; font-size: 12pt; line-height: 115%; mso-ascii-theme-font: major-bidi; mso-bidi-language: FA; mso-bidi-theme-font: major-bidi; mso-font-kerning: 12.0pt; mso-hansi-theme-font: major-bidi;">Nowadays, people are able to make fake receipts by using Artificial
Intelligence tools. On the other hand, it is possible that a customer will send
you repeated receipts. Thus, you need to take a rapid check of the invoices and
all bank accounts before sending the goods to the customer.<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-family: "Times New Roman","serif"; font-size: 12pt; line-height: 115%; mso-ascii-theme-font: major-bidi; mso-bidi-language: FA; mso-bidi-theme-font: major-bidi; mso-font-kerning: 12.0pt; mso-hansi-theme-font: major-bidi;">This analytic model helps you to find out all discrepancies very
soon. <o:p></o:p></span></p><p class="MsoNormal"><span style="font-family: "Times New Roman","serif"; font-size: 12pt; line-height: 115%; mso-ascii-theme-font: major-bidi; mso-bidi-theme-font: major-bidi; mso-hansi-theme-font: major-bidi;">By using this model, you will take
two types of the discrepancy analysis as follows:<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-family: "Times New Roman","serif"; font-size: 12pt; line-height: 115%; mso-ascii-theme-font: major-bidi; mso-bidi-theme-font: major-bidi; mso-hansi-theme-font: major-bidi;">1. When there are different amounts
of data on the sales and accounts receivable in the banking network<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-family: "Times New Roman","serif"; font-size: 12pt; line-height: 115%; mso-ascii-theme-font: major-bidi; mso-bidi-theme-font: major-bidi; mso-hansi-theme-font: major-bidi;">2. When there are the same amounts
of data on the sales and accounts receivable in the banking network but the
number of repeated amounts is different between the data on the sales and
accounts receivable in the banking network<o:p></o:p></span></p>
<p class="MsoNormal"><b><i><span style="font-family: "Times New Roman","serif"; font-size: 12pt; line-height: 115%; mso-ascii-theme-font: major-bidi; mso-bidi-theme-font: major-bidi; mso-hansi-theme-font: major-bidi;">Note: This
model does not cover the below conditions:<o:p></o:p></span></i></b></p>
<p class="MsoNormal"><b><i><span style="font-family: "Times New Roman","serif"; font-size: 12pt; line-height: 115%; mso-ascii-theme-font: major-bidi; mso-bidi-theme-font: major-bidi; mso-hansi-theme-font: major-bidi;">- If your
customer settles the sales invoice in partial payments during a period of time<o:p></o:p></span></i></b></p>
<p class="MsoNormal"><b><i><span style="font-family: "Times New Roman","serif"; font-size: 12pt; line-height: 115%; mso-ascii-theme-font: major-bidi; mso-bidi-theme-font: major-bidi; mso-hansi-theme-font: major-bidi;">- The partial
payments made by your customer are not exactly equal to the total sum mentioned
in the credit section of your bank account<o:p></o:p></span></i></b></p>
<p class="MsoNormal"><b><i><span style="font-family: "Times New Roman","serif"; font-size: 12pt; line-height: 115%; mso-ascii-theme-font: major-bidi; mso-bidi-theme-font: major-bidi; mso-hansi-theme-font: major-bidi;">These
conditions will be covered by a new analytic model that I will post next time.
(See Discrepancy Analysis (2): A Model Made by Microsoft Excel)<o:p></o:p></span></i></b></p><p class="MsoNormal"><b><span style="font-family: "Times New Roman","serif"; font-size: 12pt; line-height: 115%; mso-ascii-theme-font: major-bidi; mso-bidi-theme-font: major-bidi; mso-hansi-theme-font: major-bidi;">How does this
model work?<o:p></o:p></span></b></p>
<p class="MsoNormal"><span style="font-family: "Times New Roman","serif"; font-size: 12pt; line-height: 115%; mso-ascii-theme-font: major-bidi; mso-bidi-theme-font: major-bidi; mso-hansi-theme-font: major-bidi;">You only need to collect the sales
data from all stores and banking data from your entire bank network accompanied
by the dates and copy them into appropriate columns of this model. <o:p></o:p></span></p><p class="MsoNormal"><b><i><span style="font-family: "Times New Roman","serif"; font-size: 12pt; line-height: 115%; mso-ascii-theme-font: major-bidi; mso-bidi-theme-font: major-bidi; mso-hansi-theme-font: major-bidi;">Note: </span>There are varieties of applications for this analytic model,
in which you can compare two columns of texts or two columns of dates.
Therefore, before starting, you need to define four titles for columns as shown
in the below figure:</i></b></p><p class="MsoNormal"><b><i><br /></i></b></p><p class="MsoNormal"><b></b></p><div class="separator" style="clear: both; text-align: center;"><b><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiXEbcCCWwilt1LRCeAeVrZS7O1JzE4OIF46aICdE8AYHEShhwO_wWOb4Fu7CyNIbh8Gcoa4EksBJiUTdb7XMCrS1pNR930r2ddsLLUwPz1EA7bJ4qjp6IzqPjW-3Ey3GPrxdlx9XeEgqVzVoS-yZ9Aj8ZNbsa2rnfC_ZQQogX1fmDs_l2CsdtyYsiQF9A/s498/111.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="373" data-original-width="498" height="240" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiXEbcCCWwilt1LRCeAeVrZS7O1JzE4OIF46aICdE8AYHEShhwO_wWOb4Fu7CyNIbh8Gcoa4EksBJiUTdb7XMCrS1pNR930r2ddsLLUwPz1EA7bJ4qjp6IzqPjW-3Ey3GPrxdlx9XeEgqVzVoS-yZ9Aj8ZNbsa2rnfC_ZQQogX1fmDs_l2CsdtyYsiQF9A/s320/111.png" width="320" /></a></b></div><b><br /><i><br /></i></b><p></p><p class="MsoNormal"><o:p></o:p></p>
<p class="MsoNormal"><b><span style="font-family: "Times New Roman","serif"; font-size: 12pt; line-height: 115%; mso-ascii-theme-font: major-bidi; mso-bidi-theme-font: major-bidi; mso-hansi-theme-font: major-bidi;">Examples: <o:p></o:p></span></b></p>
<p class="MsoNormal"><span style="font-family: "Times New Roman","serif"; font-size: 12pt; line-height: 115%; mso-ascii-theme-font: major-bidi; mso-bidi-theme-font: major-bidi; mso-hansi-theme-font: major-bidi;">I copy and paste the data into 4
columns. As you can see, firstly there is not any discrepancy. But I manually
changed some of the amounts in column sales and then changed some of the
amounts in column account receivable. You can see the results in Discrepancy
Analysis_2.<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-family: "Times New Roman","serif"; font-size: 12pt; line-height: 115%; mso-ascii-theme-font: major-bidi; mso-bidi-theme-font: major-bidi; mso-hansi-theme-font: major-bidi;">In the next step, I will repeat some
of the numbers in both columns. You can find the results in Discrepancy
analysis_ 1. For instance, when you see “3 or -3”, it means that there is this
amount in both columns but in one column 3 times more than another column.
<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-family: "Times New Roman","serif"; font-size: 12pt; line-height: 115%; mso-ascii-theme-font: major-bidi; mso-bidi-theme-font: major-bidi; mso-hansi-theme-font: major-bidi;">Please see below video:<o:p></o:p></span></p><br /><div class="separator" style="clear: both; text-align: center;"><iframe allowfullscreen='allowfullscreen' webkitallowfullscreen='webkitallowfullscreen' mozallowfullscreen='mozallowfullscreen' width='320' height='266' src='https://www.blogger.com/video.g?token=AD6v5dwSbdZYeRtJtUki1Ni4rmx8ZTJTQ60tf-fKCEGHYLIaR2p4jPUn4idyNPaERLcO9DJ2xHQxFD-wW9xY4zbLYQ' class='b-hbp-video b-uploaded' frameborder='0'></iframe></div><div class="separator" style="clear: both; text-align: center;"><br /></div><div class="separator" style="clear: both; text-align: center;">See this Video on youtube:</div><div class="separator" style="clear: both; text-align: center;"><br /></div><div class="separator" style="clear: both; text-align: center;"><iframe allowfullscreen="" class="BLOG_video_class" height="266" src="https://www.youtube.com/embed/QxTXEDh9QAY" width="320" youtube-src-id="QxTXEDh9QAY"></iframe></div><br /><div class="separator" style="clear: both; text-align: center;"><br /></div><p class="MsoNormal"><span style="font-family: "Times New Roman","serif"; font-size: 12pt; line-height: 115%; mso-ascii-theme-font: major-bidi; mso-bidi-theme-font: major-bidi; mso-hansi-theme-font: major-bidi;">You can also utilize this model to
find out the discrepancies among the texts. <o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-family: "Times New Roman","serif"; font-size: 12pt; line-height: 115%; mso-ascii-theme-font: major-bidi; mso-bidi-theme-font: major-bidi; mso-hansi-theme-font: major-bidi;">Please see below video:<o:p></o:p></span></p><br /><div class="separator" style="clear: both; text-align: center;"><iframe allowfullscreen='allowfullscreen' webkitallowfullscreen='webkitallowfullscreen' mozallowfullscreen='mozallowfullscreen' width='320' height='266' src='https://www.blogger.com/video.g?token=AD6v5dxAWx87bqpMHmrfUywPfTew1t_MWMD8DXGYt1boD1Ey-JtfQgiJPYPg-8dRKzIHs7_cqgbQ86N8r_rWsoeG2A' class='b-hbp-video b-uploaded' frameborder='0'></iframe></div><div class="separator" style="clear: both; text-align: center;"><br /></div><div class="separator" style="clear: both; text-align: center;"><br /></div><div class="separator" style="clear: both; text-align: center;">See this Video on youtube:</div><div class="separator" style="clear: both; text-align: center;"><br /></div><div class="separator" style="clear: both; text-align: center;"><iframe allowfullscreen="" class="BLOG_video_class" height="266" src="https://www.youtube.com/embed/tMxt9un8yRc" width="320" youtube-src-id="tMxt9un8yRc"></iframe></div><br /><div class="separator" style="clear: both; text-align: center;"><br /></div><p class="MsoNormal"><span style="font-family: "Times New Roman","serif"; font-size: 12pt; line-height: 115%; mso-ascii-theme-font: major-bidi; mso-bidi-theme-font: major-bidi; mso-hansi-theme-font: major-bidi;">If you have any questions, please do
not hesitate to send them to my email address: </span><a href="mailto:Soleimani_gh@hotmail.com"><span style="font-family: "Times New Roman","serif"; font-size: 12pt; line-height: 115%; mso-ascii-theme-font: major-bidi; mso-bidi-theme-font: major-bidi; mso-hansi-theme-font: major-bidi;">Soleimani_gh@hotmail.com</span></a><span style="font-family: "Times New Roman","serif"; font-size: 12pt; line-height: 115%; mso-ascii-theme-font: major-bidi; mso-bidi-theme-font: major-bidi; mso-hansi-theme-font: major-bidi;"><o:p></o:p></span></p><br />Gholamreza Soleimanihttp://www.blogger.com/profile/03273527405719420253noreply@blogger.com0tag:blogger.com,1999:blog-392703582366288634.post-50908364263971799852023-06-15T17:42:00.001+03:302023-06-15T17:42:58.840+03:30Solving COMPLEX CAPTCHAs by Using an Analytic Model Made by Microsoft Excel<p> </p><p class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0mm; mso-layout-grid-align: none; text-autospace: none;"><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; mso-ascii-theme-font: major-bidi; mso-bidi-theme-font: major-bidi; mso-font-kerning: 12.0pt; mso-hansi-theme-font: major-bidi;">Nowadays, there are three types of CAPTCHAs, including text-based,
picture-based, and sound-based. One of the most complicated picture-based
CAPTCHAs is to match a given number which is equal to the total sum of many
other numbers into a picture. <o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%; mso-ascii-theme-font: major-bidi; mso-bidi-theme-font: major-bidi; mso-font-kerning: 12.0pt; mso-hansi-theme-font: major-bidi;">Suppose
CAPTCHA gives you a picture of twelve dices </span><span style="color: black; font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%; mso-ascii-theme-font: major-bidi; mso-bidi-theme-font: major-bidi; mso-fareast-font-family: "Times New Roman"; mso-hansi-theme-font: major-bidi;">and asks you to match a given
number such as 48 which is equal to the total sum of some dices in the picture.
<o:p></o:p></span></p><p class="MsoNormal"><span style="color: black; font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%; mso-ascii-theme-font: major-bidi; mso-bidi-theme-font: major-bidi; mso-fareast-font-family: "Times New Roman"; mso-hansi-theme-font: major-bidi;"><br /></span></p><p class="MsoNormal"></p><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh5GbopR5s3U6e0W34uA4Ci_uf3IgfIQFf93gdBfUklDX_93D76cxHaHJ-x2GlT6rgMpimxDZvWUSX_u68wyPQ9nM-uNAGkSWLEAcKlIvah4w1E8uaMr4_oLBVrGCLqHdrHKOyQnJpbx5Tv1a6FNZn3JSA21iauznWWIO2KUQXFvjloBuDyK3ndmWgi/s236/Dices%20(2).png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="236" data-original-width="233" height="236" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh5GbopR5s3U6e0W34uA4Ci_uf3IgfIQFf93gdBfUklDX_93D76cxHaHJ-x2GlT6rgMpimxDZvWUSX_u68wyPQ9nM-uNAGkSWLEAcKlIvah4w1E8uaMr4_oLBVrGCLqHdrHKOyQnJpbx5Tv1a6FNZn3JSA21iauznWWIO2KUQXFvjloBuDyK3ndmWgi/s1600/Dices%20(2).png" width="233" /></a></div><br /><div class="separator" style="clear: both; text-align: center;"><br /></div><br /><span style="color: black; font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%; mso-ascii-theme-font: major-bidi; mso-bidi-theme-font: major-bidi; mso-fareast-font-family: "Times New Roman"; mso-hansi-theme-font: major-bidi;"><p class="MsoNormal"><span style="color: black; font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%; mso-ascii-theme-font: major-bidi; mso-bidi-theme-font: major-bidi; mso-fareast-font-family: "Times New Roman"; mso-hansi-theme-font: major-bidi;">It could be impossible because you have to solve 2^12 scenarios (4096
scenarios) </span><span style="color: black; font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%; mso-ascii-theme-font: major-bidi; mso-bidi-language: FA; mso-bidi-theme-font: major-bidi; mso-fareast-font-family: "Times New Roman"; mso-hansi-theme-font: major-bidi;">in a very short time. <o:p></o:p></span></p>
<p class="MsoNormal"><span style="color: black; font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%; mso-ascii-theme-font: major-bidi; mso-bidi-language: FA; mso-bidi-theme-font: major-bidi; mso-fareast-font-family: "Times New Roman"; mso-hansi-theme-font: major-bidi;">This analytic model can help us to find the
answer. <o:p></o:p></span></p><p class="MsoNormal"><span style="color: black; font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%; mso-ascii-theme-font: major-bidi; mso-bidi-language: FA; mso-bidi-theme-font: major-bidi; mso-fareast-font-family: "Times New Roman"; mso-hansi-theme-font: major-bidi;"><br /></span></p><p class="MsoNormal"></p><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhzhMWk0VxCb47p8nxlwGseo3fVk8StBUU9d-WFgujN-vzj0VLZJwmDtvZZyaTze-96ojYU3dHWYeuhRk9HAANbGOCeC4vjWIG4WxtYnilHN9MTMOsLcJqmABS7a9s6J7ixJJWUVgNjUDgOVCB8dUnq4ny5lDazx80exkm_3jsbI05F7XHm9B9pSm3-/s1175/Analytic%20Model.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="423" data-original-width="1175" height="205" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhzhMWk0VxCb47p8nxlwGseo3fVk8StBUU9d-WFgujN-vzj0VLZJwmDtvZZyaTze-96ojYU3dHWYeuhRk9HAANbGOCeC4vjWIG4WxtYnilHN9MTMOsLcJqmABS7a9s6J7ixJJWUVgNjUDgOVCB8dUnq4ny5lDazx80exkm_3jsbI05F7XHm9B9pSm3-/w478-h205/Analytic%20Model.png" width="478" /></a></div><p class="MsoNormal"><br /></p><p></p><p class="MsoNormal"><span style="font-size: 12pt; line-height: 115%;">As you can see, we enter the given number
into cell “B2” then all numbers of the dices into cell “B3”. If the status is
“OK”, this is the answer. Otherwise, the answer is negative or “REJECTED”.<o:p></o:p></span></p></span><p></p><p class="MsoNormal"><span style="font-family: "Times New Roman", "serif"; font-size: 12pt; line-height: 115%;">Please see the video of this model:<o:p></o:p></span></p><p class="MsoNormal"><span style="font-family: "Times New Roman", "serif"; font-size: 12pt; line-height: 115%;"><br /></span></p><p class="MsoNormal"></p><div class="separator" style="clear: both; text-align: center;"><iframe allowfullscreen='allowfullscreen' webkitallowfullscreen='webkitallowfullscreen' mozallowfullscreen='mozallowfullscreen' width='320' height='266' src='https://www.blogger.com/video.g?token=AD6v5dxVSly38wTjq2TS4359jQaTcw0I69OuuH4vTDAwoJnWhD1bHDiuKol3qsBJ8d3WBabb4ExV-Qdv_3D_aH9bIg' class='b-hbp-video b-uploaded' frameborder='0'></iframe></div><br /><span style="font-family: "Times New Roman", "serif"; font-size: 12pt; line-height: 115%;"><br /></span><p></p><p class="MsoNormal"><span style="font-family: "Times New Roman", "serif"; font-size: 12pt; line-height: 115%;">First, I assume all 12 dices are equal to 6.
Then I changed some numbers where the total sum would be equal to the given
number.<o:p></o:p></span></p><p class="MsoNormal"><span style="font-family: "Times New Roman", "serif"; font-size: 12pt; line-height: 115%;">When the status returns to “OK”, we can
obtain one answer or more, which are the alternative answers. <o:p></o:p></span></p><p class="MsoNormal"><span style="font-family: "Times New Roman", "serif"; font-size: 12pt; line-height: 115%;">If you have any question, please do not
hesitate to send it to my email:<o:p></o:p></span></p><p class="MsoNormal">
<span style="font-family: "Times New Roman", "serif"; font-size: 12pt; line-height: 115%;">
</span></p><p class="MsoNormal"><span style="font-family: "Times New Roman", "serif"; font-size: 12pt; line-height: 115%;"><a href="mailto:Soleimani_gh@hotmail.com">Soleimani_gh@hotmail.com</a><o:p></o:p></span></p><p class="MsoNormal"><span style="color: black; font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%; mso-ascii-theme-font: major-bidi; mso-bidi-theme-font: major-bidi; mso-fareast-font-family: "Times New Roman"; mso-hansi-theme-font: major-bidi;"></span></p><p class="MsoNormal"><span style="color: black; font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%; mso-ascii-theme-font: major-bidi; mso-bidi-language: FA; mso-bidi-theme-font: major-bidi; mso-fareast-font-family: "Times New Roman"; mso-hansi-theme-font: major-bidi;"><br /></span></p><br /><p></p>Gholamreza Soleimanihttp://www.blogger.com/profile/03273527405719420253noreply@blogger.com0tag:blogger.com,1999:blog-392703582366288634.post-48054628434369759602023-06-03T14:12:00.006+03:302023-06-04T20:56:17.666+03:30Decision Making Methods: Shanon Entropy, AHP, ANP, ISM, SAW, TOPSIS, VIKOR, ELECTRE, DEMATEL<div><span style="background-color: white; color: #414141; font-family: sans-serif; font-size: 16px;">You can find attached the links to the excel spreadsheets which include at least a sample of the decision-making methods below:</span></div><div><span style="color: #414141; font-family: sans-serif;"><br /></span></div><div><span style="color: #414141; font-family: sans-serif;"><br /></span><div> AHP: </div><div> https://docs.google.com/spreadsheets/d/16k7sfeXzS5vjxZT0R8syksFKlBhXGzty/edit#gid=107806602</div><div><br /></div><div><br /></div><div> ANP:
https://docs.google.com/spreadsheets/d/1j766DLGXSkyODCr08VGN3z5y9roc4llX/edit#gid=2105940568</div><div><br /></div><div> ISM:
https://docs.google.com/spreadsheets/d/1U1ZaBVDtkN29mZz6ur-HbsotZVNy82OS/edit#gid=1639052690</div><div><br /></div><div> SAW:
https://docs.google.com/spreadsheets/d/1Jjnoz79mxKbD5GbkyD8rgJdmok81hTGh/edit#gid=398772179</div><div><br /></div><div> TOPSIS:
https://docs.google.com/spreadsheets/d/1Jjnoz79mxKbD5GbkyD8rgJdmok81hTGh/edit#gid=398772179</div><div><br /></div><div> VIKOR:
https://docs.google.com/spreadsheets/d/1Jjnoz79mxKbD5GbkyD8rgJdmok81hTGh/edit#gid=398772179</div><div><br /></div><div> ELECTRE:
https://docs.google.com/spreadsheets/d/1Jjnoz79mxKbD5GbkyD8rgJdmok81hTGh/edit#gid=398772179</div><div><br /></div><div> DEMATEL:
https://docs.google.com/spreadsheets/d/1jrHhC2PJJRqF6FTmB2CQgB-GgHvsWuvq/edit#gid=476016403</div><div><br /></div><div><br /></div><div> 10 C Model Decision Making method of ELECTRE:
https://docs.google.com/spreadsheets/d/1JI0u4Gu3frs2kBmNmdbyb05xvYrW8BfX/edit#gid=404290178</div><div><br /></div><div><br /></div><div><br /></div><h2 style="text-align: left;">
<b>If you need any support do not hesitate to send your request to my email:
soleimani_gh@hotmail.com<i></i></b></h2></div>Gholamreza Soleimanihttp://www.blogger.com/profile/03273527405719420253noreply@blogger.com0tag:blogger.com,1999:blog-392703582366288634.post-41156559205771022992020-04-27T18:52:00.001+04:302020-04-27T18:52:28.958+04:30Artificial Intelligence by Using Microsoft Excel Controlling Accounts<div dir="ltr" style="text-align: left;" trbidi="on">
Suppose your job is controlling and auditing accounts to find out the discrepancies between account receivables (sales) and saving accounts in banking systems. Now, consider a manufacturing company which has the network of chain stores (retail chains) and saving accounts in different banks so that all payments made by customers (Sales) in each store can be distributes and deposited among different saving accounts (below figure) something like a network. There are two types of payment: 1. ATM system 2. POS machines. Assume you are willing to compare the payments of customers (account receivables) with different saving accounts in banks for preparing a trial balance to ensure accuracy and reach the balance to zero for a period of three months. What are your challenges? For example:
1. It is possible, there will be simultaneously the transactions which show exactly the same numbers among different stores and banks.
2. The POS systems usually accumulate the payments made by customers. It means that you will not be able to control the accounts item to item and one by one.
3. Sometimes a customer send to you a payment several times. You are expected to recognize these frauds and to claim on the customer.
And maybe other challenges.
I have designed a model which is able to resolve all above challenges. I name this model something like the Artificial Intelligence by using Microsoft Excel.
If you are interested in having this model, please do not hesitate to send your request to my email: soleimani_gh@hotmail.com
Phone number: +98 9109250225<br />
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Gholamreza Soleimanihttp://www.blogger.com/profile/03273527405719420253noreply@blogger.com0tag:blogger.com,1999:blog-392703582366288634.post-30087195838420260722018-10-17T10:35:00.000+03:302018-10-18T12:10:39.612+03:30Creating New Logic’s Laws by Using Coding in Microsoft Excel<div dir="ltr" style="text-align: left;" trbidi="on">
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<span style="font-family: "times new roman" , "serif"; font-size: 12.0pt; line-height: 115%;"><u><b>Law (1):</b></u><o:p></o:p></span></div>
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<span style="font-family: "times new roman" , "serif"; font-size: 12.0pt; line-height: 115%;">(p </span><span style="font-size: 12.0pt; line-height: 115%; mso-ascii-font-family: Calibri; mso-bidi-font-family: "Times New Roman"; mso-bidi-theme-font: major-bidi; mso-hansi-font-family: Calibri;">→
q) I (</span><span style="font-family: "times new roman" , "serif"; font-size: 12.0pt; line-height: 115%;">(p </span><span style="font-size: 12.0pt; line-height: 115%; mso-ascii-font-family: Calibri; mso-bidi-font-family: "Times New Roman"; mso-bidi-theme-font: major-bidi; mso-hansi-font-family: Calibri;">→ q) → r) I ((</span><span style="font-family: "times new roman" , "serif"; font-size: 12.0pt; line-height: 115%;">(p </span><span style="font-size: 12.0pt; line-height: 115%; mso-ascii-font-family: Calibri; mso-bidi-font-family: "Times New Roman"; mso-bidi-theme-font: major-bidi; mso-hansi-font-family: Calibri;">→ q) → r)) → s) I (((</span><span style="font-family: "times new roman" , "serif"; font-size: 12.0pt; line-height: 115%;">(p </span><span style="font-size: 12.0pt; line-height: 115%; mso-ascii-font-family: Calibri; mso-bidi-font-family: "Times New Roman"; mso-bidi-theme-font: major-bidi; mso-hansi-font-family: Calibri;">→ q) → r)) → s) → t) I……<o:p></o:p></span></div>
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<span style="font-size: 12.0pt; line-height: 115%; mso-ascii-font-family: Calibri; mso-bidi-font-family: "Times New Roman"; mso-bidi-theme-font: major-bidi; mso-hansi-font-family: Calibri;"><br /></span></div>
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<span style="font-size: 12.0pt; line-height: 115%; mso-ascii-font-family: Calibri; mso-bidi-font-family: "Times New Roman"; mso-bidi-theme-font: major-bidi; mso-hansi-font-family: Calibri;">This Logic always “TRUE”<o:p></o:p></span><br />
<span style="font-size: 12.0pt; line-height: 115%; mso-ascii-font-family: Calibri; mso-bidi-font-family: "Times New Roman"; mso-bidi-theme-font: major-bidi; mso-hansi-font-family: Calibri;"><br /></span>
<span style="font-size: 12.0pt; line-height: 115%; mso-ascii-font-family: Calibri; mso-bidi-font-family: "Times New Roman"; mso-bidi-theme-font: major-bidi; mso-hansi-font-family: Calibri;"><b>Examples:</b></span><br />
<span style="font-size: 12.0pt; line-height: 115%; mso-ascii-font-family: Calibri; mso-bidi-font-family: "Times New Roman"; mso-bidi-theme-font: major-bidi; mso-hansi-font-family: Calibri;"><br /></span>
<span style="font-size: 12.0pt; line-height: 115%; mso-ascii-font-family: Calibri; mso-bidi-font-family: "Times New Roman"; mso-bidi-theme-font: major-bidi; mso-hansi-font-family: Calibri;">Law (1) for three propositions (variables)</span><br />
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhwSFOZHtrJGsl7H0PWDvnIJ7t13SiU2t6eVc6eZHkL4diRFOYndn-ErkDifrPg6LdI6dLmXmDkmyGWIj11eo_15mC2_cdthxP6VcWbt3A6SF9Fx_m7SdkyNKAHns-YEOzOV__4gab5Q4U/s1600/1.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="224" data-original-width="358" height="200" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhwSFOZHtrJGsl7H0PWDvnIJ7t13SiU2t6eVc6eZHkL4diRFOYndn-ErkDifrPg6LdI6dLmXmDkmyGWIj11eo_15mC2_cdthxP6VcWbt3A6SF9Fx_m7SdkyNKAHns-YEOzOV__4gab5Q4U/s320/1.png" width="320" /></a></div>
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<span style="font-size: 12.0pt; line-height: 115%; mso-ascii-font-family: Calibri; mso-bidi-font-family: "Times New Roman"; mso-bidi-theme-font: major-bidi; mso-hansi-font-family: Calibri;">Law (1) for four propositions (variables)</span><br />
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<span style="font-size: 12.0pt; line-height: 115%; mso-ascii-font-family: Calibri; mso-bidi-font-family: "Times New Roman"; mso-bidi-theme-font: major-bidi; mso-hansi-font-family: Calibri;"><br /></span>
<span style="font-size: 12.0pt; line-height: 115%; mso-ascii-font-family: Calibri; mso-bidi-font-family: "Times New Roman"; mso-bidi-theme-font: major-bidi; mso-hansi-font-family: Calibri;">Law (1) for five propositions (variables)</span><br />
<span style="font-size: 12.0pt; line-height: 115%; mso-ascii-font-family: Calibri; mso-bidi-font-family: "Times New Roman"; mso-bidi-theme-font: major-bidi; mso-hansi-font-family: Calibri;"><br /></span>
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<span style="font-size: 12.0pt; line-height: 115%; mso-ascii-font-family: Calibri; mso-bidi-font-family: "Times New Roman"; mso-bidi-theme-font: major-bidi; mso-hansi-font-family: Calibri;"><br /></span></div>
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<span style="font-size: 12.0pt; line-height: 115%; mso-ascii-font-family: Calibri; mso-bidi-font-family: "Times New Roman"; mso-bidi-theme-font: major-bidi; mso-hansi-font-family: Calibri;"><b><u><br /></u></b></span></div>
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<span style="font-size: 12.0pt; line-height: 115%; mso-ascii-font-family: Calibri; mso-bidi-font-family: "Times New Roman"; mso-bidi-theme-font: major-bidi; mso-hansi-font-family: Calibri;"><br /></span></div>
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<span style="font-family: "times new roman" , "serif"; font-size: 12.0pt; line-height: 115%;">(p </span><span style="font-size: 12.0pt; line-height: 115%; mso-ascii-font-family: Calibri; mso-bidi-font-family: "Times New Roman"; mso-bidi-theme-font: major-bidi; mso-hansi-font-family: Calibri;">→
q) & (</span><span style="font-family: "times new roman" , "serif"; font-size: 12.0pt; line-height: 115%;">(p </span><span style="font-size: 12.0pt; line-height: 115%; mso-ascii-font-family: Calibri; mso-bidi-font-family: "Times New Roman"; mso-bidi-theme-font: major-bidi; mso-hansi-font-family: Calibri;">→
q) → r) & ((</span><span style="font-family: "times new roman" , "serif"; font-size: 12.0pt; line-height: 115%;">(p </span><span style="font-size: 12.0pt; line-height: 115%; mso-ascii-font-family: Calibri; mso-bidi-font-family: "Times New Roman"; mso-bidi-theme-font: major-bidi; mso-hansi-font-family: Calibri;">→ q) → r)) → s) & (((</span><span style="font-family: "times new roman" , "serif"; font-size: 12.0pt; line-height: 115%;">(p </span><span style="font-size: 12.0pt; line-height: 115%; mso-ascii-font-family: Calibri; mso-bidi-font-family: "Times New Roman"; mso-bidi-theme-font: major-bidi; mso-hansi-font-family: Calibri;">→ q) → r)) → s) → t) &……<o:p></o:p></span></div>
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<span style="font-size: 12.0pt; line-height: 115%; mso-ascii-font-family: Calibri; mso-bidi-font-family: "Times New Roman"; mso-bidi-theme-font: major-bidi; mso-hansi-font-family: Calibri;"><br /></span></div>
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<span style="font-size: 12.0pt; line-height: 115%; mso-ascii-font-family: Calibri; mso-bidi-font-family: "Times New Roman"; mso-bidi-theme-font: major-bidi; mso-hansi-font-family: Calibri;">This logic, under below conditions always is
“TRUE”:<o:p></o:p></span></div>
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<!--[if !supportLists]--><span style="font-family: "symbol"; font-size: 12.0pt; line-height: 115%;"><span style="mso-list: Ignore;">·<span style="font: 7.0pt "Times New Roman";"> - </span></span></span><!--[endif]--><span dir="LTR"></span><span style="font-size: 12.0pt; line-height: 115%; mso-ascii-font-family: Calibri; mso-bidi-font-family: "Times New Roman"; mso-bidi-theme-font: major-bidi; mso-hansi-font-family: Calibri;">p
= False and other propositions (variables) are “TRUE”<o:p></o:p></span></div>
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<span style="font-size: 12.0pt; line-height: 115%; mso-ascii-font-family: Calibri; mso-bidi-font-family: "Times New Roman"; mso-bidi-theme-font: major-bidi; mso-hansi-font-family: Calibri;"><br /></span></div>
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<!--[if !supportLists]--><span style="font-family: "symbol"; font-size: 12.0pt; line-height: 115%;"><span style="mso-list: Ignore;">·<span style="font: 7.0pt "Times New Roman";"> - </span></span></span><!--[endif]--><span dir="LTR"></span><span style="font-size: 12.0pt; line-height: 115%; mso-ascii-font-family: Calibri; mso-bidi-font-family: "Times New Roman"; mso-bidi-theme-font: major-bidi; mso-hansi-font-family: Calibri;">p
and q = False and other propositions (variables) are “TRUE”<o:p></o:p></span></div>
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<span style="font-size: 12.0pt; line-height: 115%; mso-ascii-font-family: Calibri; mso-bidi-font-family: "Times New Roman"; mso-bidi-theme-font: major-bidi; mso-hansi-font-family: Calibri;"><br /></span></div>
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<!--[if !supportLists]--><span style="font-family: "symbol"; font-size: 12.0pt; line-height: 115%;"><span style="mso-list: Ignore;">·<span style="font: 7.0pt "Times New Roman";"> - </span></span></span><!--[endif]--><span dir="LTR"></span><span style="font-size: 12.0pt; line-height: 115%; mso-ascii-font-family: Calibri; mso-bidi-font-family: "Times New Roman"; mso-bidi-theme-font: major-bidi; mso-hansi-font-family: Calibri;">All
propositions (variables) are “TRUE”<o:p></o:p></span><br />
<span style="font-size: 12.0pt; line-height: 115%; mso-ascii-font-family: Calibri; mso-bidi-font-family: "Times New Roman"; mso-bidi-theme-font: major-bidi; mso-hansi-font-family: Calibri;"><br /></span>
<span style="font-size: 12.0pt; line-height: 115%; mso-ascii-font-family: Calibri; mso-bidi-font-family: "Times New Roman"; mso-bidi-theme-font: major-bidi; mso-hansi-font-family: Calibri;"><br /></span></div>
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<b>Examples:</b><br />
<b><br /></b></div>
<span style="font-size: 16px;">Law (2) for three propositions (variables)</span><br />
<span style="font-size: 16px;"><br /></span>
<span style="font-size: 16px;"><br /></span>
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgsowcZcHq7emcOQ3qfmHqTEGDB5Ucqn7jOmFXZfpnNi-WnnO2C_yIS4TuIycDm4wt_Slv6ZGoknE7Ya0EAZfGpbRkGRkWoTn-qbWKJrsv9qbfwWrNZvsYjhm_32wr48zrcgHqvOWz7VZA/s1600/4.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="209" data-original-width="354" height="188" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgsowcZcHq7emcOQ3qfmHqTEGDB5Ucqn7jOmFXZfpnNi-WnnO2C_yIS4TuIycDm4wt_Slv6ZGoknE7Ya0EAZfGpbRkGRkWoTn-qbWKJrsv9qbfwWrNZvsYjhm_32wr48zrcgHqvOWz7VZA/s320/4.png" width="320" /></a></div>
<span style="font-size: 16px;"><br /></span>
<span style="font-size: 16px;"><br /></span>
<span style="font-size: 16px;">Law (2) for four propositions (variables)</span><br />
<span style="font-size: 16px;"><br /></span>
<span style="font-size: 16px;"><br /></span>
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhQlBfVKvun2W0dQdugXc6KlN5VUUVQ0wQWuktm1GvzCS50-vGb1H0Kac6YI3APk1yzZOeKHMG4hA-aoWlQNy4h0cHlVNcAb0_gxb4k5650xtm6hgf-REnZQNOyZwjuivWpVoR6rABOatE/s1600/5.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="363" data-original-width="538" height="215" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhQlBfVKvun2W0dQdugXc6KlN5VUUVQ0wQWuktm1GvzCS50-vGb1H0Kac6YI3APk1yzZOeKHMG4hA-aoWlQNy4h0cHlVNcAb0_gxb4k5650xtm6hgf-REnZQNOyZwjuivWpVoR6rABOatE/s320/5.png" width="320" /></a></div>
<span style="font-size: 16px;"><br /></span>
<span style="font-size: 16px;"><br /></span>
<span style="font-size: 16px;">Law (2) for five propositions (variables)</span><br />
<span style="font-size: 16px;"><br /></span>
<span style="font-size: 16px;"><br /></span>
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEj5fhTnfgojh21Ln6_jSGYIGewZLiH2U3L4M0JvcAzst8QAVPRnxB7Vb0MTsFhmXMOKc0KGchZMWpjcAg87416BSGCFuUKHqC8bYrdAL12R1iiISQe7wZPfSxhpBlgF5cStzToi9qxQjcc/s1600/6.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="480" data-original-width="381" height="320" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEj5fhTnfgojh21Ln6_jSGYIGewZLiH2U3L4M0JvcAzst8QAVPRnxB7Vb0MTsFhmXMOKc0KGchZMWpjcAg87416BSGCFuUKHqC8bYrdAL12R1iiISQe7wZPfSxhpBlgF5cStzToi9qxQjcc/s320/6.png" width="254" /></a></div>
<span style="font-size: 16px;"><br /></span>
<span style="font-size: 16px;"><br /></span>
<span style="font-size: 16px;"><b>To be continued .....</b></span><br />
<span style="font-size: 16px;"><br /></span></div>
Gholamreza Soleimanihttp://www.blogger.com/profile/03273527405719420253noreply@blogger.com0tag:blogger.com,1999:blog-392703582366288634.post-28942859228507157942018-09-25T15:42:00.003+03:302023-12-19T20:44:08.425+03:30Analysis and Design Open Oscillatory Systems with Forced Harmonic Motion (3)<div dir="ltr" style="text-align: left;" trbidi="on">
<br />
<br />
<div class="MsoNormal" style="direction: ltr; text-align: left; unicode-bidi: embed;"><span style="font-family: "Times New Roman", serif; font-size: 12pt;"> </span><span data-preserver-spaces="true" style="background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial; background-position: initial; background-repeat: initial; background-size: initial; color: #0e101a; margin-bottom: 0pt; margin-top: 0pt;">Following the article of <a href="https://emfps.blogspot.com/2018/09/analysis-and-design-open-oscillatory.html">Analysis and Design Open Oscillatory Systems with Forced Harmonic Motion (2)</a></span><span data-preserver-spaces="true" style="background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial; background-position: initial; background-repeat: initial; background-size: initial; color: #0e101a; margin-bottom: 0pt; margin-top: 0pt;">, the purpose of this article is to present a model for finding the characteristics of an oscillatory system with forced harmonic motion where the acceleration will be equal zero. In this case, there is an interesting point that is related to an important difference between SHM and an oscillatory system with forced harmonic motion.</span></div><p style="background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial; background-position: initial; background-repeat: initial; background-size: initial; color: #0e101a; margin-bottom: 0pt; margin-top: 0pt;"><br /></p><p style="background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial; background-position: initial; background-repeat: initial; background-size: initial; color: #0e101a; margin-bottom: 0pt; margin-top: 0pt;"><span data-preserver-spaces="true" style="background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial; background-position: initial; background-repeat: initial; background-size: initial; margin-bottom: 0pt; margin-top: 0pt;">If an object is oscillating under simple harmonic motion, its linear velocity will be zero at the highest and lowest points where we have maximum displacement which is named the amplitude (A).On the other hand; at the maximum level of the displacement (x = A), the acceleration has also its maximum magnitude while at the middle (x = 0), acceleration is zero due to stop at those points in order to change direction while velocity gains its maximum magnitude at the equilibrium point (x = 0). At the extreme ends (x = A), when we have the maximum force and kinetic energy, the acceleration has its maximum magnitude. Therefore, the maximum of acceleration magnitude in simple harmonic motion occurs at maximum displacement (A) and acceleration at the middle is zero when we have the displacement equal to zero just like the below diagrams: </span></p>
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiVCi33lshHGQ9IoGGoICmPcMzS4rhKrql3RzVP7K0YQHJm-TnLBEDL2bgVy6oY2Kh4uyFxFLPjrXMHvQNgkA0Aa095o-X_8yKgJ_jW4tpkHaJvzyU-2A_oKCHG8FFHyxzqs2rLWQRN93A/s1600/2.png" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="413" data-original-width="603" height="219" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiVCi33lshHGQ9IoGGoICmPcMzS4rhKrql3RzVP7K0YQHJm-TnLBEDL2bgVy6oY2Kh4uyFxFLPjrXMHvQNgkA0Aa095o-X_8yKgJ_jW4tpkHaJvzyU-2A_oKCHG8FFHyxzqs2rLWQRN93A/s320/2.png" width="320" /></a></div>
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<span style="font-family: "Times New Roman","serif"; font-size: 12pt; line-height: 107%; mso-ascii-theme-font: major-bidi; mso-bidi-theme-font: major-bidi; mso-hansi-theme-font: major-bidi;"><span style="mso-spacerun: yes;"><br /></span></span></div>
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<span style="font-family: "Times New Roman","serif"; font-size: 12pt; line-height: 107%; mso-ascii-theme-font: major-bidi; mso-bidi-theme-font: major-bidi; mso-hansi-theme-font: major-bidi;"></span></div>
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<span style="font-family: "Times New Roman","serif"; font-size: 12pt; line-height: 107%; mso-ascii-theme-font: major-bidi; mso-bidi-theme-font: major-bidi; mso-hansi-theme-font: major-bidi;">But there is a different story about the oscillatory systems with
forced harmonic motion. In this case, at the some points where the displacement
is not zero (x = a), we have the acceleration equal to zero. Please see below
diagrams:<o:p></o:p></span></div>
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<span style="font-family: "Times New Roman","serif"; font-size: 12pt; line-height: 107%; mso-ascii-theme-font: major-bidi; mso-bidi-theme-font: major-bidi; mso-hansi-theme-font: major-bidi;"><br /></span></div>
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<span style="font-family: "Times New Roman","serif"; font-size: 12pt; line-height: 107%; mso-ascii-theme-font: major-bidi; mso-bidi-theme-font: major-bidi; mso-hansi-theme-font: major-bidi;">Now, the question is: What are the characteristics of an
oscillatory system with forced harmonic motion where we have the acceleration
equal to zero at the point of x = a?<o:p></o:p></span></div>
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<span style="font-family: "Times New Roman","serif"; font-size: 12pt; line-height: 107%; mso-ascii-theme-font: major-bidi; mso-bidi-theme-font: major-bidi; mso-hansi-theme-font: major-bidi;">Below model is able to answer above question:<o:p></o:p></span></div>
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEg8WfaSIgr0rSS-s6c1x4kc4baCTWjMZTkAqGBRVij1FJ9jRPro4GRUZAXVIzsVOSs2v3GO-YpaXtU8-CchxDQLizVyokIaQVGoYF4FKxkCn5_dG63HcCD0FX1A3zRlaWYztlvwaE-Cmk4/s1600/5.png" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="458" data-original-width="733" height="199" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEg8WfaSIgr0rSS-s6c1x4kc4baCTWjMZTkAqGBRVij1FJ9jRPro4GRUZAXVIzsVOSs2v3GO-YpaXtU8-CchxDQLizVyokIaQVGoYF4FKxkCn5_dG63HcCD0FX1A3zRlaWYztlvwaE-Cmk4/s320/5.png" width="320" /></a></div>
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<span style="font-family: "Times New Roman","serif"; font-size: 12pt; line-height: 107%; mso-ascii-theme-font: major-bidi; mso-bidi-theme-font: major-bidi; mso-hansi-theme-font: major-bidi;">The components of above model are as follows:<o:p></o:p></span></div>
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<span style="font-family: "Times New Roman","serif"; font-size: 12pt; line-height: 107%; mso-ascii-theme-font: major-bidi; mso-bidi-theme-font: major-bidi; mso-hansi-theme-font: major-bidi;"><br /></span></div>
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<span style="font-family: "Times New Roman","serif"; font-size: 12pt; line-height: 115%; mso-ascii-theme-font: major-bidi; mso-bidi-language: AR-SA; mso-bidi-theme-font: major-bidi; mso-fareast-font-family: "Times New Roman"; mso-fareast-theme-font: minor-fareast; mso-hansi-theme-font: major-bidi;">1. In right side on cells L6:M6, we have inputs
including </span><span style="font-family: "Times New Roman","serif"; font-size: 12pt; line-height: 115%; mso-ascii-theme-font: major-bidi; mso-bidi-language: AR-SA; mso-bidi-theme-font: major-bidi; mso-hansi-theme-font: major-bidi;">given data
of “F</span><span style="font-family: "Times New Roman","serif"; font-size: 9pt; line-height: 115%; mso-ascii-theme-font: major-bidi; mso-bidi-language: AR-SA; mso-bidi-theme-font: major-bidi; mso-hansi-theme-font: major-bidi;">m</span><span style="font-family: "Times New Roman","serif"; font-size: 12pt; line-height: 115%; mso-ascii-theme-font: major-bidi; mso-bidi-language: AR-SA; mso-bidi-theme-font: major-bidi; mso-hansi-theme-font: major-bidi;">”, and “t”.<o:p></o:p></span></div>
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<span style="font-family: "Times New Roman","serif"; font-size: 12pt; line-height: 115%; mso-ascii-theme-font: major-bidi; mso-bidi-language: AR-SA; mso-bidi-theme-font: major-bidi; mso-fareast-font-family: "Times New Roman"; mso-fareast-theme-font: minor-fareast; mso-hansi-theme-font: major-bidi;">2. In left side on cells H6:J7, we have other inputs
including lower and upper ranges for independent variables of “m”, “b” and </span><span style="font-family: "Times New Roman","serif"; font-size: 12pt; line-height: 115%; mso-ascii-theme-font: major-bidi; mso-bidi-language: AR-SA; mso-bidi-theme-font: major-bidi; mso-hansi-theme-font: major-bidi;">“ω″/ω” </span><span style="font-family: "Times New Roman","serif"; font-size: 12pt; line-height: 115%; mso-ascii-theme-font: major-bidi; mso-bidi-language: AR-SA; mso-bidi-theme-font: major-bidi; mso-fareast-font-family: "Times New Roman"; mso-fareast-theme-font: minor-fareast; mso-hansi-theme-font: major-bidi;">to reach the answers for the acceleration equal to
zero which are the characteristics of driven oscillatory </span><span style="font-family: "Times New Roman","serif"; font-size: 12pt; line-height: 115%; mso-ascii-theme-font: major-bidi; mso-bidi-language: AR-SA; mso-bidi-theme-font: major-bidi; mso-hansi-theme-font: major-bidi;">system. Here, there are lower and upper
ranges which are changed by click on cell A2 and also this change will again go
back by click on cell B2 (Go & Back). <span style="background: white;"><o:p></o:p></span></span></div>
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<span style="background: white; font-family: "Times New Roman","serif"; font-size: 12pt; line-height: 115%; mso-ascii-theme-font: major-bidi; mso-bidi-language: AR-SA; mso-bidi-theme-font: major-bidi; mso-hansi-theme-font: major-bidi;">3. On cells I9:I18, we have outputs
which are the characteristics </span><span style="font-family: "Times New Roman","serif"; font-size: 12pt; line-height: 115%; mso-ascii-theme-font: major-bidi; mso-bidi-language: AR-SA; mso-bidi-theme-font: major-bidi; mso-fareast-font-family: "Times New Roman"; mso-fareast-theme-font: minor-fareast; mso-hansi-theme-font: major-bidi;">for driven oscillatory </span><span style="font-family: "Times New Roman","serif"; font-size: 12pt; line-height: 115%; mso-ascii-theme-font: major-bidi; mso-bidi-language: AR-SA; mso-bidi-theme-font: major-bidi; mso-hansi-theme-font: major-bidi;">system responding to the acceleration equal to zero. <o:p></o:p></span></div>
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<span style="font-family: "Times New Roman","serif"; font-size: 12pt; line-height: 115%; mso-ascii-theme-font: major-bidi; mso-bidi-language: AR-SA; mso-bidi-theme-font: major-bidi; mso-hansi-theme-font: major-bidi;">You can see below clip as the example for this model:<o:p></o:p></span></div>
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<span style="font-family: "Times New Roman","serif"; font-size: 12pt; line-height: 115%; mso-ascii-theme-font: major-bidi; mso-bidi-language: AR-SA; mso-bidi-theme-font: major-bidi; mso-hansi-theme-font: major-bidi;"><br /></span></div>
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<iframe allowfullscreen='allowfullscreen' webkitallowfullscreen='webkitallowfullscreen' mozallowfullscreen='mozallowfullscreen' width='320' height='266' src='https://www.blogger.com/video.g?token=AD6v5dz1qjWNiS5kLtTjRi40gcKIZlWncSmyeg-A-61a5-AJNw_mY-DhWUsyi6v_K0uphmbWQFwNF91Qm9Y14gRxmw' class='b-hbp-video b-uploaded' frameborder='0'></iframe></div>
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<span style="font-family: "Times New Roman","serif"; font-size: 12pt; line-height: 115%; mso-ascii-theme-font: major-bidi; mso-bidi-language: AR-SA; mso-bidi-theme-font: major-bidi; mso-hansi-theme-font: major-bidi;"><br /></span></div>
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<span dir="LTR" style="font-family: "Times New Roman","serif"; font-size: 12pt; line-height: 107%; mso-ascii-theme-font: major-bidi; mso-bidi-theme-font: major-bidi; mso-hansi-theme-font: major-bidi;">All researchers and individual people, who are interested in having
this model, don’t hesitate to send their request to below addresses:<o:p></o:p></span></div>
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjDAZKAbEuboLPvt30sErQnyVT2oljrGNRPNd4r-otkc3Rm5tzU6tQV7zQFY5f8pPAfeO5W-oGvt-x4qeqv_x2Re9NLvLBG91RWzdifw_Ub2gJqPun4hhAWaZiLKGbDC90sFDHumyu4_7Q/s1600/%25D8%25AF%25D8%25B1%25DB%258C%25D8%25A7%25D9%2581%25D8%25AA+%25D9%2581%25D8%25A7%25DB%258C%25D9%2584+%25D8%25A7%25DA%25A9%25D8%25B3%25D9%2584.png" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="240" data-original-width="592" height="129" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjDAZKAbEuboLPvt30sErQnyVT2oljrGNRPNd4r-otkc3Rm5tzU6tQV7zQFY5f8pPAfeO5W-oGvt-x4qeqv_x2Re9NLvLBG91RWzdifw_Ub2gJqPun4hhAWaZiLKGbDC90sFDHumyu4_7Q/s320/%25D8%25AF%25D8%25B1%25DB%258C%25D8%25A7%25D9%2581%25D8%25AA+%25D9%2581%25D8%25A7%25DB%258C%25D9%2584+%25D8%25A7%25DA%25A9%25D8%25B3%25D9%2584.png" width="320" /></a></div>
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Gholamreza Soleimanihttp://www.blogger.com/profile/03273527405719420253noreply@blogger.com0tag:blogger.com,1999:blog-392703582366288634.post-16719236919717720192018-09-02T16:27:00.000+04:302018-09-02T16:40:33.927+04:30Analysis and Design Open Oscillatory Systems with Forced Harmonic Motion (2)<div dir="ltr" style="text-align: left;" trbidi="on">
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhrMaoYk-TJK8Ukm9TJqpk9A4xnlcuUDXFDKO73omlbK5q0iKANeGovhIivgUjdUp1ekXWaH8b6Pq2hw-WW2fY-oRknG_LLBbS46yTrd3J6STPr4-uVRRqrktVZKgJNwy9m78xy7zigycI/s1600/1.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="535" data-original-width="803" height="266" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhrMaoYk-TJK8Ukm9TJqpk9A4xnlcuUDXFDKO73omlbK5q0iKANeGovhIivgUjdUp1ekXWaH8b6Pq2hw-WW2fY-oRknG_LLBbS46yTrd3J6STPr4-uVRRqrktVZKgJNwy9m78xy7zigycI/s400/1.png" width="400" /></a></div>
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<span style="font-family: "times new roman" , "serif"; font-size: 12.0pt; line-height: 107%;">Following to articles of “Analysis and Design Open Oscillatory
Systems with Forced Harmonic Motion (1)” (</span><a href="https://emfps.blogspot.com/2014/02/analysis-and-design-open-oscillatory.html"><span style="font-family: "times new roman" , "serif"; font-size: 12.0pt; line-height: 107%;">https://emfps.blogspot.com/2014/02/analysis-and-design-open-oscillatory.html</span></a><u><span style="color: blue; font-family: "times new roman" , "serif"; font-size: 12.0pt; line-height: 107%;">)</span></u><span style="font-family: "times new roman" , "serif"; font-size: 12.0pt; line-height: 107%;"> and “A Model to Solve a System of SHM Equations” (</span><a href="https://emfps.blogspot.com/2018/08/a-model-to-solve-system-of-shm-equations_23.html"><span style="font-family: "times new roman" , "serif"; font-size: 12.0pt; line-height: 107%;">https://emfps.blogspot.com/2018/08/a-model-to-solve-system-of-shm-equations_23.html</span></a><u><span style="color: blue; font-family: "times new roman" , "serif"; font-size: 12.0pt; line-height: 107%;">)</span></u><span style="font-family: "times new roman" , "serif"; font-size: 12.0pt; line-height: 107%;">, the purpose of this article is, to find out the characteristics
of unknown open oscillatory system which is under forced harmonic motion in the
moment of close to resonance. In this case, three models have been designed.
One model presents the results for two independent variables “m”, “b” and<span style="mso-spacerun: yes;"> </span>another model gives us the results for three
independent variables “m”, “b” and “</span><span style="color: black; font-family: "times new roman" , "serif"; font-size: 12.0pt; line-height: 107%;">ω''/ω” and
the third model shows us the results for higher than a specific velocity.<o:p></o:p></span></div>
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<b><span style="color: black; font-family: "times new roman" , "serif"; font-size: 12.0pt; line-height: 107%;">Statement of the problem<o:p></o:p></span></b></div>
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<span style="color: black; font-family: "times new roman" , "serif"; font-size: 12.0pt; line-height: 107%;">In many situations of oscillatory motions, we have to
control the point of the resonance to prevent a huge collapse of system. On the
other hand, sometimes we need to know the width of the resonance curve and the
characteristics of the system such as natural frequency to increase the
velocity of the system by using a forced harmonic motion. In fact, the question
is: What is the amount of the force and angular frequency for a forced harmonic
motion where the amplitude and velocity of an oscillatory system will
significantly increase? These two models are able to answer to this question.<o:p></o:p></span></div>
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<b><span style="color: black; font-family: "times new roman" , "serif"; font-size: 12.0pt; line-height: 107%;">Model (1): </span></b><b><span style="font-family: "times new roman" , "serif"; font-size: 12.0pt; line-height: 107%;">The
results for two independent variables “mass” and “linear damping constant”<o:p></o:p></span></b></div>
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<span style="font-family: "times new roman" , "serif"; font-size: 12.0pt; line-height: 107%;">Please be informed that here we encounter with seven independent
variables and we have to process all these variables simultaneously for solving
the nonlinear equations. For first try, I breakdown the problem and start my
analysis by using the most important independent variables which are “m” and “b”
and also utilizing the method mentioned in article of “A Model to Solve a
System of SHM Equations” (</span><a href="https://emfps.blogspot.com/2018/08/a-model-to-solve-system-of-shm-equations_23.html"><span style="font-family: "times new roman" , "serif"; font-size: 12.0pt; line-height: 107%;">https://emfps.blogspot.com/2018/08/a-model-to-solve-system-of-shm-equations_23.html</span></a><u><span style="color: blue; font-family: "times new roman" , "serif"; font-size: 12.0pt; line-height: 107%;">)</span></u><span style="font-family: "times new roman" , "serif"; font-size: 12.0pt; line-height: 107%;"> accompanied by some tricks in Microsoft excel. I think this is the
easiest way. This model says us what are maximum displacement and velocity for
a defined range of “m” and “b” </span><span style="font-family: "times new roman" , "serif"; font-size: 12.0pt; line-height: 107%;">close to the point of the resonance</span><span style="font-family: "times new roman" , "serif"; font-size: 12.0pt; line-height: 107%;">.<o:p></o:p></span></div>
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<span style="font-family: "times new roman" , "serif"; font-size: 12.0pt; line-height: 115%;">Below figure as well as shows you the components of
this model:<o:p></o:p></span></div>
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgcV3MK1y3dA5HyikSps9MDoukSX3vRsjJPnKZKGJobJ2-8vIe5CM0CVhEVGTSLvNjyYcopREz9vfgvMufJVfDeDEeSyQgmtcezjPRaDlwTiIvPH7DOJlcij4G2_xcFnGkS6jXTMzqV_0s/s1600/2.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em; text-align: center;"><img border="0" data-original-height="437" data-original-width="601" height="232" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgcV3MK1y3dA5HyikSps9MDoukSX3vRsjJPnKZKGJobJ2-8vIe5CM0CVhEVGTSLvNjyYcopREz9vfgvMufJVfDeDEeSyQgmtcezjPRaDlwTiIvPH7DOJlcij4G2_xcFnGkS6jXTMzqV_0s/s320/2.png" width="320" /></a><br />
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<span style="font-family: "times new roman" , "serif"; font-size: 12.0pt; line-height: 115%;">The components of above model are as follows:<o:p></o:p></span></div>
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<span style="font-family: "times new roman" , "serif"; font-size: 12.0pt; line-height: 115%;">1. In right side on cells K6:M6, we have inputs
including </span><span style="font-family: "times new roman" , "serif"; font-size: 12.0pt; line-height: 115%;">given data
of “ω″/ω”, “F</span><span style="font-family: "times new roman" , "serif"; font-size: 9.0pt; line-height: 115%;">m</span><span style="font-family: "times new roman" , "serif"; font-size: 12.0pt; line-height: 115%;">”, and “t”.<o:p></o:p></span></div>
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<span style="font-family: "times new roman" , "serif"; font-size: 12.0pt; line-height: 115%;">2. In left side on cells H6:I7, we have other inputs
including lower and upper ranges for independent variables of “m” and “b” to
reach the answers which are the solution for driven oscillatory </span><span style="font-family: "times new roman" , "serif"; font-size: 12.0pt; line-height: 115%;">system close to the point of the resonance.
Here, there are lower and upper ranges which are changed by click on cell A2
and also this change will again go back by click on cell B2 (Go & Back). <span style="background: white;"><o:p></o:p></span></span></div>
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<span style="background: white; font-family: "times new roman" , "serif"; font-size: 12.0pt; line-height: 115%;">3. On cells I9:I17, we have outputs
which are maximum displacement and velocity </span><span style="font-family: "times new roman" , "serif"; font-size: 12.0pt; line-height: 115%;">for driven oscillatory </span><span style="font-family: "times new roman" , "serif"; font-size: 12.0pt; line-height: 115%;">system close to the point of the resonance. <o:p></o:p></span></div>
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<b><i><span style="font-family: "times new roman" , "serif"; font-size: 12.0pt; line-height: 107%;">Note: On I9 and I10, we have maximum
displacement and velocity for </span></i></b><b><i><span style="font-family: "times new roman" , "serif"; font-size: 12.0pt; line-height: 107%;">a
defined range of “m” and “b”. </span></i></b><b><i><span style="font-family: "times new roman" , "serif"; font-size: 12.0pt; line-height: 107%;">Please do not consider them as the amplitude of
harmonic motion. On cell I16 and I17, we have the amplitude of displacement (A)
and the amplitude of velocity (Av). <o:p></o:p></span></i></b></div>
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<br /></div>
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<span style="font-family: "times new roman" , "serif"; font-size: 12.0pt; line-height: 115%;">You can see below clip as the examples for this model:<o:p></o:p></span></div>
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<iframe allowfullscreen='allowfullscreen' webkitallowfullscreen='webkitallowfullscreen' mozallowfullscreen='mozallowfullscreen' width='320' height='266' src='https://www.blogger.com/video.g?token=AD6v5dzp744FbEHfCzHCiu8-Q2gDgfhGx2Zrp8v-j0Ogjaw8_reIS41NZuul4TeKAdoN_bA5udDMQGYuokdWrS0jTg' class='b-hbp-video b-uploaded' frameborder='0'></iframe></div>
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<b><span style="color: black; font-family: "times new roman" , "serif"; font-size: 12.0pt; line-height: 107%;">Model (2): </span></b><b><span style="font-family: "times new roman" , "serif"; font-size: 12.0pt; line-height: 107%;">The
results for three independent variables “mass”, “linear damping constant” and </span></b><b><span style="font-family: "times new roman" , "serif"; font-size: 12.0pt; line-height: 107%;">“ω″/ω”<o:p></o:p></span></b></div>
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<span style="font-family: "times new roman" , "serif"; font-size: 12.0pt; line-height: 107%;">In this model, there are the defined ranges
for “m”, “b” and “ω″/ω” which are our three independent variables and by
changing the forced harmonic motion (F</span><span style="font-family: "times new roman" , "serif"; font-size: 9.0pt; line-height: 107%;">m</span><span style="font-family: "times new roman" , "serif"; font-size: 12.0pt; line-height: 107%;">) and time (t), we are willing to know what are the characteristics of a
unknown oscillatory system that give us the maximum displacement and velocity
close to the point of the resonance.<o:p></o:p></span></div>
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<span style="font-family: "times new roman" , "serif"; font-size: 12.0pt; line-height: 115%;">Below figure as well as shows you the components of
this model:<o:p></o:p></span></div>
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<span style="font-family: "times new roman" , "serif"; font-size: 12.0pt; line-height: 115%;"><br /></span></div>
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhAAmUGSrNzcGJOX4VOnuJxxHGgrfLx5zE3jjKcDOgNSeSb9Jzu9jJWdcUD5-sEYoQSRefDoYcdKO2HHd0sQ-Zz4X3gsjvys3kJUDBeBhzXYcZLljHt3AJAZc8ohie46WTKWzoPzjeyRwY/s1600/3.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="434" data-original-width="594" height="233" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhAAmUGSrNzcGJOX4VOnuJxxHGgrfLx5zE3jjKcDOgNSeSb9Jzu9jJWdcUD5-sEYoQSRefDoYcdKO2HHd0sQ-Zz4X3gsjvys3kJUDBeBhzXYcZLljHt3AJAZc8ohie46WTKWzoPzjeyRwY/s320/3.png" width="320" /></a></div>
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<span style="font-family: "times new roman" , "serif"; font-size: 12.0pt; line-height: 115%;"><br /></span></div>
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<span style="font-family: "times new roman" , "serif"; font-size: 12.0pt; line-height: 115%;"><br /></span></div>
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<span style="font-family: "times new roman" , "serif"; font-size: 12.0pt; line-height: 115%;">The components of above model are as follows:<o:p></o:p></span></div>
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<span style="font-family: "times new roman" , "serif"; font-size: 12.0pt; line-height: 115%;">1. In right side on cells L6:M6, we have inputs
including </span><span style="font-family: "times new roman" , "serif"; font-size: 12.0pt; line-height: 115%;">given data
of “F</span><span style="font-family: "times new roman" , "serif"; font-size: 9.0pt; line-height: 115%;">m</span><span style="font-family: "times new roman" , "serif"; font-size: 12.0pt; line-height: 115%;">”, and “t”.<o:p></o:p></span></div>
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<span style="font-family: "times new roman" , "serif"; font-size: 12.0pt; line-height: 115%;">2. In left side on cells H6:J7, we have other inputs
including lower and upper ranges for independent variables of “m”, “b” and </span><span style="font-family: "times new roman" , "serif"; font-size: 12.0pt; line-height: 115%;">“ω″/ω” </span><span style="font-family: "times new roman" , "serif"; font-size: 12.0pt; line-height: 115%;">to reach the answers which are the solution for driven
oscillatory </span><span style="font-family: "times new roman" , "serif"; font-size: 12.0pt; line-height: 115%;">system close
to the point of the resonance. Here, there are lower and upper ranges which are
changed by click on cell A2 and also this change will again go back by click on
cell B2 (Go & Back). <span style="background: white;"><o:p></o:p></span></span></div>
<div class="MsoNormal" style="direction: ltr; line-height: 115%; margin-bottom: 10pt; unicode-bidi: embed;">
<span style="background: white; font-family: "times new roman" , "serif"; font-size: 12.0pt; line-height: 115%;">3. On cells J9:J17, we have outputs
which are maximum displacement and velocity </span><span style="font-family: "times new roman" , "serif"; font-size: 12.0pt; line-height: 115%;">for driven oscillatory </span><span style="font-family: "times new roman" , "serif"; font-size: 12.0pt; line-height: 115%;">system close to the point of the resonance. <o:p></o:p></span></div>
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<span style="font-family: "times new roman" , "serif"; font-size: 12.0pt; line-height: 115%;">
</span></div>
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<b><i><span style="font-family: "times new roman" , "serif"; font-size: 12.0pt; line-height: 107%;">Note: On J9 and J10, we have maximum
displacement and velocity for </span></i></b><b><i><span style="font-family: "times new roman" , "serif"; font-size: 12.0pt; line-height: 107%;">a
defined range of “m”, “b” and </span></i></b><b><span style="font-family: "times new roman" , "serif"; font-size: 12.0pt; line-height: 107%;">“ω″/ω”</span></b><b><i><span style="font-family: "times new roman" , "serif"; font-size: 12.0pt; line-height: 107%;">. </span></i></b><b><i><span style="font-family: "times new roman" , "serif"; font-size: 12.0pt; line-height: 107%;">Please do not consider them as the amplitude
of harmonic motion. On cell J16 and J17, we have the amplitude of displacement
(A) and the amplitude of velocity (Av).</span></i></b></div>
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<b><i><span style="font-family: "times new roman" , "serif"; font-size: 12.0pt; line-height: 107%;"><br /></span></i></b></div>
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<b><i><span style="font-family: "times new roman" , "serif"; font-size: 12.0pt; line-height: 107%;"> <o:p></o:p></span></i></b><span style="font-family: "times new roman" , serif; font-size: 12pt;">You can see below clip as the examples for this model:</span></div>
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<span style="font-family: "times new roman" , "serif"; font-size: 12.0pt; line-height: 115%;"><o:p></o:p></span></div>
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<span style="font-family: "times new roman" , "serif"; font-size: 12.0pt; line-height: 115%;"><o:p><br /></o:p></span></div>
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<iframe allowfullscreen='allowfullscreen' webkitallowfullscreen='webkitallowfullscreen' mozallowfullscreen='mozallowfullscreen' width='320' height='266' src='https://www.blogger.com/video.g?token=AD6v5dwZerykbtcESUkgsMj5t3CTAufV1L68wPDQyFxrtWEkS4Zk4v_aWl98ZrbfkYP2JhZaccoRgH1Xd0G8-NAuKw' class='b-hbp-video b-uploaded' frameborder='0'></iframe></div>
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<b><span style="font-family: "times new roman" , serif; font-size: 12pt; line-height: 107%;">Model (3): </span></b><b><span style="font-family: "times new roman" , "serif"; font-size: 12.0pt; line-height: 107%;">The
results of three independent variables “mass”, “linear damping constant” and </span></b><b><span style="font-family: "times new roman" , "serif"; font-size: 12.0pt; line-height: 107%;">“ω″/ω” </span></b><b><span style="font-family: "times new roman" , serif; font-size: 12pt; line-height: 107%;">for higher than a specific velocity</span></b><span style="font-family: "times new roman" , "serif"; font-size: 12.0pt; line-height: 107%;"><o:p></o:p></span></div>
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<span style="font-family: "times new roman" , "serif"; font-size: 12.0pt; line-height: 107%;">In this model, we want to design an unknown oscillatory system for
a specific velocity. We can have all characteristics of the system for focus,
lower and higher than a specific velocity. Here, I consider it for a higher
than specific velocity. Since there are many answers, I have only fixed 15
answers for this model.<o:p></o:p></span></div>
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<span style="font-family: "times new roman" , "serif"; font-size: 12.0pt; line-height: 115%;"> </span><span style="font-family: "times new roman" , "serif"; font-size: 12.0pt; line-height: 115%;">Below figure as well as shows you the components of
this model:<o:p></o:p></span></div>
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEj8WxTPLHb4WTYNhFV6ySjRW0PGai1FS6huZF3Ce1AoYWhSq-YjB7dbh3PbvkNr20H37dSBEb97g4P_FHaebo1AK3tHrwdtpZk5aopz3DudKRDv-vwEZ8tkWO3TB21Yr7eKCM8IICbymvc/s1600/4.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="565" data-original-width="1021" height="177" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEj8WxTPLHb4WTYNhFV6ySjRW0PGai1FS6huZF3Ce1AoYWhSq-YjB7dbh3PbvkNr20H37dSBEb97g4P_FHaebo1AK3tHrwdtpZk5aopz3DudKRDv-vwEZ8tkWO3TB21Yr7eKCM8IICbymvc/s320/4.png" width="320" /></a></div>
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<span style="font-family: "times new roman" , "serif"; font-size: 12.0pt; line-height: 107%;">As you can see, all components of this model are the similar to
model (2). Only I have added15 absolute value for velocities more than a
specific velocity and also on cell M7, we have specific amount of velocity.<o:p></o:p></span></div>
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<span style="font-family: "times new roman" , "serif"; font-size: 12.0pt; line-height: 107%;"><br /></span></div>
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<span style="font-family: "times new roman" , "serif"; font-size: 12.0pt; line-height: 115%;">You can see below clip as the examples for this model:<o:p></o:p></span></div>
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<span style="font-family: "times new roman" , "serif"; font-size: 12.0pt; line-height: 115%;">
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<iframe allowfullscreen='allowfullscreen' webkitallowfullscreen='webkitallowfullscreen' mozallowfullscreen='mozallowfullscreen' width='320' height='266' src='https://www.blogger.com/video.g?token=AD6v5dxrIIiJuUTmRmZOorAmI0dcWR-A5m2OlkNQ7PoliclAMKAEAjXgRpKKv4Xa7H-RQNjYcnkafN5ZbuvdWLXN7g' class='b-hbp-video b-uploaded' frameborder='0'></iframe></div>
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<b><span dir="LTR" style="font-family: "times new roman" , "serif"; font-size: 12.0pt; line-height: 107%;">Data Analysis and Conclusion<o:p></o:p></span></b></div>
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<span dir="LTR"> One of the most important applications of above models
is to create the value from data analysis. Please see below results:<o:p></o:p></span></div>
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiCjdLOLNZosAL86DyoFr5lF4KORue28el3Yyg_MBZpT73a7E5c3Bdzn8ah6T5dcZ9N-OfpiYnHCeX3mcwzn0kZBdpMZRX2seL51tImoCdaBNbRCqbLXvkWShU0anRN9bDIRmUcl8NVL8k/s1600/5.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="545" data-original-width="518" height="320" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiCjdLOLNZosAL86DyoFr5lF4KORue28el3Yyg_MBZpT73a7E5c3Bdzn8ah6T5dcZ9N-OfpiYnHCeX3mcwzn0kZBdpMZRX2seL51tImoCdaBNbRCqbLXvkWShU0anRN9bDIRmUcl8NVL8k/s320/5.png" width="304" /></a></div>
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<span dir="LTR" style="font-family: "times new roman" , "serif"; font-size: 12.0pt; line-height: 107%;">Above table shows us that there are many answers for a constant
velocity. But if you carefully focus on the results, you will find out an
interesting property about driven oscillations and resonance.<o:p></o:p></span></div>
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<span dir="LTR" style="font-family: "times new roman" , "serif"; font-size: 12.0pt; line-height: 107%;"><br /></span></div>
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<b><span dir="LTR" style="font-family: "times new roman" , "serif"; font-size: 12.0pt; line-height: 107%;">What is this property?<o:p></o:p></span></b></div>
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<b><span dir="LTR" style="font-family: "times new roman" , "serif"; font-size: 12.0pt; line-height: 107%;"><br /></span></b></div>
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<span dir="LTR" style="font-family: "times new roman" , "serif"; font-size: 12.0pt; line-height: 107%;">If an oscillatory system has very low angular frequency (ω) and
linear damping constant (b) in the conditions close to the point of the
resonance and in zero time (t =0), surprisingly by increasing the mass, the
displacement (x) will go up and by
decreasing the mass, the displacement will go down. In this situation, the
amplitude for any changes on mass will stay the constant forever.<o:p></o:p></span></div>
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</span></div>
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<span dir="LTR" style="font-family: "times new roman" , "serif"; font-size: 12.0pt; line-height: 107%;">All researchers and individual people, who are interested in having
these models, don’t hesitate to send their request to below addresses:<o:p></o:p></span></div>
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgu1xkNcQDHfyo5C3QYEOKicVkwdblXHzijXJ-QN-5Zve8hvC7tMKrdeVq4zFQ2Xp5EJW-Y86EUJQlEJXkWqZLXVEFSO_HWGhc_Yfm8kKLJUQ8BlD6MhzapFNeRdP3x3FQxwla4z1eI7IA/s1600/%25D8%25AF%25D8%25B1%25DB%258C%25D8%25A7%25D9%2581%25D8%25AA+%25D9%2581%25D8%25A7%25DB%258C%25D9%2584+%25D8%25A7%25DA%25A9%25D8%25B3%25D9%2584.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="240" data-original-width="592" height="129" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgu1xkNcQDHfyo5C3QYEOKicVkwdblXHzijXJ-QN-5Zve8hvC7tMKrdeVq4zFQ2Xp5EJW-Y86EUJQlEJXkWqZLXVEFSO_HWGhc_Yfm8kKLJUQ8BlD6MhzapFNeRdP3x3FQxwla4z1eI7IA/s320/%25D8%25AF%25D8%25B1%25DB%258C%25D8%25A7%25D9%2581%25D8%25AA+%25D9%2581%25D8%25A7%25DB%258C%25D9%2584+%25D8%25A7%25DA%25A9%25D8%25B3%25D9%2584.png" width="320" /></a></div>
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Gholamreza Soleimanihttp://www.blogger.com/profile/03273527405719420253noreply@blogger.com0tag:blogger.com,1999:blog-392703582366288634.post-56758839575099096462018-08-22T01:09:00.001+04:302018-08-22T16:13:30.054+04:30A Model to Solve a System of SHM Equations<div dir="ltr" style="text-align: left;" trbidi="on">
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<span style="font-family: "times new roman" , "serif"; font-size: 12.0pt; line-height: 115%;">Following to article of “A Model to
Solve a System of Nonlinear Equations by Using Microsoft Excel plus VBA” (</span><a href="http://emfps.blogspot.com/2018/02/a-model-to-track-location-of-particle.html"><span style="font-family: "times new roman" , "serif"; font-size: 12.0pt; line-height: 115%;">http://emfps.blogspot.com/2018/02/a-model-to-track-location-of-particle.html</span></a><span class="MsoHyperlink"><span style="font-family: "times new roman" , "serif"; font-size: 12.0pt; line-height: 115%;">), the purpose of this article is,
to present another example about solving a system of nonlinear equations for
Simple Harmonic Motion (SHM). <o:p></o:p></span></span></div>
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<span class="MsoHyperlink"><span style="font-family: "times new roman" , "serif"; font-size: 12.0pt; line-height: 115%;">Suppose
we have two oscillatory motions which are in two perpendicular directions. We
can write a system of equations for them as follows:<o:p></o:p></span></span></div>
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Assume the angular frequency for both SHMs is the same and
also there is the difference between initial phases equal 90 degree. In this
case, we will have below system of equations:<o:p></o:p></div>
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<span style="font-family: "times new roman" , "serif"; font-size: 12.0pt; line-height: 115%;">This model is able to solve above
system of two equations for given data of “x”, “y”, “Ax” and “Ay”.</span></div>
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<span style="font-family: "times new roman" , "serif"; font-size: 12.0pt; line-height: 115%;"><br /></span></div>
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<span style="font-family: "times new roman" , "serif"; font-size: 12.0pt; line-height: 115%;"> <o:p></o:p></span><span style="font-family: "times new roman" , serif; font-size: 12pt;">There are two methods for finding
“ω”, “t” and “φ”. </span></div>
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<b><span style="font-family: "times new roman" , "serif"; font-size: 12.0pt; line-height: 115%;">Method (1):<o:p></o:p></span></b></div>
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<span style="font-family: "times new roman" , "serif"; font-size: 12.0pt; line-height: 115%;">The convert of two equations to one equation
and solving only one equation for three independent variables in accordance
with the method mentioned in article of “</span><span style="font-family: "times new roman" , "serif"; font-size: 12.0pt; line-height: 115%;">Solving
a Nonlinear Equation with Many Independent Variables by Using Microsoft Excel
plus VBA” (</span><a href="https://emfps.blogspot.com/2016/10/can-we-solve-nonlinear-equation-with.html"><span style="font-family: "times new roman" , "serif"; font-size: 12.0pt; line-height: 115%;">https://emfps.blogspot.com/2016/10/can-we-solve-nonlinear-equation-with.html</span></a><span class="MsoHyperlink"><span style="font-family: "times new roman" , "serif"; font-size: 12.0pt; line-height: 115%;">) as follows:<o:p></o:p></span></span></div>
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<span style="font-family: "times new roman" , "serif"; font-size: 12.0pt; line-height: 115%;"><o:p></o:p></span></div>
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<span style="font-family: "times new roman" , "serif"; font-size: 12.0pt; line-height: 115%;">Below figure as well as shows you
the components of this model:<o:p></o:p></span></div>
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<span style="font-family: "times new roman" , "serif"; font-size: 12.0pt; line-height: 115%;">Let me explain you about the
components of above model as follows:<o:p></o:p></span></div>
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<span style="font-family: "times new roman" , "serif"; font-size: 12.0pt; line-height: 115%;"><br /></span></div>
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<span style="font-family: "times new roman" , "serif"; font-size: 12.0pt; line-height: 115%;">1. In right side on cells L6:O6, we
have inputs including </span><span style="font-family: "times new roman" , "serif"; font-size: 12.0pt; line-height: 115%;">given data of
“x”, “y”, “Ax” and “Ay”. <o:p></o:p></span></div>
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<span style="font-family: "times new roman" , "serif"; font-size: 12.0pt; line-height: 115%;"><br /></span></div>
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<span style="font-family: "times new roman" , "serif"; font-size: 12.0pt; line-height: 115%;">2. In left side on cells H6:J7, we
have other inputs including lower and upper ranges for independent variables of
“ω”, “t” and “φ” to reach the answers which are the solution for </span><span style="font-family: "times new roman" , "serif"; font-size: 12.0pt; line-height: 115%;">system of two nonlinear equations. Here, there are lower and upper
ranges which are changed by click on cell A2 and also this change will again go
back by click on cell B2 (Go & Back). <span style="background: white;"><o:p></o:p></span></span></div>
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<span style="font-family: "times new roman" , "serif"; font-size: 12.0pt; line-height: 115%;"><br /></span></div>
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<span style="background: white; font-family: "times new roman" , "serif"; font-size: 12.0pt; line-height: 115%;">3. On cells H10:J24,
we have outputs which are the answers to above </span><span style="font-family: "times new roman" , "serif"; font-size: 12.0pt; line-height: 115%;">system
of two nonlinear equations.<o:p></o:p></span></div>
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<span style="font-family: "times new roman" , "serif"; font-size: 12.0pt; line-height: 115%;"><br /></span></div>
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<span style="font-family: "times new roman" , "serif"; font-size: 12.0pt; line-height: 115%;">4. On cell M7, we have Error which
is the difference between equation of outputs (-y.Ax /x.Ay) and equation of
inputs (Tan (ωt+φ)) <o:p></o:p></span></div>
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<span style="font-family: "times new roman" , "serif"; font-size: 12.0pt; line-height: 115%;"><br /></span></div>
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<span style="font-family: "times new roman" , "serif"; font-size: 12.0pt; line-height: 115%;">5. On cells K10:K24, we have the
solution of “x” by replacing the answers.<o:p></o:p></span></div>
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<span style="font-family: "times new roman" , "serif"; font-size: 12.0pt; line-height: 115%;"><br /></span></div>
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<span style="font-family: "times new roman" , "serif"; font-size: 12.0pt; line-height: 115%;">6. On cells M10:M24, we have the
solution of “y” by replacing the answers.<o:p></o:p></span></div>
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<span style="font-family: "times new roman" , "serif"; font-size: 12.0pt; line-height: 115%;"><br /></span></div>
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<span style="font-family: "times new roman" , "serif"; font-size: 12.0pt; line-height: 115%;">7. On cells O10:O24, we have the
difference between item 5 (“x”) and cell L6 which are the errors of our answers.<o:p></o:p></span></div>
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<span style="font-family: "times new roman" , "serif"; font-size: 12.0pt; line-height: 115%;"><br /></span></div>
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<span style="font-family: "times new roman" , "serif"; font-size: 12.0pt; line-height: 115%;">8. On cells P10:P24, we have the
difference between item 6 (“y”) and cell M6 which are the errors of our answers.<o:p></o:p></span></div>
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<span style="font-family: "times new roman" , "serif"; font-size: 12.0pt; line-height: 115%;">You can see below clip as the
examples for this model:<o:p></o:p></span></div>
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<iframe allowfullscreen='allowfullscreen' webkitallowfullscreen='webkitallowfullscreen' mozallowfullscreen='mozallowfullscreen' width='320' height='266' src='https://www.blogger.com/video.g?token=AD6v5dwgH1C1XSsK2V465oR769TIHaAOm70Qlx_ABN1V9PgQacEcGTrPgxTobtTh6R8L-d0S71GIQuBqydVsJ63tXg' class='b-hbp-video b-uploaded' frameborder='0'></iframe></div>
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<b><span style="font-family: "times new roman" , "serif"; font-size: 12.0pt; line-height: 115%;">Method (2):<o:p></o:p></span></b></div>
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<b><span style="font-family: "times new roman" , "serif"; font-size: 12.0pt; line-height: 115%;"><br /></span></b></div>
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<span style="font-family: "times new roman" , "serif"; font-size: 12.0pt; line-height: 115%;">Using the method stated in article
of “A Model to Solve a System of Nonlinear Equations by Using Microsoft Excel
plus VBA” (</span><span style="font-family: "times new roman" , "serif"; font-size: 12.0pt; line-height: 115%;"><a href="http://emfps.blogspot.com/2018/02/a-model-to-track-location-of-particle.html">http://emfps.blogspot.com/2018/02/a-model-to-track-location-of-particle.html</a></span><span class="MsoHyperlink"><span style="font-family: "times new roman" , "serif"; font-size: 12.0pt; line-height: 115%;"><o:p></o:p></span></span></div>
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<span class="MsoHyperlink"><span style="font-family: "times new roman" , "serif"; font-size: 12.0pt; line-height: 115%;">In</span></span><span style="font-family: "times new roman" , "serif"; font-size: 12.0pt; line-height: 115%;"> this method, we directly solve a system of two nonlinear
equations. <o:p></o:p></span></div>
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<span style="font-family: "times new roman" , "serif"; font-size: 12.0pt; line-height: 115%;"><br /></span></div>
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<span style="font-family: "times new roman" , "serif"; font-size: 12.0pt; line-height: 115%;">Below figure as well as shows you
the components of this model:<o:p></o:p></span></div>
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<span style="font-family: "times new roman" , "serif"; font-size: 12.0pt; line-height: 115%;"><br /></span></div>
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<span style="font-family: "times new roman" , "serif"; font-size: 12.0pt; line-height: 115%;">The explanations of the components
are the same with method (1) except the error.<o:p></o:p></span></div>
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<span style="font-family: "times new roman" , "serif"; font-size: 12.0pt; line-height: 115%;">You can see below clip as the
examples for this model:<o:p></o:p></span></div>
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<span dir="LTR" style="font-family: "times new roman" , "serif"; font-size: 12.0pt; line-height: 107%;">All researchers and individual people, who are interested in having
this model, don’t hesitate to send </span></div>
<div class="MsoNormal" dir="RTL" style="text-align: left;">
<span dir="LTR" style="font-family: "times new roman" , "serif"; font-size: 12.0pt; line-height: 107%;">their request to below addresses:<o:p></o:p></span></div>
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Gholamreza Soleimanihttp://www.blogger.com/profile/03273527405719420253noreply@blogger.com0tag:blogger.com,1999:blog-392703582366288634.post-53350052361332663972018-08-06T18:41:00.000+04:302018-08-06T18:41:47.243+04:30Is Angular Frequency a Vector or Scalar Quantity?<div dir="ltr" style="text-align: left;" trbidi="on">
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgnobm0-BHdFBwtJqhIcKwM7UzGGY2TfEVxKE-MCQNj00uQUUtKVeAuFzfFbPdf3XL4kYf5UDDJrnrmyhHvw9jtKrjnjzVSrTQXjETBVPgunm16G_76SbXeHzvUMwaQ7fvLAlFilOh1qxA/s1600/machinery.png" imageanchor="1" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgnobm0-BHdFBwtJqhIcKwM7UzGGY2TfEVxKE-MCQNj00uQUUtKVeAuFzfFbPdf3XL4kYf5UDDJrnrmyhHvw9jtKrjnjzVSrTQXjETBVPgunm16G_76SbXeHzvUMwaQ7fvLAlFilOh1qxA/s320/machinery.png" /></a></div>
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<span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 107%; mso-ascii-theme-font: major-bidi; mso-bidi-theme-font: major-bidi; mso-hansi-theme-font: major-bidi;">Angular frequency is the changes of angular displacement to the changes
of time:<o:p></o:p></span></div>
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<span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 107%; mso-ascii-theme-font: major-bidi; mso-bidi-theme-font: major-bidi; mso-hansi-theme-font: major-bidi;"><br /></span></div>
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<span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 107%; mso-ascii-theme-font: major-bidi; mso-bidi-theme-font: major-bidi; mso-hansi-theme-font: major-bidi;"><br /></span></div>
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<span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 107%; mso-ascii-theme-font: major-bidi; mso-bidi-theme-font: major-bidi; mso-hansi-theme-font: major-bidi;">Therefore, if we say that the angular frequency is a vector, then
an angle should be also a vector. In all reference books in physics, you can
find that only <b><i>a very small angles</i></b> can be considered as a vector.
But I am willing to tell you that there are several another factors (<b><i>except
very small angles</i></b>) which can be defined as impact factors such as <b><i>Amplitude</i></b>
of an oscillatory motion in which high amplitude does not allow you to use the
rules dominated on vectors to analyze an oscillatory system with combination of
many harmonic motions. <o:p></o:p></span></div>
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<span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 107%; mso-ascii-theme-font: major-bidi; mso-bidi-theme-font: major-bidi; mso-hansi-theme-font: major-bidi;"><br /></span></div>
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<span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 107%; mso-ascii-theme-font: major-bidi; mso-bidi-theme-font: major-bidi; mso-hansi-theme-font: major-bidi;">The surprising news is: "The most important impact factors are not <b><i>very
small angles and amplitude</i></b> but <b><i>the direction of the motion</i></b>.
In some situations and conditions, you can even consider a very large angle as
a vector where this reverses the concept defined in reference books in Physics."<o:p></o:p></span></div>
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<span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 107%; mso-ascii-theme-font: major-bidi; mso-bidi-theme-font: major-bidi; mso-hansi-theme-font: major-bidi;"><br /></span></div>
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<b><i><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 107%; mso-ascii-theme-font: major-bidi; mso-bidi-theme-font: major-bidi; mso-hansi-theme-font: major-bidi;">If you do not truly apply the concept of vector for angular
frequency, the result of your analysis and design for an oscillatory system
with combination of many harmonic motions, will go in wrong way.<o:p></o:p></span></i></b></div>
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Gholamreza Soleimanihttp://www.blogger.com/profile/03273527405719420253noreply@blogger.com0tag:blogger.com,1999:blog-392703582366288634.post-11714784986523942362018-05-20T21:55:00.000+04:302018-05-22T16:54:39.717+04:30Workshop Series: The Big Data Science Analysis with Microsoft Excel plus VBA<div dir="ltr" style="text-align: left;" trbidi="on">
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<span dir="LTR"></span><span dir="LTR"></span><b><i><span dir="LTR" style="font-family: "Times New Roman", serif; font-size: 13.5pt;"><span dir="LTR"></span><span dir="LTR"></span>"The Big Data Science Analysis with Microsoft Excel plus
VBA"</span></i></b><span lang="FA" style="font-family: "Times New Roman", serif; font-size: 13.5pt;"><o:p></o:p></span></div>
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<span dir="LTR"> There are two big strategies for
these workshop series as follows:<o:p></o:p></span></div>
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<span dir="LTR">1. Solving the complicated problems by producing new methods and models<o:p></o:p></span></div>
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<span dir="LTR">2. Creating the value from the
big data <o:p></o:p></span></div>
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<span dir="LTR"><br /></span></div>
Here is PowerPoint movie about<b> "<i><span style="font-family: "calibri" , "sans-serif"; font-size: 11.0pt; line-height: 107%;">The Big Data Science
Analysis with Microsoft Excel plus VBA"</span></i></b><br />
<b><i><span style="font-family: "calibri" , "sans-serif"; font-size: 11.0pt; line-height: 107%;"><br /></span></i></b>
<b><i><span style="font-family: "calibri" , "sans-serif"; font-size: 11.0pt; line-height: 107%;"><br /></span></i></b>
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<iframe allowfullscreen='allowfullscreen' webkitallowfullscreen='webkitallowfullscreen' mozallowfullscreen='mozallowfullscreen' width='320' height='266' src='https://www.blogger.com/video.g?token=AD6v5dwBxE-2kIc9vIL263YyF2HRYcbG9rHL9Gs7spIrSCHN6buUmY1zfoNEg3_uHoldA9wwhcMC2agAKKcwuqTGLA' class='b-hbp-video b-uploaded' frameborder='0'></iframe></div>
<b><i><span style="font-family: "calibri" , "sans-serif"; font-size: 11.0pt; line-height: 107%;"><br /></span></i></b></div>
Gholamreza Soleimanihttp://www.blogger.com/profile/03273527405719420253noreply@blogger.com0tag:blogger.com,1999:blog-392703582366288634.post-9164283101717053512018-04-30T04:33:00.003+04:302018-04-30T04:33:53.693+04:30The Distances among The Particles in The Space (3)<div dir="ltr" style="text-align: left;" trbidi="on">
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<span dir="LTR" style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 107%; mso-ascii-theme-font: major-bidi; mso-bidi-theme-font: major-bidi; mso-hansi-theme-font: major-bidi;">You can preview the conjectures (1), (2), (3) and (4) on below
links:<o:p></o:p></span></div>
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<span dir="LTR" style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 107%; mso-ascii-theme-font: major-bidi; mso-bidi-theme-font: major-bidi; mso-hansi-theme-font: major-bidi;"><br /></span></div>
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<span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 107%; mso-ascii-theme-font: major-bidi; mso-bidi-theme-font: major-bidi; mso-hansi-theme-font: major-bidi;"><span style="mso-spacerun: yes;"> </span></span><a href="http://www.emfps.org/2018/04/the-distances-among-particles-in-space.html" style="font-family: "Times New Roman", serif; font-size: 12pt;">http://www.emfps.org/2018/04/the-distances-among-particles-in-space.html</a></div>
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<span dir="LTR"></span><span dir="LTR"></span><span lang="FA" style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 107%; mso-ascii-theme-font: major-bidi; mso-bidi-theme-font: major-bidi; mso-hansi-theme-font: major-bidi;"><span dir="LTR"></span><span dir="LTR"></span><span style="mso-spacerun: yes;"> </span></span><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 107%; mso-ascii-theme-font: major-bidi; mso-bidi-theme-font: major-bidi; mso-hansi-theme-font: major-bidi;"><a href="http://www.emfps.org/2018/04/the-distances-among-particles-in-space-2.html">http://www.emfps.org/2018/04/the-distances-among-particles-in-space-2.html</a><o:p></o:p></span></div>
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<b><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 107%; mso-ascii-theme-font: major-bidi; mso-bidi-theme-font: major-bidi; mso-hansi-theme-font: major-bidi;">Conjecture (5):</span></b><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 107%; mso-ascii-theme-font: major-bidi; mso-bidi-theme-font: major-bidi; mso-hansi-theme-font: major-bidi;"><span style="mso-spacerun: yes;"> </span><o:p></o:p></span></div>
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<span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 107%; mso-ascii-theme-font: major-bidi; mso-bidi-theme-font: major-bidi; mso-hansi-theme-font: major-bidi;"><span style="mso-spacerun: yes;"><br /></span></span></div>
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<span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 107%; mso-ascii-theme-font: major-bidi; mso-bidi-theme-font: major-bidi; mso-hansi-theme-font: major-bidi;">By using this theorem or conjecture,
I am willing to show you that there is below figure among five points in the
space:<o:p></o:p></span></div>
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh6MOkRB_h_x-n9wYW-ItEZ6ceGplz_WuVA2beLQgn72L4DcBipDBPJfs56WkbQLTOznkivioO7o_jJ0mKVkagLMDgC-qAJQdpYTqh18wGPVMOZtzOL078xU1BG9ILC2u9VfMBecCVdEYg/s1600/14.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="500" data-original-width="972" height="164" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh6MOkRB_h_x-n9wYW-ItEZ6ceGplz_WuVA2beLQgn72L4DcBipDBPJfs56WkbQLTOznkivioO7o_jJ0mKVkagLMDgC-qAJQdpYTqh18wGPVMOZtzOL078xU1BG9ILC2u9VfMBecCVdEYg/s320/14.png" width="320" /></a></div>
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<span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 107%; mso-ascii-theme-font: major-bidi; mso-bidi-theme-font: major-bidi; mso-hansi-theme-font: major-bidi;"><br /></span></div>
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<span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 107%; mso-ascii-theme-font: major-bidi; mso-bidi-theme-font: major-bidi; mso-hansi-theme-font: major-bidi;">Suppose we have point P1 (x, y, z)
and an independent variable “t” where there is below functions between them:<o:p></o:p></span></div>
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh3sMuJfTPAfvWlHYHk7iJalRxw4qiG71Qp2VC26bZWowKy_n8xTPegSlV2XP2kHwkbOp9yo2jxabcDaY2jUPSqAEzYk4wZEfHUi1UWM8CytCGsWQ_gbxyAzXYdRoCW_vdNNgGvMLKA_BM/s1600/15.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="296" data-original-width="699" height="135" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh3sMuJfTPAfvWlHYHk7iJalRxw4qiG71Qp2VC26bZWowKy_n8xTPegSlV2XP2kHwkbOp9yo2jxabcDaY2jUPSqAEzYk4wZEfHUi1UWM8CytCGsWQ_gbxyAzXYdRoCW_vdNNgGvMLKA_BM/s320/15.png" width="320" /></a><br />
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<b><i><span style="font-family: "Times New Roman","serif"; font-size: 14.0pt; line-height: 107%; mso-ascii-theme-font: major-bidi; mso-bidi-theme-font: major-bidi; mso-fareast-font-family: "Times New Roman"; mso-fareast-theme-font: minor-fareast; mso-hansi-theme-font: major-bidi;">If points Pm
and Pn have below coordination:<o:p></o:p></span></i></b></div>
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<b><i><span style="font-family: "Times New Roman","serif"; font-size: 14.0pt; line-height: 107%; mso-ascii-theme-font: major-bidi; mso-bidi-theme-font: major-bidi; mso-fareast-font-family: "Times New Roman"; mso-fareast-theme-font: minor-fareast; mso-hansi-theme-font: major-bidi;">Pm (f(x,y,z,t),
f(x,y,z,t), f(x,y,z,t))<o:p></o:p></span></i></b></div>
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<b><i><span style="font-family: "Times New Roman","serif"; font-size: 14.0pt; line-height: 107%; mso-ascii-theme-font: major-bidi; mso-bidi-theme-font: major-bidi; mso-fareast-font-family: "Times New Roman"; mso-fareast-theme-font: minor-fareast; mso-hansi-theme-font: major-bidi;"><br /></span></i></b></div>
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<b><i><span style="font-family: "Times New Roman","serif"; font-size: 14.0pt; line-height: 107%; mso-ascii-theme-font: major-bidi; mso-bidi-theme-font: major-bidi; mso-fareast-font-family: "Times New Roman"; mso-fareast-theme-font: minor-fareast; mso-hansi-theme-font: major-bidi;">Pn (g(x,y,z,t),
g(x,y,z,t), g(x,y,z,t))<o:p></o:p></span></i></b></div>
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<b><i><span style="font-family: "Times New Roman","serif"; font-size: 14.0pt; line-height: 107%; mso-ascii-theme-font: major-bidi; mso-bidi-theme-font: major-bidi; mso-fareast-font-family: "Times New Roman"; mso-fareast-theme-font: minor-fareast; mso-hansi-theme-font: major-bidi;"><br /></span></i></b></div>
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<b><i><span style="font-family: "Times New Roman","serif"; font-size: 14.0pt; line-height: 107%; mso-ascii-theme-font: major-bidi; mso-bidi-theme-font: major-bidi; mso-fareast-font-family: "Times New Roman"; mso-fareast-theme-font: minor-fareast; mso-hansi-theme-font: major-bidi;">Then, in
according to conjecture (3), the distance of points Pm and Pn will be equal
with the points P1, P2 and P3 stated in conjecture (3). (Please see conjecture
(3) on above links).<o:p></o:p></span></i></b></div>
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<b><i><span style="font-family: "Times New Roman","serif"; font-size: 14.0pt; line-height: 107%; mso-ascii-theme-font: major-bidi; mso-bidi-theme-font: major-bidi; mso-fareast-font-family: "Times New Roman"; mso-fareast-theme-font: minor-fareast; mso-hansi-theme-font: major-bidi;"><br /></span></i></b></div>
<div class="MsoNormal" style="direction: ltr; tab-stops: 319.15pt; text-align: left; unicode-bidi: embed;">
<b><i><span style="font-family: "Times New Roman","serif"; font-size: 14.0pt; line-height: 107%; mso-ascii-theme-font: major-bidi; mso-bidi-theme-font: major-bidi; mso-fareast-font-family: "Times New Roman"; mso-fareast-theme-font: minor-fareast; mso-hansi-theme-font: major-bidi;">It means:<o:p></o:p></span></i></b></div>
<div class="MsoNormal" style="direction: ltr; tab-stops: 319.15pt; text-align: left; unicode-bidi: embed;">
<b><i><span style="font-family: "Times New Roman","serif"; font-size: 14.0pt; line-height: 107%; mso-ascii-theme-font: major-bidi; mso-bidi-theme-font: major-bidi; mso-fareast-font-family: "Times New Roman"; mso-fareast-theme-font: minor-fareast; mso-hansi-theme-font: major-bidi;"><br /></span></i></b></div>
<div class="MsoNormal" style="direction: ltr; tab-stops: 319.15pt; text-align: left; unicode-bidi: embed;">
<b><i><span style="font-family: "Times New Roman","serif"; font-size: 14.0pt; line-height: 107%; mso-ascii-theme-font: major-bidi; mso-bidi-theme-font: major-bidi; mso-fareast-font-family: "Times New Roman"; mso-fareast-theme-font: minor-fareast; mso-hansi-theme-font: major-bidi;">d(Pm,P1)= d(Pm,P2)
= d(Pm,P3) = d(Pn,P1) = d(Pn,P2) = d(Pn,P3) =R</span></i></b><b><span style="font-family: "Times New Roman","serif"; font-size: 14.0pt; line-height: 107%; mso-ascii-theme-font: major-bidi; mso-bidi-theme-font: major-bidi; mso-hansi-theme-font: major-bidi;"><o:p></o:p></span></b></div>
<div class="MsoNormal" style="direction: ltr; tab-stops: 319.15pt; text-align: left; unicode-bidi: embed;">
<br /></div>
<div class="MsoNormal" style="direction: ltr; tab-stops: 319.15pt; text-align: left; unicode-bidi: embed;">
<span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 107%; mso-ascii-theme-font: major-bidi; mso-bidi-theme-font: major-bidi; mso-hansi-theme-font: major-bidi;">Example (1):<o:p></o:p></span></div>
<div class="MsoNormal" style="direction: ltr; tab-stops: 319.15pt; text-align: left; unicode-bidi: embed;">
<span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 107%; mso-ascii-theme-font: major-bidi; mso-bidi-theme-font: major-bidi; mso-hansi-theme-font: major-bidi;"><br /></span></div>
<div class="MsoNormal" style="direction: ltr; tab-stops: 319.15pt; text-align: left; unicode-bidi: embed;">
<span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 107%; mso-ascii-theme-font: major-bidi; mso-bidi-theme-font: major-bidi; mso-hansi-theme-font: major-bidi;">Suppose we have below data:<o:p></o:p></span></div>
<div class="MsoNormal" style="direction: ltr; tab-stops: 319.15pt; text-align: left; unicode-bidi: embed;">
<span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 107%; mso-ascii-theme-font: major-bidi; mso-bidi-theme-font: major-bidi; mso-hansi-theme-font: major-bidi;"><br /></span></div>
<div class="MsoNormal" style="direction: ltr; tab-stops: 319.15pt; text-align: left; unicode-bidi: embed;">
<span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 107%; mso-ascii-theme-font: major-bidi; mso-bidi-theme-font: major-bidi; mso-hansi-theme-font: major-bidi;">P1 (-11, 3, 31)<o:p></o:p></span></div>
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<span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 107%; mso-ascii-theme-font: major-bidi; mso-bidi-theme-font: major-bidi; mso-hansi-theme-font: major-bidi;"><br /></span></div>
<div class="MsoNormal" style="direction: ltr; tab-stops: 319.15pt; text-align: left; unicode-bidi: embed;">
<span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 107%; mso-ascii-theme-font: major-bidi; mso-bidi-theme-font: major-bidi; mso-hansi-theme-font: major-bidi;">t = 129<o:p></o:p></span></div>
<div class="MsoNormal" style="direction: ltr; tab-stops: 319.15pt; text-align: left; unicode-bidi: embed;">
<span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 107%; mso-ascii-theme-font: major-bidi; mso-bidi-theme-font: major-bidi; mso-hansi-theme-font: major-bidi;"><br /></span></div>
<div class="MsoNormal" style="direction: ltr; tab-stops: 319.15pt; text-align: left; unicode-bidi: embed;">
<span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 107%; mso-ascii-theme-font: major-bidi; mso-bidi-theme-font: major-bidi; mso-hansi-theme-font: major-bidi;">The results will be as follows:<o:p></o:p></span></div>
<div class="MsoNormal" style="direction: ltr; tab-stops: 319.15pt; text-align: left; unicode-bidi: embed;">
<span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 107%; mso-ascii-theme-font: major-bidi; mso-bidi-theme-font: major-bidi; mso-hansi-theme-font: major-bidi;"><br /></span></div>
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh5f9sJ6m7iIxau1eM3Ki3wtf84MyEpdrRudHuayKdGrKt2HCO_nZxNAjTofL1QFLQrA-Qdm5jeJlHqS9yVEaOvaer7B_NZEDtqbeMI3evflJYsUFfW-s93BE1X-InyBB0amSY0HBYi2nw/s1600/16.png" imageanchor="1" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;"><img border="0" data-original-height="491" data-original-width="459" height="320" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh5f9sJ6m7iIxau1eM3Ki3wtf84MyEpdrRudHuayKdGrKt2HCO_nZxNAjTofL1QFLQrA-Qdm5jeJlHqS9yVEaOvaer7B_NZEDtqbeMI3evflJYsUFfW-s93BE1X-InyBB0amSY0HBYi2nw/s320/16.png" width="299" /></a></div>
<div class="MsoNormal" style="direction: ltr; tab-stops: 319.15pt; text-align: left; unicode-bidi: embed;">
<span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 107%; mso-ascii-theme-font: major-bidi; mso-bidi-theme-font: major-bidi; mso-hansi-theme-font: major-bidi;"><br /></span></div>
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<div class="MsoNormal" style="direction: ltr; tab-stops: 319.15pt; text-align: left; unicode-bidi: embed;">
<span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 107%; mso-ascii-theme-font: major-bidi; mso-bidi-theme-font: major-bidi; mso-hansi-theme-font: major-bidi;">Example (2):<o:p></o:p></span></div>
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<span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 107%; mso-ascii-theme-font: major-bidi; mso-bidi-theme-font: major-bidi; mso-hansi-theme-font: major-bidi;"><br /></span></div>
<div class="MsoNormal" style="direction: ltr; tab-stops: 319.15pt; text-align: left; unicode-bidi: embed;">
<span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 107%; mso-ascii-theme-font: major-bidi; mso-bidi-theme-font: major-bidi; mso-hansi-theme-font: major-bidi;">Suppose we have below data:<o:p></o:p></span></div>
<div class="MsoNormal" style="direction: ltr; tab-stops: 319.15pt; text-align: left; unicode-bidi: embed;">
<span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 107%; mso-ascii-theme-font: major-bidi; mso-bidi-theme-font: major-bidi; mso-hansi-theme-font: major-bidi;"><br /></span></div>
<div class="MsoNormal" style="direction: ltr; tab-stops: 319.15pt; text-align: left; unicode-bidi: embed;">
<span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 107%; mso-ascii-theme-font: major-bidi; mso-bidi-theme-font: major-bidi; mso-hansi-theme-font: major-bidi;">P1 (-3.57, 9.4, -1.84)<o:p></o:p></span></div>
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<span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 107%; mso-ascii-theme-font: major-bidi; mso-bidi-theme-font: major-bidi; mso-hansi-theme-font: major-bidi;"><br /></span></div>
<div class="MsoNormal" style="direction: ltr; tab-stops: 319.15pt; text-align: left; unicode-bidi: embed;">
<span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 107%; mso-ascii-theme-font: major-bidi; mso-bidi-theme-font: major-bidi; mso-hansi-theme-font: major-bidi;">t = 32.83<o:p></o:p></span></div>
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<span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 107%; mso-ascii-theme-font: major-bidi; mso-bidi-theme-font: major-bidi; mso-hansi-theme-font: major-bidi;"><br /></span></div>
<div class="MsoNormal" style="direction: ltr; tab-stops: 319.15pt; text-align: left; unicode-bidi: embed;">
<span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 107%; mso-ascii-theme-font: major-bidi; mso-bidi-theme-font: major-bidi; mso-hansi-theme-font: major-bidi;">The results will be as follows:<o:p></o:p></span></div>
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<span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 107%; mso-ascii-theme-font: major-bidi; mso-bidi-theme-font: major-bidi; mso-hansi-theme-font: major-bidi;"><br /></span></div>
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgwOwwhcgCfnbQZedg89dGqfqN_WnKx7BdbC1iNv2TpYkbcU_8x6PVQbEloRCDeMWtSWIz0lQ4Fljx0VNlpYs-80ThG9dapcyNjmthr9QJUhKsVVvpd0mzpAsaLKGeraw_3kJIv4VdkxSQ/s1600/17.png" imageanchor="1" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;"><img border="0" data-original-height="495" data-original-width="440" height="320" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgwOwwhcgCfnbQZedg89dGqfqN_WnKx7BdbC1iNv2TpYkbcU_8x6PVQbEloRCDeMWtSWIz0lQ4Fljx0VNlpYs-80ThG9dapcyNjmthr9QJUhKsVVvpd0mzpAsaLKGeraw_3kJIv4VdkxSQ/s320/17.png" width="284" /></a></div>
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<span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 107%; mso-ascii-theme-font: major-bidi; mso-bidi-theme-font: major-bidi; mso-hansi-theme-font: major-bidi;"><br /></span></div>
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<div align="right" class="MsoNormal" dir="RTL" style="text-align: left;">
<b><span dir="LTR" style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 107%; mso-ascii-theme-font: major-bidi; mso-bidi-theme-font: major-bidi; mso-hansi-theme-font: major-bidi;"><br /></span></b></div>
<div align="right" class="MsoNormal" dir="RTL" style="text-align: left;">
<b><span dir="LTR" style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 107%; mso-ascii-theme-font: major-bidi; mso-bidi-theme-font: major-bidi; mso-hansi-theme-font: major-bidi;">The Mapping A System of five Particle for Given Gravity Potential
Energy <o:p></o:p></span></b></div>
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<b><span dir="LTR" style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 107%; mso-ascii-theme-font: major-bidi; mso-bidi-theme-font: major-bidi; mso-hansi-theme-font: major-bidi;"><br /></span></b></div>
<div align="right" class="MsoNormal" dir="RTL" style="text-align: left;">
<span dir="LTR" style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 107%; mso-ascii-theme-font: major-bidi; mso-bidi-theme-font: major-bidi; mso-hansi-theme-font: major-bidi;">Suppose we have five particles Pm, Pn, P1, P2 and P3 with the
distances among them in infinity which have the same masses of “m”. If an
external force brings all these particles in new location just like above figure,
how can we map the location of these particles for a constant gravity potential </span></div>
<div align="right" class="MsoNormal" dir="RTL" style="text-align: left;">
<span dir="LTR" style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 107%; mso-ascii-theme-font: major-bidi; mso-bidi-theme-font: major-bidi; mso-hansi-theme-font: major-bidi;">energy?<o:p></o:p></span></div>
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<span dir="LTR" style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 107%; mso-ascii-theme-font: major-bidi; mso-bidi-theme-font: major-bidi; mso-hansi-theme-font: major-bidi;"><br /></span></div>
<div class="MsoNormal" style="direction: ltr; text-align: left; unicode-bidi: embed;">
<span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 107%; mso-ascii-theme-font: major-bidi; mso-bidi-theme-font: major-bidi; mso-hansi-theme-font: major-bidi;">The method of analysis is just like the steps stated in previous
article </span></div>
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<span style="font-family: "Times New Roman", serif; font-size: 12pt; line-height: 107%;">(</span><a href="http://www.emfps.org/2018/04/the-distances-among-particles-in-space-2.html"><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 107%; mso-ascii-theme-font: major-bidi; mso-bidi-theme-font: major-bidi; mso-hansi-theme-font: major-bidi;">http://www.emfps.org/2018/04/the-distances-among-particles-in-space-2.html</span></a><span class="MsoHyperlink"><span style="color: windowtext; font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 107%; mso-ascii-theme-font: major-bidi; mso-bidi-theme-font: major-bidi; mso-hansi-theme-font: major-bidi;">)</span></span></div>
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<span class="MsoHyperlink"><span style="color: windowtext; font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 107%; mso-ascii-theme-font: major-bidi; mso-bidi-theme-font: major-bidi; mso-hansi-theme-font: major-bidi;"><br /></span></span></div>
<div class="MsoNormal" style="direction: ltr; text-align: left; unicode-bidi: embed;">
<span class="MsoHyperlink"><span style="color: windowtext; font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 107%; mso-ascii-theme-font: major-bidi; mso-bidi-theme-font: major-bidi; mso-hansi-theme-font: major-bidi; text-decoration: none; text-underline: none;">The only difference is to solve </span></span><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 107%; mso-ascii-theme-font: major-bidi; mso-bidi-theme-font: major-bidi; mso-hansi-theme-font: major-bidi;">a system of three nonlinear equations instead of a system of two
nonlinear equations in previous articles as follows:<o:p></o:p></span></div>
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<span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 107%; mso-ascii-theme-font: major-bidi; mso-bidi-theme-font: major-bidi; mso-hansi-theme-font: major-bidi;"><br /></span></div>
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh62MMk5Lvfbm8jtcGcvDQH5FkIHff_uy68E2BJ6ghL_OGqPhdtMR16TC5_6q-Vk7xq-bXcItE-Pn7_b2l1xMFGjgtyL6i2jtfVN6Wbe_hFbcR-riyOY1OQJq2HjRUBPaFf6VnrPJKy-LY/s1600/18_1.png" imageanchor="1" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;"><img border="0" data-original-height="160" data-original-width="479" height="106" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh62MMk5Lvfbm8jtcGcvDQH5FkIHff_uy68E2BJ6ghL_OGqPhdtMR16TC5_6q-Vk7xq-bXcItE-Pn7_b2l1xMFGjgtyL6i2jtfVN6Wbe_hFbcR-riyOY1OQJq2HjRUBPaFf6VnrPJKy-LY/s320/18_1.png" width="320" /></a></div>
<div class="MsoNormal" style="direction: ltr; text-align: left; unicode-bidi: embed;">
<span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 107%; mso-ascii-theme-font: major-bidi; mso-bidi-theme-font: major-bidi; mso-hansi-theme-font: major-bidi;"><br /></span></div>
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<div class="MsoNormal" style="direction: ltr; tab-stops: 319.15pt; text-align: left; unicode-bidi: embed;">
<span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 107%; mso-ascii-theme-font: major-bidi; mso-bidi-theme-font: major-bidi; mso-hansi-theme-font: major-bidi;">Example:<o:p></o:p></span></div>
<div class="MsoNormal" style="direction: ltr; tab-stops: 319.15pt; text-align: left; unicode-bidi: embed;">
<span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 107%; mso-ascii-theme-font: major-bidi; mso-bidi-theme-font: major-bidi; mso-hansi-theme-font: major-bidi;"><br /></span></div>
<div class="MsoNormal" style="direction: ltr; tab-stops: 319.15pt; text-align: left; unicode-bidi: embed;">
<span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 107%; mso-ascii-theme-font: major-bidi; mso-bidi-theme-font: major-bidi; mso-hansi-theme-font: major-bidi;">To simplify above system of
equations, I consider “t” as a constant number.<o:p></o:p></span></div>
<div class="MsoNormal" style="direction: ltr; tab-stops: 319.15pt; text-align: left; unicode-bidi: embed;">
<span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 107%; mso-ascii-theme-font: major-bidi; mso-bidi-theme-font: major-bidi; mso-hansi-theme-font: major-bidi;"><br /></span></div>
<div class="MsoNormal" style="direction: ltr; tab-stops: 319.15pt; text-align: left; unicode-bidi: embed;">
<span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 107%; mso-ascii-theme-font: major-bidi; mso-bidi-theme-font: major-bidi; mso-hansi-theme-font: major-bidi;">Assume we have:<o:p></o:p></span></div>
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<span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 107%; mso-ascii-theme-font: major-bidi; mso-bidi-theme-font: major-bidi; mso-hansi-theme-font: major-bidi;"><br /></span></div>
<div class="MsoNormal" style="direction: ltr; tab-stops: 319.15pt; text-align: left; unicode-bidi: embed;">
<span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 107%; mso-ascii-theme-font: major-bidi; mso-bidi-theme-font: major-bidi; mso-hansi-theme-font: major-bidi;">r = 0.24 m<o:p></o:p></span></div>
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<span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 107%; mso-ascii-theme-font: major-bidi; mso-bidi-theme-font: major-bidi; mso-hansi-theme-font: major-bidi;"><br /></span></div>
<div class="MsoNormal" style="direction: ltr; tab-stops: 319.15pt; text-align: left; unicode-bidi: embed;">
<span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 107%; mso-ascii-theme-font: major-bidi; mso-bidi-theme-font: major-bidi; mso-hansi-theme-font: major-bidi;">t = 3<o:p></o:p></span></div>
<div class="MsoNormal" style="direction: ltr; tab-stops: 319.15pt; text-align: left; unicode-bidi: embed;">
<span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 107%; mso-ascii-theme-font: major-bidi; mso-bidi-theme-font: major-bidi; mso-hansi-theme-font: major-bidi;"><br /></span></div>
<div class="MsoNormal" style="direction: ltr; tab-stops: 319.15pt; text-align: left; unicode-bidi: embed;">
<span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 107%; mso-ascii-theme-font: major-bidi; mso-bidi-theme-font: major-bidi; mso-hansi-theme-font: major-bidi;">Thus, we should solve below system
of three equations:<o:p></o:p></span></div>
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<span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 107%; mso-ascii-theme-font: major-bidi; mso-bidi-theme-font: major-bidi; mso-hansi-theme-font: major-bidi;"><br /></span></div>
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjElk2cyNbmv5hqCK932kvMXesAxwOkyI4JzZvovrz-JeD8OhNaXZnQ1k2yubSi_aSHGSZRXPkynLo3srQyPzo8inUFza8dInlyRGsKnCIhsRlelNInJ2Mm7tjJV3oM_oQVAxwooa1jazU/s1600/18_2.png" imageanchor="1" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;"><img border="0" data-original-height="173" data-original-width="528" height="104" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjElk2cyNbmv5hqCK932kvMXesAxwOkyI4JzZvovrz-JeD8OhNaXZnQ1k2yubSi_aSHGSZRXPkynLo3srQyPzo8inUFza8dInlyRGsKnCIhsRlelNInJ2Mm7tjJV3oM_oQVAxwooa1jazU/s320/18_2.png" width="320" /></a></div>
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<span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 107%; mso-ascii-theme-font: major-bidi; mso-bidi-theme-font: major-bidi; mso-hansi-theme-font: major-bidi;"><br /></span></div>
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<span class="MsoHyperlink"><span style="color: windowtext; font-family: "Times New Roman", serif; font-size: 12pt; line-height: 107%;">I found 190 models that some of them are as follows:<o:p></o:p></span></span></div>
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<span class="MsoHyperlink"><span style="color: windowtext; font-family: "Times New Roman", serif; font-size: 12pt; line-height: 107%;"><br /></span></span></div>
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgdxu4jMDeRahWp4BBuewYDQSoTrEYMnFgqrvLw6ulcmZT_giwL7rpdzeqKeBPEhr29Evsn9lUDPcOVM9obNWfR-n72Wyd-N5PHKyS93J0bI1_Du-z9QihTr-GUnEC_keKACpwIiqiuAhM/s1600/19.png" imageanchor="1" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;"><img border="0" data-original-height="523" data-original-width="450" height="320" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgdxu4jMDeRahWp4BBuewYDQSoTrEYMnFgqrvLw6ulcmZT_giwL7rpdzeqKeBPEhr29Evsn9lUDPcOVM9obNWfR-n72Wyd-N5PHKyS93J0bI1_Du-z9QihTr-GUnEC_keKACpwIiqiuAhM/s320/19.png" width="275" /></a></div>
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<span class="MsoHyperlink"><span style="color: windowtext; font-family: "Times New Roman", serif; font-size: 12pt; line-height: 107%;"><br /></span></span></div>
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<span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 107%; mso-ascii-theme-font: major-bidi; mso-bidi-theme-font: major-bidi; mso-hansi-theme-font: major-bidi;">For testing of these models, I use model (1) in above table and we
can see the results as follows:<o:p></o:p></span></div>
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<span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 107%; mso-ascii-theme-font: major-bidi; mso-bidi-theme-font: major-bidi; mso-hansi-theme-font: major-bidi;"><br /></span></div>
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<span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 107%; mso-ascii-theme-font: major-bidi; mso-bidi-theme-font: major-bidi; mso-hansi-theme-font: major-bidi;"><br /></span></div>
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEga0WhMjYf5ZAW0yGGy-63F8FdydoqBDNSs7RmP1BHCXFcfSkmMkNvDJquDQhcigcY3WEg0CL3ji5pZHOKITtpAe4tlNWr3HnVc8cSolGZirhsp8iX5Zt-LR6jxMr3rhjLWJ4N5wiO-HXQ/s1600/20.png" imageanchor="1" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;"><img border="0" data-original-height="469" data-original-width="420" height="320" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEga0WhMjYf5ZAW0yGGy-63F8FdydoqBDNSs7RmP1BHCXFcfSkmMkNvDJquDQhcigcY3WEg0CL3ji5pZHOKITtpAe4tlNWr3HnVc8cSolGZirhsp8iX5Zt-LR6jxMr3rhjLWJ4N5wiO-HXQ/s320/20.png" width="286" /></a></div>
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<span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 107%; mso-ascii-theme-font: major-bidi; mso-bidi-theme-font: major-bidi; mso-hansi-theme-font: major-bidi;"><br /></span></div>
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Gholamreza Soleimanihttp://www.blogger.com/profile/03273527405719420253noreply@blogger.com1tag:blogger.com,1999:blog-392703582366288634.post-2741343996791691332018-04-28T18:43:00.002+04:302018-04-28T18:43:57.021+04:30The Distances among The Particles in The Space (2)<div dir="ltr" style="text-align: left;" trbidi="on">
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<span dir="LTR" style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 107%; mso-ascii-theme-font: major-bidi; mso-bidi-theme-font: major-bidi; mso-hansi-theme-font: major-bidi;"><br /></span></div>
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<span dir="LTR" style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 107%; mso-ascii-theme-font: major-bidi; mso-bidi-theme-font: major-bidi; mso-hansi-theme-font: major-bidi;">You can preview the conjectures (1) and (2) and (3) on below link:<o:p></o:p></span></div>
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<span dir="LTR" style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 107%; mso-ascii-theme-font: major-bidi; mso-bidi-theme-font: major-bidi; mso-hansi-theme-font: major-bidi;"><br /></span></div>
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<span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 107%; mso-ascii-theme-font: major-bidi; mso-bidi-theme-font: major-bidi; mso-hansi-theme-font: major-bidi;"><span style="mso-spacerun: yes;"> </span></span><a href="http://www.emfps.org/2018/04/the-distances-among-particles-in-space.html">http://www.emfps.org/2018/04/the-distances-among-particles-in-space.html</a><span dir="RTL" lang="FA" style="font-family: "Arial","sans-serif"; mso-ascii-font-family: Calibri; mso-ascii-theme-font: minor-latin; mso-bidi-font-family: Arial; mso-bidi-theme-font: minor-bidi; mso-hansi-font-family: Calibri; mso-hansi-theme-font: minor-latin;"><o:p></o:p></span></div>
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<br /></div>
<div align="right" class="MsoNormal" dir="RTL" style="text-align: left;">
<b><span dir="LTR" style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 107%; mso-ascii-theme-font: major-bidi; mso-bidi-theme-font: major-bidi; mso-hansi-theme-font: major-bidi;">Conjecture (4):<o:p></o:p></span></b></div>
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<div class="MsoNormal" style="direction: ltr; text-align: left; unicode-bidi: embed;">
<b><i><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 107%; mso-ascii-theme-font: major-bidi; mso-bidi-theme-font: major-bidi; mso-hansi-theme-font: major-bidi;">The distances between the point P0 (a, a, a) and the points
mentioned in conjecture (3) are always the same where “a” is a member of real
number.<o:p></o:p></span></i></b></div>
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<br /></div>
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<span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 107%; mso-ascii-theme-font: major-bidi; mso-bidi-theme-font: major-bidi; mso-hansi-theme-font: major-bidi;">Example:<o:p></o:p></span></div>
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<span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 107%; mso-ascii-theme-font: major-bidi; mso-bidi-theme-font: major-bidi; mso-hansi-theme-font: major-bidi;"><br /></span></div>
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<span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 107%; mso-ascii-theme-font: major-bidi; mso-bidi-theme-font: major-bidi; mso-hansi-theme-font: major-bidi;">Suppose we have point P1 with below coordination:<o:p></o:p></span></div>
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<span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 107%; mso-ascii-theme-font: major-bidi; mso-bidi-theme-font: major-bidi; mso-hansi-theme-font: major-bidi;"><br /></span></div>
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<span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 107%; mso-ascii-theme-font: major-bidi; mso-bidi-theme-font: major-bidi; mso-hansi-theme-font: major-bidi;">P1 (-3, 15, 34)<o:p></o:p></span></div>
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<span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 107%; mso-ascii-theme-font: major-bidi; mso-bidi-theme-font: major-bidi; mso-hansi-theme-font: major-bidi;"><br /></span></div>
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<span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 107%; mso-ascii-theme-font: major-bidi; mso-bidi-theme-font: major-bidi; mso-hansi-theme-font: major-bidi;">According to conjecture (3), the points P2 and P3 will be:<o:p></o:p></span></div>
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<span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 107%; mso-ascii-theme-font: major-bidi; mso-bidi-theme-font: major-bidi; mso-hansi-theme-font: major-bidi;"><br /></span></div>
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<span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 107%; mso-ascii-theme-font: major-bidi; mso-bidi-theme-font: major-bidi; mso-hansi-theme-font: major-bidi;">P2 (34, -3, 15)<o:p></o:p></span></div>
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<span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 107%; mso-ascii-theme-font: major-bidi; mso-bidi-theme-font: major-bidi; mso-hansi-theme-font: major-bidi;"><br /></span></div>
<div class="MsoNormal" style="direction: ltr; text-align: left; unicode-bidi: embed;">
<span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 107%; mso-ascii-theme-font: major-bidi; mso-bidi-theme-font: major-bidi; mso-hansi-theme-font: major-bidi;">P3 (15, 34, -3)<o:p></o:p></span></div>
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<span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 107%; mso-ascii-theme-font: major-bidi; mso-bidi-theme-font: major-bidi; mso-hansi-theme-font: major-bidi;"><br /></span></div>
<div class="MsoNormal" style="direction: ltr; text-align: left; unicode-bidi: embed;">
<span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 107%; mso-ascii-theme-font: major-bidi; mso-bidi-theme-font: major-bidi; mso-hansi-theme-font: major-bidi;">The distances among the points P1 and P2 and P3 are equal to </span><span style="color: black; mso-ascii-font-family: Calibri; mso-bidi-font-family: "Times New Roman"; mso-bidi-language: AR-SA; mso-fareast-font-family: "Times New Roman"; mso-hansi-font-family: Calibri;">45.32108.<o:p></o:p></span></div>
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<span style="color: black; mso-ascii-font-family: Calibri; mso-bidi-font-family: "Times New Roman"; mso-bidi-language: AR-SA; mso-fareast-font-family: "Times New Roman"; mso-hansi-font-family: Calibri;"><br /></span></div>
<div class="MsoNormal" style="direction: ltr; text-align: left; unicode-bidi: embed;">
<span style="color: black; font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 107%; mso-ascii-theme-font: major-bidi; mso-bidi-language: AR-SA; mso-bidi-theme-font: major-bidi; mso-fareast-font-family: "Times New Roman"; mso-hansi-theme-font: major-bidi;">Assume we have point P0 with below coordination:<o:p></o:p></span></div>
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<span style="color: black; font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 107%; mso-ascii-theme-font: major-bidi; mso-bidi-language: AR-SA; mso-bidi-theme-font: major-bidi; mso-fareast-font-family: "Times New Roman"; mso-hansi-theme-font: major-bidi;"><br /></span></div>
<div class="MsoNormal" style="direction: ltr; text-align: left; unicode-bidi: embed;">
<span style="color: black; font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 107%; mso-ascii-theme-font: major-bidi; mso-bidi-language: AR-SA; mso-bidi-theme-font: major-bidi; mso-fareast-font-family: "Times New Roman"; mso-hansi-theme-font: major-bidi;">P0 (56, 56, 56)<o:p></o:p></span></div>
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<span style="color: black; font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 107%; mso-ascii-theme-font: major-bidi; mso-bidi-language: AR-SA; mso-bidi-theme-font: major-bidi; mso-fareast-font-family: "Times New Roman"; mso-hansi-theme-font: major-bidi;"><br /></span></div>
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<span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 107%; mso-ascii-theme-font: major-bidi; mso-bidi-theme-font: major-bidi; mso-hansi-theme-font: major-bidi;">The distances between the point P0 (56, 56, 56) and the points P1
and P2 and P3 is the same and </span></div>
<div class="MsoNormal" style="direction: ltr; text-align: left; unicode-bidi: embed;">
<span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 107%; mso-ascii-theme-font: major-bidi; mso-bidi-theme-font: major-bidi; mso-hansi-theme-font: major-bidi;">equal to </span><span style="color: black; mso-ascii-font-family: Calibri; mso-bidi-font-family: "Times New Roman"; mso-bidi-language: AR-SA; mso-fareast-font-family: "Times New Roman"; mso-hansi-font-family: Calibri;">75.13987.<o:p></o:p></span></div>
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<span style="color: black; mso-ascii-font-family: Calibri; mso-bidi-font-family: "Times New Roman"; mso-bidi-language: AR-SA; mso-fareast-font-family: "Times New Roman"; mso-hansi-font-family: Calibri;"><br /></span></div>
<div class="MsoNormal" style="direction: ltr; text-align: left; unicode-bidi: embed;">
<span style="color: black; mso-ascii-font-family: Calibri; mso-bidi-font-family: "Times New Roman"; mso-bidi-language: AR-SA; mso-fareast-font-family: "Times New Roman"; mso-hansi-font-family: Calibri;">d (P0, P1 ) = 75.13987<o:p></o:p></span></div>
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<span style="color: black; mso-ascii-font-family: Calibri; mso-bidi-font-family: "Times New Roman"; mso-bidi-language: AR-SA; mso-fareast-font-family: "Times New Roman"; mso-hansi-font-family: Calibri;">d (P0, P2) = 75.13987<o:p></o:p></span></div>
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<span style="color: black; mso-ascii-font-family: Calibri; mso-bidi-font-family: "Times New Roman"; mso-bidi-language: AR-SA; mso-fareast-font-family: "Times New Roman"; mso-hansi-font-family: Calibri;">d (P0, P3 ) = 75.13987<o:p></o:p></span></div>
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<b><span dir="LTR" style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 107%; mso-ascii-theme-font: major-bidi; mso-bidi-theme-font: major-bidi; mso-hansi-theme-font: major-bidi;">The Mapping A System of Four Particle for Given Gravity Potential
Energy <o:p></o:p></span></b></div>
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<b><span dir="LTR" style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 107%; mso-ascii-theme-font: major-bidi; mso-bidi-theme-font: major-bidi; mso-hansi-theme-font: major-bidi;"><br /></span></b></div>
<div align="right" class="MsoNormal" dir="RTL" style="text-align: left;">
<span dir="LTR" style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 107%; mso-ascii-theme-font: major-bidi; mso-bidi-theme-font: major-bidi; mso-hansi-theme-font: major-bidi;">Suppose we have four particles P0, P1, P2 and P3 with the distances
among them in infinity<span style="mso-spacerun: yes;"> </span>which have the
same masses of “m”. If an external force brings all these particles in new
location just like </span></div>
<div align="right" class="MsoNormal" dir="RTL" style="text-align: left;">
<span dir="LTR" style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 107%; mso-ascii-theme-font: major-bidi; mso-bidi-theme-font: major-bidi; mso-hansi-theme-font: major-bidi;">below figure, how can we map the location of these particles
for a constant gravity potential energy?<o:p></o:p></span></div>
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<span dir="LTR" style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 107%; mso-ascii-theme-font: major-bidi; mso-bidi-theme-font: major-bidi; mso-hansi-theme-font: major-bidi;"><br /></span></div>
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjmDoEqyIHtNH5-I8_jjQyjW3Ew0y9BarqcdILqhvUiO7LknI9SyoOittfrdftRNRbIVEdYJaMHjJblXmXrrTFFfZqh9O_YT2zNN5HmTbpGr_F6FxrIJDRk765I6GjhzvqAjYjG41cBh4U/s1600/4.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="404" data-original-width="731" height="176" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjmDoEqyIHtNH5-I8_jjQyjW3Ew0y9BarqcdILqhvUiO7LknI9SyoOittfrdftRNRbIVEdYJaMHjJblXmXrrTFFfZqh9O_YT2zNN5HmTbpGr_F6FxrIJDRk765I6GjhzvqAjYjG41cBh4U/s320/4.png" width="320" /></a></div>
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<span dir="LTR" style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 107%; mso-ascii-theme-font: major-bidi; mso-bidi-theme-font: major-bidi; mso-hansi-theme-font: major-bidi;"> </span><span style="font-family: "Times New Roman", serif; font-size: 12pt;"> </span><span style="font-family: "Times New Roman", serif; font-size: 12pt;">As I told you, suppose that
mass of all particles is the same. Therefore, for our analysis, we have three
independent variables of “m”, “r” and “R”.</span></div>
<div class="MsoNormal" style="text-align: left;">
<br /></div>
<br />
<div class="MsoNormal" style="text-align: left;">
<span dir="LTR" style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 107%; mso-ascii-theme-font: major-bidi; mso-bidi-theme-font: major-bidi; mso-hansi-theme-font: major-bidi;">Suppose the constant gravity
potential energy is equal -</span><span dir="LTR">1.008E-08
J</span></div>
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<span dir="LTR" style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 107%; mso-ascii-theme-font: major-bidi; mso-bidi-theme-font: major-bidi; mso-fareast-font-family: "Times New Roman"; mso-fareast-theme-font: minor-fareast; mso-hansi-theme-font: major-bidi;"><br /></span></div>
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<span dir="LTR" style="font-family: "Times New Roman", serif; font-size: 12pt; line-height: 107%;">U (r) = </span><span dir="LTR" style="font-family: "Times New Roman", serif; font-size: 12pt; line-height: 107%;">-</span><span dir="LTR">1.008E-08 J</span></div>
<div class="MsoNormal" style="text-align: left;">
<span dir="LTR"><br /></span></div>
<div class="MsoNormal" style="text-align: left;">
<span dir="LTR" style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 107%; mso-ascii-theme-font: major-bidi; mso-bidi-theme-font: major-bidi; mso-hansi-theme-font: major-bidi;"> As I stated in my previous
article, </span><span dir="LTR">to find the coordination and mapping the
particles, we should take two steps:<o:p></o:p></span></div>
<div class="MsoNormal" style="text-align: left;">
<span dir="LTR"><br /></span></div>
<div class="MsoNormal" style="text-align: left; unicode-bidi: embed;">
<b><span style="font-family: "Times New Roman", serif; font-size: 12pt; line-height: 107%;">Step (1)</span></b><span style="font-family: "Times New Roman", serif; font-size: 12pt; line-height: 107%;">: <o:p></o:p></span></div>
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<span style="font-family: "Times New Roman", serif; font-size: 12pt; line-height: 107%;"><br /></span></div>
<div style="text-align: left;">
</div>
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<span style="font-family: "Times New Roman", serif; font-size: 12pt; line-height: 107%;">To find the mass of particles accompanied by the
distances of “r” and “R”, we should apply the method mentioned in article of “</span><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 107%; mso-ascii-theme-font: major-bidi; mso-bidi-theme-font: major-bidi; mso-hansi-theme-font: major-bidi;">Solving a Nonlinear Equation with Many Independent Variables” (</span><a href="http://www.emfps.org/2016/10/can-we-solve-nonlinear-equation-with.html"><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 107%; mso-ascii-theme-font: major-bidi; mso-bidi-theme-font: major-bidi; mso-hansi-theme-font: major-bidi;">http://www.emfps.org/2016/10/can-we-solve-nonlinear-equation-with.html</span></a><span class="MsoHyperlink"><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 107%; mso-ascii-theme-font: major-bidi; mso-bidi-theme-font: major-bidi; mso-hansi-theme-font: major-bidi;">)<o:p></o:p></span></span></div>
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<span class="MsoHyperlink"><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 107%; mso-ascii-theme-font: major-bidi; mso-bidi-theme-font: major-bidi; mso-hansi-theme-font: major-bidi;"><br /></span></span></div>
<div class="MsoNormal" style="text-align: left; unicode-bidi: embed;">
<span class="MsoHyperlink"><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 107%; mso-ascii-theme-font: major-bidi; mso-bidi-theme-font: major-bidi; mso-hansi-theme-font: major-bidi;"></span></span></div>
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<span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 107%; mso-ascii-theme-font: major-bidi; mso-bidi-theme-font: major-bidi; mso-hansi-theme-font: major-bidi;">I found 8 answers for three independent variables of the particles:<o:p></o:p></span></div>
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<span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 107%; mso-ascii-theme-font: major-bidi; mso-bidi-theme-font: major-bidi; mso-hansi-theme-font: major-bidi;"><br /></span></div>
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEj9VDRJFfEPx0LLUoo-e0HYrPoz94IsJpZdbUclGDjit73DOy08gtqD5Bi6H0LBfO3w-vtjLgbzfUSF5M3CO3jO9fPF3yMyYN0SCJl_ZaUWHgc22NEk_BN9tL3rEFSeWxdZY52Pmt1Hhqs/s1600/5.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="298" data-original-width="469" height="203" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEj9VDRJFfEPx0LLUoo-e0HYrPoz94IsJpZdbUclGDjit73DOy08gtqD5Bi6H0LBfO3w-vtjLgbzfUSF5M3CO3jO9fPF3yMyYN0SCJl_ZaUWHgc22NEk_BN9tL3rEFSeWxdZY52Pmt1Hhqs/s320/5.png" width="320" /></a></div>
<div class="separator" style="clear: both; text-align: center;">
<br /></div>
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<span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 107%; mso-ascii-theme-font: major-bidi; mso-bidi-theme-font: major-bidi; mso-hansi-theme-font: major-bidi;"></span></div>
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<span style="font-family: "Times New Roman", serif; font-size: 12pt; line-height: 107%;">For example, I choose below three variables from above
table:<o:p></o:p></span><span style="font-family: "Times New Roman", serif; font-size: 12pt; line-height: 107%;"><br /></span></div>
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<span style="font-family: "Times New Roman", serif; font-size: 12pt; line-height: 107%;"><br /></span></div>
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<span style="font-family: "Times New Roman", serif; font-size: 12pt; line-height: 107%;"></span></div>
<table border="0" cellpadding="0" cellspacing="0" class="MsoNormalTable" style="border-collapse: collapse; margin-left: 4.65pt; mso-padding-alt: 0cm 5.4pt 0cm 5.4pt; mso-yfti-tbllook: 1184; width: 256px;">
<tbody>
<tr style="height: 15.75pt; mso-yfti-firstrow: yes; mso-yfti-irow: 0;">
<td nowrap="" style="border: solid windowtext 1.0pt; height: 15.75pt; mso-border-alt: solid windowtext .5pt; padding: 0cm 5.4pt 0cm 5.4pt; width: 26.0pt;" width="35">
<div align="center" class="MsoNormal" style="direction: ltr; line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; text-align: center; unicode-bidi: embed;">
<b>m<o:p></o:p></b></div>
</td>
<td nowrap="" style="border-left: none; border: solid windowtext 1.0pt; height: 15.75pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt; padding: 0cm 5.4pt 0cm 5.4pt; width: 35.0pt;" width="47">
<div align="center" class="MsoNormal" style="direction: ltr; line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; text-align: center; unicode-bidi: embed;">
<b>r<o:p></o:p></b></div>
</td>
<td nowrap="" style="border-left: none; border: solid windowtext 1.0pt; height: 15.75pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt; padding: 0cm 5.4pt 0cm 5.4pt; width: 28.0pt;" width="37">
<div align="center" class="MsoNormal" style="direction: ltr; line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; text-align: center; unicode-bidi: embed;">
<b>R<o:p></o:p></b></div>
</td>
<td nowrap="" style="border-left: none; border: solid windowtext 1.0pt; height: 15.75pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt; padding: 0cm 5.4pt 0cm 5.4pt; width: 103.15pt;" width="138">
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<b><span style="font-size: 12pt;">T_G_P_E<o:p></o:p></span></b></div>
</td>
</tr>
<tr style="height: 15.0pt; mso-yfti-irow: 1;">
<td nowrap="" style="border-top: none; border: solid windowtext 1.0pt; height: 15.0pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; padding: 0cm 5.4pt 0cm 5.4pt; width: 26.0pt;" width="35">
<div align="center" class="MsoNormal" style="direction: ltr; line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; text-align: center; unicode-bidi: embed;">
1<o:p></o:p></div>
</td>
<td nowrap="" style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 15.0pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; padding: 0cm 5.4pt 0cm 5.4pt; width: 35.0pt;" width="47">
<div align="center" class="MsoNormal" style="direction: ltr; line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; text-align: center; unicode-bidi: embed;">
0.02<o:p></o:p></div>
</td>
<td nowrap="" style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 15.0pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; padding: 0cm 5.4pt 0cm 5.4pt; width: 28.0pt;" width="37">
<div align="center" class="MsoNormal" style="direction: ltr; line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; text-align: center; unicode-bidi: embed;">
2.8<o:p></o:p></div>
</td>
<td nowrap="" style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 15.0pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; padding: 0cm 5.4pt 0cm 5.4pt; width: 103.15pt;" width="138">
<div align="center" class="MsoNormal" style="direction: ltr; line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; text-align: center; unicode-bidi: embed;">
-1.007949E-08<o:p></o:p></div>
</td>
</tr>
<tr style="height: 15.0pt; mso-yfti-irow: 2;">
<td nowrap="" style="border-top: none; border: solid windowtext 1.0pt; height: 15.0pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; padding: 0cm 5.4pt 0cm 5.4pt; width: 26.0pt;" width="35">
<div align="center" class="MsoNormal" style="direction: ltr; line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; text-align: center; unicode-bidi: embed;">
3<o:p></o:p></div>
</td>
<td nowrap="" style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 15.0pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; padding: 0cm 5.4pt 0cm 5.4pt; width: 35.0pt;" width="47">
<div align="center" class="MsoNormal" style="direction: ltr; line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; text-align: center; unicode-bidi: embed;">
0.21<o:p></o:p></div>
</td>
<td nowrap="" style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 15.0pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; padding: 0cm 5.4pt 0cm 5.4pt; width: 28.0pt;" width="37">
<div align="center" class="MsoNormal" style="direction: ltr; line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; text-align: center; unicode-bidi: embed;">
1.2<o:p></o:p></div>
</td>
<td nowrap="" style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 15.0pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; padding: 0cm 5.4pt 0cm 5.4pt; width: 103.15pt;" width="138">
<div align="center" class="MsoNormal" style="direction: ltr; line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; text-align: center; unicode-bidi: embed;">
-1.007949E-08<o:p></o:p></div>
</td>
</tr>
<tr style="height: 15.0pt; mso-yfti-irow: 3; mso-yfti-lastrow: yes;">
<td nowrap="" style="border-top: none; border: solid windowtext 1.0pt; height: 15.0pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; padding: 0cm 5.4pt 0cm 5.4pt; width: 26.0pt;" width="35">
<div align="center" class="MsoNormal" style="direction: ltr; line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; text-align: center; unicode-bidi: embed;">
3<o:p></o:p></div>
</td>
<td nowrap="" style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 15.0pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; padding: 0cm 5.4pt 0cm 5.4pt; width: 35.0pt;" width="47">
<div align="center" class="MsoNormal" style="direction: ltr; line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; text-align: center; unicode-bidi: embed;">
0.24<o:p></o:p></div>
</td>
<td nowrap="" style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 15.0pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; padding: 0cm 5.4pt 0cm 5.4pt; width: 28.0pt;" width="37">
<div align="center" class="MsoNormal" style="direction: ltr; line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; text-align: center; unicode-bidi: embed;">
0.7<o:p></o:p></div>
</td>
<td nowrap="" style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 15.0pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; padding: 0cm 5.4pt 0cm 5.4pt; width: 103.15pt;" width="138">
<div align="center" class="MsoNormal" style="direction: ltr; line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; text-align: center; unicode-bidi: embed;">
-1.007949E-08<o:p></o:p></div>
</td>
</tr>
</tbody></table>
<div class="MsoNormal" style="direction: ltr; unicode-bidi: embed;">
<span style="font-family: "Times New Roman", serif; font-size: 12pt; line-height: 107%;"><br /></span></div>
<br />
<div class="MsoNormal" style="direction: ltr; text-align: left; unicode-bidi: embed;">
<span style="color: black; font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 107%; mso-ascii-theme-font: major-bidi; mso-bidi-language: AR-SA; mso-bidi-theme-font: major-bidi; mso-fareast-font-family: "Times New Roman"; mso-hansi-theme-font: major-bidi;">And by using these three set, I start step 2.<o:p></o:p></span></div>
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<span style="color: black; font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 107%; mso-ascii-theme-font: major-bidi; mso-bidi-language: AR-SA; mso-bidi-theme-font: major-bidi; mso-fareast-font-family: "Times New Roman"; mso-hansi-theme-font: major-bidi;"><br /></span></div>
<div class="MsoNormal" style="direction: ltr; text-align: left; unicode-bidi: embed;">
<b><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 107%; mso-ascii-theme-font: major-bidi; mso-bidi-theme-font: major-bidi; mso-hansi-theme-font: major-bidi;">Step (2)</span></b><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 107%; mso-ascii-theme-font: major-bidi; mso-bidi-theme-font: major-bidi; mso-hansi-theme-font: major-bidi;">: <o:p></o:p></span></div>
<div class="MsoNormal" style="direction: ltr; text-align: left; unicode-bidi: embed;">
<span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 107%; mso-ascii-theme-font: major-bidi; mso-bidi-theme-font: major-bidi; mso-hansi-theme-font: major-bidi;"><br /></span></div>
<div class="MsoNormal" style="direction: ltr; text-align: left; unicode-bidi: embed;">
<span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 107%; mso-ascii-theme-font: major-bidi; mso-bidi-theme-font: major-bidi; mso-hansi-theme-font: major-bidi;">Since we should get the coordination of particles by using the
distances “r’ and “R”, therefore, we have to solve </span>a system of two
nonlinear equations as follows:<o:p></o:p></div>
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<br /></div>
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhmMhxVwcbWU2zW5pHNaEXMZ-_ZhhidA0fbe2EdhH-ZzdnYvHkaJoeAE80gfN7iW1ZKLU18tWFwvJU6kZ483HHxkmpoeFTsSjVXz_2ekZZH0akeGKfo0Lskt7C9VENcwDiMow5lYfciCsw/s1600/6.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="121" data-original-width="590" height="65" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhmMhxVwcbWU2zW5pHNaEXMZ-_ZhhidA0fbe2EdhH-ZzdnYvHkaJoeAE80gfN7iW1ZKLU18tWFwvJU6kZ483HHxkmpoeFTsSjVXz_2ekZZH0akeGKfo0Lskt7C9VENcwDiMow5lYfciCsw/s320/6.png" width="320" /></a></div>
<div class="MsoNormal" style="direction: ltr; text-align: left; unicode-bidi: embed;">
<br /></div>
<div class="MsoNormal" style="direction: ltr; text-align: left; unicode-bidi: embed;">
<span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 107%; mso-ascii-theme-font: major-bidi; mso-bidi-theme-font: major-bidi; mso-hansi-theme-font: major-bidi;">By using the model presented in article of “A Model to Track the
Location of a Particle in the Space” (</span><a href="http://www.emfps.org/2018/02/a-model-to-track-location-of-particle.html"><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 107%; mso-ascii-theme-font: major-bidi; mso-bidi-theme-font: major-bidi; mso-hansi-theme-font: major-bidi;">http://www.emfps.org/2018/02/a-model-to-track-location-of-particle.html</span></a><span class="MsoHyperlink"><span style="color: windowtext; font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 107%; mso-ascii-theme-font: major-bidi; mso-bidi-theme-font: major-bidi; mso-hansi-theme-font: major-bidi;">), </span></span><span class="MsoHyperlink"><span style="color: windowtext; font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 107%; mso-ascii-theme-font: major-bidi; mso-bidi-theme-font: major-bidi; mso-hansi-theme-font: major-bidi; text-decoration: none; text-underline: none;">we can easily find the coordination of the particles.<o:p></o:p></span></span></div>
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<span class="MsoHyperlink"><span style="color: windowtext; font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 107%; mso-ascii-theme-font: major-bidi; mso-bidi-theme-font: major-bidi; mso-hansi-theme-font: major-bidi; text-decoration: none; text-underline: none;"><br /></span></span></div>
<div class="MsoNormal" style="direction: ltr; text-align: left; unicode-bidi: embed;">
<span class="MsoHyperlink"><span style="color: windowtext; font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 107%; mso-ascii-theme-font: major-bidi; mso-bidi-theme-font: major-bidi; mso-hansi-theme-font: major-bidi; text-decoration: none; text-underline: none;">For instance, if we have:<o:p></o:p></span></span></div>
<div class="MsoNormal" style="direction: ltr; text-align: left; unicode-bidi: embed;">
<span class="MsoHyperlink"><span style="color: windowtext; font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 107%; mso-ascii-theme-font: major-bidi; mso-bidi-theme-font: major-bidi; mso-hansi-theme-font: major-bidi; text-decoration: none; text-underline: none;"><br /></span></span></div>
<div class="MsoNormal" style="direction: ltr; text-align: left; unicode-bidi: embed;">
<span class="MsoHyperlink"><span style="color: windowtext; font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 107%; mso-ascii-theme-font: major-bidi; mso-bidi-theme-font: major-bidi; mso-hansi-theme-font: major-bidi; text-decoration: none; text-underline: none;"><span style="mso-spacerun: yes;"> </span>m = 1kg<o:p></o:p></span></span></div>
<div class="MsoNormal" style="direction: ltr; text-align: left; unicode-bidi: embed;">
<span class="MsoHyperlink"><span style="color: windowtext; font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 107%; mso-ascii-theme-font: major-bidi; mso-bidi-theme-font: major-bidi; mso-hansi-theme-font: major-bidi; text-decoration: none; text-underline: none;"><br /></span></span></div>
<div class="MsoNormal" style="direction: ltr; text-align: left; unicode-bidi: embed;">
<span class="MsoHyperlink"><span style="color: windowtext; font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 107%; mso-ascii-theme-font: major-bidi; mso-bidi-theme-font: major-bidi; mso-hansi-theme-font: major-bidi; text-decoration: none; text-underline: none;">r = 0.02 m<o:p></o:p></span></span></div>
<div class="MsoNormal" style="direction: ltr; text-align: left; unicode-bidi: embed;">
<span class="MsoHyperlink"><span style="color: windowtext; font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 107%; mso-ascii-theme-font: major-bidi; mso-bidi-theme-font: major-bidi; mso-hansi-theme-font: major-bidi; text-decoration: none; text-underline: none;"><br /></span></span></div>
<div class="MsoNormal" style="direction: ltr; text-align: left; unicode-bidi: embed;">
<span class="MsoHyperlink"><span style="color: windowtext; font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 107%; mso-ascii-theme-font: major-bidi; mso-bidi-theme-font: major-bidi; mso-hansi-theme-font: major-bidi; text-decoration: none; text-underline: none;">R = 2.8 m <span style="mso-spacerun: yes;"> </span><o:p></o:p></span></span></div>
<div class="MsoNormal" style="direction: ltr; text-align: left; unicode-bidi: embed;">
<span class="MsoHyperlink"><span style="color: windowtext; font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 107%; mso-ascii-theme-font: major-bidi; mso-bidi-theme-font: major-bidi; mso-hansi-theme-font: major-bidi; text-decoration: none; text-underline: none;"><span style="mso-spacerun: yes;"><br /></span></span></span></div>
<div class="MsoNormal" style="direction: ltr; text-align: left; unicode-bidi: embed;">
<span class="MsoHyperlink"><span style="color: windowtext; font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 107%; mso-ascii-theme-font: major-bidi; mso-bidi-theme-font: major-bidi; mso-hansi-theme-font: major-bidi; text-decoration: none; text-underline: none;">I found 444 models that some of them are as follows:<o:p></o:p></span></span></div>
<div class="MsoNormal" style="direction: ltr; text-align: left; unicode-bidi: embed;">
<span class="MsoHyperlink"><span style="color: windowtext; font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 107%; mso-ascii-theme-font: major-bidi; mso-bidi-theme-font: major-bidi; mso-hansi-theme-font: major-bidi; text-decoration: none; text-underline: none;"><br /></span></span></div>
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgteJ_6neF_v1jbKd__qJMY3sSpsHPCS0hJtaxDJLFHDCLQx-6JbLvRMs2v9ZgdmxUPLrVNs_GGhCrUemBvrErp7O8EuqHD9Q5oNmtLou_Slwn4Fof3JJq3HhJQZGOJz9hzpw94uTX8HhM/s1600/7.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="519" data-original-width="391" height="320" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgteJ_6neF_v1jbKd__qJMY3sSpsHPCS0hJtaxDJLFHDCLQx-6JbLvRMs2v9ZgdmxUPLrVNs_GGhCrUemBvrErp7O8EuqHD9Q5oNmtLou_Slwn4Fof3JJq3HhJQZGOJz9hzpw94uTX8HhM/s320/7.png" width="241" /></a></div>
<div class="MsoNormal" style="direction: ltr; text-align: left; unicode-bidi: embed;">
<span class="MsoHyperlink"><span style="color: windowtext; font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 107%; mso-ascii-theme-font: major-bidi; mso-bidi-theme-font: major-bidi; mso-hansi-theme-font: major-bidi; text-decoration: none; text-underline: none;"><br /></span></span></div>
<div class="MsoNormal" style="direction: ltr; text-align: left; unicode-bidi: embed;">
<span class="MsoHyperlink"><span style="color: windowtext; font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 107%; mso-ascii-theme-font: major-bidi; mso-bidi-theme-font: major-bidi; mso-hansi-theme-font: major-bidi; text-decoration: none; text-underline: none;"></span></span></div>
<div class="MsoNormal" style="direction: ltr; unicode-bidi: embed;">
<span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 107%; mso-ascii-theme-font: major-bidi; mso-bidi-theme-font: major-bidi; mso-hansi-theme-font: major-bidi;">For testing of these models, I use model (1) in above table and we
can see the results as follows:<o:p></o:p></span></div>
<div class="MsoNormal" style="direction: ltr; unicode-bidi: embed;">
<span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 107%; mso-ascii-theme-font: major-bidi; mso-bidi-theme-font: major-bidi; mso-hansi-theme-font: major-bidi;"><br /></span></div>
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjMH3EMermiMtz9hKbZB6NjdOeX5zpG0PcdWXmyXWSLOO-pjO-RkH_vwgScPAZ10F1ToFpoSNNYnK0YLLgHx_Y4JzzWuAKix_ljX8U9mmJHMfaGGwEqK5wTCVF6W5JNKdG7WxUj3kIgmyI/s1600/8.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="175" data-original-width="416" height="134" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjMH3EMermiMtz9hKbZB6NjdOeX5zpG0PcdWXmyXWSLOO-pjO-RkH_vwgScPAZ10F1ToFpoSNNYnK0YLLgHx_Y4JzzWuAKix_ljX8U9mmJHMfaGGwEqK5wTCVF6W5JNKdG7WxUj3kIgmyI/s320/8.png" width="320" /></a></div>
<div class="MsoNormal" style="direction: ltr; unicode-bidi: embed;">
<span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 107%; mso-ascii-theme-font: major-bidi; mso-bidi-theme-font: major-bidi; mso-hansi-theme-font: major-bidi;"><br /></span></div>
<div class="MsoNormal" style="direction: ltr; unicode-bidi: embed;">
<span class="MsoHyperlink"><span style="color: windowtext; font-family: "Times New Roman", serif; font-size: 12pt; line-height: 107%;">If we have:<o:p></o:p></span></span></div>
<div class="MsoNormal" style="direction: ltr; unicode-bidi: embed;">
<span class="MsoHyperlink"><span style="color: windowtext; font-family: "Times New Roman", serif; font-size: 12pt; line-height: 107%;"><br /></span></span></div>
<br />
<div class="MsoNormal" style="direction: ltr; unicode-bidi: embed;">
<span class="MsoHyperlink"><span style="color: windowtext; font-family: "Times New Roman", serif; font-size: 12pt; line-height: 107%;"> m = 3kg<o:p></o:p></span></span></div>
<div class="MsoNormal" style="direction: ltr; unicode-bidi: embed;">
<span class="MsoHyperlink"><span style="color: windowtext; font-family: "Times New Roman", serif; font-size: 12pt; line-height: 107%;"><br /></span></span></div>
<div class="MsoNormal" style="direction: ltr; unicode-bidi: embed;">
<span class="MsoHyperlink"><span style="color: windowtext; font-family: "Times New Roman", serif; font-size: 12pt; line-height: 107%;">r = 0.21 m<o:p></o:p></span></span></div>
<div class="MsoNormal" style="direction: ltr; unicode-bidi: embed;">
<span class="MsoHyperlink"><span style="color: windowtext; font-family: "Times New Roman", serif; font-size: 12pt; line-height: 107%;"><br /></span></span></div>
<div class="MsoNormal" style="direction: ltr; unicode-bidi: embed;">
<span class="MsoHyperlink"><span style="color: windowtext; font-family: "Times New Roman", serif; font-size: 12pt; line-height: 107%;">R = 1.2 m <o:p></o:p></span></span></div>
<div class="MsoNormal" style="direction: ltr; unicode-bidi: embed;">
<span class="MsoHyperlink"><span style="color: windowtext; font-family: "Times New Roman", serif; font-size: 12pt; line-height: 107%;"><br /></span></span></div>
<div class="MsoNormal" style="direction: ltr; unicode-bidi: embed;">
<span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 107%; mso-ascii-theme-font: major-bidi; mso-bidi-theme-font: major-bidi; mso-hansi-theme-font: major-bidi;">
</span></div>
<div class="MsoNormal" style="direction: ltr; unicode-bidi: embed;">
<span class="MsoHyperlink"><span style="color: windowtext; font-family: "Times New Roman", serif; font-size: 12pt; line-height: 107%;">I found 276 models that some of them are as follows:<o:p></o:p></span></span></div>
<div class="MsoNormal" style="direction: ltr; unicode-bidi: embed;">
<span class="MsoHyperlink"><span style="color: windowtext; font-family: "Times New Roman", serif; font-size: 12pt; line-height: 107%;"><br /></span></span></div>
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiNV6D6nVSYr4iwKmvI89o3q6Dhnjyf29yUE_ku_UXw_9j7SHmCLCX6gopUqeiMnXZhTpM1Ca-EN-GJ9DWH8eb07zsMQtpo_D-QqSQzzmW1zWpnsSxWyTjaFvWLl2XiZ9fHvsydfZKkHKU/s1600/9.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="521" data-original-width="357" height="320" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiNV6D6nVSYr4iwKmvI89o3q6Dhnjyf29yUE_ku_UXw_9j7SHmCLCX6gopUqeiMnXZhTpM1Ca-EN-GJ9DWH8eb07zsMQtpo_D-QqSQzzmW1zWpnsSxWyTjaFvWLl2XiZ9fHvsydfZKkHKU/s320/9.png" width="219" /></a></div>
<div class="MsoNormal" style="direction: ltr; unicode-bidi: embed;">
<span class="MsoHyperlink"><span style="color: windowtext; font-family: "Times New Roman", serif; font-size: 12pt; line-height: 107%;"><br /></span></span></div>
<div class="MsoNormal" style="direction: ltr; unicode-bidi: embed;">
<span class="MsoHyperlink"><span style="color: windowtext; font-family: "Times New Roman", serif; font-size: 12pt; line-height: 107%;"></span></span></div>
<div class="MsoNormal" style="direction: ltr; unicode-bidi: embed;">
<span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 107%; mso-ascii-theme-font: major-bidi; mso-bidi-theme-font: major-bidi; mso-hansi-theme-font: major-bidi;">For testing of these models, I use model (1) in above table and we
can see the results as follows:<o:p></o:p></span></div>
<div class="MsoNormal" style="direction: ltr; unicode-bidi: embed;">
<span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 107%; mso-ascii-theme-font: major-bidi; mso-bidi-theme-font: major-bidi; mso-hansi-theme-font: major-bidi;"><br /></span></div>
<div class="MsoNormal" style="direction: ltr; unicode-bidi: embed;">
<br /></div>
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjkamTKO2aU0CgnXi5PuiHYnm3WaPftvKDkpPsBlYyJiq82UdHG4ZLx24cpzgremaIp9Z-VXWADlQfgsOKWxL_vVkjBztgmKbkM6LdAZDO4L-wvbReSRSGonkw4igPPR-DYp8y5rqCtDiQ/s1600/10.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="211" data-original-width="457" height="147" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjkamTKO2aU0CgnXi5PuiHYnm3WaPftvKDkpPsBlYyJiq82UdHG4ZLx24cpzgremaIp9Z-VXWADlQfgsOKWxL_vVkjBztgmKbkM6LdAZDO4L-wvbReSRSGonkw4igPPR-DYp8y5rqCtDiQ/s320/10.png" width="320" /></a></div>
<div class="MsoNormal" style="direction: ltr; unicode-bidi: embed;">
<span class="MsoHyperlink"><span style="color: windowtext; font-family: "Times New Roman", serif; font-size: 12pt; line-height: 107%;">If we have:<o:p></o:p></span></span></div>
<div class="MsoNormal" style="direction: ltr; unicode-bidi: embed;">
<span class="MsoHyperlink"><span style="color: windowtext; font-family: "Times New Roman", serif; font-size: 12pt; line-height: 107%;"><br /></span></span></div>
<div class="MsoNormal" style="direction: ltr; unicode-bidi: embed;">
<span class="MsoHyperlink"><span style="color: windowtext; font-family: "Times New Roman", serif; font-size: 12pt; line-height: 107%;"> m = 3kg<o:p></o:p></span></span></div>
<div class="MsoNormal" style="direction: ltr; unicode-bidi: embed;">
<span class="MsoHyperlink"><span style="color: windowtext; font-family: "Times New Roman", serif; font-size: 12pt; line-height: 107%;"><br /></span></span></div>
<div class="MsoNormal" style="direction: ltr; unicode-bidi: embed;">
<span class="MsoHyperlink"><span style="color: windowtext; font-family: "Times New Roman", serif; font-size: 12pt; line-height: 107%;">r = 0.24 m<o:p></o:p></span></span></div>
<div class="MsoNormal" style="direction: ltr; unicode-bidi: embed;">
<span class="MsoHyperlink"><span style="color: windowtext; font-family: "Times New Roman", serif; font-size: 12pt; line-height: 107%;"><br /></span></span></div>
<div class="MsoNormal" style="direction: ltr; unicode-bidi: embed;">
<span class="MsoHyperlink"><span style="color: windowtext; font-family: "Times New Roman", serif; font-size: 12pt; line-height: 107%;">R = 0.7 m <o:p></o:p></span></span></div>
<div class="MsoNormal" style="direction: ltr; unicode-bidi: embed;">
<span class="MsoHyperlink"><span style="color: windowtext; font-family: "Times New Roman", serif; font-size: 12pt; line-height: 107%;"><br /></span></span></div>
<div class="MsoNormal" style="direction: ltr; unicode-bidi: embed;">
</div>
<div class="MsoNormal" style="direction: ltr; unicode-bidi: embed;">
<span class="MsoHyperlink"><span style="color: windowtext; font-family: "Times New Roman", serif; font-size: 12pt; line-height: 107%;">I found 276 models that some of them are as follows:<o:p></o:p></span></span></div>
<div class="MsoNormal" style="direction: ltr; unicode-bidi: embed;">
<span class="MsoHyperlink"><span style="color: windowtext; font-family: "Times New Roman", serif; font-size: 12pt; line-height: 107%;"><br /></span></span></div>
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiAcxWys4xDxdBmMLZ0xfO_tsII0UdTUZ-TPUKZbg0qOMlrNPkwHoR5ZUdgzLtjNTa5FuBR_TGI0VxRgyfvpIvEiNuR_LjurzKNbWiyuCSD3F5RYLbQOLLGtnSPZ4BJjCuiWYi8lzKYqhQ/s1600/11.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="522" data-original-width="420" height="320" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiAcxWys4xDxdBmMLZ0xfO_tsII0UdTUZ-TPUKZbg0qOMlrNPkwHoR5ZUdgzLtjNTa5FuBR_TGI0VxRgyfvpIvEiNuR_LjurzKNbWiyuCSD3F5RYLbQOLLGtnSPZ4BJjCuiWYi8lzKYqhQ/s320/11.png" width="257" /></a></div>
<div class="MsoNormal" style="direction: ltr; unicode-bidi: embed;">
<span class="MsoHyperlink"><span style="color: windowtext; font-family: "Times New Roman", serif; font-size: 12pt; line-height: 107%;"><br /></span></span></div>
<div class="MsoNormal" style="direction: ltr; unicode-bidi: embed;">
<span class="MsoHyperlink"><span style="color: windowtext; font-family: "Times New Roman", serif; font-size: 12pt; line-height: 107%;"></span></span></div>
<div class="MsoNormal" style="direction: ltr; unicode-bidi: embed;">
<span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 107%; mso-ascii-theme-font: major-bidi; mso-bidi-theme-font: major-bidi; mso-hansi-theme-font: major-bidi;">For testing of these models, I use model (1) in above table and we
can see the results as follows:<o:p></o:p></span></div>
<div class="MsoNormal" style="direction: ltr; unicode-bidi: embed;">
<span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 107%; mso-ascii-theme-font: major-bidi; mso-bidi-theme-font: major-bidi; mso-hansi-theme-font: major-bidi;"><br /></span></div>
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhASgwqyCfrjVsymLDSOJNgTouh3dbw7MxbYfiTP6kUd5gZ7qr2Qr9JAhoICHcLRThJzWRO68TtB9G04Z9l_pvELroa8w2WQdzFEVUzCTN2FuVBcK1RuMZ28M9WlxzSoUyRf0LYzT6d0GI/s1600/12.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="226" data-original-width="535" height="135" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhASgwqyCfrjVsymLDSOJNgTouh3dbw7MxbYfiTP6kUd5gZ7qr2Qr9JAhoICHcLRThJzWRO68TtB9G04Z9l_pvELroa8w2WQdzFEVUzCTN2FuVBcK1RuMZ28M9WlxzSoUyRf0LYzT6d0GI/s320/12.png" width="320" /></a></div>
<div class="MsoNormal" style="direction: ltr; unicode-bidi: embed;">
<span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 107%; mso-ascii-theme-font: major-bidi; mso-bidi-theme-font: major-bidi; mso-hansi-theme-font: major-bidi;"><br /></span></div>
<div class="MsoNormal" style="direction: ltr; unicode-bidi: embed;">
<b><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 107%; mso-ascii-theme-font: major-bidi; mso-bidi-theme-font: major-bidi; mso-hansi-theme-font: major-bidi;">Conclusion<o:p></o:p></span></b></div>
<div class="MsoNormal" style="direction: ltr; unicode-bidi: embed;">
<b><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 107%; mso-ascii-theme-font: major-bidi; mso-bidi-theme-font: major-bidi; mso-hansi-theme-font: major-bidi;"><br /></span></b></div>
<div class="MsoNormal" style="direction: ltr; unicode-bidi: embed;">
<span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 107%; mso-ascii-theme-font: major-bidi; mso-bidi-theme-font: major-bidi; mso-hansi-theme-font: major-bidi;">
</span></div>
<div class="MsoNormal" style="direction: ltr; unicode-bidi: embed;">
<span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 107%; mso-ascii-theme-font: major-bidi; mso-bidi-theme-font: major-bidi; mso-hansi-theme-font: major-bidi;">Suppose you are squeezing a sponge by your hand and assume that the
work done by your hand will stay the constant. How can you say that you are
controlling the potential energy throughout the sponge when you deform the
sponge and change the location of particles of the sponge?<o:p></o:p></span></div>
<div class="MsoNormal" style="direction: ltr; unicode-bidi: embed;">
<span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 107%; mso-ascii-theme-font: major-bidi; mso-bidi-theme-font: major-bidi; mso-hansi-theme-font: major-bidi;"><br /></span></div>
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhFlfWkOH3GtGlqCdevjgyGRtHEiltErMSpAP074m88TOU6EjyvCNJSsWZgLzz3j7GIZeykOIqQnBi_tWihrVOakT5rtjvrtq0bF51ru5yej2JG-tDyIOenjtiyNH95HJnOHvdxvpr9jU0/s1600/13.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="665" data-original-width="947" height="224" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhFlfWkOH3GtGlqCdevjgyGRtHEiltErMSpAP074m88TOU6EjyvCNJSsWZgLzz3j7GIZeykOIqQnBi_tWihrVOakT5rtjvrtq0bF51ru5yej2JG-tDyIOenjtiyNH95HJnOHvdxvpr9jU0/s320/13.png" width="320" /></a></div>
<div class="MsoNormal" style="direction: ltr; unicode-bidi: embed;">
<span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 107%; mso-ascii-theme-font: major-bidi; mso-bidi-theme-font: major-bidi; mso-hansi-theme-font: major-bidi;"><br /></span></div>
<div class="MsoNormal" dir="LTR" style="direction: ltr; unicode-bidi: embed;">
<span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 107%; mso-ascii-theme-font: major-bidi; mso-bidi-theme-font: major-bidi; mso-hansi-theme-font: major-bidi;">In physics, the
people usually use the vector fields, gradient vectors, curl and so on. But the
problem is, to encounter with the chaos systems in the nature in which you are
not able to find a real function for your subject. In this case, the people
usually use the methods of the boundary conditions. <o:p></o:p></span></div>
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<span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 107%; mso-ascii-theme-font: major-bidi; mso-bidi-theme-font: major-bidi; mso-hansi-theme-font: major-bidi;">
</span></div>
<div class="MsoNormal" dir="LTR" style="direction: ltr; unicode-bidi: embed;">
<span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 107%; mso-ascii-theme-font: major-bidi; mso-bidi-theme-font: major-bidi; mso-hansi-theme-font: major-bidi;">I think that
the method mentioned in above article can help us to solve the problems which are
defined as the chaos systems. <o:p></o:p></span></div>
<br /></div>
Gholamreza Soleimanihttp://www.blogger.com/profile/03273527405719420253noreply@blogger.com0tag:blogger.com,1999:blog-392703582366288634.post-8019366624608234042018-04-25T19:27:00.002+04:302018-05-14T15:04:09.232+04:30The Distances among The Particles in The Space (1)<div dir="ltr" style="text-align: left;" trbidi="on">
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<span dir="LTR" style="font-family: "times new roman" , "serif"; font-size: 12.0pt; line-height: 107%;">In physics and engineering, the distances among the particles is
usually an important factor for analysis of the subject especially when we are
studying Newton’s law of universal gravitation in mechanic, Coulomb’s law in
electricity, Maxwell’s equations in electromagnetic theory and so on. But, do you think that the application of the theorems in related to the distances among the particles is limited to above laws in classic physics? Definitely no. The most crucial thing is to predict a flexible system which is moving. For instance, suppose you have a bowl filled by water in your hand. When you move, how can you predict the motion of water system into the bowl? Of course, when we are speaking about a rigid system, the prediction and analysis of this system is easy just like when you are moving by a car (an approximately rigid system).</span></div>
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<span dir="LTR" style="font-family: "times new roman" , "serif"; font-size: 12.0pt; line-height: 107%;">In the reference with article of “A Specific Permutation And
Applications (1)” (</span><span dir="LTR"><a href="http://www.emfps.org/2018/03/a-specific-permutation.html"><span style="font-family: "times new roman" , "serif"; font-size: 12.0pt; line-height: 107%;">http://www.emfps.org/2018/03/a-specific-permutation.html</span></a></span><span dir="LTR" style="font-family: "times new roman" , "serif"; font-size: 12.0pt; line-height: 107%;">), we can derive many conjectures (or theorems) or properties in
related to the distances among the particles in the space. Consequently, this
could be conducted as a big project in which I will not be able to handle this
project alone.<o:p></o:p></span></div>
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<span dir="LTR" style="font-family: "times new roman" , "serif"; font-size: 12.0pt; line-height: 107%;"><span style="mso-spacerun: yes;"> </span>In this series, I will post
little by little these new properties accompanied by examples only related to Newton's law of universal gravitation in mechanic. Since I am using
the big data analysis to extract these properties, I have not any pure
mathematics proof for them. Therefore, I will mark up them as the Conjectures
instead of the Theorems.<b><i> As the matter of fact, this is the Big Data Analysis with Microsoft excel to create the value from data.</i></b><o:p></o:p></span></div>
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<span dir="LTR" style="font-family: "times new roman" , "serif"; font-size: 12.0pt; line-height: 107%;"><br /></span>
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<b><span dir="LTR" style="font-family: "times new roman" , "serif"; font-size: 12.0pt; line-height: 107%;">Conjecture (1): <o:p></o:p></span></b></div>
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<b><span dir="LTR" style="font-family: "times new roman" , "serif"; font-size: 12.0pt; line-height: 107%;"><br /></span></b></div>
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<span dir="LTR" style="font-family: "times new roman" , "serif"; font-size: 12.0pt; line-height: 107%;">
</span></div>
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<span dir="LTR" style="font-family: "times new roman" , "serif"; font-size: 12.0pt; line-height: 107%;">If above article (A Specific Permutation…) has been applied for
only three choices from many events (sample space), we will have the concentric
spheres or layered spheres just like below figure:<o:p></o:p></span></div>
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<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjd74ZVHfIl6lO_YZMPvtcFLcw-Nsz4c9hL-Dz5bxSHqIESsfG3ZFlZBW3c0_NIl-XdajijOA8I70K59kC8FVGuTqlkSd1r650RDmPi518V173nzhl7c3rsSEuLABD9gjze4vr96BwVHxE/s1600/1.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="499" data-original-width="588" height="271" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjd74ZVHfIl6lO_YZMPvtcFLcw-Nsz4c9hL-Dz5bxSHqIESsfG3ZFlZBW3c0_NIl-XdajijOA8I70K59kC8FVGuTqlkSd1r650RDmPi518V173nzhl7c3rsSEuLABD9gjze4vr96BwVHxE/s320/1.png" width="320" /></a></div>
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<span dir="LTR" style="font-family: "times new roman" , "serif"; font-size: 12.0pt; line-height: 107%;"><br /></span></div>
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<span dir="LTR" style="font-family: "times new roman" , "serif"; font-size: 12.0pt; line-height: 107%;">In previous article, I told you a specific permutation with n = 6
and r =3, gives us 48 points on a sphere, If we increase the sample space (n)
to 8 and r = 3, we will have 4 concentric spheres which gives us 48 points on
each sphere and for n = 10, we will have 10 concentric spheres which gives us
48 points on each sphere and for n = 12, we will have 20 concentric spheres
which gives us 48 points on each sphere and etc..<o:p></o:p></span></div>
<div align="right" class="MsoNormal" dir="RTL" style="text-align: left;">
<b><i><span dir="LTR" style="font-family: "times new roman" , "serif"; font-size: 12.0pt; line-height: 107%;">In fact, the number of the layered spheres can be calculated by
using previous equation divided to </span></i></b></div>
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<b><i><span dir="LTR" style="font-family: "times new roman" , "serif"; font-size: 12.0pt; line-height: 107%;">48.<o:p></o:p></span></i></b></div>
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<b><i><span dir="LTR" style="font-family: "times new roman" , "serif"; font-size: 12.0pt; line-height: 107%;"><br /></span></i></b></div>
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<b><i><span dir="LTR" style="font-family: "times new roman" , "serif"; font-size: 12.0pt; line-height: 107%;">Note: I will again comeback to this conjecture as soon as possible.<o:p></o:p></span></i></b></div>
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<b><i><span dir="LTR" style="font-family: "times new roman" , "serif"; font-size: 12.0pt; line-height: 107%;"><br /></span></i></b></div>
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<b><span dir="LTR" style="font-family: "times new roman" , "serif"; font-size: 12.0pt; line-height: 107%;">Conjecture (2): <o:p></o:p></span></b></div>
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<b><span dir="LTR" style="font-family: "times new roman" , "serif"; font-size: 12.0pt; line-height: 107%;"><br /></span></b></div>
<br />
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<b><i><span dir="LTR" style="font-family: "times new roman" , "serif"; font-size: 12.0pt; line-height: 107%;">The distance of each point on a sphere is equal to at least five
pair points on the same sphere.</span></i></b><span dir="LTR" style="font-family: "times new roman" , "serif"; font-size: 12.0pt; line-height: 107%;"> <o:p></o:p></span></div>
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<b><i><span dir="LTR" style="font-family: "times new roman" , "serif"; font-size: 12.0pt; line-height: 107%;">Suppose points P1, P2, P3, P4, P5, P6, P7, P8, P9, P10, P11 have
been located on a sphere. This conjecture says to us:<o:p></o:p></span></i></b></div>
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<b><i><span dir="LTR" style="font-family: "times new roman" , "serif"; font-size: 12.0pt; line-height: 107%;"><br /></span></i></b></div>
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<b><i><span dir="LTR" style="font-family: "times new roman" , "serif"; font-size: 12.0pt; line-height: 107%;">d (P1, P2) = d (P1, P3) = A<o:p></o:p></span></i></b></div>
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<b><i><span dir="LTR" style="font-family: "times new roman" , "serif"; font-size: 12.0pt; line-height: 107%;"><br /></span></i></b></div>
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<b><i><span dir="LTR" style="font-family: "times new roman" , "serif"; font-size: 12.0pt; line-height: 107%;">d (P1, P4) = d (P1, P5) = B<o:p></o:p></span></i></b></div>
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<b><i><span dir="LTR" style="font-family: "times new roman" , "serif"; font-size: 12.0pt; line-height: 107%;"><br /></span></i></b></div>
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<b><i><span dir="LTR" style="font-family: "times new roman" , "serif"; font-size: 12.0pt; line-height: 107%;">d (P1, P6) = d (P1, P7) = C<o:p></o:p></span></i></b></div>
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<b><i><span dir="LTR" style="font-family: "times new roman" , "serif"; font-size: 12.0pt; line-height: 107%;"><br /></span></i></b></div>
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<b><i><span dir="LTR" style="font-family: "times new roman" , "serif"; font-size: 12.0pt; line-height: 107%;">d (P1, P8) = d (P1, P9) = D<o:p></o:p></span></i></b></div>
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<b><i><span dir="LTR" style="font-family: "times new roman" , "serif"; font-size: 12.0pt; line-height: 107%;"><br /></span></i></b></div>
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<b><i><span dir="LTR" style="font-family: "times new roman" , "serif"; font-size: 12.0pt; line-height: 107%;">d (P1, P10) = d (P1, P11) =
E<o:p></o:p></span></i></b></div>
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<b><i><span dir="LTR" style="font-family: "times new roman" , "serif"; font-size: 12.0pt; line-height: 107%;"><br /></span></i></b></div>
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<b><i><span dir="LTR" style="font-family: "times new roman" , "serif"; font-size: 12.0pt; line-height: 107%;">Where: <o:p></o:p></span></i></b></div>
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<b><i><span dir="LTR" style="font-family: "times new roman" , "serif"; font-size: 12.0pt; line-height: 107%;"><br /></span></i></b></div>
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<b><i><span dir="LTR" style="font-family: "times new roman" , "serif"; font-size: 12.0pt; line-height: 107%;">d (P1, P2) = the distance between point P1 to P2<o:p></o:p></span></i></b></div>
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<b><i><span dir="LTR" style="font-family: "times new roman" , "serif"; font-size: 12.0pt; line-height: 107%;"><br /></span></i></b></div>
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<b><i><span dir="LTR" style="font-family: "times new roman" , "serif"; font-size: 12.0pt; line-height: 107%;">The amounts of A, B, C, D, E are the members of real number</span></i></b><b><i><span lang="FA" style="font-family: "times new roman" , "serif"; font-size: 12.0pt; line-height: 107%;"><o:p></o:p></span></i></b></div>
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<b><i><span dir="LTR" style="font-family: "times new roman" , "serif"; font-size: 12.0pt; line-height: 107%;"><br /></span></i></b></div>
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<b><i><span dir="LTR" style="font-family: "times new roman" , "serif"; font-size: 12.0pt; line-height: 107%;">Note: I will again comeback to this conjecture as soon as possible.</span></i></b><b><i><span dir="LTR" style="font-family: "times new roman" , "serif"; mso-ascii-theme-font: major-bidi; mso-bidi-theme-font: major-bidi; mso-hansi-theme-font: major-bidi;"><o:p></o:p></span></i></b></div>
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<br /></div>
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<b><span dir="LTR" style="font-family: "times new roman" , "serif"; font-size: 12.0pt; line-height: 107%;">Conjecture (3): <o:p></o:p></span></b></div>
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<b><span dir="LTR" style="font-family: "times new roman" , "serif"; font-size: 12.0pt; line-height: 107%;"><br /></span></b></div>
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<b><i><span dir="LTR" style="font-family: "times new roman" , "serif"; font-size: 12.0pt; line-height: 107%;">The distances among the points P1(x, y, z), P2 (z, x, y) and P3(y,
z, x) are always the same.<o:p></o:p></span></i></b></div>
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<b><i><span dir="LTR" style="font-family: "times new roman" , "serif"; font-size: 12.0pt; line-height: 107%;">d (P1, P2) = d (P1, P3) = d (P2, P3)<o:p></o:p></span></i></b></div>
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<b><i><span dir="LTR" style="font-family: "times new roman" , "serif"; font-size: 12.0pt; line-height: 107%;"><br /></span></i></b></div>
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<span dir="LTR" style="font-family: "times new roman" , "serif"; font-size: 12.0pt; line-height: 107%;">Example:<o:p></o:p></span></div>
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<span dir="LTR" style="font-family: "times new roman" , "serif"; font-size: 12.0pt; line-height: 107%;"><br /></span></div>
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<span dir="LTR" style="font-family: "times new roman" , "serif"; font-size: 12.0pt; line-height: 107%;">Suppose point P1 has below coordination:<o:p></o:p></span></div>
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<span dir="LTR" style="font-family: "times new roman" , "serif"; font-size: 12.0pt; line-height: 107%;"><br /></span></div>
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<span dir="LTR" style="font-family: "times new roman" , "serif"; font-size: 12.0pt; line-height: 107%;">P1 (3, -5, 11)<o:p></o:p></span></div>
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<span dir="LTR" style="font-family: "times new roman" , "serif"; font-size: 12.0pt; line-height: 107%;"><br /></span></div>
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<span dir="LTR" style="font-family: "times new roman" , "serif"; font-size: 12.0pt; line-height: 107%;">Therefore, the coordination P1 and P2 will be:<o:p></o:p></span></div>
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<span dir="LTR" style="font-family: "times new roman" , "serif"; font-size: 12.0pt; line-height: 107%;"><br /></span></div>
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<span dir="LTR" style="font-family: "times new roman" , "serif"; font-size: 12.0pt; line-height: 107%;">P2 (11, 3, -5)<o:p></o:p></span></div>
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<span dir="LTR" style="font-family: "times new roman" , "serif"; font-size: 12.0pt; line-height: 107%;"><br /></span></div>
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<span dir="LTR" style="font-family: "times new roman" , "serif"; font-size: 12.0pt; line-height: 107%;">P3 (-5, 11, 3)<o:p></o:p></span></div>
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<span dir="LTR" style="font-family: "times new roman" , "serif"; font-size: 12.0pt; line-height: 107%;"><br /></span></div>
<div class="MsoNormal" style="text-align: left;">
<span dir="LTR" style="font-family: "times new roman" , "serif"; font-size: 12.0pt; line-height: 107%;">d (P1, P2) = d (P1, P3) = d (P2, P3) = 19.59592<o:p></o:p></span></div>
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<span dir="LTR" style="font-family: "times new roman" , "serif"; font-size: 12.0pt; line-height: 107%;"><br /></span></div>
<div class="MsoNormal" style="text-align: left;">
<span dir="LTR" style="font-family: "times new roman" , "serif"; font-size: 12.0pt; line-height: 107%;">Let me tell you an example about Newton’s law of universal
gravitation as follows:<o:p></o:p></span></div>
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<br /></div>
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<b><span dir="LTR" style="font-family: "times new roman" , "serif"; font-size: 12.0pt; line-height: 107%;">The Mapping A System of Three Particles for Given Gravity Potential
Energy And The Distance<o:p></o:p></span></b></div>
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<b><span dir="LTR" style="font-family: "times new roman" , "serif"; font-size: 12.0pt; line-height: 107%;"><br /></span></b></div>
<div class="MsoNormal" style="text-align: left;">
<span style="font-family: "times new roman" , "serif"; font-size: 12.0pt; line-height: 107%;">Suppose
we have three particles P1, P2 and P3 with the distances among them in
infinity which have the masses of m1,
m2 and m3. If an external force brings all these particles in new location just
like below figure, how can we calculate total work done on them?</span></div>
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<span style="font-family: "times new roman" , "serif"; font-size: 12.0pt; line-height: 107%;"><br /></span></div>
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<span style="font-family: "times new roman" , "serif"; font-size: 12.0pt; line-height: 107%;"><br /></span></div>
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEg6-s7sXLiXAp8TUSv27V3v1yjdLZzFSU4JBIqeFKevgOnrDad6XFQO7rPCBGQOnlKrENZ88Dw1W47B2uBh0NvBEl7WW3bAqGPPwNrHCcVgnukSlLxS5FnVMMZUjGdmWnOrRlE1bdEmjDo/s1600/2.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="358" data-original-width="601" height="190" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEg6-s7sXLiXAp8TUSv27V3v1yjdLZzFSU4JBIqeFKevgOnrDad6XFQO7rPCBGQOnlKrENZ88Dw1W47B2uBh0NvBEl7WW3bAqGPPwNrHCcVgnukSlLxS5FnVMMZUjGdmWnOrRlE1bdEmjDo/s320/2.png" width="320" /></a></div>
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<span style="font-family: "times new roman" , "serif"; font-size: 12.0pt; line-height: 107%;"><br /></span></div>
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<span style="font-family: "times new roman" , "serif"; font-size: 12.0pt; line-height: 107%;"></span></div>
<div class="MsoNormal" style="text-align: left;">
<span dir="LTR" style="font-family: "times new roman" , "serif"; font-size: 12.0pt; line-height: 107%;">It is clear; the work done on particles is equal to total gravity
potential energy of system but in opposite direction in which we can write
below equation for total gravity potential energy of system:<o:p></o:p></span></div>
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjRVjiNywWq2e_hz7NpLJJrrV7I00AMxnMVf6qX60gjHTRneQ3myFKSV2_Imbi86VLC7ryJvVeHntAWoBWIfOIo37cEmFLiEhyphenhyphenOB8sjnvuJV0AfGnCbso9U4yt6PSb6n3fVZa0ZrqVvDm8/s1600/3.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="114" data-original-width="537" height="67" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjRVjiNywWq2e_hz7NpLJJrrV7I00AMxnMVf6qX60gjHTRneQ3myFKSV2_Imbi86VLC7ryJvVeHntAWoBWIfOIo37cEmFLiEhyphenhyphenOB8sjnvuJV0AfGnCbso9U4yt6PSb6n3fVZa0ZrqVvDm8/s320/3.png" width="320" /></a></div>
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<span dir="LTR" style="font-family: "times new roman" , "serif"; font-size: 12.0pt; line-height: 107%;">Where:<o:p></o:p></span></div>
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<span dir="LTR" style="font-family: "times new roman" , "serif"; font-size: 12.0pt; line-height: 107%;">G = Gravitational constant = </span><span dir="LTR">6.672E-11
(N.m2/kg2)<o:p></o:p></span></div>
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<span dir="LTR"><br /></span></div>
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<span dir="LTR" style="font-family: "times new roman" , "serif"; font-size: 12.0pt; line-height: 107%;">U (r) = </span><span dir="LTR" style="font-family: "times new roman" , "serif"; font-size: 12.0pt; line-height: 107%;">total
gravity potential energy of system (J) <o:p></o:p></span></div>
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<span dir="LTR" style="font-family: "times new roman" , "serif"; font-size: 12.0pt; line-height: 107%;">r = the distance among the particles (m)</span></div>
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<span dir="LTR" style="font-family: "times new roman" , "serif"; font-size: 12.0pt; line-height: 107%;"><o:p></o:p></span><span dir="LTR" style="font-family: "times new roman" , "serif"; font-size: 12.0pt; line-height: 107%;">m1, m2,m3 = mass (kg)</span><span dir="LTR" style="font-family: "times new roman" , "serif"; font-size: 12.0pt; line-height: 107%;"><o:p></o:p></span></div>
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<b><u><span dir="LTR" style="font-family: "times new roman" , "serif"; font-size: 12.0pt; line-height: 107%;">Question (1):<o:p></o:p></span></u></b></div>
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<b><u><span dir="LTR" style="font-family: "times new roman" , "serif"; font-size: 12.0pt; line-height: 107%;"><br /></span></u></b></div>
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<span dir="LTR" style="font-family: "times new roman" , "serif"; font-size: 12.0pt; line-height: 107%;">If we have:<o:p></o:p></span></div>
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<span dir="LTR" style="font-family: "times new roman" , "serif"; font-size: 12.0pt; line-height: 107%;">U (r) = </span><span dir="LTR" style="font-family: "times new roman" , serif; font-size: 12pt; line-height: 107%;">-0.04143312
J<o:p></o:p></span></div>
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<span dir="LTR" style="font-family: "times new roman" , serif; font-size: 12pt; line-height: 107%;">r = 0.0002 m<o:p></o:p></span></div>
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<span dir="LTR" style="font-family: "times new roman" , serif; font-size: 12pt; line-height: 107%;">How can we map these particles in the space?<o:p></o:p></span></div>
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<b><span style="font-family: "times new roman" , serif; font-size: 12pt; line-height: 107%;">Step (1)</span></b><span style="font-family: "times new roman" , serif; font-size: 12pt; line-height: 107%;">: <o:p></o:p></span></div>
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<span style="font-family: "times new roman" , serif; font-size: 12pt; line-height: 107%;">To find masses of particles, we should apply the
method mentioned in article of “</span><span style="font-family: "times new roman" , "serif"; font-size: 12.0pt; line-height: 107%;">Solving
a Nonlinear Equation with Many Independent Variables” (</span><a href="http://www.emfps.org/2016/10/can-we-solve-nonlinear-equation-with.html"><span style="font-family: "times new roman" , "serif"; font-size: 12.0pt; line-height: 107%;">http://www.emfps.org/2016/10/can-we-solve-nonlinear-equation-with.html</span></a><span class="MsoHyperlink"><span style="font-family: "times new roman" , "serif"; font-size: 12.0pt; line-height: 107%;">)<o:p></o:p></span></span></div>
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<span style="font-family: "times new roman" , "serif"; font-size: 12.0pt; line-height: 107%;">I found 6 answers for mass of the particles:<o:p></o:p></span></div>
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<b><span style="font-family: "times new roman" , serif; font-size: 12pt;">m1<o:p></o:p></span></b></div>
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<b><span style="font-family: "times new roman" , serif; font-size: 12pt;">m2<o:p></o:p></span></b></div>
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<b><span style="font-family: "times new roman" , serif; font-size: 12pt;">m3<o:p></o:p></span></b></div>
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<span style="font-family: "times new roman" , serif; font-size: 12pt;">6<o:p></o:p></span></div>
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<span style="font-family: "times new roman" , serif; font-size: 12pt;">300<o:p></o:p></span></div>
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<span style="font-family: "times new roman" , serif; font-size: 12pt;">400<o:p></o:p></span></div>
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<span style="font-family: "times new roman" , serif; font-size: 12pt;">6<o:p></o:p></span></div>
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<span style="font-family: "times new roman" , serif; font-size: 12pt;">400<o:p></o:p></span></div>
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<span style="font-family: "times new roman" , serif; font-size: 12pt;">300<o:p></o:p></span></div>
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<span style="font-family: "times new roman" , serif; font-size: 12pt;">15<o:p></o:p></span></div>
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<span style="font-family: "times new roman" , serif; font-size: 12pt;">380<o:p></o:p></span></div>
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<span style="font-family: "times new roman" , serif; font-size: 12pt;">300<o:p></o:p></span></div>
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<span style="font-family: "times new roman" , serif; font-size: 12pt;">22<o:p></o:p></span></div>
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<span style="font-family: "times new roman" , serif; font-size: 12pt;">100<o:p></o:p></span></div>
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<span style="font-family: "times new roman" , serif; font-size: 12pt;">1000<o:p></o:p></span></div>
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<span style="font-family: "times new roman" , serif; font-size: 12pt;">40<o:p></o:p></span></div>
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<span style="font-family: "times new roman" , serif; font-size: 12pt;">130<o:p></o:p></span></div>
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<span style="font-family: "times new roman" , serif; font-size: 12pt;">700<o:p></o:p></span></div>
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<span style="font-family: "times new roman" , serif; font-size: 12pt;">40<o:p></o:p></span></div>
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<span style="font-family: "times new roman" , serif; font-size: 12pt;">330<o:p></o:p></span></div>
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<span style="font-family: "times new roman" , serif; font-size: 12pt;">300<o:p></o:p></span></div>
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<br /></div>
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<b><span style="font-family: "times new roman" , "serif"; font-size: 12.0pt; line-height: 107%;">Step (2)</span></b><span style="font-family: "times new roman" , "serif"; font-size: 12.0pt; line-height: 107%;">: <o:p></o:p></span></div>
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<span style="font-family: "times new roman" , "serif"; font-size: 12.0pt; line-height: 107%;">Since the distance is equal to 0.0002 m, we can find the
coordination of particle P1 by using the model presented in article of “A Model
to Track the Location of a Particle in the Space” (</span><a href="http://www.emfps.org/2018/02/a-model-to-track-location-of-particle.html"><span style="font-family: "times new roman" , "serif"; font-size: 12.0pt; line-height: 107%;">http://www.emfps.org/2018/02/a-model-to-track-location-of-particle.html</span></a><span class="MsoHyperlink"><span style="font-family: "times new roman" , "serif"; font-size: 12.0pt; line-height: 107%;">)</span></span><span class="MsoHyperlink"><span style="font-family: "times new roman" , serif; font-size: 12pt; line-height: 107%;"><o:p></o:p></span></span></div>
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<span dir="LTR" style="font-family: "times new roman" , "serif"; font-size: 12.0pt; line-height: 107%;">
</span></div>
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<span class="MsoHyperlink"><span style="font-family: "times new roman" , serif; font-size: 12pt; line-height: 107%;">I found 408 answers for coordination of particle P1
as follows:<o:p></o:p></span></span></div>
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<span class="MsoHyperlink"><span style="font-family: "times new roman" , serif; font-size: 12pt; line-height: 107%;"><br /></span></span></div>
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<span class="MsoHyperlink"><span style="font-family: "times new roman" , serif; font-size: 12pt; line-height: 107%;">Here I have posted some of the results:</span></span></div>
<div class="MsoNormal" style="text-align: left; unicode-bidi: embed;">
<span class="MsoHyperlink"><span style="font-family: "times new roman" , serif; font-size: 12pt; line-height: 107%;"><br /></span></span></div>
<div class="MsoNormal" style="text-align: left; unicode-bidi: embed;">
<span class="MsoHyperlink"><span style="font-family: "times new roman" , serif; font-size: 12pt; line-height: 107%;"></span></span></div>
<table border="0" cellpadding="0" cellspacing="0" class="MsoNormalTable" style="border-collapse: collapse; margin-left: 4.65pt; mso-padding-alt: 0cm 5.4pt 0cm 5.4pt; mso-yfti-tbllook: 1184; width: 256px;">
<tbody>
<tr style="height: 15.0pt; mso-yfti-firstrow: yes; mso-yfti-irow: 0;">
<td nowrap="" style="border: solid windowtext 1.0pt; height: 15.0pt; mso-border-alt: solid windowtext .5pt; padding: 0cm 5.4pt 0cm 5.4pt; width: 48.0pt;" width="64"><div align="center" class="MsoNormal" style="direction: ltr; line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; text-align: center; unicode-bidi: embed;">
<b>Models<o:p></o:p></b></div>
</td>
<td nowrap="" style="border-left: none; border: solid windowtext 1.0pt; height: 15.0pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt; padding: 0cm 5.4pt 0cm 5.4pt; width: 48.0pt;" width="64"><div align="center" class="MsoNormal" style="direction: ltr; line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; text-align: center; unicode-bidi: embed;">
<b>x<o:p></o:p></b></div>
</td>
<td nowrap="" style="border-left: none; border: solid windowtext 1.0pt; height: 15.0pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt; padding: 0cm 5.4pt 0cm 5.4pt; width: 48.0pt;" width="64"><div align="center" class="MsoNormal" style="direction: ltr; line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; text-align: center; unicode-bidi: embed;">
<b>y<o:p></o:p></b></div>
</td>
<td nowrap="" style="border-left: none; border: solid windowtext 1.0pt; height: 15.0pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt; padding: 0cm 5.4pt 0cm 5.4pt; width: 48.0pt;" width="64"><div align="center" class="MsoNormal" style="direction: ltr; line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; text-align: center; unicode-bidi: embed;">
<b>z<o:p></o:p></b></div>
</td>
</tr>
<tr style="height: 15.0pt; mso-yfti-irow: 1;">
<td nowrap="" style="border-top: none; border: solid windowtext 1.0pt; height: 15.0pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; padding: 0cm 5.4pt 0cm 5.4pt; width: 48.0pt;" valign="bottom" width="64"><div align="right" class="MsoNormal" style="direction: ltr; line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; text-align: right; unicode-bidi: embed;">
1<o:p></o:p></div>
</td>
<td nowrap="" style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 15.0pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; padding: 0cm 5.4pt 0cm 5.4pt; width: 48.0pt;" valign="bottom" width="64"><div align="right" class="MsoNormal" style="direction: ltr; line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; text-align: right; unicode-bidi: embed;">
-0.0005<o:p></o:p></div>
</td>
<td nowrap="" style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 15.0pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; padding: 0cm 5.4pt 0cm 5.4pt; width: 48.0pt;" valign="bottom" width="64"><div align="right" class="MsoNormal" style="direction: ltr; line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; text-align: right; unicode-bidi: embed;">
-0.00047<o:p></o:p></div>
</td>
<td nowrap="" style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 15.0pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; padding: 0cm 5.4pt 0cm 5.4pt; width: 48.0pt;" valign="bottom" width="64"><div align="right" class="MsoNormal" style="direction: ltr; line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; text-align: right; unicode-bidi: embed;">
-0.00035<o:p></o:p></div>
</td>
</tr>
<tr style="height: 15.0pt; mso-yfti-irow: 2;">
<td nowrap="" style="border-top: none; border: solid windowtext 1.0pt; height: 15.0pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; padding: 0cm 5.4pt 0cm 5.4pt; width: 48.0pt;" valign="bottom" width="64"><div align="right" class="MsoNormal" style="direction: ltr; line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; text-align: right; unicode-bidi: embed;">
2<o:p></o:p></div>
</td>
<td nowrap="" style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 15.0pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; padding: 0cm 5.4pt 0cm 5.4pt; width: 48.0pt;" valign="bottom" width="64"><div align="right" class="MsoNormal" style="direction: ltr; line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; text-align: right; unicode-bidi: embed;">
-0.0005<o:p></o:p></div>
</td>
<td nowrap="" style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 15.0pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; padding: 0cm 5.4pt 0cm 5.4pt; width: 48.0pt;" valign="bottom" width="64"><div align="right" class="MsoNormal" style="direction: ltr; line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; text-align: right; unicode-bidi: embed;">
-0.00037<o:p></o:p></div>
</td>
<td nowrap="" style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 15.0pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; padding: 0cm 5.4pt 0cm 5.4pt; width: 48.0pt;" valign="bottom" width="64"><div align="right" class="MsoNormal" style="direction: ltr; line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; text-align: right; unicode-bidi: embed;">
-0.00035<o:p></o:p></div>
</td>
</tr>
<tr style="height: 15.0pt; mso-yfti-irow: 3;">
<td nowrap="" style="border-top: none; border: solid windowtext 1.0pt; height: 15.0pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; padding: 0cm 5.4pt 0cm 5.4pt; width: 48.0pt;" valign="bottom" width="64"><div align="right" class="MsoNormal" style="direction: ltr; line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; text-align: right; unicode-bidi: embed;">
3<o:p></o:p></div>
</td>
<td nowrap="" style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 15.0pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; padding: 0cm 5.4pt 0cm 5.4pt; width: 48.0pt;" valign="bottom" width="64"><div align="right" class="MsoNormal" style="direction: ltr; line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; text-align: right; unicode-bidi: embed;">
-0.0005<o:p></o:p></div>
</td>
<td nowrap="" style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 15.0pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; padding: 0cm 5.4pt 0cm 5.4pt; width: 48.0pt;" valign="bottom" width="64"><div align="right" class="MsoNormal" style="direction: ltr; line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; text-align: right; unicode-bidi: embed;">
-0.00035<o:p></o:p></div>
</td>
<td nowrap="" style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 15.0pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; padding: 0cm 5.4pt 0cm 5.4pt; width: 48.0pt;" valign="bottom" width="64"><div align="right" class="MsoNormal" style="direction: ltr; line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; text-align: right; unicode-bidi: embed;">
-0.00047<o:p></o:p></div>
</td>
</tr>
<tr style="height: 15.0pt; mso-yfti-irow: 4;">
<td nowrap="" style="border-top: none; border: solid windowtext 1.0pt; height: 15.0pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; padding: 0cm 5.4pt 0cm 5.4pt; width: 48.0pt;" valign="bottom" width="64"><div align="right" class="MsoNormal" style="direction: ltr; line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; text-align: right; unicode-bidi: embed;">
4<o:p></o:p></div>
</td>
<td nowrap="" style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 15.0pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; padding: 0cm 5.4pt 0cm 5.4pt; width: 48.0pt;" valign="bottom" width="64"><div align="right" class="MsoNormal" style="direction: ltr; line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; text-align: right; unicode-bidi: embed;">
-0.0005<o:p></o:p></div>
</td>
<td nowrap="" style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 15.0pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; padding: 0cm 5.4pt 0cm 5.4pt; width: 48.0pt;" valign="bottom" width="64"><div align="right" class="MsoNormal" style="direction: ltr; line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; text-align: right; unicode-bidi: embed;">
-0.00035<o:p></o:p></div>
</td>
<td nowrap="" style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 15.0pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; padding: 0cm 5.4pt 0cm 5.4pt; width: 48.0pt;" valign="bottom" width="64"><div align="right" class="MsoNormal" style="direction: ltr; line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; text-align: right; unicode-bidi: embed;">
-0.00037<o:p></o:p></div>
</td>
</tr>
<tr style="height: 15.0pt; mso-yfti-irow: 5;">
<td nowrap="" style="border-top: none; border: solid windowtext 1.0pt; height: 15.0pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; padding: 0cm 5.4pt 0cm 5.4pt; width: 48.0pt;" valign="bottom" width="64"><div align="right" class="MsoNormal" style="direction: ltr; line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; text-align: right; unicode-bidi: embed;">
5<o:p></o:p></div>
</td>
<td nowrap="" style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 15.0pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; padding: 0cm 5.4pt 0cm 5.4pt; width: 48.0pt;" valign="bottom" width="64"><div align="right" class="MsoNormal" style="direction: ltr; line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; text-align: right; unicode-bidi: embed;">
-0.00047<o:p></o:p></div>
</td>
<td nowrap="" style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 15.0pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; padding: 0cm 5.4pt 0cm 5.4pt; width: 48.0pt;" valign="bottom" width="64"><div align="right" class="MsoNormal" style="direction: ltr; line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; text-align: right; unicode-bidi: embed;">
-0.0005<o:p></o:p></div>
</td>
<td nowrap="" style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 15.0pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; padding: 0cm 5.4pt 0cm 5.4pt; width: 48.0pt;" valign="bottom" width="64"><div align="right" class="MsoNormal" style="direction: ltr; line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; text-align: right; unicode-bidi: embed;">
-0.00035<o:p></o:p></div>
</td>
</tr>
<tr style="height: 15.0pt; mso-yfti-irow: 6;">
<td nowrap="" style="border-top: none; border: solid windowtext 1.0pt; height: 15.0pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; padding: 0cm 5.4pt 0cm 5.4pt; width: 48.0pt;" valign="bottom" width="64"><div align="right" class="MsoNormal" style="direction: ltr; line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; text-align: right; unicode-bidi: embed;">
6<o:p></o:p></div>
</td>
<td nowrap="" style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 15.0pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; padding: 0cm 5.4pt 0cm 5.4pt; width: 48.0pt;" valign="bottom" width="64"><div align="right" class="MsoNormal" style="direction: ltr; line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; text-align: right; unicode-bidi: embed;">
-0.00047<o:p></o:p></div>
</td>
<td nowrap="" style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 15.0pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; padding: 0cm 5.4pt 0cm 5.4pt; width: 48.0pt;" valign="bottom" width="64"><div align="right" class="MsoNormal" style="direction: ltr; line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; text-align: right; unicode-bidi: embed;">
-0.00045<o:p></o:p></div>
</td>
<td nowrap="" style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 15.0pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; padding: 0cm 5.4pt 0cm 5.4pt; width: 48.0pt;" valign="bottom" width="64"><div align="right" class="MsoNormal" style="direction: ltr; line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; text-align: right; unicode-bidi: embed;">
-0.00032<o:p></o:p></div>
</td>
</tr>
<tr style="height: 15.0pt; mso-yfti-irow: 7;">
<td nowrap="" style="border-top: none; border: solid windowtext 1.0pt; height: 15.0pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; padding: 0cm 5.4pt 0cm 5.4pt; width: 48.0pt;" valign="bottom" width="64"><div align="right" class="MsoNormal" style="direction: ltr; line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; text-align: right; unicode-bidi: embed;">
7<o:p></o:p></div>
</td>
<td nowrap="" style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 15.0pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; padding: 0cm 5.4pt 0cm 5.4pt; width: 48.0pt;" valign="bottom" width="64"><div align="right" class="MsoNormal" style="direction: ltr; line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; text-align: right; unicode-bidi: embed;">
-0.00047<o:p></o:p></div>
</td>
<td nowrap="" style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 15.0pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; padding: 0cm 5.4pt 0cm 5.4pt; width: 48.0pt;" valign="bottom" width="64"><div align="right" class="MsoNormal" style="direction: ltr; line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; text-align: right; unicode-bidi: embed;">
-0.00035<o:p></o:p></div>
</td>
<td nowrap="" style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 15.0pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; padding: 0cm 5.4pt 0cm 5.4pt; width: 48.0pt;" valign="bottom" width="64"><div align="right" class="MsoNormal" style="direction: ltr; line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; text-align: right; unicode-bidi: embed;">
-0.0005<o:p></o:p></div>
</td>
</tr>
<tr style="height: 15.0pt; mso-yfti-irow: 8;">
<td nowrap="" style="border-top: none; border: solid windowtext 1.0pt; height: 15.0pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; padding: 0cm 5.4pt 0cm 5.4pt; width: 48.0pt;" valign="bottom" width="64"><div align="right" class="MsoNormal" style="direction: ltr; line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; text-align: right; unicode-bidi: embed;">
8<o:p></o:p></div>
</td>
<td nowrap="" style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 15.0pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; padding: 0cm 5.4pt 0cm 5.4pt; width: 48.0pt;" valign="bottom" width="64"><div align="right" class="MsoNormal" style="direction: ltr; line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; text-align: right; unicode-bidi: embed;">
-0.00047<o:p></o:p></div>
</td>
<td nowrap="" style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 15.0pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; padding: 0cm 5.4pt 0cm 5.4pt; width: 48.0pt;" valign="bottom" width="64"><div align="right" class="MsoNormal" style="direction: ltr; line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; text-align: right; unicode-bidi: embed;">
-0.00035<o:p></o:p></div>
</td>
<td nowrap="" style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 15.0pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; padding: 0cm 5.4pt 0cm 5.4pt; width: 48.0pt;" valign="bottom" width="64"><div align="right" class="MsoNormal" style="direction: ltr; line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; text-align: right; unicode-bidi: embed;">
-0.00032<o:p></o:p></div>
</td>
</tr>
<tr style="height: 15.0pt; mso-yfti-irow: 9;">
<td nowrap="" style="border-top: none; border: solid windowtext 1.0pt; height: 15.0pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; padding: 0cm 5.4pt 0cm 5.4pt; width: 48.0pt;" valign="bottom" width="64"><div align="right" class="MsoNormal" style="direction: ltr; line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; text-align: right; unicode-bidi: embed;">
9<o:p></o:p></div>
</td>
<td nowrap="" style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 15.0pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; padding: 0cm 5.4pt 0cm 5.4pt; width: 48.0pt;" valign="bottom" width="64"><div align="right" class="MsoNormal" style="direction: ltr; line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; text-align: right; unicode-bidi: embed;">
-0.00047<o:p></o:p></div>
</td>
<td nowrap="" style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 15.0pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; padding: 0cm 5.4pt 0cm 5.4pt; width: 48.0pt;" valign="bottom" width="64"><div align="right" class="MsoNormal" style="direction: ltr; line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; text-align: right; unicode-bidi: embed;">
-0.00032<o:p></o:p></div>
</td>
<td nowrap="" style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 15.0pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; padding: 0cm 5.4pt 0cm 5.4pt; width: 48.0pt;" valign="bottom" width="64"><div align="right" class="MsoNormal" style="direction: ltr; line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; text-align: right; unicode-bidi: embed;">
-0.00045<o:p></o:p></div>
</td>
</tr>
<tr style="height: 15.0pt; mso-yfti-irow: 10;">
<td nowrap="" style="border-top: none; border: solid windowtext 1.0pt; height: 15.0pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; padding: 0cm 5.4pt 0cm 5.4pt; width: 48.0pt;" valign="bottom" width="64"><div align="right" class="MsoNormal" style="direction: ltr; line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; text-align: right; unicode-bidi: embed;">
10<o:p></o:p></div>
</td>
<td nowrap="" style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 15.0pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; padding: 0cm 5.4pt 0cm 5.4pt; width: 48.0pt;" valign="bottom" width="64"><div align="right" class="MsoNormal" style="direction: ltr; line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; text-align: right; unicode-bidi: embed;">
-0.00047<o:p></o:p></div>
</td>
<td nowrap="" style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 15.0pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; padding: 0cm 5.4pt 0cm 5.4pt; width: 48.0pt;" valign="bottom" width="64"><div align="right" class="MsoNormal" style="direction: ltr; line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; text-align: right; unicode-bidi: embed;">
-0.00032<o:p></o:p></div>
</td>
<td nowrap="" style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 15.0pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; padding: 0cm 5.4pt 0cm 5.4pt; width: 48.0pt;" valign="bottom" width="64"><div align="right" class="MsoNormal" style="direction: ltr; line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; text-align: right; unicode-bidi: embed;">
-0.00035<o:p></o:p></div>
</td>
</tr>
<tr style="height: 15.0pt; mso-yfti-irow: 11;">
<td nowrap="" style="border-top: none; border: solid windowtext 1.0pt; height: 15.0pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; padding: 0cm 5.4pt 0cm 5.4pt; width: 48.0pt;" valign="bottom" width="64"><div align="right" class="MsoNormal" style="direction: ltr; line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; text-align: right; unicode-bidi: embed;">
11<o:p></o:p></div>
</td>
<td nowrap="" style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 15.0pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; padding: 0cm 5.4pt 0cm 5.4pt; width: 48.0pt;" valign="bottom" width="64"><div align="right" class="MsoNormal" style="direction: ltr; line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; text-align: right; unicode-bidi: embed;">
-0.00045<o:p></o:p></div>
</td>
<td nowrap="" style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 15.0pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; padding: 0cm 5.4pt 0cm 5.4pt; width: 48.0pt;" valign="bottom" width="64"><div align="right" class="MsoNormal" style="direction: ltr; line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; text-align: right; unicode-bidi: embed;">
-0.00047<o:p></o:p></div>
</td>
<td nowrap="" style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 15.0pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; padding: 0cm 5.4pt 0cm 5.4pt; width: 48.0pt;" valign="bottom" width="64"><div align="right" class="MsoNormal" style="direction: ltr; line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; text-align: right; unicode-bidi: embed;">
-0.00032<o:p></o:p></div>
</td>
</tr>
<tr style="height: 15.0pt; mso-yfti-irow: 12;">
<td nowrap="" style="border-top: none; border: solid windowtext 1.0pt; height: 15.0pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; padding: 0cm 5.4pt 0cm 5.4pt; width: 48.0pt;" valign="bottom" width="64"><div align="right" class="MsoNormal" style="direction: ltr; line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; text-align: right; unicode-bidi: embed;">
12<o:p></o:p></div>
</td>
<td nowrap="" style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 15.0pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; padding: 0cm 5.4pt 0cm 5.4pt; width: 48.0pt;" valign="bottom" width="64"><div align="right" class="MsoNormal" style="direction: ltr; line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; text-align: right; unicode-bidi: embed;">
-0.00045<o:p></o:p></div>
</td>
<td nowrap="" style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 15.0pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; padding: 0cm 5.4pt 0cm 5.4pt; width: 48.0pt;" valign="bottom" width="64"><div align="right" class="MsoNormal" style="direction: ltr; line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; text-align: right; unicode-bidi: embed;">
-0.00042<o:p></o:p></div>
</td>
<td nowrap="" style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 15.0pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; padding: 0cm 5.4pt 0cm 5.4pt; width: 48.0pt;" valign="bottom" width="64"><div align="right" class="MsoNormal" style="direction: ltr; line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; text-align: right; unicode-bidi: embed;">
-0.00029<o:p></o:p></div>
</td>
</tr>
<tr style="height: 15.0pt; mso-yfti-irow: 13; mso-yfti-lastrow: yes;">
<td nowrap="" style="border-top: none; border: solid windowtext 1.0pt; height: 15.0pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; padding: 0cm 5.4pt 0cm 5.4pt; width: 48.0pt;" valign="bottom" width="64"><div align="right" class="MsoNormal" style="direction: ltr; line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; text-align: right; unicode-bidi: embed;">
13<o:p></o:p></div>
</td>
<td nowrap="" style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 15.0pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; padding: 0cm 5.4pt 0cm 5.4pt; width: 48.0pt;" valign="bottom" width="64"><div align="right" class="MsoNormal" style="direction: ltr; line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; text-align: right; unicode-bidi: embed;">
-0.00045<o:p></o:p></div>
</td>
<td nowrap="" style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 15.0pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; padding: 0cm 5.4pt 0cm 5.4pt; width: 48.0pt;" valign="bottom" width="64"><div align="right" class="MsoNormal" style="direction: ltr; line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; text-align: right; unicode-bidi: embed;">
-0.00032<o:p></o:p></div>
</td>
<td nowrap="" style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 15.0pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; padding: 0cm 5.4pt 0cm 5.4pt; width: 48.0pt;" valign="bottom" width="64"><div align="right" class="MsoNormal" style="direction: ltr; line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; text-align: right; unicode-bidi: embed;">
-0.00047<o:p></o:p></div>
</td>
</tr>
</tbody></table>
<div class="MsoNormal" style="text-align: left;">
<span style="font-family: "times new roman" , "serif"; font-size: 12.0pt; line-height: 107%;"><br /></span></div>
<table border="0" cellpadding="0" cellspacing="0" class="MsoNormalTable" style="border-collapse: collapse; margin-left: 4.65pt; mso-padding-alt: 0cm 5.4pt 0cm 5.4pt; mso-yfti-tbllook: 1184; width: 256px;">
<tbody>
<tr style="height: 15.0pt; mso-yfti-firstrow: yes; mso-yfti-irow: 0;">
<td nowrap="" style="border-top: none; border: solid windowtext 1.0pt; height: 15.0pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; padding: 0cm 5.4pt 0cm 5.4pt; width: 48.0pt;" valign="bottom" width="64"><div align="right" class="MsoNormal" style="direction: ltr; line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; text-align: right; unicode-bidi: embed;">
14<o:p></o:p></div>
</td>
<td nowrap="" style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 15.0pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; padding: 0cm 5.4pt 0cm 5.4pt; width: 48.0pt;" valign="bottom" width="64"><div align="right" class="MsoNormal" style="direction: ltr; line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; text-align: right; unicode-bidi: embed;">
-0.00045<o:p></o:p></div>
</td>
<td nowrap="" style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 15.0pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; padding: 0cm 5.4pt 0cm 5.4pt; width: 48.0pt;" valign="bottom" width="64"><div align="right" class="MsoNormal" style="direction: ltr; line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; text-align: right; unicode-bidi: embed;">
-0.00032<o:p></o:p></div>
</td>
<td nowrap="" style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 15.0pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; padding: 0cm 5.4pt 0cm 5.4pt; width: 48.0pt;" valign="bottom" width="64"><div align="right" class="MsoNormal" style="direction: ltr; line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; text-align: right; unicode-bidi: embed;">
-0.00029<o:p></o:p></div>
</td>
</tr>
<tr style="height: 15.0pt; mso-yfti-irow: 1;">
<td nowrap="" style="border-top: none; border: solid windowtext 1.0pt; height: 15.0pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; padding: 0cm 5.4pt 0cm 5.4pt; width: 48.0pt;" valign="bottom" width="64"><div align="right" class="MsoNormal" style="direction: ltr; line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; text-align: right; unicode-bidi: embed;">
15<o:p></o:p></div>
</td>
<td nowrap="" style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 15.0pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; padding: 0cm 5.4pt 0cm 5.4pt; width: 48.0pt;" valign="bottom" width="64"><div align="right" class="MsoNormal" style="direction: ltr; line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; text-align: right; unicode-bidi: embed;">
-0.00045<o:p></o:p></div>
</td>
<td nowrap="" style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 15.0pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; padding: 0cm 5.4pt 0cm 5.4pt; width: 48.0pt;" valign="bottom" width="64"><div align="right" class="MsoNormal" style="direction: ltr; line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; text-align: right; unicode-bidi: embed;">
-0.00029<o:p></o:p></div>
</td>
<td nowrap="" style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 15.0pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; padding: 0cm 5.4pt 0cm 5.4pt; width: 48.0pt;" valign="bottom" width="64"><div align="right" class="MsoNormal" style="direction: ltr; line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; text-align: right; unicode-bidi: embed;">
-0.00042<o:p></o:p></div>
</td>
</tr>
<tr style="height: 15.0pt; mso-yfti-irow: 2;">
<td nowrap="" style="border-top: none; border: solid windowtext 1.0pt; height: 15.0pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; padding: 0cm 5.4pt 0cm 5.4pt; width: 48.0pt;" valign="bottom" width="64"><div align="right" class="MsoNormal" style="direction: ltr; line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; text-align: right; unicode-bidi: embed;">
16<o:p></o:p></div>
</td>
<td nowrap="" style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 15.0pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; padding: 0cm 5.4pt 0cm 5.4pt; width: 48.0pt;" valign="bottom" width="64"><div align="right" class="MsoNormal" style="direction: ltr; line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; text-align: right; unicode-bidi: embed;">
-0.00045<o:p></o:p></div>
</td>
<td nowrap="" style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 15.0pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; padding: 0cm 5.4pt 0cm 5.4pt; width: 48.0pt;" valign="bottom" width="64"><div align="right" class="MsoNormal" style="direction: ltr; line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; text-align: right; unicode-bidi: embed;">
-0.00029<o:p></o:p></div>
</td>
<td nowrap="" style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 15.0pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; padding: 0cm 5.4pt 0cm 5.4pt; width: 48.0pt;" valign="bottom" width="64"><div align="right" class="MsoNormal" style="direction: ltr; line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; text-align: right; unicode-bidi: embed;">
-0.00032<o:p></o:p></div>
</td>
</tr>
<tr style="height: 15.0pt; mso-yfti-irow: 3;">
<td nowrap="" style="border-top: none; border: solid windowtext 1.0pt; height: 15.0pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; padding: 0cm 5.4pt 0cm 5.4pt; width: 48.0pt;" valign="bottom" width="64"><div align="right" class="MsoNormal" style="direction: ltr; line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; text-align: right; unicode-bidi: embed;">
17<o:p></o:p></div>
</td>
<td nowrap="" style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 15.0pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; padding: 0cm 5.4pt 0cm 5.4pt; width: 48.0pt;" valign="bottom" width="64"><div align="right" class="MsoNormal" style="direction: ltr; line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; text-align: right; unicode-bidi: embed;">
-0.00042<o:p></o:p></div>
</td>
<td nowrap="" style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 15.0pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; padding: 0cm 5.4pt 0cm 5.4pt; width: 48.0pt;" valign="bottom" width="64"><div align="right" class="MsoNormal" style="direction: ltr; line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; text-align: right; unicode-bidi: embed;">
-0.00045<o:p></o:p></div>
</td>
<td nowrap="" style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 15.0pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; padding: 0cm 5.4pt 0cm 5.4pt; width: 48.0pt;" valign="bottom" width="64"><div align="right" class="MsoNormal" style="direction: ltr; line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; text-align: right; unicode-bidi: embed;">
-0.00029<o:p></o:p></div>
</td>
</tr>
<tr style="height: 15.0pt; mso-yfti-irow: 4;">
<td nowrap="" style="border-top: none; border: solid windowtext 1.0pt; height: 15.0pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; padding: 0cm 5.4pt 0cm 5.4pt; width: 48.0pt;" valign="bottom" width="64"><div align="right" class="MsoNormal" style="direction: ltr; line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; text-align: right; unicode-bidi: embed;">
18<o:p></o:p></div>
</td>
<td nowrap="" style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 15.0pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; padding: 0cm 5.4pt 0cm 5.4pt; width: 48.0pt;" valign="bottom" width="64"><div align="right" class="MsoNormal" style="direction: ltr; line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; text-align: right; unicode-bidi: embed;">
-0.00042<o:p></o:p></div>
</td>
<td nowrap="" style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 15.0pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; padding: 0cm 5.4pt 0cm 5.4pt; width: 48.0pt;" valign="bottom" width="64"><div align="right" class="MsoNormal" style="direction: ltr; line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; text-align: right; unicode-bidi: embed;">
-0.0004<o:p></o:p></div>
</td>
<td nowrap="" style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 15.0pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; padding: 0cm 5.4pt 0cm 5.4pt; width: 48.0pt;" valign="bottom" width="64"><div align="right" class="MsoNormal" style="direction: ltr; line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; text-align: right; unicode-bidi: embed;">
-0.00027<o:p></o:p></div>
</td>
</tr>
<tr style="height: 15.0pt; mso-yfti-irow: 5;">
<td nowrap="" style="border-top: none; border: solid windowtext 1.0pt; height: 15.0pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; padding: 0cm 5.4pt 0cm 5.4pt; width: 48.0pt;" valign="bottom" width="64"><div align="right" class="MsoNormal" style="direction: ltr; line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; text-align: right; unicode-bidi: embed;">
19<o:p></o:p></div>
</td>
<td nowrap="" style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 15.0pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; padding: 0cm 5.4pt 0cm 5.4pt; width: 48.0pt;" valign="bottom" width="64"><div align="right" class="MsoNormal" style="direction: ltr; line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; text-align: right; unicode-bidi: embed;">
-0.00042<o:p></o:p></div>
</td>
<td nowrap="" style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 15.0pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; padding: 0cm 5.4pt 0cm 5.4pt; width: 48.0pt;" valign="bottom" width="64"><div align="right" class="MsoNormal" style="direction: ltr; line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; text-align: right; unicode-bidi: embed;">
-0.00029<o:p></o:p></div>
</td>
<td nowrap="" style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 15.0pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; padding: 0cm 5.4pt 0cm 5.4pt; width: 48.0pt;" valign="bottom" width="64"><div align="right" class="MsoNormal" style="direction: ltr; line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; text-align: right; unicode-bidi: embed;">
-0.00045<o:p></o:p></div>
</td>
</tr>
<tr style="height: 15.0pt; mso-yfti-irow: 6;">
<td nowrap="" style="border-top: none; border: solid windowtext 1.0pt; height: 15.0pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; padding: 0cm 5.4pt 0cm 5.4pt; width: 48.0pt;" valign="bottom" width="64"><div align="right" class="MsoNormal" style="direction: ltr; line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; text-align: right; unicode-bidi: embed;">
20<o:p></o:p></div>
</td>
<td nowrap="" style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 15.0pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; padding: 0cm 5.4pt 0cm 5.4pt; width: 48.0pt;" valign="bottom" width="64"><div align="right" class="MsoNormal" style="direction: ltr; line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; text-align: right; unicode-bidi: embed;">
-0.00042<o:p></o:p></div>
</td>
<td nowrap="" style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 15.0pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; padding: 0cm 5.4pt 0cm 5.4pt; width: 48.0pt;" valign="bottom" width="64"><div align="right" class="MsoNormal" style="direction: ltr; line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; text-align: right; unicode-bidi: embed;">
-0.00029<o:p></o:p></div>
</td>
<td nowrap="" style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 15.0pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; padding: 0cm 5.4pt 0cm 5.4pt; width: 48.0pt;" valign="bottom" width="64"><div align="right" class="MsoNormal" style="direction: ltr; line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; text-align: right; unicode-bidi: embed;">
-0.00027<o:p></o:p></div>
</td>
</tr>
<tr style="height: 15.0pt; mso-yfti-irow: 7;">
<td nowrap="" style="border-top: none; border: solid windowtext 1.0pt; height: 15.0pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; padding: 0cm 5.4pt 0cm 5.4pt; width: 48.0pt;" valign="bottom" width="64"><div align="right" class="MsoNormal" style="direction: ltr; line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; text-align: right; unicode-bidi: embed;">
21<o:p></o:p></div>
</td>
<td nowrap="" style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 15.0pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; padding: 0cm 5.4pt 0cm 5.4pt; width: 48.0pt;" valign="bottom" width="64"><div align="right" class="MsoNormal" style="direction: ltr; line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; text-align: right; unicode-bidi: embed;">
-0.00042<o:p></o:p></div>
</td>
<td nowrap="" style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 15.0pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; padding: 0cm 5.4pt 0cm 5.4pt; width: 48.0pt;" valign="bottom" width="64"><div align="right" class="MsoNormal" style="direction: ltr; line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; text-align: right; unicode-bidi: embed;">
-0.00027<o:p></o:p></div>
</td>
<td nowrap="" style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 15.0pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; padding: 0cm 5.4pt 0cm 5.4pt; width: 48.0pt;" valign="bottom" width="64"><div align="right" class="MsoNormal" style="direction: ltr; line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; text-align: right; unicode-bidi: embed;">
-0.0004<o:p></o:p></div>
</td>
</tr>
<tr style="height: 15.0pt; mso-yfti-irow: 8;">
<td nowrap="" style="border-top: none; border: solid windowtext 1.0pt; height: 15.0pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; padding: 0cm 5.4pt 0cm 5.4pt; width: 48.0pt;" valign="bottom" width="64"><div align="right" class="MsoNormal" style="direction: ltr; line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; text-align: right; unicode-bidi: embed;">
22<o:p></o:p></div>
</td>
<td nowrap="" style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 15.0pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; padding: 0cm 5.4pt 0cm 5.4pt; width: 48.0pt;" valign="bottom" width="64"><div align="right" class="MsoNormal" style="direction: ltr; line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; text-align: right; unicode-bidi: embed;">
-0.00042<o:p></o:p></div>
</td>
<td nowrap="" style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 15.0pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; padding: 0cm 5.4pt 0cm 5.4pt; width: 48.0pt;" valign="bottom" width="64"><div align="right" class="MsoNormal" style="direction: ltr; line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; text-align: right; unicode-bidi: embed;">
-0.00027<o:p></o:p></div>
</td>
<td nowrap="" style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 15.0pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; padding: 0cm 5.4pt 0cm 5.4pt; width: 48.0pt;" valign="bottom" width="64"><div align="right" class="MsoNormal" style="direction: ltr; line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; text-align: right; unicode-bidi: embed;">
-0.00029<o:p></o:p></div>
</td>
</tr>
<tr style="height: 15.0pt; mso-yfti-irow: 9;">
<td nowrap="" style="border-top: none; border: solid windowtext 1.0pt; height: 15.0pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; padding: 0cm 5.4pt 0cm 5.4pt; width: 48.0pt;" valign="bottom" width="64"><div align="right" class="MsoNormal" style="direction: ltr; line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; text-align: right; unicode-bidi: embed;">
23<o:p></o:p></div>
</td>
<td nowrap="" style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 15.0pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; padding: 0cm 5.4pt 0cm 5.4pt; width: 48.0pt;" valign="bottom" width="64"><div align="right" class="MsoNormal" style="direction: ltr; line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; text-align: right; unicode-bidi: embed;">
-0.0004<o:p></o:p></div>
</td>
<td nowrap="" style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 15.0pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; padding: 0cm 5.4pt 0cm 5.4pt; width: 48.0pt;" valign="bottom" width="64"><div align="right" class="MsoNormal" style="direction: ltr; line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; text-align: right; unicode-bidi: embed;">
-0.00042<o:p></o:p></div>
</td>
<td nowrap="" style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 15.0pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; padding: 0cm 5.4pt 0cm 5.4pt; width: 48.0pt;" valign="bottom" width="64"><div align="right" class="MsoNormal" style="direction: ltr; line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; text-align: right; unicode-bidi: embed;">
-0.00027<o:p></o:p></div>
</td>
</tr>
<tr style="height: 15.0pt; mso-yfti-irow: 10;">
<td nowrap="" style="border-top: none; border: solid windowtext 1.0pt; height: 15.0pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; padding: 0cm 5.4pt 0cm 5.4pt; width: 48.0pt;" valign="bottom" width="64"><div align="right" class="MsoNormal" style="direction: ltr; line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; text-align: right; unicode-bidi: embed;">
24<o:p></o:p></div>
</td>
<td nowrap="" style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 15.0pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; padding: 0cm 5.4pt 0cm 5.4pt; width: 48.0pt;" valign="bottom" width="64"><div align="right" class="MsoNormal" style="direction: ltr; line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; text-align: right; unicode-bidi: embed;">
-0.0004<o:p></o:p></div>
</td>
<td nowrap="" style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 15.0pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; padding: 0cm 5.4pt 0cm 5.4pt; width: 48.0pt;" valign="bottom" width="64"><div align="right" class="MsoNormal" style="direction: ltr; line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; text-align: right; unicode-bidi: embed;">
-0.00037<o:p></o:p></div>
</td>
<td nowrap="" style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 15.0pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; padding: 0cm 5.4pt 0cm 5.4pt; width: 48.0pt;" valign="bottom" width="64"><div align="right" class="MsoNormal" style="direction: ltr; line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; text-align: right; unicode-bidi: embed;">
-0.00024<o:p></o:p></div>
</td>
</tr>
<tr style="height: 15.0pt; mso-yfti-irow: 11;">
<td nowrap="" style="border-top: none; border: solid windowtext 1.0pt; height: 15.0pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; padding: 0cm 5.4pt 0cm 5.4pt; width: 48.0pt;" valign="bottom" width="64"><div align="right" class="MsoNormal" style="direction: ltr; line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; text-align: right; unicode-bidi: embed;">
25<o:p></o:p></div>
</td>
<td nowrap="" style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 15.0pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; padding: 0cm 5.4pt 0cm 5.4pt; width: 48.0pt;" valign="bottom" width="64"><div align="right" class="MsoNormal" style="direction: ltr; line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; text-align: right; unicode-bidi: embed;">
-0.0004<o:p></o:p></div>
</td>
<td nowrap="" style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 15.0pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; padding: 0cm 5.4pt 0cm 5.4pt; width: 48.0pt;" valign="bottom" width="64"><div align="right" class="MsoNormal" style="direction: ltr; line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; text-align: right; unicode-bidi: embed;">
-0.00027<o:p></o:p></div>
</td>
<td nowrap="" style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 15.0pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; padding: 0cm 5.4pt 0cm 5.4pt; width: 48.0pt;" valign="bottom" width="64"><div align="right" class="MsoNormal" style="direction: ltr; line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; text-align: right; unicode-bidi: embed;">
-0.00042<o:p></o:p></div>
</td>
</tr>
<tr style="height: 15.0pt; mso-yfti-irow: 12;">
<td nowrap="" style="border-top: none; border: solid windowtext 1.0pt; height: 15.0pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; padding: 0cm 5.4pt 0cm 5.4pt; width: 48.0pt;" valign="bottom" width="64"><div align="right" class="MsoNormal" style="direction: ltr; line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; text-align: right; unicode-bidi: embed;">
26<o:p></o:p></div>
</td>
<td nowrap="" style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 15.0pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; padding: 0cm 5.4pt 0cm 5.4pt; width: 48.0pt;" valign="bottom" width="64"><div align="right" class="MsoNormal" style="direction: ltr; line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; text-align: right; unicode-bidi: embed;">
-0.0004<o:p></o:p></div>
</td>
<td nowrap="" style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 15.0pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; padding: 0cm 5.4pt 0cm 5.4pt; width: 48.0pt;" valign="bottom" width="64"><div align="right" class="MsoNormal" style="direction: ltr; line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; text-align: right; unicode-bidi: embed;">
-0.00027<o:p></o:p></div>
</td>
<td nowrap="" style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 15.0pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; padding: 0cm 5.4pt 0cm 5.4pt; width: 48.0pt;" valign="bottom" width="64"><div align="right" class="MsoNormal" style="direction: ltr; line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; text-align: right; unicode-bidi: embed;">
-0.00024<o:p></o:p></div>
</td>
</tr>
<tr style="height: 15.0pt; mso-yfti-irow: 13;">
<td nowrap="" style="border-top: none; border: solid windowtext 1.0pt; height: 15.0pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; padding: 0cm 5.4pt 0cm 5.4pt; width: 48.0pt;" valign="bottom" width="64"><div align="right" class="MsoNormal" style="direction: ltr; line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; text-align: right; unicode-bidi: embed;">
27<o:p></o:p></div>
</td>
<td nowrap="" style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 15.0pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; padding: 0cm 5.4pt 0cm 5.4pt; width: 48.0pt;" valign="bottom" width="64"><div align="right" class="MsoNormal" style="direction: ltr; line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; text-align: right; unicode-bidi: embed;">
-0.0004<o:p></o:p></div>
</td>
<td nowrap="" style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 15.0pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; padding: 0cm 5.4pt 0cm 5.4pt; width: 48.0pt;" valign="bottom" width="64"><div align="right" class="MsoNormal" style="direction: ltr; line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; text-align: right; unicode-bidi: embed;">
-0.00024<o:p></o:p></div>
</td>
<td nowrap="" style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 15.0pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; padding: 0cm 5.4pt 0cm 5.4pt; width: 48.0pt;" valign="bottom" width="64"><div align="right" class="MsoNormal" style="direction: ltr; line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; text-align: right; unicode-bidi: embed;">
-0.00037<o:p></o:p></div>
</td>
</tr>
<tr style="height: 15.0pt; mso-yfti-irow: 14;">
<td nowrap="" style="border-top: none; border: solid windowtext 1.0pt; height: 15.0pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; padding: 0cm 5.4pt 0cm 5.4pt; width: 48.0pt;" valign="bottom" width="64"><div align="right" class="MsoNormal" style="direction: ltr; line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; text-align: right; unicode-bidi: embed;">
28<o:p></o:p></div>
</td>
<td nowrap="" style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 15.0pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; padding: 0cm 5.4pt 0cm 5.4pt; width: 48.0pt;" valign="bottom" width="64"><div align="right" class="MsoNormal" style="direction: ltr; line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; text-align: right; unicode-bidi: embed;">
-0.0004<o:p></o:p></div>
</td>
<td nowrap="" style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 15.0pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; padding: 0cm 5.4pt 0cm 5.4pt; width: 48.0pt;" valign="bottom" width="64"><div align="right" class="MsoNormal" style="direction: ltr; line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; text-align: right; unicode-bidi: embed;">
-0.00024<o:p></o:p></div>
</td>
<td nowrap="" style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 15.0pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; padding: 0cm 5.4pt 0cm 5.4pt; width: 48.0pt;" valign="bottom" width="64"><div align="right" class="MsoNormal" style="direction: ltr; line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; text-align: right; unicode-bidi: embed;">
-0.00027<o:p></o:p></div>
</td>
</tr>
<tr style="height: 15.0pt; mso-yfti-irow: 15;">
<td nowrap="" style="border-top: none; border: solid windowtext 1.0pt; height: 15.0pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; padding: 0cm 5.4pt 0cm 5.4pt; width: 48.0pt;" valign="bottom" width="64"><div align="right" class="MsoNormal" style="direction: ltr; line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; text-align: right; unicode-bidi: embed;">
29<o:p></o:p></div>
</td>
<td nowrap="" style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 15.0pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; padding: 0cm 5.4pt 0cm 5.4pt; width: 48.0pt;" valign="bottom" width="64"><div align="right" class="MsoNormal" style="direction: ltr; line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; text-align: right; unicode-bidi: embed;">
-0.00037<o:p></o:p></div>
</td>
<td nowrap="" style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 15.0pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; padding: 0cm 5.4pt 0cm 5.4pt; width: 48.0pt;" valign="bottom" width="64"><div align="right" class="MsoNormal" style="direction: ltr; line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; text-align: right; unicode-bidi: embed;">
-0.0005<o:p></o:p></div>
</td>
<td nowrap="" style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 15.0pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; padding: 0cm 5.4pt 0cm 5.4pt; width: 48.0pt;" valign="bottom" width="64"><div align="right" class="MsoNormal" style="direction: ltr; line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; text-align: right; unicode-bidi: embed;">
-0.00035<o:p></o:p></div>
</td>
</tr>
<tr style="height: 15.0pt; mso-yfti-irow: 16;">
<td nowrap="" style="border-top: none; border: solid windowtext 1.0pt; height: 15.0pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; padding: 0cm 5.4pt 0cm 5.4pt; width: 48.0pt;" valign="bottom" width="64"><div align="right" class="MsoNormal" style="direction: ltr; line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; text-align: right; unicode-bidi: embed;">
30<o:p></o:p></div>
</td>
<td nowrap="" style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 15.0pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; padding: 0cm 5.4pt 0cm 5.4pt; width: 48.0pt;" valign="bottom" width="64"><div align="right" class="MsoNormal" style="direction: ltr; line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; text-align: right; unicode-bidi: embed;">
-0.00037<o:p></o:p></div>
</td>
<td nowrap="" style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 15.0pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; padding: 0cm 5.4pt 0cm 5.4pt; width: 48.0pt;" valign="bottom" width="64"><div align="right" class="MsoNormal" style="direction: ltr; line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; text-align: right; unicode-bidi: embed;">
-0.0004<o:p></o:p></div>
</td>
<td nowrap="" style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 15.0pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; padding: 0cm 5.4pt 0cm 5.4pt; width: 48.0pt;" valign="bottom" width="64"><div align="right" class="MsoNormal" style="direction: ltr; line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; text-align: right; unicode-bidi: embed;">
-0.00024<o:p></o:p></div>
</td>
</tr>
<tr style="height: 15.0pt; mso-yfti-irow: 17;">
<td nowrap="" style="border-top: none; border: solid windowtext 1.0pt; height: 15.0pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; padding: 0cm 5.4pt 0cm 5.4pt; width: 48.0pt;" valign="bottom" width="64"><div align="right" class="MsoNormal" style="direction: ltr; line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; text-align: right; unicode-bidi: embed;">
31<o:p></o:p></div>
</td>
<td nowrap="" style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 15.0pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; padding: 0cm 5.4pt 0cm 5.4pt; width: 48.0pt;" valign="bottom" width="64"><div align="right" class="MsoNormal" style="direction: ltr; line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; text-align: right; unicode-bidi: embed;">
-0.00037<o:p></o:p></div>
</td>
<td nowrap="" style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 15.0pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; padding: 0cm 5.4pt 0cm 5.4pt; width: 48.0pt;" valign="bottom" width="64"><div align="right" class="MsoNormal" style="direction: ltr; line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; text-align: right; unicode-bidi: embed;">
-0.00035<o:p></o:p></div>
</td>
<td nowrap="" style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 15.0pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; padding: 0cm 5.4pt 0cm 5.4pt; width: 48.0pt;" valign="bottom" width="64"><div align="right" class="MsoNormal" style="direction: ltr; line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; text-align: right; unicode-bidi: embed;">
-0.0005<o:p></o:p></div>
</td>
</tr>
<tr style="height: 15.0pt; mso-yfti-irow: 18;">
<td nowrap="" style="border-top: none; border: solid windowtext 1.0pt; height: 15.0pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; padding: 0cm 5.4pt 0cm 5.4pt; width: 48.0pt;" valign="bottom" width="64"><div align="right" class="MsoNormal" style="direction: ltr; line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; text-align: right; unicode-bidi: embed;">
32<o:p></o:p></div>
</td>
<td nowrap="" style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 15.0pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; padding: 0cm 5.4pt 0cm 5.4pt; width: 48.0pt;" valign="bottom" width="64"><div align="right" class="MsoNormal" style="direction: ltr; line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; text-align: right; unicode-bidi: embed;">
-0.00037<o:p></o:p></div>
</td>
<td nowrap="" style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 15.0pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; padding: 0cm 5.4pt 0cm 5.4pt; width: 48.0pt;" valign="bottom" width="64"><div align="right" class="MsoNormal" style="direction: ltr; line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; text-align: right; unicode-bidi: embed;">
-0.00035<o:p></o:p></div>
</td>
<td nowrap="" style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 15.0pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; padding: 0cm 5.4pt 0cm 5.4pt; width: 48.0pt;" valign="bottom" width="64"><div align="right" class="MsoNormal" style="direction: ltr; line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; text-align: right; unicode-bidi: embed;">
-0.00022<o:p></o:p></div>
</td>
</tr>
<tr style="height: 15.0pt; mso-yfti-irow: 19;">
<td nowrap="" style="border-top: none; border: solid windowtext 1.0pt; height: 15.0pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; padding: 0cm 5.4pt 0cm 5.4pt; width: 48.0pt;" valign="bottom" width="64"><div align="right" class="MsoNormal" style="direction: ltr; line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; text-align: right; unicode-bidi: embed;">
33<o:p></o:p></div>
</td>
<td nowrap="" style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 15.0pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; padding: 0cm 5.4pt 0cm 5.4pt; width: 48.0pt;" valign="bottom" width="64"><div align="right" class="MsoNormal" style="direction: ltr; line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; text-align: right; unicode-bidi: embed;">
-0.00037<o:p></o:p></div>
</td>
<td nowrap="" style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 15.0pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; padding: 0cm 5.4pt 0cm 5.4pt; width: 48.0pt;" valign="bottom" width="64"><div align="right" class="MsoNormal" style="direction: ltr; line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; text-align: right; unicode-bidi: embed;">
-0.00024<o:p></o:p></div>
</td>
<td nowrap="" style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 15.0pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; padding: 0cm 5.4pt 0cm 5.4pt; width: 48.0pt;" valign="bottom" width="64"><div align="right" class="MsoNormal" style="direction: ltr; line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; text-align: right; unicode-bidi: embed;">
-0.0004<o:p></o:p></div>
</td>
</tr>
<tr style="height: 15.0pt; mso-yfti-irow: 20;">
<td nowrap="" style="border-top: none; border: solid windowtext 1.0pt; height: 15.0pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; padding: 0cm 5.4pt 0cm 5.4pt; width: 48.0pt;" valign="bottom" width="64"><div align="right" class="MsoNormal" style="direction: ltr; line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; text-align: right; unicode-bidi: embed;">
34<o:p></o:p></div>
</td>
<td nowrap="" style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 15.0pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; padding: 0cm 5.4pt 0cm 5.4pt; width: 48.0pt;" valign="bottom" width="64"><div align="right" class="MsoNormal" style="direction: ltr; line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; text-align: right; unicode-bidi: embed;">
-0.00037<o:p></o:p></div>
</td>
<td nowrap="" style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 15.0pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; padding: 0cm 5.4pt 0cm 5.4pt; width: 48.0pt;" valign="bottom" width="64"><div align="right" class="MsoNormal" style="direction: ltr; line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; text-align: right; unicode-bidi: embed;">
-0.00024<o:p></o:p></div>
</td>
<td nowrap="" style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 15.0pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; padding: 0cm 5.4pt 0cm 5.4pt; width: 48.0pt;" valign="bottom" width="64"><div align="right" class="MsoNormal" style="direction: ltr; line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; text-align: right; unicode-bidi: embed;">
-0.00022<o:p></o:p></div>
</td>
</tr>
<tr style="height: 15.0pt; mso-yfti-irow: 21;">
<td nowrap="" style="border-top: none; border: solid windowtext 1.0pt; height: 15.0pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; padding: 0cm 5.4pt 0cm 5.4pt; width: 48.0pt;" valign="bottom" width="64"><div align="right" class="MsoNormal" style="direction: ltr; line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; text-align: right; unicode-bidi: embed;">
35<o:p></o:p></div>
</td>
<td nowrap="" style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 15.0pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; padding: 0cm 5.4pt 0cm 5.4pt; width: 48.0pt;" valign="bottom" width="64"><div align="right" class="MsoNormal" style="direction: ltr; line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; text-align: right; unicode-bidi: embed;">
-0.00037<o:p></o:p></div>
</td>
<td nowrap="" style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 15.0pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; padding: 0cm 5.4pt 0cm 5.4pt; width: 48.0pt;" valign="bottom" width="64"><div align="right" class="MsoNormal" style="direction: ltr; line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; text-align: right; unicode-bidi: embed;">
-0.00022<o:p></o:p></div>
</td>
<td nowrap="" style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 15.0pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; padding: 0cm 5.4pt 0cm 5.4pt; width: 48.0pt;" valign="bottom" width="64"><div align="right" class="MsoNormal" style="direction: ltr; line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; text-align: right; unicode-bidi: embed;">
-0.00035<o:p></o:p></div>
</td>
</tr>
<tr style="height: 15.0pt; mso-yfti-irow: 22;">
<td nowrap="" style="border-top: none; border: solid windowtext 1.0pt; height: 15.0pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; padding: 0cm 5.4pt 0cm 5.4pt; width: 48.0pt;" valign="bottom" width="64"><div align="right" class="MsoNormal" style="direction: ltr; line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; text-align: right; unicode-bidi: embed;">
36<o:p></o:p></div>
</td>
<td nowrap="" style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 15.0pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; padding: 0cm 5.4pt 0cm 5.4pt; width: 48.0pt;" valign="bottom" width="64"><div align="right" class="MsoNormal" style="direction: ltr; line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; text-align: right; unicode-bidi: embed;">
-0.00037<o:p></o:p></div>
</td>
<td nowrap="" style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 15.0pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; padding: 0cm 5.4pt 0cm 5.4pt; width: 48.0pt;" valign="bottom" width="64"><div align="right" class="MsoNormal" style="direction: ltr; line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; text-align: right; unicode-bidi: embed;">
-0.00022<o:p></o:p></div>
</td>
<td nowrap="" style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 15.0pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; padding: 0cm 5.4pt 0cm 5.4pt; width: 48.0pt;" valign="bottom" width="64"><div align="right" class="MsoNormal" style="direction: ltr; line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; text-align: right; unicode-bidi: embed;">
-0.00024<o:p></o:p></div>
</td>
</tr>
<tr style="height: 15.0pt; mso-yfti-irow: 23;">
<td nowrap="" style="border-top: none; border: solid windowtext 1.0pt; height: 15.0pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; padding: 0cm 5.4pt 0cm 5.4pt; width: 48.0pt;" valign="bottom" width="64"><div align="right" class="MsoNormal" style="direction: ltr; line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; text-align: right; unicode-bidi: embed;">
37<o:p></o:p></div>
</td>
<td nowrap="" style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 15.0pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; padding: 0cm 5.4pt 0cm 5.4pt; width: 48.0pt;" valign="bottom" width="64"><div align="right" class="MsoNormal" style="direction: ltr; line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; text-align: right; unicode-bidi: embed;">
-0.00035<o:p></o:p></div>
</td>
<td nowrap="" style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 15.0pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; padding: 0cm 5.4pt 0cm 5.4pt; width: 48.0pt;" valign="bottom" width="64"><div align="right" class="MsoNormal" style="direction: ltr; line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; text-align: right; unicode-bidi: embed;">
-0.0005<o:p></o:p></div>
</td>
<td nowrap="" style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 15.0pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; padding: 0cm 5.4pt 0cm 5.4pt; width: 48.0pt;" valign="bottom" width="64"><div align="right" class="MsoNormal" style="direction: ltr; line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; text-align: right; unicode-bidi: embed;">
-0.00047<o:p></o:p></div>
</td>
</tr>
<tr style="height: 15.0pt; mso-yfti-irow: 24;">
<td nowrap="" style="border-top: none; border: solid windowtext 1.0pt; height: 15.0pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; padding: 0cm 5.4pt 0cm 5.4pt; width: 48.0pt;" valign="bottom" width="64"><div align="right" class="MsoNormal" style="direction: ltr; line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; text-align: right; unicode-bidi: embed;">
38<o:p></o:p></div>
</td>
<td nowrap="" style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 15.0pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; padding: 0cm 5.4pt 0cm 5.4pt; width: 48.0pt;" valign="bottom" width="64"><div align="right" class="MsoNormal" style="direction: ltr; line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; text-align: right; unicode-bidi: embed;">
-0.00035<o:p></o:p></div>
</td>
<td nowrap="" style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 15.0pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; padding: 0cm 5.4pt 0cm 5.4pt; width: 48.0pt;" valign="bottom" width="64"><div align="right" class="MsoNormal" style="direction: ltr; line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; text-align: right; unicode-bidi: embed;">
-0.0005<o:p></o:p></div>
</td>
<td nowrap="" style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 15.0pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; padding: 0cm 5.4pt 0cm 5.4pt; width: 48.0pt;" valign="bottom" width="64"><div align="right" class="MsoNormal" style="direction: ltr; line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; text-align: right; unicode-bidi: embed;">
-0.00037<o:p></o:p></div>
</td>
</tr>
<tr style="height: 15.0pt; mso-yfti-irow: 25;">
<td nowrap="" style="border-top: none; border: solid windowtext 1.0pt; height: 15.0pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; padding: 0cm 5.4pt 0cm 5.4pt; width: 48.0pt;" valign="bottom" width="64"><div align="right" class="MsoNormal" style="direction: ltr; line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; text-align: right; unicode-bidi: embed;">
39<o:p></o:p></div>
</td>
<td nowrap="" style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 15.0pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; padding: 0cm 5.4pt 0cm 5.4pt; width: 48.0pt;" valign="bottom" width="64"><div align="right" class="MsoNormal" style="direction: ltr; line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; text-align: right; unicode-bidi: embed;">
-0.00035<o:p></o:p></div>
</td>
<td nowrap="" style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 15.0pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; padding: 0cm 5.4pt 0cm 5.4pt; width: 48.0pt;" valign="bottom" width="64"><div align="right" class="MsoNormal" style="direction: ltr; line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; text-align: right; unicode-bidi: embed;">
-0.00047<o:p></o:p></div>
</td>
<td nowrap="" style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 15.0pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; padding: 0cm 5.4pt 0cm 5.4pt; width: 48.0pt;" valign="bottom" width="64"><div align="right" class="MsoNormal" style="direction: ltr; line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; text-align: right; unicode-bidi: embed;">
-0.0005<o:p></o:p></div>
</td>
</tr>
<tr style="height: 15.0pt; mso-yfti-irow: 26;">
<td nowrap="" style="border-top: none; border: solid windowtext 1.0pt; height: 15.0pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; padding: 0cm 5.4pt 0cm 5.4pt; width: 48.0pt;" valign="bottom" width="64"><div align="right" class="MsoNormal" style="direction: ltr; line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; text-align: right; unicode-bidi: embed;">
40<o:p></o:p></div>
</td>
<td nowrap="" style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 15.0pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; padding: 0cm 5.4pt 0cm 5.4pt; width: 48.0pt;" valign="bottom" width="64"><div align="right" class="MsoNormal" style="direction: ltr; line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; text-align: right; unicode-bidi: embed;">
-0.00035<o:p></o:p></div>
</td>
<td nowrap="" style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 15.0pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; padding: 0cm 5.4pt 0cm 5.4pt; width: 48.0pt;" valign="bottom" width="64"><div align="right" class="MsoNormal" style="direction: ltr; line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; text-align: right; unicode-bidi: embed;">
-0.00047<o:p></o:p></div>
</td>
<td nowrap="" style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 15.0pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; padding: 0cm 5.4pt 0cm 5.4pt; width: 48.0pt;" valign="bottom" width="64"><div align="right" class="MsoNormal" style="direction: ltr; line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; text-align: right; unicode-bidi: embed;">
-0.00032<o:p></o:p></div>
</td>
</tr>
<tr style="height: 15.0pt; mso-yfti-irow: 27;">
<td nowrap="" style="border-top: none; border: solid windowtext 1.0pt; height: 15.0pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; padding: 0cm 5.4pt 0cm 5.4pt; width: 48.0pt;" valign="bottom" width="64"><div align="right" class="MsoNormal" style="direction: ltr; line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; text-align: right; unicode-bidi: embed;">
41<o:p></o:p></div>
</td>
<td nowrap="" style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 15.0pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; padding: 0cm 5.4pt 0cm 5.4pt; width: 48.0pt;" valign="bottom" width="64"><div align="right" class="MsoNormal" style="direction: ltr; line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; text-align: right; unicode-bidi: embed;">
-0.00035<o:p></o:p></div>
</td>
<td nowrap="" style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 15.0pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; padding: 0cm 5.4pt 0cm 5.4pt; width: 48.0pt;" valign="bottom" width="64"><div align="right" class="MsoNormal" style="direction: ltr; line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; text-align: right; unicode-bidi: embed;">
-0.00037<o:p></o:p></div>
</td>
<td nowrap="" style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 15.0pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; padding: 0cm 5.4pt 0cm 5.4pt; width: 48.0pt;" valign="bottom" width="64"><div align="right" class="MsoNormal" style="direction: ltr; line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; text-align: right; unicode-bidi: embed;">
-0.0005<o:p></o:p></div>
</td>
</tr>
<tr style="height: 15.0pt; mso-yfti-irow: 28;">
<td nowrap="" style="border-top: none; border: solid windowtext 1.0pt; height: 15.0pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; padding: 0cm 5.4pt 0cm 5.4pt; width: 48.0pt;" valign="bottom" width="64"><div align="right" class="MsoNormal" style="direction: ltr; line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; text-align: right; unicode-bidi: embed;">
42<o:p></o:p></div>
</td>
<td nowrap="" style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 15.0pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; padding: 0cm 5.4pt 0cm 5.4pt; width: 48.0pt;" valign="bottom" width="64"><div align="right" class="MsoNormal" style="direction: ltr; line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; text-align: right; unicode-bidi: embed;">
-0.00035<o:p></o:p></div>
</td>
<td nowrap="" style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 15.0pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; padding: 0cm 5.4pt 0cm 5.4pt; width: 48.0pt;" valign="bottom" width="64"><div align="right" class="MsoNormal" style="direction: ltr; line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; text-align: right; unicode-bidi: embed;">
-0.00037<o:p></o:p></div>
</td>
<td nowrap="" style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 15.0pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; padding: 0cm 5.4pt 0cm 5.4pt; width: 48.0pt;" valign="bottom" width="64"><div align="right" class="MsoNormal" style="direction: ltr; line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; text-align: right; unicode-bidi: embed;">
-0.00022<o:p></o:p></div>
</td>
</tr>
<tr style="height: 15.0pt; mso-yfti-irow: 29;">
<td nowrap="" style="border-top: none; border: solid windowtext 1.0pt; height: 15.0pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; padding: 0cm 5.4pt 0cm 5.4pt; width: 48.0pt;" valign="bottom" width="64"><div align="right" class="MsoNormal" style="direction: ltr; line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; text-align: right; unicode-bidi: embed;">
43<o:p></o:p></div>
</td>
<td nowrap="" style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 15.0pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; padding: 0cm 5.4pt 0cm 5.4pt; width: 48.0pt;" valign="bottom" width="64"><div align="right" class="MsoNormal" style="direction: ltr; line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; text-align: right; unicode-bidi: embed;">
-0.00035<o:p></o:p></div>
</td>
<td nowrap="" style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 15.0pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; padding: 0cm 5.4pt 0cm 5.4pt; width: 48.0pt;" valign="bottom" width="64"><div align="right" class="MsoNormal" style="direction: ltr; line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; text-align: right; unicode-bidi: embed;">
-0.00032<o:p></o:p></div>
</td>
<td nowrap="" style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 15.0pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; padding: 0cm 5.4pt 0cm 5.4pt; width: 48.0pt;" valign="bottom" width="64"><div align="right" class="MsoNormal" style="direction: ltr; line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; text-align: right; unicode-bidi: embed;">
-0.00047<o:p></o:p></div>
</td>
</tr>
<tr style="height: 15.0pt; mso-yfti-irow: 30;">
<td nowrap="" style="border-top: none; border: solid windowtext 1.0pt; height: 15.0pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; padding: 0cm 5.4pt 0cm 5.4pt; width: 48.0pt;" valign="bottom" width="64"><div align="right" class="MsoNormal" style="direction: ltr; line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; text-align: right; unicode-bidi: embed;">
44<o:p></o:p></div>
</td>
<td nowrap="" style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 15.0pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; padding: 0cm 5.4pt 0cm 5.4pt; width: 48.0pt;" valign="bottom" width="64"><div align="right" class="MsoNormal" style="direction: ltr; line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; text-align: right; unicode-bidi: embed;">
-0.00035<o:p></o:p></div>
</td>
<td nowrap="" style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 15.0pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; padding: 0cm 5.4pt 0cm 5.4pt; width: 48.0pt;" valign="bottom" width="64"><div align="right" class="MsoNormal" style="direction: ltr; line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; text-align: right; unicode-bidi: embed;">
-0.00032<o:p></o:p></div>
</td>
<td nowrap="" style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 15.0pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; padding: 0cm 5.4pt 0cm 5.4pt; width: 48.0pt;" valign="bottom" width="64"><div align="right" class="MsoNormal" style="direction: ltr; line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; text-align: right; unicode-bidi: embed;">
-0.00019<o:p></o:p></div>
</td>
</tr>
<tr style="height: 15.0pt; mso-yfti-irow: 31;">
<td nowrap="" style="border-top: none; border: solid windowtext 1.0pt; height: 15.0pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; padding: 0cm 5.4pt 0cm 5.4pt; width: 48.0pt;" valign="bottom" width="64"><div align="right" class="MsoNormal" style="direction: ltr; line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; text-align: right; unicode-bidi: embed;">
45<o:p></o:p></div>
</td>
<td nowrap="" style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 15.0pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; padding: 0cm 5.4pt 0cm 5.4pt; width: 48.0pt;" valign="bottom" width="64"><div align="right" class="MsoNormal" style="direction: ltr; line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; text-align: right; unicode-bidi: embed;">
-0.00035<o:p></o:p></div>
</td>
<td nowrap="" style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 15.0pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; padding: 0cm 5.4pt 0cm 5.4pt; width: 48.0pt;" valign="bottom" width="64"><div align="right" class="MsoNormal" style="direction: ltr; line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; text-align: right; unicode-bidi: embed;">
-0.00022<o:p></o:p></div>
</td>
<td nowrap="" style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 15.0pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; padding: 0cm 5.4pt 0cm 5.4pt; width: 48.0pt;" valign="bottom" width="64"><div align="right" class="MsoNormal" style="direction: ltr; line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; text-align: right; unicode-bidi: embed;">
-0.00037<o:p></o:p></div>
</td>
</tr>
<tr style="height: 15.0pt; mso-yfti-irow: 32;">
<td nowrap="" style="border-top: none; border: solid windowtext 1.0pt; height: 15.0pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; padding: 0cm 5.4pt 0cm 5.4pt; width: 48.0pt;" valign="bottom" width="64"><div align="right" class="MsoNormal" style="direction: ltr; line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; text-align: right; unicode-bidi: embed;">
46<o:p></o:p></div>
</td>
<td nowrap="" style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 15.0pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; padding: 0cm 5.4pt 0cm 5.4pt; width: 48.0pt;" valign="bottom" width="64"><div align="right" class="MsoNormal" style="direction: ltr; line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; text-align: right; unicode-bidi: embed;">
-0.00035<o:p></o:p></div>
</td>
<td nowrap="" style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 15.0pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; padding: 0cm 5.4pt 0cm 5.4pt; width: 48.0pt;" valign="bottom" width="64"><div align="right" class="MsoNormal" style="direction: ltr; line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; text-align: right; unicode-bidi: embed;">
-0.00022<o:p></o:p></div>
</td>
<td nowrap="" style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 15.0pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; padding: 0cm 5.4pt 0cm 5.4pt; width: 48.0pt;" valign="bottom" width="64"><div align="right" class="MsoNormal" style="direction: ltr; line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; text-align: right; unicode-bidi: embed;">
-0.00019<o:p></o:p></div>
</td>
</tr>
<tr style="height: 15.0pt; mso-yfti-irow: 33;">
<td nowrap="" style="border-top: none; border: solid windowtext 1.0pt; height: 15.0pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; padding: 0cm 5.4pt 0cm 5.4pt; width: 48.0pt;" valign="bottom" width="64"><div align="right" class="MsoNormal" style="direction: ltr; line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; text-align: right; unicode-bidi: embed;">
47<o:p></o:p></div>
</td>
<td nowrap="" style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 15.0pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; padding: 0cm 5.4pt 0cm 5.4pt; width: 48.0pt;" valign="bottom" width="64"><div align="right" class="MsoNormal" style="direction: ltr; line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; text-align: right; unicode-bidi: embed;">
-0.00035<o:p></o:p></div>
</td>
<td nowrap="" style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 15.0pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; padding: 0cm 5.4pt 0cm 5.4pt; width: 48.0pt;" valign="bottom" width="64"><div align="right" class="MsoNormal" style="direction: ltr; line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; text-align: right; unicode-bidi: embed;">
-0.00019<o:p></o:p></div>
</td>
<td nowrap="" style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 15.0pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; padding: 0cm 5.4pt 0cm 5.4pt; width: 48.0pt;" valign="bottom" width="64"><div align="right" class="MsoNormal" style="direction: ltr; line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; text-align: right; unicode-bidi: embed;">
-0.00032<o:p></o:p></div>
</td>
</tr>
<tr style="height: 15.0pt; mso-yfti-irow: 34;">
<td nowrap="" style="border-top: none; border: solid windowtext 1.0pt; height: 15.0pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; padding: 0cm 5.4pt 0cm 5.4pt; width: 48.0pt;" valign="bottom" width="64"><div align="right" class="MsoNormal" style="direction: ltr; line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; text-align: right; unicode-bidi: embed;">
48<o:p></o:p></div>
</td>
<td nowrap="" style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 15.0pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; padding: 0cm 5.4pt 0cm 5.4pt; width: 48.0pt;" valign="bottom" width="64"><div align="right" class="MsoNormal" style="direction: ltr; line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; text-align: right; unicode-bidi: embed;">
-0.00035<o:p></o:p></div>
</td>
<td nowrap="" style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 15.0pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; padding: 0cm 5.4pt 0cm 5.4pt; width: 48.0pt;" valign="bottom" width="64"><div align="right" class="MsoNormal" style="direction: ltr; line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; text-align: right; unicode-bidi: embed;">
-0.00019<o:p></o:p></div>
</td>
<td nowrap="" style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 15.0pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; padding: 0cm 5.4pt 0cm 5.4pt; width: 48.0pt;" valign="bottom" width="64"><div align="right" class="MsoNormal" style="direction: ltr; line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; text-align: right; unicode-bidi: embed;">
-0.00022<o:p></o:p></div>
</td>
</tr>
<tr style="height: 15.0pt; mso-yfti-irow: 35;">
<td nowrap="" style="border-top: none; border: solid windowtext 1.0pt; height: 15.0pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; padding: 0cm 5.4pt 0cm 5.4pt; width: 48.0pt;" valign="bottom" width="64"><div align="right" class="MsoNormal" style="direction: ltr; line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; text-align: right; unicode-bidi: embed;">
49<o:p></o:p></div>
</td>
<td nowrap="" style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 15.0pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; padding: 0cm 5.4pt 0cm 5.4pt; width: 48.0pt;" valign="bottom" width="64"><div align="right" class="MsoNormal" style="direction: ltr; line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; text-align: right; unicode-bidi: embed;">
-0.00032<o:p></o:p></div>
</td>
<td nowrap="" style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 15.0pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; padding: 0cm 5.4pt 0cm 5.4pt; width: 48.0pt;" valign="bottom" width="64"><div align="right" class="MsoNormal" style="direction: ltr; line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; text-align: right; unicode-bidi: embed;">
-0.00047<o:p></o:p></div>
</td>
<td nowrap="" style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 15.0pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; padding: 0cm 5.4pt 0cm 5.4pt; width: 48.0pt;" valign="bottom" width="64"><div align="right" class="MsoNormal" style="direction: ltr; line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; text-align: right; unicode-bidi: embed;">
-0.00045<o:p></o:p></div>
</td>
</tr>
<tr style="height: 15.0pt; mso-yfti-irow: 36;">
<td nowrap="" style="border-top: none; border: solid windowtext 1.0pt; height: 15.0pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; padding: 0cm 5.4pt 0cm 5.4pt; width: 48.0pt;" valign="bottom" width="64"><div align="right" class="MsoNormal" style="direction: ltr; line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; text-align: right; unicode-bidi: embed;">
50<o:p></o:p></div>
</td>
<td nowrap="" style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 15.0pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; padding: 0cm 5.4pt 0cm 5.4pt; width: 48.0pt;" valign="bottom" width="64"><div align="right" class="MsoNormal" style="direction: ltr; line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; text-align: right; unicode-bidi: embed;">
-0.00032<o:p></o:p></div>
</td>
<td nowrap="" style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 15.0pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; padding: 0cm 5.4pt 0cm 5.4pt; width: 48.0pt;" valign="bottom" width="64"><div align="right" class="MsoNormal" style="direction: ltr; line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; text-align: right; unicode-bidi: embed;">
-0.00047<o:p></o:p></div>
</td>
<td nowrap="" style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 15.0pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; padding: 0cm 5.4pt 0cm 5.4pt; width: 48.0pt;" valign="bottom" width="64"><div align="right" class="MsoNormal" style="direction: ltr; line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; text-align: right; unicode-bidi: embed;">
-0.00035<o:p></o:p></div>
</td>
</tr>
<tr style="height: 15.0pt; mso-yfti-irow: 37;">
<td nowrap="" style="border-top: none; border: solid windowtext 1.0pt; height: 15.0pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; padding: 0cm 5.4pt 0cm 5.4pt; width: 48.0pt;" valign="bottom" width="64"><div align="right" class="MsoNormal" style="direction: ltr; line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; text-align: right; unicode-bidi: embed;">
51<o:p></o:p></div>
</td>
<td nowrap="" style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 15.0pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; padding: 0cm 5.4pt 0cm 5.4pt; width: 48.0pt;" valign="bottom" width="64"><div align="right" class="MsoNormal" style="direction: ltr; line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; text-align: right; unicode-bidi: embed;">
-0.00032<o:p></o:p></div>
</td>
<td nowrap="" style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 15.0pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; padding: 0cm 5.4pt 0cm 5.4pt; width: 48.0pt;" valign="bottom" width="64"><div align="right" class="MsoNormal" style="direction: ltr; line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; text-align: right; unicode-bidi: embed;">
-0.00045<o:p></o:p></div>
</td>
<td nowrap="" style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 15.0pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; padding: 0cm 5.4pt 0cm 5.4pt; width: 48.0pt;" valign="bottom" width="64"><div align="right" class="MsoNormal" style="direction: ltr; line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; text-align: right; unicode-bidi: embed;">
-0.00047<o:p></o:p></div>
</td>
</tr>
<tr style="height: 15.0pt; mso-yfti-irow: 38;">
<td nowrap="" style="border-top: none; border: solid windowtext 1.0pt; height: 15.0pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; padding: 0cm 5.4pt 0cm 5.4pt; width: 48.0pt;" valign="bottom" width="64"><div align="right" class="MsoNormal" style="direction: ltr; line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; text-align: right; unicode-bidi: embed;">
52<o:p></o:p></div>
</td>
<td nowrap="" style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 15.0pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; padding: 0cm 5.4pt 0cm 5.4pt; width: 48.0pt;" valign="bottom" width="64"><div align="right" class="MsoNormal" style="direction: ltr; line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; text-align: right; unicode-bidi: embed;">
-0.00032<o:p></o:p></div>
</td>
<td nowrap="" style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 15.0pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; padding: 0cm 5.4pt 0cm 5.4pt; width: 48.0pt;" valign="bottom" width="64"><div align="right" class="MsoNormal" style="direction: ltr; line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; text-align: right; unicode-bidi: embed;">
-0.00045<o:p></o:p></div>
</td>
<td nowrap="" style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 15.0pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; padding: 0cm 5.4pt 0cm 5.4pt; width: 48.0pt;" valign="bottom" width="64"><div align="right" class="MsoNormal" style="direction: ltr; line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; text-align: right; unicode-bidi: embed;">
-0.00029<o:p></o:p></div>
</td>
</tr>
<tr style="height: 15.0pt; mso-yfti-irow: 39;">
<td nowrap="" style="border-top: none; border: solid windowtext 1.0pt; height: 15.0pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; padding: 0cm 5.4pt 0cm 5.4pt; width: 48.0pt;" valign="bottom" width="64"><div align="right" class="MsoNormal" style="direction: ltr; line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; text-align: right; unicode-bidi: embed;">
53<o:p></o:p></div>
</td>
<td nowrap="" style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 15.0pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; padding: 0cm 5.4pt 0cm 5.4pt; width: 48.0pt;" valign="bottom" width="64"><div align="right" class="MsoNormal" style="direction: ltr; line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; text-align: right; unicode-bidi: embed;">
-0.00032<o:p></o:p></div>
</td>
<td nowrap="" style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 15.0pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; padding: 0cm 5.4pt 0cm 5.4pt; width: 48.0pt;" valign="bottom" width="64"><div align="right" class="MsoNormal" style="direction: ltr; line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; text-align: right; unicode-bidi: embed;">
-0.00035<o:p></o:p></div>
</td>
<td nowrap="" style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 15.0pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; padding: 0cm 5.4pt 0cm 5.4pt; width: 48.0pt;" valign="bottom" width="64"><div align="right" class="MsoNormal" style="direction: ltr; line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; text-align: right; unicode-bidi: embed;">
-0.00047<o:p></o:p></div>
</td>
</tr>
<tr style="height: 15.0pt; mso-yfti-irow: 40;">
<td nowrap="" style="border-top: none; border: solid windowtext 1.0pt; height: 15.0pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; padding: 0cm 5.4pt 0cm 5.4pt; width: 48.0pt;" valign="bottom" width="64"><div align="right" class="MsoNormal" style="direction: ltr; line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; text-align: right; unicode-bidi: embed;">
54<o:p></o:p></div>
</td>
<td nowrap="" style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 15.0pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; padding: 0cm 5.4pt 0cm 5.4pt; width: 48.0pt;" valign="bottom" width="64"><div align="right" class="MsoNormal" style="direction: ltr; line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; text-align: right; unicode-bidi: embed;">
-0.00032<o:p></o:p></div>
</td>
<td nowrap="" style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 15.0pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; padding: 0cm 5.4pt 0cm 5.4pt; width: 48.0pt;" valign="bottom" width="64"><div align="right" class="MsoNormal" style="direction: ltr; line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; text-align: right; unicode-bidi: embed;">
-0.00035<o:p></o:p></div>
</td>
<td nowrap="" style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 15.0pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; padding: 0cm 5.4pt 0cm 5.4pt; width: 48.0pt;" valign="bottom" width="64"><div align="right" class="MsoNormal" style="direction: ltr; line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; text-align: right; unicode-bidi: embed;">
-0.00019<o:p></o:p></div>
</td>
</tr>
<tr style="height: 15.0pt; mso-yfti-irow: 41;">
<td nowrap="" style="border-top: none; border: solid windowtext 1.0pt; height: 15.0pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; padding: 0cm 5.4pt 0cm 5.4pt; width: 48.0pt;" valign="bottom" width="64"><div align="right" class="MsoNormal" style="direction: ltr; line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; text-align: right; unicode-bidi: embed;">
55<o:p></o:p></div>
</td>
<td nowrap="" style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 15.0pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; padding: 0cm 5.4pt 0cm 5.4pt; width: 48.0pt;" valign="bottom" width="64"><div align="right" class="MsoNormal" style="direction: ltr; line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; text-align: right; unicode-bidi: embed;">
-0.00032<o:p></o:p></div>
</td>
<td nowrap="" style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 15.0pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; padding: 0cm 5.4pt 0cm 5.4pt; width: 48.0pt;" valign="bottom" width="64"><div align="right" class="MsoNormal" style="direction: ltr; line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; text-align: right; unicode-bidi: embed;">
-0.00029<o:p></o:p></div>
</td>
<td nowrap="" style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 15.0pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; padding: 0cm 5.4pt 0cm 5.4pt; width: 48.0pt;" valign="bottom" width="64"><div align="right" class="MsoNormal" style="direction: ltr; line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; text-align: right; unicode-bidi: embed;">
-0.00045<o:p></o:p></div>
</td>
</tr>
<tr style="height: 15.0pt; mso-yfti-irow: 42;">
<td nowrap="" style="border-top: none; border: solid windowtext 1.0pt; height: 15.0pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; padding: 0cm 5.4pt 0cm 5.4pt; width: 48.0pt;" valign="bottom" width="64"><div align="right" class="MsoNormal" style="direction: ltr; line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; text-align: right; unicode-bidi: embed;">
56<o:p></o:p></div>
</td>
<td nowrap="" style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 15.0pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; padding: 0cm 5.4pt 0cm 5.4pt; width: 48.0pt;" valign="bottom" width="64"><div align="right" class="MsoNormal" style="direction: ltr; line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; text-align: right; unicode-bidi: embed;">
-0.00032<o:p></o:p></div>
</td>
<td nowrap="" style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 15.0pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; padding: 0cm 5.4pt 0cm 5.4pt; width: 48.0pt;" valign="bottom" width="64"><div align="right" class="MsoNormal" style="direction: ltr; line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; text-align: right; unicode-bidi: embed;">
-0.00029<o:p></o:p></div>
</td>
<td nowrap="" style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 15.0pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; padding: 0cm 5.4pt 0cm 5.4pt; width: 48.0pt;" valign="bottom" width="64"><div align="right" class="MsoNormal" style="direction: ltr; line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; text-align: right; unicode-bidi: embed;">
-0.00017<o:p></o:p></div>
</td>
</tr>
<tr style="height: 15.0pt; mso-yfti-irow: 43;">
<td nowrap="" style="border-top: none; border: solid windowtext 1.0pt; height: 15.0pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; padding: 0cm 5.4pt 0cm 5.4pt; width: 48.0pt;" valign="bottom" width="64"><div align="right" class="MsoNormal" style="direction: ltr; line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; text-align: right; unicode-bidi: embed;">
57<o:p></o:p></div>
</td>
<td nowrap="" style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 15.0pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; padding: 0cm 5.4pt 0cm 5.4pt; width: 48.0pt;" valign="bottom" width="64"><div align="right" class="MsoNormal" style="direction: ltr; line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; text-align: right; unicode-bidi: embed;">
-0.00032<o:p></o:p></div>
</td>
<td nowrap="" style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 15.0pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; padding: 0cm 5.4pt 0cm 5.4pt; width: 48.0pt;" valign="bottom" width="64"><div align="right" class="MsoNormal" style="direction: ltr; line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; text-align: right; unicode-bidi: embed;">
-0.00019<o:p></o:p></div>
</td>
<td nowrap="" style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 15.0pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; padding: 0cm 5.4pt 0cm 5.4pt; width: 48.0pt;" valign="bottom" width="64"><div align="right" class="MsoNormal" style="direction: ltr; line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; text-align: right; unicode-bidi: embed;">
-0.00035<o:p></o:p></div>
</td>
</tr>
<tr style="height: 15.0pt; mso-yfti-irow: 44; mso-yfti-lastrow: yes;">
<td nowrap="" style="border-top: none; border: solid windowtext 1.0pt; height: 15.0pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; padding: 0cm 5.4pt 0cm 5.4pt; width: 48.0pt;" valign="bottom" width="64"><div align="right" class="MsoNormal" style="direction: ltr; line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; text-align: right; unicode-bidi: embed;">
58<o:p></o:p></div>
</td>
<td nowrap="" style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 15.0pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; padding: 0cm 5.4pt 0cm 5.4pt; width: 48.0pt;" valign="bottom" width="64"><div align="right" class="MsoNormal" style="direction: ltr; line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; text-align: right; unicode-bidi: embed;">
-0.00032<o:p></o:p></div>
</td>
<td nowrap="" style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 15.0pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; padding: 0cm 5.4pt 0cm 5.4pt; width: 48.0pt;" valign="bottom" width="64"><div align="right" class="MsoNormal" style="direction: ltr; line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; text-align: right; unicode-bidi: embed;">
-0.00019<o:p></o:p></div>
</td>
<td nowrap="" style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 15.0pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; padding: 0cm 5.4pt 0cm 5.4pt; width: 48.0pt;" valign="bottom" width="64"><div align="right" class="MsoNormal" style="direction: ltr; line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; text-align: right; unicode-bidi: embed;">
-0.00017<o:p></o:p></div>
</td>
</tr>
</tbody></table>
<div style="text-align: left;">
<br /></div>
<div style="text-align: left;">
</div>
<div class="MsoNormal" style="direction: ltr; text-align: left; unicode-bidi: embed;">
Please
be informed that each answer gives us a model of three particles P1, P2 and P3.
For instance, look at Model (1) in above table. By applying the conjecture (3),
you can find below system of articles:<o:p></o:p></div>
<br />
<br />
<div style="text-align: left;">
<table border="0" cellpadding="0" cellspacing="0" class="MsoNormalTable" style="border-collapse: collapse; margin-left: 4.65pt; mso-padding-alt: 0cm 5.4pt 0cm 5.4pt; mso-yfti-tbllook: 1184; width: 323px;">
<tbody>
<tr style="height: 15.0pt; mso-yfti-firstrow: yes; mso-yfti-irow: 0;">
<td nowrap="" style="height: 15.0pt; padding: 0cm 5.4pt 0cm 5.4pt; width: 26.0pt;" valign="bottom" width="35"></td>
<td nowrap="" style="border: solid windowtext 1.0pt; height: 15.0pt; mso-border-alt: solid windowtext .5pt; padding: 0cm 5.4pt 0cm 5.4pt; width: 60.25pt;" width="80"><div align="center" class="MsoNormal" style="direction: ltr; line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; text-align: center; unicode-bidi: embed;">
<b><span style="color: black; mso-ascii-font-family: Calibri; mso-bidi-font-family: "Times New Roman"; mso-bidi-language: AR-SA; mso-fareast-font-family: "Times New Roman"; mso-hansi-font-family: Calibri;">x<o:p></o:p></span></b></div>
</td>
<td nowrap="" style="border-left: none; border: solid windowtext 1.0pt; height: 15.0pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt; padding: 0cm 5.4pt 0cm 5.4pt; width: 58.5pt;" width="78"><div align="center" class="MsoNormal" style="direction: ltr; line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; text-align: center; unicode-bidi: embed;">
<b><span style="color: black; mso-ascii-font-family: Calibri; mso-bidi-font-family: "Times New Roman"; mso-bidi-language: AR-SA; mso-fareast-font-family: "Times New Roman"; mso-hansi-font-family: Calibri;">y<o:p></o:p></span></b></div>
</td>
<td nowrap="" style="border-left: none; border: solid windowtext 1.0pt; height: 15.0pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt; padding: 0cm 5.4pt 0cm 5.4pt; width: 58.5pt;" width="78"><div align="center" class="MsoNormal" style="direction: ltr; line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; text-align: center; unicode-bidi: embed;">
<b><span style="color: black; mso-ascii-font-family: Calibri; mso-bidi-font-family: "Times New Roman"; mso-bidi-language: AR-SA; mso-fareast-font-family: "Times New Roman"; mso-hansi-font-family: Calibri;">z<o:p></o:p></span></b></div>
</td>
<td nowrap="" style="border-left: none; border: solid windowtext 1.0pt; height: 15.0pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt; padding: 0cm 5.4pt 0cm 5.4pt; width: 38.85pt;" width="52"><div align="center" class="MsoNormal" style="direction: ltr; line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; text-align: center; unicode-bidi: embed;">
<b><span style="color: black; mso-ascii-font-family: Calibri; mso-bidi-font-family: "Times New Roman"; mso-bidi-language: AR-SA; mso-fareast-font-family: "Times New Roman"; mso-hansi-font-family: Calibri;">Distance<o:p></o:p></span></b></div>
</td>
</tr>
<tr style="height: 15.0pt; mso-yfti-irow: 1;">
<td nowrap="" style="border: solid windowtext 1.0pt; height: 15.0pt; mso-border-alt: solid windowtext .5pt; padding: 0cm 5.4pt 0cm 5.4pt; width: 26.0pt;" width="35"><div align="center" class="MsoNormal" style="direction: ltr; line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; text-align: center; unicode-bidi: embed;">
<b><span style="color: black; mso-ascii-font-family: Calibri; mso-bidi-font-family: "Times New Roman"; mso-bidi-language: AR-SA; mso-fareast-font-family: "Times New Roman"; mso-hansi-font-family: Calibri;">P1<o:p></o:p></span></b></div>
</td>
<td nowrap="" style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 15.0pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; padding: 0cm 5.4pt 0cm 5.4pt; width: 60.25pt;" valign="bottom" width="80"><div align="right" class="MsoNormal" style="direction: ltr; line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; text-align: right; unicode-bidi: embed;">
<b><span style="color: black; mso-ascii-font-family: Calibri; mso-bidi-font-family: "Times New Roman"; mso-bidi-language: AR-SA; mso-fareast-font-family: "Times New Roman"; mso-hansi-font-family: Calibri;">-0.0005<o:p></o:p></span></b></div>
</td>
<td nowrap="" style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 15.0pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; padding: 0cm 5.4pt 0cm 5.4pt; width: 58.5pt;" valign="bottom" width="78"><div align="right" class="MsoNormal" style="direction: ltr; line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; text-align: right; unicode-bidi: embed;">
<b><span style="color: black; mso-ascii-font-family: Calibri; mso-bidi-font-family: "Times New Roman"; mso-bidi-language: AR-SA; mso-fareast-font-family: "Times New Roman"; mso-hansi-font-family: Calibri;">-0.00047<o:p></o:p></span></b></div>
</td>
<td nowrap="" style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 15.0pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; padding: 0cm 5.4pt 0cm 5.4pt; width: 58.5pt;" valign="bottom" width="78"><div align="right" class="MsoNormal" style="direction: ltr; line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; text-align: right; unicode-bidi: embed;">
<b><span style="color: black; mso-ascii-font-family: Calibri; mso-bidi-font-family: "Times New Roman"; mso-bidi-language: AR-SA; mso-fareast-font-family: "Times New Roman"; mso-hansi-font-family: Calibri;">-0.00035<o:p></o:p></span></b></div>
</td>
<td nowrap="" style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 15.0pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; padding: 0cm 5.4pt 0cm 5.4pt; width: 38.85pt;" width="52"><div align="center" class="MsoNormal" style="direction: ltr; line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; text-align: center; unicode-bidi: embed;">
<b><span style="color: black; mso-ascii-font-family: Calibri; mso-bidi-font-family: "Times New Roman"; mso-bidi-language: AR-SA; mso-fareast-font-family: "Times New Roman"; mso-hansi-font-family: Calibri;">0.00020<o:p></o:p></span></b></div>
</td>
</tr>
<tr style="height: 15.0pt; mso-yfti-irow: 2;">
<td nowrap="" style="border-top: none; border: solid windowtext 1.0pt; height: 15.0pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; padding: 0cm 5.4pt 0cm 5.4pt; width: 26.0pt;" width="35"><div align="center" class="MsoNormal" style="direction: ltr; line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; text-align: center; unicode-bidi: embed;">
<b><span style="color: black; mso-ascii-font-family: Calibri; mso-bidi-font-family: "Times New Roman"; mso-bidi-language: AR-SA; mso-fareast-font-family: "Times New Roman"; mso-hansi-font-family: Calibri;">P2<o:p></o:p></span></b></div>
</td>
<td nowrap="" style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 15.0pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; padding: 0cm 5.4pt 0cm 5.4pt; width: 60.25pt;" valign="bottom" width="80"><div align="right" class="MsoNormal" style="direction: ltr; line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; text-align: right; unicode-bidi: embed;">
<b><span style="color: black; mso-ascii-font-family: Calibri; mso-bidi-font-family: "Times New Roman"; mso-bidi-language: AR-SA; mso-fareast-font-family: "Times New Roman"; mso-hansi-font-family: Calibri;">-0.00035<o:p></o:p></span></b></div>
</td>
<td nowrap="" style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 15.0pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; padding: 0cm 5.4pt 0cm 5.4pt; width: 58.5pt;" valign="bottom" width="78"><div align="right" class="MsoNormal" style="direction: ltr; line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; text-align: right; unicode-bidi: embed;">
<b><span style="color: black; mso-ascii-font-family: Calibri; mso-bidi-font-family: "Times New Roman"; mso-bidi-language: AR-SA; mso-fareast-font-family: "Times New Roman"; mso-hansi-font-family: Calibri;">-0.0005<o:p></o:p></span></b></div>
</td>
<td nowrap="" style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 15.0pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; padding: 0cm 5.4pt 0cm 5.4pt; width: 58.5pt;" valign="bottom" width="78"><div align="right" class="MsoNormal" style="direction: ltr; line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; text-align: right; unicode-bidi: embed;">
<b><span style="color: black; mso-ascii-font-family: Calibri; mso-bidi-font-family: "Times New Roman"; mso-bidi-language: AR-SA; mso-fareast-font-family: "Times New Roman"; mso-hansi-font-family: Calibri;">-0.00047<o:p></o:p></span></b></div>
</td>
<td nowrap="" style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 15.0pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; padding: 0cm 5.4pt 0cm 5.4pt; width: 38.85pt;" width="52"><div align="center" class="MsoNormal" style="direction: ltr; line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; text-align: center; unicode-bidi: embed;">
<b><span style="color: black; mso-ascii-font-family: Calibri; mso-bidi-font-family: "Times New Roman"; mso-bidi-language: AR-SA; mso-fareast-font-family: "Times New Roman"; mso-hansi-font-family: Calibri;">0.00020<o:p></o:p></span></b></div>
</td>
</tr>
<tr style="height: 15.0pt; mso-yfti-irow: 3; mso-yfti-lastrow: yes;">
<td nowrap="" style="border-top: none; border: solid windowtext 1.0pt; height: 15.0pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; padding: 0cm 5.4pt 0cm 5.4pt; width: 26.0pt;" width="35"><div align="center" class="MsoNormal" style="direction: ltr; line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; text-align: center; unicode-bidi: embed;">
<b><span style="color: black; mso-ascii-font-family: Calibri; mso-bidi-font-family: "Times New Roman"; mso-bidi-language: AR-SA; mso-fareast-font-family: "Times New Roman"; mso-hansi-font-family: Calibri;">P3<o:p></o:p></span></b></div>
</td>
<td nowrap="" style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 15.0pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; padding: 0cm 5.4pt 0cm 5.4pt; width: 60.25pt;" valign="bottom" width="80"><div align="right" class="MsoNormal" style="direction: ltr; line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; text-align: right; unicode-bidi: embed;">
<b><span style="color: black; mso-ascii-font-family: Calibri; mso-bidi-font-family: "Times New Roman"; mso-bidi-language: AR-SA; mso-fareast-font-family: "Times New Roman"; mso-hansi-font-family: Calibri;">-0.00047<o:p></o:p></span></b></div>
</td>
<td nowrap="" style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 15.0pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; padding: 0cm 5.4pt 0cm 5.4pt; width: 58.5pt;" valign="bottom" width="78"><div align="right" class="MsoNormal" style="direction: ltr; line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; text-align: right; unicode-bidi: embed;">
<b><span style="color: black; mso-ascii-font-family: Calibri; mso-bidi-font-family: "Times New Roman"; mso-bidi-language: AR-SA; mso-fareast-font-family: "Times New Roman"; mso-hansi-font-family: Calibri;">-0.00035<o:p></o:p></span></b></div>
</td>
<td nowrap="" style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 15.0pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; padding: 0cm 5.4pt 0cm 5.4pt; width: 58.5pt;" valign="bottom" width="78"><div align="right" class="MsoNormal" style="direction: ltr; line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; text-align: right; unicode-bidi: embed;">
<b><span style="color: black; mso-ascii-font-family: Calibri; mso-bidi-font-family: "Times New Roman"; mso-bidi-language: AR-SA; mso-fareast-font-family: "Times New Roman"; mso-hansi-font-family: Calibri;">-0.0005<o:p></o:p></span></b></div>
</td>
<td nowrap="" style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 15.0pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; padding: 0cm 5.4pt 0cm 5.4pt; width: 38.85pt;" width="52"><div align="center" class="MsoNormal" style="direction: ltr; line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; text-align: center; unicode-bidi: embed;">
<b><span style="color: black; mso-ascii-font-family: Calibri; mso-bidi-font-family: "Times New Roman"; mso-bidi-language: AR-SA; mso-fareast-font-family: "Times New Roman"; mso-hansi-font-family: Calibri;">0.00020<o:p></o:p></span></b></div>
</td>
</tr>
</tbody></table>
</div>
<div style="text-align: left;">
</div>
<div align="right" class="MsoNormal" dir="RTL" style="text-align: left;">
<span dir="LTR" style="font-family: "times new roman" , "serif"; font-size: 12.0pt; line-height: 107%;">As you can see, the distance among P1, P2 and P3 is equal to 0.0002
m.<o:p></o:p></span></div>
<div align="right" class="MsoNormal" dir="RTL" style="text-align: left;">
<span dir="LTR" style="font-family: "times new roman" , "serif"; font-size: 12.0pt; line-height: 107%;"><br /></span></div>
<div align="right" class="MsoNormal" dir="RTL" style="text-align: left;">
<span dir="LTR" style="font-family: "times new roman" , "serif"; font-size: 12.0pt; line-height: 107%;">Now, please comeback to step (1), we have 6 answers for the masses
and for each answer of masses, we have 408 models. It means that we found 2448
systems of three particles which have the same total gravity potential energy. <o:p></o:p></span></div>
<div class="MsoNormal" style="text-align: left;">
<span dir="LTR" style="font-family: "times new roman" , "serif"; font-size: 12.0pt; line-height: 107%;"><br /></span></div>
<div class="MsoNormal" style="text-align: left;">
<b><u><span dir="LTR" style="font-family: "times new roman" , "serif"; font-size: 12.0pt; line-height: 107%;">Question (2):<o:p></o:p></span></u></b></div>
<div class="MsoNormal" style="text-align: left;">
<b><u><span dir="LTR" style="font-family: "times new roman" , "serif"; font-size: 12.0pt; line-height: 107%;"><br /></span></u></b></div>
<br />
<div class="MsoNormal" style="text-align: left;">
<span dir="LTR" style="font-family: "times new roman" , "serif"; font-size: 12.0pt; line-height: 107%;">If we have:<o:p></o:p></span></div>
<div class="MsoNormal" style="text-align: left;">
<span dir="LTR" style="font-family: "times new roman" , "serif"; font-size: 12.0pt; line-height: 107%;"><br /></span></div>
<div class="MsoNormal" style="text-align: left;">
<span dir="LTR" style="font-family: "times new roman" , "serif"; font-size: 12.0pt; line-height: 107%;">U (r) = </span><span dir="LTR">-0.01748064
</span><span dir="LTR" style="font-family: "times new roman" , serif; font-size: 12pt; line-height: 107%;">J</span><span dir="LTR"><o:p></o:p></span></div>
<div class="MsoNormal" style="text-align: left;">
<span dir="LTR" style="font-family: "times new roman" , serif; font-size: 12pt; line-height: 107%;"><br /></span></div>
<div class="MsoNormal" style="text-align: left;">
<span dir="LTR" style="font-family: "times new roman" , serif; font-size: 12pt; line-height: 107%;">r = 0.0002 m<o:p></o:p></span></div>
<div class="MsoNormal" style="text-align: left;">
<span dir="LTR" style="font-family: "times new roman" , serif; font-size: 12pt; line-height: 107%;"><br /></span></div>
<div class="MsoNormal" style="text-align: left;">
<span dir="LTR" style="font-family: "times new roman" , serif; font-size: 12pt; line-height: 107%;">How can we map these particles in the space?<o:p></o:p></span></div>
<div class="MsoNormal" style="text-align: left;">
<span dir="LTR" style="font-family: "times new roman" , serif; font-size: 12pt; line-height: 107%;"><br /></span></div>
<div class="MsoNormal" style="text-align: left;">
<span dir="LTR" style="font-family: "times new roman" , "serif"; font-size: 12.0pt; line-height: 107%;">It is clear, the number of models is 408 but the answers of masses
are as follows:<o:p></o:p></span></div>
<div class="MsoNormal" style="text-align: left;">
<br /></div>
<table border="0" cellpadding="0" cellspacing="0" class="MsoNormalTable" style="border-collapse: collapse; margin-left: 4.65pt; text-align: left; width: 192px;">
<tbody>
<tr style="height: 15.0pt; mso-yfti-firstrow: yes; mso-yfti-irow: 0;">
<td nowrap="" style="border: solid windowtext 1.0pt; height: 15.0pt; mso-border-alt: solid windowtext .5pt; padding: 0cm 5.4pt 0cm 5.4pt; width: 48.0pt;" width="64"><div class="MsoNormal" style="line-height: normal; margin-bottom: 0.0001pt; text-align: center; unicode-bidi: embed;">
<b>m1<o:p></o:p></b></div>
</td>
<td nowrap="" style="border-left: none; border: solid windowtext 1.0pt; height: 15.0pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt; padding: 0cm 5.4pt 0cm 5.4pt; width: 48.0pt;" width="64"><div class="MsoNormal" style="line-height: normal; margin-bottom: 0.0001pt; text-align: center; unicode-bidi: embed;">
<b>m2<o:p></o:p></b></div>
</td>
<td nowrap="" style="border-left: none; border: solid windowtext 1.0pt; height: 15.0pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt; padding: 0cm 5.4pt 0cm 5.4pt; width: 48.0pt;" width="64"><div class="MsoNormal" style="line-height: normal; margin-bottom: 0.0001pt; text-align: center; unicode-bidi: embed;">
<b>m3<o:p></o:p></b></div>
</td>
</tr>
<tr style="height: 15.0pt; mso-yfti-irow: 1;">
<td nowrap="" style="border-top: none; border: solid windowtext 1.0pt; height: 15.0pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; padding: 0cm 5.4pt 0cm 5.4pt; width: 48.0pt;" valign="bottom" width="64"><div class="MsoNormal" style="line-height: normal; margin-bottom: 0.0001pt; text-align: left; unicode-bidi: embed;">
4<o:p></o:p></div>
</td>
<td nowrap="" style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 15.0pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; padding: 0cm 5.4pt 0cm 5.4pt; width: 48.0pt;" valign="bottom" width="64"><div class="MsoNormal" style="line-height: normal; margin-bottom: 0.0001pt; text-align: left; unicode-bidi: embed;">
100<o:p></o:p></div>
</td>
<td nowrap="" style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 15.0pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; padding: 0cm 5.4pt 0cm 5.4pt; width: 48.0pt;" valign="bottom" width="64"><div class="MsoNormal" style="line-height: normal; margin-bottom: 0.0001pt; text-align: left; unicode-bidi: embed;">
500<o:p></o:p></div>
</td>
</tr>
<tr style="height: 15.75pt; mso-yfti-irow: 2;">
<td nowrap="" style="border-top: none; border: solid windowtext 1.0pt; height: 15.75pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; padding: 0cm 5.4pt 0cm 5.4pt; width: 48.0pt;" valign="bottom" width="64"><div class="MsoNormal" style="line-height: normal; margin-bottom: 0.0001pt; text-align: left; unicode-bidi: embed;">
10<o:p></o:p></div>
</td>
<td nowrap="" style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 15.75pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; padding: 0cm 5.4pt 0cm 5.4pt; width: 48.0pt;" valign="bottom" width="64"><div class="MsoNormal" style="line-height: normal; margin-bottom: 0.0001pt; text-align: left; unicode-bidi: embed;">
240<o:p></o:p></div>
</td>
<td nowrap="" style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 15.75pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; padding: 0cm 5.4pt 0cm 5.4pt; width: 48.0pt;" valign="bottom" width="64"><div class="MsoNormal" style="line-height: normal; margin-bottom: 0.0001pt; text-align: left; unicode-bidi: embed;">
200<o:p></o:p></div>
</td>
</tr>
<tr style="height: 15.75pt; mso-yfti-irow: 3;">
<td nowrap="" style="border-top: none; border: solid windowtext 1.0pt; height: 15.75pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; padding: 0cm 5.4pt 0cm 5.4pt; width: 48.0pt;" valign="bottom" width="64"><div class="MsoNormal" style="line-height: normal; margin-bottom: 0.0001pt; text-align: left; unicode-bidi: embed;">
20<o:p></o:p></div>
</td>
<td nowrap="" style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 15.75pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; padding: 0cm 5.4pt 0cm 5.4pt; width: 48.0pt;" valign="bottom" width="64"><div class="MsoNormal" style="line-height: normal; margin-bottom: 0.0001pt; text-align: left; unicode-bidi: embed;">
20<o:p></o:p></div>
</td>
<td nowrap="" style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 15.75pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; padding: 0cm 5.4pt 0cm 5.4pt; width: 48.0pt;" valign="bottom" width="64"><div class="MsoNormal" style="line-height: normal; margin-bottom: 0.0001pt; text-align: left; unicode-bidi: embed;">
1300<o:p></o:p></div>
</td>
</tr>
<tr style="height: 15.75pt; mso-yfti-irow: 4;">
<td nowrap="" style="border-top: none; border: solid windowtext 1.0pt; height: 15.75pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; padding: 0cm 5.4pt 0cm 5.4pt; width: 48.0pt;" valign="bottom" width="64"><div class="MsoNormal" style="line-height: normal; margin-bottom: 0.0001pt; text-align: left; unicode-bidi: embed;">
20<o:p></o:p></div>
</td>
<td nowrap="" style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 15.75pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; padding: 0cm 5.4pt 0cm 5.4pt; width: 48.0pt;" valign="bottom" width="64"><div class="MsoNormal" style="line-height: normal; margin-bottom: 0.0001pt; text-align: left; unicode-bidi: embed;">
220<o:p></o:p></div>
</td>
<td nowrap="" style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 15.75pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; padding: 0cm 5.4pt 0cm 5.4pt; width: 48.0pt;" valign="bottom" width="64"><div class="MsoNormal" style="line-height: normal; margin-bottom: 0.0001pt; text-align: left; unicode-bidi: embed;">
200<o:p></o:p></div>
</td>
</tr>
<tr style="height: 18.75pt; mso-yfti-irow: 5;">
<td nowrap="" style="border-top: none; border: solid windowtext 1.0pt; height: 18.75pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; padding: 0cm 5.4pt 0cm 5.4pt; width: 48.0pt;" valign="bottom" width="64"><div class="MsoNormal" style="line-height: normal; margin-bottom: 0.0001pt; text-align: left; unicode-bidi: embed;">
30<o:p></o:p></div>
</td>
<td nowrap="" style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 18.75pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; padding: 0cm 5.4pt 0cm 5.4pt; width: 48.0pt;" valign="bottom" width="64"><div class="MsoNormal" style="line-height: normal; margin-bottom: 0.0001pt; text-align: left; unicode-bidi: embed;">
380<o:p></o:p></div>
</td>
<td nowrap="" style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 18.75pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; padding: 0cm 5.4pt 0cm 5.4pt; width: 48.0pt;" valign="bottom" width="64"><div class="MsoNormal" style="line-height: normal; margin-bottom: 0.0001pt; text-align: left; unicode-bidi: embed;">
100<o:p></o:p></div>
</td>
</tr>
<tr style="height: 15.0pt; mso-yfti-irow: 6;">
<td nowrap="" style="border-top: none; border: solid windowtext 1.0pt; height: 15.0pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; padding: 0cm 5.4pt 0cm 5.4pt; width: 48.0pt;" valign="bottom" width="64"><div class="MsoNormal" style="line-height: normal; margin-bottom: 0.0001pt; text-align: left; unicode-bidi: embed;">
31<o:p></o:p></div>
</td>
<td nowrap="" style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 15.0pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; padding: 0cm 5.4pt 0cm 5.4pt; width: 48.0pt;" valign="bottom" width="64"><div class="MsoNormal" style="line-height: normal; margin-bottom: 0.0001pt; text-align: left; unicode-bidi: embed;">
200<o:p></o:p></div>
</td>
<td nowrap="" style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 15.0pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; padding: 0cm 5.4pt 0cm 5.4pt; width: 48.0pt;" valign="bottom" width="64"><div class="MsoNormal" style="line-height: normal; margin-bottom: 0.0001pt; text-align: left; unicode-bidi: embed;">
200<o:p></o:p></div>
</td>
</tr>
<tr style="height: 15.0pt; mso-yfti-irow: 7; mso-yfti-lastrow: yes;">
<td nowrap="" style="border-top: none; border: solid windowtext 1.0pt; height: 15.0pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; padding: 0cm 5.4pt 0cm 5.4pt; width: 48.0pt;" valign="bottom" width="64"><div class="MsoNormal" style="line-height: normal; margin-bottom: 0.0001pt; text-align: left; unicode-bidi: embed;">
40<o:p></o:p></div>
</td>
<td nowrap="" style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 15.0pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; padding: 0cm 5.4pt 0cm 5.4pt; width: 48.0pt;" valign="bottom" width="64"><div class="MsoNormal" style="line-height: normal; margin-bottom: 0.0001pt; text-align: left; unicode-bidi: embed;">
60<o:p></o:p></div>
</td>
<td nowrap="" style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 15.0pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; padding: 0cm 5.4pt 0cm 5.4pt; width: 48.0pt;" valign="bottom" width="64"><div class="MsoNormal" style="line-height: normal; margin-bottom: 0.0001pt; text-align: left; unicode-bidi: embed;">
500<o:p></o:p></div>
</td>
</tr>
</tbody></table>
<div class="MsoNormal" style="text-align: left;">
<br /></div>
<div class="MsoNormal" style="text-align: left;">
<span dir="LTR" style="font-family: "times new roman" , "serif"; font-size: 12.0pt; line-height: 107%;">It means that we found 2856 systems of three particles which have
the same total gravity potential energy.<o:p></o:p></span></div>
<div class="MsoNormal" style="text-align: left;">
<span dir="LTR" style="font-family: "times new roman" , "serif"; font-size: 12.0pt; line-height: 107%;"><br /></span></div>
<div class="MsoNormal" style="text-align: left;">
<b><u><span dir="LTR" style="font-family: "times new roman" , "serif"; font-size: 12.0pt; line-height: 107%;">Question (3):<o:p></o:p></span></u></b></div>
<div class="MsoNormal" style="text-align: left;">
<b><u><span dir="LTR" style="font-family: "times new roman" , "serif"; font-size: 12.0pt; line-height: 107%;"><br /></span></u></b></div>
<div class="MsoNormal" style="text-align: left;">
<span dir="LTR" style="font-family: "times new roman" , "serif"; font-size: 12.0pt; line-height: 107%;">If we have:<o:p></o:p></span></div>
<div class="MsoNormal" style="text-align: left;">
<span dir="LTR" style="font-family: "times new roman" , "serif"; font-size: 12.0pt; line-height: 107%;"><br /></span></div>
<div class="MsoNormal" style="text-align: left;">
<span dir="LTR" style="font-family: "times new roman" , "serif"; font-size: 12.0pt; line-height: 107%;">U (r) =</span><span dir="LTR"> </span><span dir="LTR">-2.27021E-06</span><span dir="LTR" style="font-family: "times new roman" , "serif"; font-size: 12.0pt; line-height: 107%;"> </span><span dir="LTR" style="font-family: "times new roman" , serif; font-size: 12pt; line-height: 107%;">J</span><span dir="LTR"><o:p></o:p></span></div>
<div class="MsoNormal" style="text-align: left;">
<span dir="LTR" style="font-family: "times new roman" , serif; font-size: 12pt; line-height: 107%;"><br /></span></div>
<div class="MsoNormal" style="text-align: left;">
<span dir="LTR" style="font-family: "times new roman" , serif; font-size: 12pt; line-height: 107%;">r = 1.54 m<o:p></o:p></span></div>
<div class="MsoNormal" style="text-align: left;">
<span dir="LTR" style="font-family: "times new roman" , serif; font-size: 12pt; line-height: 107%;"><br /></span></div>
<div class="MsoNormal" style="text-align: left;">
<span dir="LTR" style="font-family: "times new roman" , serif; font-size: 12pt; line-height: 107%;">How can we map these particles in the space?<o:p></o:p></span></div>
<div class="MsoNormal" style="text-align: left;">
<span dir="LTR" style="font-family: "times new roman" , serif; font-size: 12pt; line-height: 107%;"><br /></span></div>
<div class="MsoNormal" style="text-align: left;">
<span dir="LTR" style="font-family: "times new roman" , "serif"; font-size: 12.0pt; line-height: 107%;">The answers for masses are just like to question (2):<o:p></o:p></span></div>
<div align="right" class="MsoNormal">
<br /></div>
<table border="0" cellpadding="0" cellspacing="0" class="MsoNormalTable" style="border-collapse: collapse; margin-left: 4.65pt; mso-padding-alt: 0cm 5.4pt 0cm 5.4pt; mso-yfti-tbllook: 1184; width: 192px;">
<tbody>
<tr style="height: 15.0pt; mso-yfti-firstrow: yes; mso-yfti-irow: 0;">
<td nowrap="" style="border: solid windowtext 1.0pt; height: 15.0pt; mso-border-alt: solid windowtext .5pt; padding: 0cm 5.4pt 0cm 5.4pt; width: 48.0pt;" width="64"><div align="center" class="MsoNormal" style="direction: ltr; line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; text-align: center; unicode-bidi: embed;">
<b>m1<o:p></o:p></b></div>
</td>
<td nowrap="" style="border-left: none; border: solid windowtext 1.0pt; height: 15.0pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt; padding: 0cm 5.4pt 0cm 5.4pt; width: 48.0pt;" width="64"><div align="center" class="MsoNormal" style="direction: ltr; line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; text-align: center; unicode-bidi: embed;">
<b>m2<o:p></o:p></b></div>
</td>
<td nowrap="" style="border-left: none; border: solid windowtext 1.0pt; height: 15.0pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt; padding: 0cm 5.4pt 0cm 5.4pt; width: 48.0pt;" width="64"><div align="center" class="MsoNormal" style="direction: ltr; line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; text-align: center; unicode-bidi: embed;">
<b>m3<o:p></o:p></b></div>
</td>
</tr>
<tr style="height: 15.0pt; mso-yfti-irow: 1;">
<td nowrap="" style="border-top: none; border: solid windowtext 1.0pt; height: 15.0pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; padding: 0cm 5.4pt 0cm 5.4pt; width: 48.0pt;" valign="bottom" width="64"><div align="right" class="MsoNormal" style="direction: ltr; line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; text-align: right; unicode-bidi: embed;">
4<o:p></o:p></div>
</td>
<td nowrap="" style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 15.0pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; padding: 0cm 5.4pt 0cm 5.4pt; width: 48.0pt;" valign="bottom" width="64"><div align="right" class="MsoNormal" style="direction: ltr; line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; text-align: right; unicode-bidi: embed;">
100<o:p></o:p></div>
</td>
<td nowrap="" style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 15.0pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; padding: 0cm 5.4pt 0cm 5.4pt; width: 48.0pt;" valign="bottom" width="64"><div align="right" class="MsoNormal" style="direction: ltr; line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; text-align: right; unicode-bidi: embed;">
500<o:p></o:p></div>
</td>
</tr>
<tr style="height: 15.75pt; mso-yfti-irow: 2;">
<td nowrap="" style="border-top: none; border: solid windowtext 1.0pt; height: 15.75pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; padding: 0cm 5.4pt 0cm 5.4pt; width: 48.0pt;" valign="bottom" width="64"><div align="right" class="MsoNormal" style="direction: ltr; line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; text-align: right; unicode-bidi: embed;">
10<o:p></o:p></div>
</td>
<td nowrap="" style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 15.75pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; padding: 0cm 5.4pt 0cm 5.4pt; width: 48.0pt;" valign="bottom" width="64"><div align="right" class="MsoNormal" style="direction: ltr; line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; text-align: right; unicode-bidi: embed;">
240<o:p></o:p></div>
</td>
<td nowrap="" style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 15.75pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; padding: 0cm 5.4pt 0cm 5.4pt; width: 48.0pt;" valign="bottom" width="64"><div align="right" class="MsoNormal" style="direction: ltr; line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; text-align: right; unicode-bidi: embed;">
200<o:p></o:p></div>
</td>
</tr>
<tr style="height: 15.75pt; mso-yfti-irow: 3;">
<td nowrap="" style="border-top: none; border: solid windowtext 1.0pt; height: 15.75pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; padding: 0cm 5.4pt 0cm 5.4pt; width: 48.0pt;" valign="bottom" width="64"><div align="right" class="MsoNormal" style="direction: ltr; line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; text-align: right; unicode-bidi: embed;">
20<o:p></o:p></div>
</td>
<td nowrap="" style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 15.75pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; padding: 0cm 5.4pt 0cm 5.4pt; width: 48.0pt;" valign="bottom" width="64"><div align="right" class="MsoNormal" style="direction: ltr; line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; text-align: right; unicode-bidi: embed;">
20<o:p></o:p></div>
</td>
<td nowrap="" style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 15.75pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; padding: 0cm 5.4pt 0cm 5.4pt; width: 48.0pt;" valign="bottom" width="64"><div align="right" class="MsoNormal" style="direction: ltr; line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; text-align: right; unicode-bidi: embed;">
1300<o:p></o:p></div>
</td>
</tr>
<tr style="height: 15.75pt; mso-yfti-irow: 4;">
<td nowrap="" style="border-top: none; border: solid windowtext 1.0pt; height: 15.75pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; padding: 0cm 5.4pt 0cm 5.4pt; width: 48.0pt;" valign="bottom" width="64"><div align="right" class="MsoNormal" style="direction: ltr; line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; text-align: right; unicode-bidi: embed;">
20<o:p></o:p></div>
</td>
<td nowrap="" style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 15.75pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; padding: 0cm 5.4pt 0cm 5.4pt; width: 48.0pt;" valign="bottom" width="64"><div align="right" class="MsoNormal" style="direction: ltr; line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; text-align: right; unicode-bidi: embed;">
220<o:p></o:p></div>
</td>
<td nowrap="" style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 15.75pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; padding: 0cm 5.4pt 0cm 5.4pt; width: 48.0pt;" valign="bottom" width="64"><div align="right" class="MsoNormal" style="direction: ltr; line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; text-align: right; unicode-bidi: embed;">
200<o:p></o:p></div>
</td>
</tr>
<tr style="height: 18.75pt; mso-yfti-irow: 5;">
<td nowrap="" style="border-top: none; border: solid windowtext 1.0pt; height: 18.75pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; padding: 0cm 5.4pt 0cm 5.4pt; width: 48.0pt;" valign="bottom" width="64"><div align="right" class="MsoNormal" style="direction: ltr; line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; text-align: right; unicode-bidi: embed;">
30<o:p></o:p></div>
</td>
<td nowrap="" style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 18.75pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; padding: 0cm 5.4pt 0cm 5.4pt; width: 48.0pt;" valign="bottom" width="64"><div align="right" class="MsoNormal" style="direction: ltr; line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; text-align: right; unicode-bidi: embed;">
380<o:p></o:p></div>
</td>
<td nowrap="" style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 18.75pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; padding: 0cm 5.4pt 0cm 5.4pt; width: 48.0pt;" valign="bottom" width="64"><div align="right" class="MsoNormal" style="direction: ltr; line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; text-align: right; unicode-bidi: embed;">
100<o:p></o:p></div>
</td>
</tr>
<tr style="height: 15.0pt; mso-yfti-irow: 6;">
<td nowrap="" style="border-top: none; border: solid windowtext 1.0pt; height: 15.0pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; padding: 0cm 5.4pt 0cm 5.4pt; width: 48.0pt;" valign="bottom" width="64"><div align="right" class="MsoNormal" style="direction: ltr; line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; text-align: right; unicode-bidi: embed;">
31<o:p></o:p></div>
</td>
<td nowrap="" style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 15.0pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; padding: 0cm 5.4pt 0cm 5.4pt; width: 48.0pt;" valign="bottom" width="64"><div align="right" class="MsoNormal" style="direction: ltr; line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; text-align: right; unicode-bidi: embed;">
200<o:p></o:p></div>
</td>
<td nowrap="" style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 15.0pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; padding: 0cm 5.4pt 0cm 5.4pt; width: 48.0pt;" valign="bottom" width="64"><div align="right" class="MsoNormal" style="direction: ltr; line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; text-align: right; unicode-bidi: embed;">
200<o:p></o:p></div>
</td>
</tr>
<tr style="height: 15.0pt; mso-yfti-irow: 7; mso-yfti-lastrow: yes;">
<td nowrap="" style="border-top: none; border: solid windowtext 1.0pt; height: 15.0pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; padding: 0cm 5.4pt 0cm 5.4pt; width: 48.0pt;" valign="bottom" width="64"><div align="right" class="MsoNormal" style="direction: ltr; line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; text-align: right; unicode-bidi: embed;">
40<o:p></o:p></div>
</td>
<td nowrap="" style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 15.0pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; padding: 0cm 5.4pt 0cm 5.4pt; width: 48.0pt;" valign="bottom" width="64"><div align="right" class="MsoNormal" style="direction: ltr; line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; text-align: right; unicode-bidi: embed;">
60<o:p></o:p></div>
</td>
<td nowrap="" style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 15.0pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; padding: 0cm 5.4pt 0cm 5.4pt; width: 48.0pt;" valign="bottom" width="64"><div align="right" class="MsoNormal" style="direction: ltr; line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; text-align: right; unicode-bidi: embed;">
500<o:p></o:p></div>
</td>
</tr>
</tbody></table>
<div align="right" class="MsoNormal" dir="RTL">
<br /></div>
<div align="right" class="MsoNormal" dir="RTL">
<span dir="LTR" style="font-family: "times new roman" , "serif"; font-size: 12.0pt; line-height: 107%;"><o:p><br /></o:p></span></div>
<div class="MsoNormal" style="text-align: left;">
<span dir="LTR" style="font-family: "times new roman" , "serif"; font-size: 12.0pt; line-height: 107%;">But the answers for step (2) are as follows:<o:p></o:p></span></div>
<div class="MsoNormal" style="text-align: left;">
<span dir="LTR" style="font-family: "times new roman" , "serif"; font-size: 12.0pt; line-height: 107%;"><br /></span></div>
<div class="MsoNormal">
<span dir="LTR" style="font-family: "times new roman" , serif; font-size: 12pt; line-height: 107%;">
</span></div>
<table border="0" cellpadding="0" cellspacing="0" class="MsoNormalTable" style="border-collapse: collapse; margin-left: 4.65pt; mso-padding-alt: 0cm 5.4pt 0cm 5.4pt; mso-yfti-tbllook: 1184; width: 256px;">
<tbody>
<tr style="height: 15.0pt; mso-yfti-firstrow: yes; mso-yfti-irow: 0;">
<td nowrap="" style="border: solid windowtext 1.0pt; height: 15.0pt; mso-border-alt: solid windowtext .5pt; padding: 0cm 5.4pt 0cm 5.4pt; width: 48.0pt;" width="64"><div align="center" class="MsoNormal" style="direction: ltr; line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; text-align: center; unicode-bidi: embed;">
<b>Models<o:p></o:p></b></div>
</td>
<td nowrap="" style="border-left: none; border: solid windowtext 1.0pt; height: 15.0pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt; padding: 0cm 5.4pt 0cm 5.4pt; width: 48.0pt;" width="64"><div align="center" class="MsoNormal" style="direction: ltr; line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; text-align: center; unicode-bidi: embed;">
<b>x<o:p></o:p></b></div>
</td>
<td nowrap="" style="border-left: none; border: solid windowtext 1.0pt; height: 15.0pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt; padding: 0cm 5.4pt 0cm 5.4pt; width: 48.0pt;" width="64"><div align="center" class="MsoNormal" style="direction: ltr; line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; text-align: center; unicode-bidi: embed;">
<b>y<o:p></o:p></b></div>
</td>
<td nowrap="" style="border-left: none; border: solid windowtext 1.0pt; height: 15.0pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt; padding: 0cm 5.4pt 0cm 5.4pt; width: 48.0pt;" width="64"><div align="center" class="MsoNormal" style="direction: ltr; line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; text-align: center; unicode-bidi: embed;">
<b>z<o:p></o:p></b></div>
</td>
</tr>
<tr style="height: 15.0pt; mso-yfti-irow: 1;">
<td nowrap="" style="border-top: none; border: solid windowtext 1.0pt; height: 15.0pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; padding: 0cm 5.4pt 0cm 5.4pt; width: 48.0pt;" valign="bottom" width="64"><div align="right" class="MsoNormal" style="direction: ltr; line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; text-align: right; unicode-bidi: embed;">
1<o:p></o:p></div>
</td>
<td nowrap="" style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 15.0pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; padding: 0cm 5.4pt 0cm 5.4pt; width: 48.0pt;" valign="bottom" width="64"><div align="right" class="MsoNormal" style="direction: ltr; line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; text-align: right; unicode-bidi: embed;">
-0.31<o:p></o:p></div>
</td>
<td nowrap="" style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 15.0pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; padding: 0cm 5.4pt 0cm 5.4pt; width: 48.0pt;" valign="bottom" width="64"><div align="right" class="MsoNormal" style="direction: ltr; line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; text-align: right; unicode-bidi: embed;">
0.09<o:p></o:p></div>
</td>
<td nowrap="" style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 15.0pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; padding: 0cm 5.4pt 0cm 5.4pt; width: 48.0pt;" valign="bottom" width="64"><div align="right" class="MsoNormal" style="direction: ltr; line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; text-align: right; unicode-bidi: embed;">
0.923333<o:p></o:p></div>
</td>
</tr>
<tr style="height: 15.0pt; mso-yfti-irow: 2;">
<td nowrap="" style="border-top: none; border: solid windowtext 1.0pt; height: 15.0pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; padding: 0cm 5.4pt 0cm 5.4pt; width: 48.0pt;" valign="bottom" width="64"><div align="right" class="MsoNormal" style="direction: ltr; line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; text-align: right; unicode-bidi: embed;">
2<o:p></o:p></div>
</td>
<td nowrap="" style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 15.0pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; padding: 0cm 5.4pt 0cm 5.4pt; width: 48.0pt;" valign="bottom" width="64"><div align="right" class="MsoNormal" style="direction: ltr; line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; text-align: right; unicode-bidi: embed;">
-0.31<o:p></o:p></div>
</td>
<td nowrap="" style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 15.0pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; padding: 0cm 5.4pt 0cm 5.4pt; width: 48.0pt;" valign="bottom" width="64"><div align="right" class="MsoNormal" style="direction: ltr; line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; text-align: right; unicode-bidi: embed;">
0.523333<o:p></o:p></div>
</td>
<td nowrap="" style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 15.0pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; padding: 0cm 5.4pt 0cm 5.4pt; width: 48.0pt;" valign="bottom" width="64"><div align="right" class="MsoNormal" style="direction: ltr; line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; text-align: right; unicode-bidi: embed;">
0.923333<o:p></o:p></div>
</td>
</tr>
<tr style="height: 15.0pt; mso-yfti-irow: 3;">
<td nowrap="" style="border-top: none; border: solid windowtext 1.0pt; height: 15.0pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; padding: 0cm 5.4pt 0cm 5.4pt; width: 48.0pt;" valign="bottom" width="64"><div align="right" class="MsoNormal" style="direction: ltr; line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; text-align: right; unicode-bidi: embed;">
3<o:p></o:p></div>
</td>
<td nowrap="" style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 15.0pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; padding: 0cm 5.4pt 0cm 5.4pt; width: 48.0pt;" valign="bottom" width="64"><div align="right" class="MsoNormal" style="direction: ltr; line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; text-align: right; unicode-bidi: embed;">
-0.31<o:p></o:p></div>
</td>
<td nowrap="" style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 15.0pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; padding: 0cm 5.4pt 0cm 5.4pt; width: 48.0pt;" valign="bottom" width="64"><div align="right" class="MsoNormal" style="direction: ltr; line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; text-align: right; unicode-bidi: embed;">
0.923333<o:p></o:p></div>
</td>
<td nowrap="" style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 15.0pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; padding: 0cm 5.4pt 0cm 5.4pt; width: 48.0pt;" valign="bottom" width="64"><div align="right" class="MsoNormal" style="direction: ltr; line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; text-align: right; unicode-bidi: embed;">
0.09<o:p></o:p></div>
</td>
</tr>
<tr style="height: 15.0pt; mso-yfti-irow: 4;">
<td nowrap="" style="border-top: none; border: solid windowtext 1.0pt; height: 15.0pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; padding: 0cm 5.4pt 0cm 5.4pt; width: 48.0pt;" valign="bottom" width="64"><div align="right" class="MsoNormal" style="direction: ltr; line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; text-align: right; unicode-bidi: embed;">
4<o:p></o:p></div>
</td>
<td nowrap="" style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 15.0pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; padding: 0cm 5.4pt 0cm 5.4pt; width: 48.0pt;" valign="bottom" width="64"><div align="right" class="MsoNormal" style="direction: ltr; line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; text-align: right; unicode-bidi: embed;">
-0.31<o:p></o:p></div>
</td>
<td nowrap="" style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 15.0pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; padding: 0cm 5.4pt 0cm 5.4pt; width: 48.0pt;" valign="bottom" width="64"><div align="right" class="MsoNormal" style="direction: ltr; line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; text-align: right; unicode-bidi: embed;">
0.923333<o:p></o:p></div>
</td>
<td nowrap="" style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 15.0pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; padding: 0cm 5.4pt 0cm 5.4pt; width: 48.0pt;" valign="bottom" width="64"><div align="right" class="MsoNormal" style="direction: ltr; line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; text-align: right; unicode-bidi: embed;">
0.523333<o:p></o:p></div>
</td>
</tr>
<tr style="height: 15.0pt; mso-yfti-irow: 5;">
<td nowrap="" style="border-top: none; border: solid windowtext 1.0pt; height: 15.0pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; padding: 0cm 5.4pt 0cm 5.4pt; width: 48.0pt;" valign="bottom" width="64"><div align="right" class="MsoNormal" style="direction: ltr; line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; text-align: right; unicode-bidi: embed;">
5<o:p></o:p></div>
</td>
<td nowrap="" style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 15.0pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; padding: 0cm 5.4pt 0cm 5.4pt; width: 48.0pt;" valign="bottom" width="64"><div align="right" class="MsoNormal" style="direction: ltr; line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; text-align: right; unicode-bidi: embed;">
-0.27667<o:p></o:p></div>
</td>
<td nowrap="" style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 15.0pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; padding: 0cm 5.4pt 0cm 5.4pt; width: 48.0pt;" valign="bottom" width="64"><div align="right" class="MsoNormal" style="direction: ltr; line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; text-align: right; unicode-bidi: embed;">
0.123333<o:p></o:p></div>
</td>
<td nowrap="" style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 15.0pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; padding: 0cm 5.4pt 0cm 5.4pt; width: 48.0pt;" valign="bottom" width="64"><div align="right" class="MsoNormal" style="direction: ltr; line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; text-align: right; unicode-bidi: embed;">
0.956667<o:p></o:p></div>
</td>
</tr>
<tr style="height: 15.0pt; mso-yfti-irow: 6;">
<td nowrap="" style="border-top: none; border: solid windowtext 1.0pt; height: 15.0pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; padding: 0cm 5.4pt 0cm 5.4pt; width: 48.0pt;" valign="bottom" width="64"><div align="right" class="MsoNormal" style="direction: ltr; line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; text-align: right; unicode-bidi: embed;">
6<o:p></o:p></div>
</td>
<td nowrap="" style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 15.0pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; padding: 0cm 5.4pt 0cm 5.4pt; width: 48.0pt;" valign="bottom" width="64"><div align="right" class="MsoNormal" style="direction: ltr; line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; text-align: right; unicode-bidi: embed;">
-0.27667<o:p></o:p></div>
</td>
<td nowrap="" style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 15.0pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; padding: 0cm 5.4pt 0cm 5.4pt; width: 48.0pt;" valign="bottom" width="64"><div align="right" class="MsoNormal" style="direction: ltr; line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; text-align: right; unicode-bidi: embed;">
0.556667<o:p></o:p></div>
</td>
<td nowrap="" style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 15.0pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; padding: 0cm 5.4pt 0cm 5.4pt; width: 48.0pt;" valign="bottom" width="64"><div align="right" class="MsoNormal" style="direction: ltr; line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; text-align: right; unicode-bidi: embed;">
0.956667<o:p></o:p></div>
</td>
</tr>
<tr style="height: 15.0pt; mso-yfti-irow: 7;">
<td nowrap="" style="border-top: none; border: solid windowtext 1.0pt; height: 15.0pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; padding: 0cm 5.4pt 0cm 5.4pt; width: 48.0pt;" valign="bottom" width="64"><div align="right" class="MsoNormal" style="direction: ltr; line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; text-align: right; unicode-bidi: embed;">
7<o:p></o:p></div>
</td>
<td nowrap="" style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 15.0pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; padding: 0cm 5.4pt 0cm 5.4pt; width: 48.0pt;" valign="bottom" width="64"><div align="right" class="MsoNormal" style="direction: ltr; line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; text-align: right; unicode-bidi: embed;">
-0.27667<o:p></o:p></div>
</td>
<td nowrap="" style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 15.0pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; padding: 0cm 5.4pt 0cm 5.4pt; width: 48.0pt;" valign="bottom" width="64"><div align="right" class="MsoNormal" style="direction: ltr; line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; text-align: right; unicode-bidi: embed;">
0.956667<o:p></o:p></div>
</td>
<td nowrap="" style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 15.0pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; padding: 0cm 5.4pt 0cm 5.4pt; width: 48.0pt;" valign="bottom" width="64"><div align="right" class="MsoNormal" style="direction: ltr; line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; text-align: right; unicode-bidi: embed;">
0.123333<o:p></o:p></div>
</td>
</tr>
<tr style="height: 15.0pt; mso-yfti-irow: 8;">
<td nowrap="" style="border-top: none; border: solid windowtext 1.0pt; height: 15.0pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; padding: 0cm 5.4pt 0cm 5.4pt; width: 48.0pt;" valign="bottom" width="64"><div align="right" class="MsoNormal" style="direction: ltr; line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; text-align: right; unicode-bidi: embed;">
8<o:p></o:p></div>
</td>
<td nowrap="" style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 15.0pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; padding: 0cm 5.4pt 0cm 5.4pt; width: 48.0pt;" valign="bottom" width="64"><div align="right" class="MsoNormal" style="direction: ltr; line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; text-align: right; unicode-bidi: embed;">
-0.27667<o:p></o:p></div>
</td>
<td nowrap="" style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 15.0pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; padding: 0cm 5.4pt 0cm 5.4pt; width: 48.0pt;" valign="bottom" width="64"><div align="right" class="MsoNormal" style="direction: ltr; line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; text-align: right; unicode-bidi: embed;">
0.956667<o:p></o:p></div>
</td>
<td nowrap="" style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 15.0pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; padding: 0cm 5.4pt 0cm 5.4pt; width: 48.0pt;" valign="bottom" width="64"><div align="right" class="MsoNormal" style="direction: ltr; line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; text-align: right; unicode-bidi: embed;">
0.556667<o:p></o:p></div>
</td>
</tr>
<tr style="height: 15.0pt; mso-yfti-irow: 9;">
<td nowrap="" style="border-top: none; border: solid windowtext 1.0pt; height: 15.0pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; padding: 0cm 5.4pt 0cm 5.4pt; width: 48.0pt;" valign="bottom" width="64"><div align="right" class="MsoNormal" style="direction: ltr; line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; text-align: right; unicode-bidi: embed;">
9<o:p></o:p></div>
</td>
<td nowrap="" style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 15.0pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; padding: 0cm 5.4pt 0cm 5.4pt; width: 48.0pt;" valign="bottom" width="64"><div align="right" class="MsoNormal" style="direction: ltr; line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; text-align: right; unicode-bidi: embed;">
-0.24333<o:p></o:p></div>
</td>
<td nowrap="" style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 15.0pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; padding: 0cm 5.4pt 0cm 5.4pt; width: 48.0pt;" valign="bottom" width="64"><div align="right" class="MsoNormal" style="direction: ltr; line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; text-align: right; unicode-bidi: embed;">
0.156667<o:p></o:p></div>
</td>
<td nowrap="" style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 15.0pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; padding: 0cm 5.4pt 0cm 5.4pt; width: 48.0pt;" valign="bottom" width="64"><div align="right" class="MsoNormal" style="direction: ltr; line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; text-align: right; unicode-bidi: embed;">
0.99<o:p></o:p></div>
</td>
</tr>
<tr style="height: 15.0pt; mso-yfti-irow: 10;">
<td nowrap="" style="border-top: none; border: solid windowtext 1.0pt; height: 15.0pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; padding: 0cm 5.4pt 0cm 5.4pt; width: 48.0pt;" valign="bottom" width="64"><div align="right" class="MsoNormal" style="direction: ltr; line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; text-align: right; unicode-bidi: embed;">
10<o:p></o:p></div>
</td>
<td nowrap="" style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 15.0pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; padding: 0cm 5.4pt 0cm 5.4pt; width: 48.0pt;" valign="bottom" width="64"><div align="right" class="MsoNormal" style="direction: ltr; line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; text-align: right; unicode-bidi: embed;">
-0.24333<o:p></o:p></div>
</td>
<td nowrap="" style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 15.0pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; padding: 0cm 5.4pt 0cm 5.4pt; width: 48.0pt;" valign="bottom" width="64"><div align="right" class="MsoNormal" style="direction: ltr; line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; text-align: right; unicode-bidi: embed;">
0.59<o:p></o:p></div>
</td>
<td nowrap="" style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 15.0pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; padding: 0cm 5.4pt 0cm 5.4pt; width: 48.0pt;" valign="bottom" width="64"><div align="right" class="MsoNormal" style="direction: ltr; line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; text-align: right; unicode-bidi: embed;">
0.99<o:p></o:p></div>
</td>
</tr>
<tr style="height: 15.0pt; mso-yfti-irow: 11;">
<td nowrap="" style="border-top: none; border: solid windowtext 1.0pt; height: 15.0pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; padding: 0cm 5.4pt 0cm 5.4pt; width: 48.0pt;" valign="bottom" width="64"><div align="right" class="MsoNormal" style="direction: ltr; line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; text-align: right; unicode-bidi: embed;">
11<o:p></o:p></div>
</td>
<td nowrap="" style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 15.0pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; padding: 0cm 5.4pt 0cm 5.4pt; width: 48.0pt;" valign="bottom" width="64"><div align="right" class="MsoNormal" style="direction: ltr; line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; text-align: right; unicode-bidi: embed;">
-0.24333<o:p></o:p></div>
</td>
<td nowrap="" style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 15.0pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; padding: 0cm 5.4pt 0cm 5.4pt; width: 48.0pt;" valign="bottom" width="64"><div align="right" class="MsoNormal" style="direction: ltr; line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; text-align: right; unicode-bidi: embed;">
0.99<o:p></o:p></div>
</td>
<td nowrap="" style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 15.0pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; padding: 0cm 5.4pt 0cm 5.4pt; width: 48.0pt;" valign="bottom" width="64"><div align="right" class="MsoNormal" style="direction: ltr; line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; text-align: right; unicode-bidi: embed;">
0.156667<o:p></o:p></div>
</td>
</tr>
<tr style="height: 15.0pt; mso-yfti-irow: 12;">
<td nowrap="" style="border-top: none; border: solid windowtext 1.0pt; height: 15.0pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; padding: 0cm 5.4pt 0cm 5.4pt; width: 48.0pt;" valign="bottom" width="64"><div align="right" class="MsoNormal" style="direction: ltr; line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; text-align: right; unicode-bidi: embed;">
12<o:p></o:p></div>
</td>
<td nowrap="" style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 15.0pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; padding: 0cm 5.4pt 0cm 5.4pt; width: 48.0pt;" valign="bottom" width="64"><div align="right" class="MsoNormal" style="direction: ltr; line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; text-align: right; unicode-bidi: embed;">
-0.24333<o:p></o:p></div>
</td>
<td nowrap="" style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 15.0pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; padding: 0cm 5.4pt 0cm 5.4pt; width: 48.0pt;" valign="bottom" width="64"><div align="right" class="MsoNormal" style="direction: ltr; line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; text-align: right; unicode-bidi: embed;">
0.99<o:p></o:p></div>
</td>
<td nowrap="" style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 15.0pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; padding: 0cm 5.4pt 0cm 5.4pt; width: 48.0pt;" valign="bottom" width="64"><div align="right" class="MsoNormal" style="direction: ltr; line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; text-align: right; unicode-bidi: embed;">
0.59<o:p></o:p></div>
</td>
</tr>
<tr style="height: 15.0pt; mso-yfti-irow: 13;">
<td nowrap="" style="border-top: none; border: solid windowtext 1.0pt; height: 15.0pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; padding: 0cm 5.4pt 0cm 5.4pt; width: 48.0pt;" valign="bottom" width="64"><div align="right" class="MsoNormal" style="direction: ltr; line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; text-align: right; unicode-bidi: embed;">
13<o:p></o:p></div>
</td>
<td nowrap="" style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 15.0pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; padding: 0cm 5.4pt 0cm 5.4pt; width: 48.0pt;" valign="bottom" width="64"><div align="right" class="MsoNormal" style="direction: ltr; line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; text-align: right; unicode-bidi: embed;">
0.09<o:p></o:p></div>
</td>
<td nowrap="" style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 15.0pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; padding: 0cm 5.4pt 0cm 5.4pt; width: 48.0pt;" valign="bottom" width="64"><div align="right" class="MsoNormal" style="direction: ltr; line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; text-align: right; unicode-bidi: embed;">
-0.31<o:p></o:p></div>
</td>
<td nowrap="" style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 15.0pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; padding: 0cm 5.4pt 0cm 5.4pt; width: 48.0pt;" valign="bottom" width="64"><div align="right" class="MsoNormal" style="direction: ltr; line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; text-align: right; unicode-bidi: embed;">
0.923333<o:p></o:p></div>
</td>
</tr>
<tr style="height: 15.0pt; mso-yfti-irow: 14;">
<td nowrap="" style="border-top: none; border: solid windowtext 1.0pt; height: 15.0pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; padding: 0cm 5.4pt 0cm 5.4pt; width: 48.0pt;" valign="bottom" width="64"><div align="right" class="MsoNormal" style="direction: ltr; line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; text-align: right; unicode-bidi: embed;">
14<o:p></o:p></div>
</td>
<td nowrap="" style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 15.0pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; padding: 0cm 5.4pt 0cm 5.4pt; width: 48.0pt;" valign="bottom" width="64"><div align="right" class="MsoNormal" style="direction: ltr; line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; text-align: right; unicode-bidi: embed;">
0.09<o:p></o:p></div>
</td>
<td nowrap="" style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 15.0pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; padding: 0cm 5.4pt 0cm 5.4pt; width: 48.0pt;" valign="bottom" width="64"><div align="right" class="MsoNormal" style="direction: ltr; line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; text-align: right; unicode-bidi: embed;">
0.923333<o:p></o:p></div>
</td>
<td nowrap="" style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 15.0pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; padding: 0cm 5.4pt 0cm 5.4pt; width: 48.0pt;" valign="bottom" width="64"><div align="right" class="MsoNormal" style="direction: ltr; line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; text-align: right; unicode-bidi: embed;">
-0.31<o:p></o:p></div>
</td>
</tr>
<tr style="height: 15.0pt; mso-yfti-irow: 15;">
<td nowrap="" style="border-top: none; border: solid windowtext 1.0pt; height: 15.0pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; padding: 0cm 5.4pt 0cm 5.4pt; width: 48.0pt;" valign="bottom" width="64"><div align="right" class="MsoNormal" style="direction: ltr; line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; text-align: right; unicode-bidi: embed;">
15<o:p></o:p></div>
</td>
<td nowrap="" style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 15.0pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; padding: 0cm 5.4pt 0cm 5.4pt; width: 48.0pt;" valign="bottom" width="64"><div align="right" class="MsoNormal" style="direction: ltr; line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; text-align: right; unicode-bidi: embed;">
0.123333<o:p></o:p></div>
</td>
<td nowrap="" style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 15.0pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; padding: 0cm 5.4pt 0cm 5.4pt; width: 48.0pt;" valign="bottom" width="64"><div align="right" class="MsoNormal" style="direction: ltr; line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; text-align: right; unicode-bidi: embed;">
-0.27667<o:p></o:p></div>
</td>
<td nowrap="" style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 15.0pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; padding: 0cm 5.4pt 0cm 5.4pt; width: 48.0pt;" valign="bottom" width="64"><div align="right" class="MsoNormal" style="direction: ltr; line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; text-align: right; unicode-bidi: embed;">
0.956667<o:p></o:p></div>
</td>
</tr>
<tr style="height: 15.0pt; mso-yfti-irow: 16;">
<td nowrap="" style="border-top: none; border: solid windowtext 1.0pt; height: 15.0pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; padding: 0cm 5.4pt 0cm 5.4pt; width: 48.0pt;" valign="bottom" width="64"><div align="right" class="MsoNormal" style="direction: ltr; line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; text-align: right; unicode-bidi: embed;">
16<o:p></o:p></div>
</td>
<td nowrap="" style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 15.0pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; padding: 0cm 5.4pt 0cm 5.4pt; width: 48.0pt;" valign="bottom" width="64"><div align="right" class="MsoNormal" style="direction: ltr; line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; text-align: right; unicode-bidi: embed;">
0.123333<o:p></o:p></div>
</td>
<td nowrap="" style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 15.0pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; padding: 0cm 5.4pt 0cm 5.4pt; width: 48.0pt;" valign="bottom" width="64"><div align="right" class="MsoNormal" style="direction: ltr; line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; text-align: right; unicode-bidi: embed;">
0.956667<o:p></o:p></div>
</td>
<td nowrap="" style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 15.0pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; padding: 0cm 5.4pt 0cm 5.4pt; width: 48.0pt;" valign="bottom" width="64"><div align="right" class="MsoNormal" style="direction: ltr; line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; text-align: right; unicode-bidi: embed;">
-0.27667<o:p></o:p></div>
</td>
</tr>
<tr style="height: 15.0pt; mso-yfti-irow: 17;">
<td nowrap="" style="border-top: none; border: solid windowtext 1.0pt; height: 15.0pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; padding: 0cm 5.4pt 0cm 5.4pt; width: 48.0pt;" valign="bottom" width="64"><div align="right" class="MsoNormal" style="direction: ltr; line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; text-align: right; unicode-bidi: embed;">
17<o:p></o:p></div>
</td>
<td nowrap="" style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 15.0pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; padding: 0cm 5.4pt 0cm 5.4pt; width: 48.0pt;" valign="bottom" width="64"><div align="right" class="MsoNormal" style="direction: ltr; line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; text-align: right; unicode-bidi: embed;">
0.156667<o:p></o:p></div>
</td>
<td nowrap="" style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 15.0pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; padding: 0cm 5.4pt 0cm 5.4pt; width: 48.0pt;" valign="bottom" width="64"><div align="right" class="MsoNormal" style="direction: ltr; line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; text-align: right; unicode-bidi: embed;">
-0.24333<o:p></o:p></div>
</td>
<td nowrap="" style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 15.0pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; padding: 0cm 5.4pt 0cm 5.4pt; width: 48.0pt;" valign="bottom" width="64"><div align="right" class="MsoNormal" style="direction: ltr; line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; text-align: right; unicode-bidi: embed;">
0.99<o:p></o:p></div>
</td>
</tr>
<tr style="height: 15.0pt; mso-yfti-irow: 18;">
<td nowrap="" style="border-top: none; border: solid windowtext 1.0pt; height: 15.0pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; padding: 0cm 5.4pt 0cm 5.4pt; width: 48.0pt;" valign="bottom" width="64"><div align="right" class="MsoNormal" style="direction: ltr; line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; text-align: right; unicode-bidi: embed;">
18<o:p></o:p></div>
</td>
<td nowrap="" style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 15.0pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; padding: 0cm 5.4pt 0cm 5.4pt; width: 48.0pt;" valign="bottom" width="64"><div align="right" class="MsoNormal" style="direction: ltr; line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; text-align: right; unicode-bidi: embed;">
0.156667<o:p></o:p></div>
</td>
<td nowrap="" style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 15.0pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; padding: 0cm 5.4pt 0cm 5.4pt; width: 48.0pt;" valign="bottom" width="64"><div align="right" class="MsoNormal" style="direction: ltr; line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; text-align: right; unicode-bidi: embed;">
0.99<o:p></o:p></div>
</td>
<td nowrap="" style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 15.0pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; padding: 0cm 5.4pt 0cm 5.4pt; width: 48.0pt;" valign="bottom" width="64"><div align="right" class="MsoNormal" style="direction: ltr; line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; text-align: right; unicode-bidi: embed;">
-0.24333<o:p></o:p></div>
</td>
</tr>
<tr style="height: 15.0pt; mso-yfti-irow: 19;">
<td nowrap="" style="border-top: none; border: solid windowtext 1.0pt; height: 15.0pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; padding: 0cm 5.4pt 0cm 5.4pt; width: 48.0pt;" valign="bottom" width="64"><div align="right" class="MsoNormal" style="direction: ltr; line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; text-align: right; unicode-bidi: embed;">
19<o:p></o:p></div>
</td>
<td nowrap="" style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 15.0pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; padding: 0cm 5.4pt 0cm 5.4pt; width: 48.0pt;" valign="bottom" width="64"><div align="right" class="MsoNormal" style="direction: ltr; line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; text-align: right; unicode-bidi: embed;">
0.523333<o:p></o:p></div>
</td>
<td nowrap="" style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 15.0pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; padding: 0cm 5.4pt 0cm 5.4pt; width: 48.0pt;" valign="bottom" width="64"><div align="right" class="MsoNormal" style="direction: ltr; line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; text-align: right; unicode-bidi: embed;">
-0.31<o:p></o:p></div>
</td>
<td nowrap="" style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 15.0pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; padding: 0cm 5.4pt 0cm 5.4pt; width: 48.0pt;" valign="bottom" width="64"><div align="right" class="MsoNormal" style="direction: ltr; line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; text-align: right; unicode-bidi: embed;">
0.923333<o:p></o:p></div>
</td>
</tr>
<tr style="height: 15.0pt; mso-yfti-irow: 20;">
<td nowrap="" style="border-top: none; border: solid windowtext 1.0pt; height: 15.0pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; padding: 0cm 5.4pt 0cm 5.4pt; width: 48.0pt;" valign="bottom" width="64"><div align="right" class="MsoNormal" style="direction: ltr; line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; text-align: right; unicode-bidi: embed;">
20<o:p></o:p></div>
</td>
<td nowrap="" style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 15.0pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; padding: 0cm 5.4pt 0cm 5.4pt; width: 48.0pt;" valign="bottom" width="64"><div align="right" class="MsoNormal" style="direction: ltr; line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; text-align: right; unicode-bidi: embed;">
0.523333<o:p></o:p></div>
</td>
<td nowrap="" style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 15.0pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; padding: 0cm 5.4pt 0cm 5.4pt; width: 48.0pt;" valign="bottom" width="64"><div align="right" class="MsoNormal" style="direction: ltr; line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; text-align: right; unicode-bidi: embed;">
0.923333<o:p></o:p></div>
</td>
<td nowrap="" style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 15.0pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; padding: 0cm 5.4pt 0cm 5.4pt; width: 48.0pt;" valign="bottom" width="64"><div align="right" class="MsoNormal" style="direction: ltr; line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; text-align: right; unicode-bidi: embed;">
-0.31<o:p></o:p></div>
</td>
</tr>
<tr style="height: 15.0pt; mso-yfti-irow: 21;">
<td nowrap="" style="border-top: none; border: solid windowtext 1.0pt; height: 15.0pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; padding: 0cm 5.4pt 0cm 5.4pt; width: 48.0pt;" valign="bottom" width="64"><div align="right" class="MsoNormal" style="direction: ltr; line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; text-align: right; unicode-bidi: embed;">
21<o:p></o:p></div>
</td>
<td nowrap="" style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 15.0pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; padding: 0cm 5.4pt 0cm 5.4pt; width: 48.0pt;" valign="bottom" width="64"><div align="right" class="MsoNormal" style="direction: ltr; line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; text-align: right; unicode-bidi: embed;">
0.556667<o:p></o:p></div>
</td>
<td nowrap="" style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 15.0pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; padding: 0cm 5.4pt 0cm 5.4pt; width: 48.0pt;" valign="bottom" width="64"><div align="right" class="MsoNormal" style="direction: ltr; line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; text-align: right; unicode-bidi: embed;">
-0.27667<o:p></o:p></div>
</td>
<td nowrap="" style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 15.0pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; padding: 0cm 5.4pt 0cm 5.4pt; width: 48.0pt;" valign="bottom" width="64"><div align="right" class="MsoNormal" style="direction: ltr; line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; text-align: right; unicode-bidi: embed;">
0.956667<o:p></o:p></div>
</td>
</tr>
<tr style="height: 15.0pt; mso-yfti-irow: 22;">
<td nowrap="" style="border-top: none; border: solid windowtext 1.0pt; height: 15.0pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; padding: 0cm 5.4pt 0cm 5.4pt; width: 48.0pt;" valign="bottom" width="64"><div align="right" class="MsoNormal" style="direction: ltr; line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; text-align: right; unicode-bidi: embed;">
22<o:p></o:p></div>
</td>
<td nowrap="" style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 15.0pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; padding: 0cm 5.4pt 0cm 5.4pt; width: 48.0pt;" valign="bottom" width="64"><div align="right" class="MsoNormal" style="direction: ltr; line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; text-align: right; unicode-bidi: embed;">
0.556667<o:p></o:p></div>
</td>
<td nowrap="" style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 15.0pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; padding: 0cm 5.4pt 0cm 5.4pt; width: 48.0pt;" valign="bottom" width="64"><div align="right" class="MsoNormal" style="direction: ltr; line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; text-align: right; unicode-bidi: embed;">
0.956667<o:p></o:p></div>
</td>
<td nowrap="" style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 15.0pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; padding: 0cm 5.4pt 0cm 5.4pt; width: 48.0pt;" valign="bottom" width="64"><div align="right" class="MsoNormal" style="direction: ltr; line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; text-align: right; unicode-bidi: embed;">
-0.27667<o:p></o:p></div>
</td>
</tr>
<tr style="height: 15.0pt; mso-yfti-irow: 23;">
<td nowrap="" style="border-top: none; border: solid windowtext 1.0pt; height: 15.0pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; padding: 0cm 5.4pt 0cm 5.4pt; width: 48.0pt;" valign="bottom" width="64"><div align="right" class="MsoNormal" style="direction: ltr; line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; text-align: right; unicode-bidi: embed;">
23<o:p></o:p></div>
</td>
<td nowrap="" style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 15.0pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; padding: 0cm 5.4pt 0cm 5.4pt; width: 48.0pt;" valign="bottom" width="64"><div align="right" class="MsoNormal" style="direction: ltr; line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; text-align: right; unicode-bidi: embed;">
0.59<o:p></o:p></div>
</td>
<td nowrap="" style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 15.0pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; padding: 0cm 5.4pt 0cm 5.4pt; width: 48.0pt;" valign="bottom" width="64"><div align="right" class="MsoNormal" style="direction: ltr; line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; text-align: right; unicode-bidi: embed;">
-0.24333<o:p></o:p></div>
</td>
<td nowrap="" style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 15.0pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; padding: 0cm 5.4pt 0cm 5.4pt; width: 48.0pt;" valign="bottom" width="64"><div align="right" class="MsoNormal" style="direction: ltr; line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; text-align: right; unicode-bidi: embed;">
0.99<o:p></o:p></div>
</td>
</tr>
<tr style="height: 15.0pt; mso-yfti-irow: 24;">
<td nowrap="" style="border-top: none; border: solid windowtext 1.0pt; height: 15.0pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; padding: 0cm 5.4pt 0cm 5.4pt; width: 48.0pt;" valign="bottom" width="64"><div align="right" class="MsoNormal" style="direction: ltr; line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; text-align: right; unicode-bidi: embed;">
24<o:p></o:p></div>
</td>
<td nowrap="" style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 15.0pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; padding: 0cm 5.4pt 0cm 5.4pt; width: 48.0pt;" valign="bottom" width="64"><div align="right" class="MsoNormal" style="direction: ltr; line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; text-align: right; unicode-bidi: embed;">
0.59<o:p></o:p></div>
</td>
<td nowrap="" style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 15.0pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; padding: 0cm 5.4pt 0cm 5.4pt; width: 48.0pt;" valign="bottom" width="64"><div align="right" class="MsoNormal" style="direction: ltr; line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; text-align: right; unicode-bidi: embed;">
0.99<o:p></o:p></div>
</td>
<td nowrap="" style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 15.0pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; padding: 0cm 5.4pt 0cm 5.4pt; width: 48.0pt;" valign="bottom" width="64"><div align="right" class="MsoNormal" style="direction: ltr; line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; text-align: right; unicode-bidi: embed;">
-0.24333<o:p></o:p></div>
</td>
</tr>
<tr style="height: 15.0pt; mso-yfti-irow: 25;">
<td nowrap="" style="border-top: none; border: solid windowtext 1.0pt; height: 15.0pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; padding: 0cm 5.4pt 0cm 5.4pt; width: 48.0pt;" valign="bottom" width="64"><div align="right" class="MsoNormal" style="direction: ltr; line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; text-align: right; unicode-bidi: embed;">
25<o:p></o:p></div>
</td>
<td nowrap="" style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 15.0pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; padding: 0cm 5.4pt 0cm 5.4pt; width: 48.0pt;" valign="bottom" width="64"><div align="right" class="MsoNormal" style="direction: ltr; line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; text-align: right; unicode-bidi: embed;">
0.923333<o:p></o:p></div>
</td>
<td nowrap="" style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 15.0pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; padding: 0cm 5.4pt 0cm 5.4pt; width: 48.0pt;" valign="bottom" width="64"><div align="right" class="MsoNormal" style="direction: ltr; line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; text-align: right; unicode-bidi: embed;">
-0.31<o:p></o:p></div>
</td>
<td nowrap="" style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 15.0pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; padding: 0cm 5.4pt 0cm 5.4pt; width: 48.0pt;" valign="bottom" width="64"><div align="right" class="MsoNormal" style="direction: ltr; line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; text-align: right; unicode-bidi: embed;">
0.09<o:p></o:p></div>
</td>
</tr>
<tr style="height: 15.0pt; mso-yfti-irow: 26;">
<td nowrap="" style="border-top: none; border: solid windowtext 1.0pt; height: 15.0pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; padding: 0cm 5.4pt 0cm 5.4pt; width: 48.0pt;" valign="bottom" width="64"><div align="right" class="MsoNormal" style="direction: ltr; line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; text-align: right; unicode-bidi: embed;">
26<o:p></o:p></div>
</td>
<td nowrap="" style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 15.0pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; padding: 0cm 5.4pt 0cm 5.4pt; width: 48.0pt;" valign="bottom" width="64"><div align="right" class="MsoNormal" style="direction: ltr; line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; text-align: right; unicode-bidi: embed;">
0.923333<o:p></o:p></div>
</td>
<td nowrap="" style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 15.0pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; padding: 0cm 5.4pt 0cm 5.4pt; width: 48.0pt;" valign="bottom" width="64"><div align="right" class="MsoNormal" style="direction: ltr; line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; text-align: right; unicode-bidi: embed;">
-0.31<o:p></o:p></div>
</td>
<td nowrap="" style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 15.0pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; padding: 0cm 5.4pt 0cm 5.4pt; width: 48.0pt;" valign="bottom" width="64"><div align="right" class="MsoNormal" style="direction: ltr; line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; text-align: right; unicode-bidi: embed;">
0.523333<o:p></o:p></div>
</td>
</tr>
<tr style="height: 15.0pt; mso-yfti-irow: 27;">
<td nowrap="" style="border-top: none; border: solid windowtext 1.0pt; height: 15.0pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; padding: 0cm 5.4pt 0cm 5.4pt; width: 48.0pt;" valign="bottom" width="64"><div align="right" class="MsoNormal" style="direction: ltr; line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; text-align: right; unicode-bidi: embed;">
27<o:p></o:p></div>
</td>
<td nowrap="" style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 15.0pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; padding: 0cm 5.4pt 0cm 5.4pt; width: 48.0pt;" valign="bottom" width="64"><div align="right" class="MsoNormal" style="direction: ltr; line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; text-align: right; unicode-bidi: embed;">
0.923333<o:p></o:p></div>
</td>
<td nowrap="" style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 15.0pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; padding: 0cm 5.4pt 0cm 5.4pt; width: 48.0pt;" valign="bottom" width="64"><div align="right" class="MsoNormal" style="direction: ltr; line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; text-align: right; unicode-bidi: embed;">
0.09<o:p></o:p></div>
</td>
<td nowrap="" style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 15.0pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; padding: 0cm 5.4pt 0cm 5.4pt; width: 48.0pt;" valign="bottom" width="64"><div align="right" class="MsoNormal" style="direction: ltr; line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; text-align: right; unicode-bidi: embed;">
-0.31<o:p></o:p></div>
</td>
</tr>
<tr style="height: 15.0pt; mso-yfti-irow: 28;">
<td nowrap="" style="border-top: none; border: solid windowtext 1.0pt; height: 15.0pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; padding: 0cm 5.4pt 0cm 5.4pt; width: 48.0pt;" valign="bottom" width="64"><div align="right" class="MsoNormal" style="direction: ltr; line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; text-align: right; unicode-bidi: embed;">
28<o:p></o:p></div>
</td>
<td nowrap="" style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 15.0pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; padding: 0cm 5.4pt 0cm 5.4pt; width: 48.0pt;" valign="bottom" width="64"><div align="right" class="MsoNormal" style="direction: ltr; line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; text-align: right; unicode-bidi: embed;">
0.923333<o:p></o:p></div>
</td>
<td nowrap="" style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 15.0pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; padding: 0cm 5.4pt 0cm 5.4pt; width: 48.0pt;" valign="bottom" width="64"><div align="right" class="MsoNormal" style="direction: ltr; line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; text-align: right; unicode-bidi: embed;">
0.523333<o:p></o:p></div>
</td>
<td nowrap="" style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 15.0pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; padding: 0cm 5.4pt 0cm 5.4pt; width: 48.0pt;" valign="bottom" width="64"><div align="right" class="MsoNormal" style="direction: ltr; line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; text-align: right; unicode-bidi: embed;">
-0.31<o:p></o:p></div>
</td>
</tr>
<tr style="height: 15.0pt; mso-yfti-irow: 29; mso-yfti-lastrow: yes;">
<td nowrap="" style="border-top: none; border: solid windowtext 1.0pt; height: 15.0pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; padding: 0cm 5.4pt 0cm 5.4pt; width: 48.0pt;" valign="bottom" width="64"><div align="right" class="MsoNormal" style="direction: ltr; line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; text-align: right; unicode-bidi: embed;">
29<o:p></o:p></div>
</td>
<td nowrap="" style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 15.0pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; padding: 0cm 5.4pt 0cm 5.4pt; width: 48.0pt;" valign="bottom" width="64"><div align="right" class="MsoNormal" style="direction: ltr; line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; text-align: right; unicode-bidi: embed;">
0.956667<o:p></o:p></div>
</td>
<td nowrap="" style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 15.0pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; padding: 0cm 5.4pt 0cm 5.4pt; width: 48.0pt;" valign="bottom" width="64"><div align="right" class="MsoNormal" style="direction: ltr; line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; text-align: right; unicode-bidi: embed;">
-0.27667<o:p></o:p></div>
</td>
<td nowrap="" style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 15.0pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; padding: 0cm 5.4pt 0cm 5.4pt; width: 48.0pt;" valign="bottom" width="64"><div align="right" class="MsoNormal" style="direction: ltr; line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; text-align: right; unicode-bidi: embed;">
0.123333<o:p></o:p></div>
</td>
</tr>
</tbody></table>
<div align="right" class="MsoNormal" dir="RTL">
<span dir="LTR" style="font-family: "times new roman" , "serif"; font-size: 12.0pt; line-height: 107%;">
</span></div>
<div align="right" class="MsoNormal" dir="RTL">
<br /></div>
<div style="text-align: left;">
<table border="0" cellpadding="0" cellspacing="0" class="MsoNormalTable" style="border-collapse: collapse; margin-left: 4.65pt; mso-padding-alt: 0cm 5.4pt 0cm 5.4pt; mso-yfti-tbllook: 1184; width: 256px;">
<tbody>
<tr style="height: 15.0pt; mso-yfti-firstrow: yes; mso-yfti-irow: 0;">
<td nowrap="" style="border-top: none; border: solid windowtext 1.0pt; height: 15.0pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; padding: 0cm 5.4pt 0cm 5.4pt; width: 48.0pt;" valign="bottom" width="64"><div align="right" class="MsoNormal" style="direction: ltr; line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; text-align: right; unicode-bidi: embed;">
<span style="color: black; mso-ascii-font-family: Calibri; mso-bidi-font-family: "Times New Roman"; mso-bidi-language: AR-SA; mso-fareast-font-family: "Times New Roman"; mso-hansi-font-family: Calibri;">30<o:p></o:p></span></div>
</td>
<td nowrap="" style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 15.0pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; padding: 0cm 5.4pt 0cm 5.4pt; width: 48.0pt;" valign="bottom" width="64"><div align="right" class="MsoNormal" style="direction: ltr; line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; text-align: right; unicode-bidi: embed;">
<span style="color: black; mso-ascii-font-family: Calibri; mso-bidi-font-family: "Times New Roman"; mso-bidi-language: AR-SA; mso-fareast-font-family: "Times New Roman"; mso-hansi-font-family: Calibri;">0.956667<o:p></o:p></span></div>
</td>
<td nowrap="" style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 15.0pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; padding: 0cm 5.4pt 0cm 5.4pt; width: 48.0pt;" valign="bottom" width="64"><div align="right" class="MsoNormal" style="direction: ltr; line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; text-align: right; unicode-bidi: embed;">
<span style="color: black; mso-ascii-font-family: Calibri; mso-bidi-font-family: "Times New Roman"; mso-bidi-language: AR-SA; mso-fareast-font-family: "Times New Roman"; mso-hansi-font-family: Calibri;">-0.27667<o:p></o:p></span></div>
</td>
<td nowrap="" style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 15.0pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; padding: 0cm 5.4pt 0cm 5.4pt; width: 48.0pt;" valign="bottom" width="64"><div align="right" class="MsoNormal" style="direction: ltr; line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; text-align: right; unicode-bidi: embed;">
<span style="color: black; mso-ascii-font-family: Calibri; mso-bidi-font-family: "Times New Roman"; mso-bidi-language: AR-SA; mso-fareast-font-family: "Times New Roman"; mso-hansi-font-family: Calibri;">0.556667<o:p></o:p></span></div>
</td>
</tr>
<tr style="height: 15.0pt; mso-yfti-irow: 1;">
<td nowrap="" style="border-top: none; border: solid windowtext 1.0pt; height: 15.0pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; padding: 0cm 5.4pt 0cm 5.4pt; width: 48.0pt;" valign="bottom" width="64"><div align="right" class="MsoNormal" style="direction: ltr; line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; text-align: right; unicode-bidi: embed;">
<span style="color: black; mso-ascii-font-family: Calibri; mso-bidi-font-family: "Times New Roman"; mso-bidi-language: AR-SA; mso-fareast-font-family: "Times New Roman"; mso-hansi-font-family: Calibri;">31<o:p></o:p></span></div>
</td>
<td nowrap="" style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 15.0pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; padding: 0cm 5.4pt 0cm 5.4pt; width: 48.0pt;" valign="bottom" width="64"><div align="right" class="MsoNormal" style="direction: ltr; line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; text-align: right; unicode-bidi: embed;">
<span style="color: black; mso-ascii-font-family: Calibri; mso-bidi-font-family: "Times New Roman"; mso-bidi-language: AR-SA; mso-fareast-font-family: "Times New Roman"; mso-hansi-font-family: Calibri;">0.956667<o:p></o:p></span></div>
</td>
<td nowrap="" style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 15.0pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; padding: 0cm 5.4pt 0cm 5.4pt; width: 48.0pt;" valign="bottom" width="64"><div align="right" class="MsoNormal" style="direction: ltr; line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; text-align: right; unicode-bidi: embed;">
<span style="color: black; mso-ascii-font-family: Calibri; mso-bidi-font-family: "Times New Roman"; mso-bidi-language: AR-SA; mso-fareast-font-family: "Times New Roman"; mso-hansi-font-family: Calibri;">0.123333<o:p></o:p></span></div>
</td>
<td nowrap="" style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 15.0pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; padding: 0cm 5.4pt 0cm 5.4pt; width: 48.0pt;" valign="bottom" width="64"><div align="right" class="MsoNormal" style="direction: ltr; line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; text-align: right; unicode-bidi: embed;">
<span style="color: black; mso-ascii-font-family: Calibri; mso-bidi-font-family: "Times New Roman"; mso-bidi-language: AR-SA; mso-fareast-font-family: "Times New Roman"; mso-hansi-font-family: Calibri;">-0.27667<o:p></o:p></span></div>
</td>
</tr>
<tr style="height: 15.0pt; mso-yfti-irow: 2;">
<td nowrap="" style="border-top: none; border: solid windowtext 1.0pt; height: 15.0pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; padding: 0cm 5.4pt 0cm 5.4pt; width: 48.0pt;" valign="bottom" width="64"><div align="right" class="MsoNormal" style="direction: ltr; line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; text-align: right; unicode-bidi: embed;">
<span style="color: black; mso-ascii-font-family: Calibri; mso-bidi-font-family: "Times New Roman"; mso-bidi-language: AR-SA; mso-fareast-font-family: "Times New Roman"; mso-hansi-font-family: Calibri;">32<o:p></o:p></span></div>
</td>
<td nowrap="" style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 15.0pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; padding: 0cm 5.4pt 0cm 5.4pt; width: 48.0pt;" valign="bottom" width="64"><div align="right" class="MsoNormal" style="direction: ltr; line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; text-align: right; unicode-bidi: embed;">
<span style="color: black; mso-ascii-font-family: Calibri; mso-bidi-font-family: "Times New Roman"; mso-bidi-language: AR-SA; mso-fareast-font-family: "Times New Roman"; mso-hansi-font-family: Calibri;">0.956667<o:p></o:p></span></div>
</td>
<td nowrap="" style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 15.0pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; padding: 0cm 5.4pt 0cm 5.4pt; width: 48.0pt;" valign="bottom" width="64"><div align="right" class="MsoNormal" style="direction: ltr; line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; text-align: right; unicode-bidi: embed;">
<span style="color: black; mso-ascii-font-family: Calibri; mso-bidi-font-family: "Times New Roman"; mso-bidi-language: AR-SA; mso-fareast-font-family: "Times New Roman"; mso-hansi-font-family: Calibri;">0.556667<o:p></o:p></span></div>
</td>
<td nowrap="" style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 15.0pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; padding: 0cm 5.4pt 0cm 5.4pt; width: 48.0pt;" valign="bottom" width="64"><div align="right" class="MsoNormal" style="direction: ltr; line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; text-align: right; unicode-bidi: embed;">
<span style="color: black; mso-ascii-font-family: Calibri; mso-bidi-font-family: "Times New Roman"; mso-bidi-language: AR-SA; mso-fareast-font-family: "Times New Roman"; mso-hansi-font-family: Calibri;">-0.27667<o:p></o:p></span></div>
</td>
</tr>
<tr style="height: 15.0pt; mso-yfti-irow: 3;">
<td nowrap="" style="border-top: none; border: solid windowtext 1.0pt; height: 15.0pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; padding: 0cm 5.4pt 0cm 5.4pt; width: 48.0pt;" valign="bottom" width="64"><div align="right" class="MsoNormal" style="direction: ltr; line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; text-align: right; unicode-bidi: embed;">
<span style="color: black; mso-ascii-font-family: Calibri; mso-bidi-font-family: "Times New Roman"; mso-bidi-language: AR-SA; mso-fareast-font-family: "Times New Roman"; mso-hansi-font-family: Calibri;">33<o:p></o:p></span></div>
</td>
<td nowrap="" style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 15.0pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; padding: 0cm 5.4pt 0cm 5.4pt; width: 48.0pt;" valign="bottom" width="64"><div align="right" class="MsoNormal" style="direction: ltr; line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; text-align: right; unicode-bidi: embed;">
<span style="color: black; mso-ascii-font-family: Calibri; mso-bidi-font-family: "Times New Roman"; mso-bidi-language: AR-SA; mso-fareast-font-family: "Times New Roman"; mso-hansi-font-family: Calibri;">0.99<o:p></o:p></span></div>
</td>
<td nowrap="" style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 15.0pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; padding: 0cm 5.4pt 0cm 5.4pt; width: 48.0pt;" valign="bottom" width="64"><div align="right" class="MsoNormal" style="direction: ltr; line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; text-align: right; unicode-bidi: embed;">
<span style="color: black; mso-ascii-font-family: Calibri; mso-bidi-font-family: "Times New Roman"; mso-bidi-language: AR-SA; mso-fareast-font-family: "Times New Roman"; mso-hansi-font-family: Calibri;">-0.24333<o:p></o:p></span></div>
</td>
<td nowrap="" style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 15.0pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; padding: 0cm 5.4pt 0cm 5.4pt; width: 48.0pt;" valign="bottom" width="64"><div align="right" class="MsoNormal" style="direction: ltr; line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; text-align: right; unicode-bidi: embed;">
<span style="color: black; mso-ascii-font-family: Calibri; mso-bidi-font-family: "Times New Roman"; mso-bidi-language: AR-SA; mso-fareast-font-family: "Times New Roman"; mso-hansi-font-family: Calibri;">0.156667<o:p></o:p></span></div>
</td>
</tr>
<tr style="height: 15.0pt; mso-yfti-irow: 4;">
<td nowrap="" style="border-top: none; border: solid windowtext 1.0pt; height: 15.0pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; padding: 0cm 5.4pt 0cm 5.4pt; width: 48.0pt;" valign="bottom" width="64"><div align="right" class="MsoNormal" style="direction: ltr; line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; text-align: right; unicode-bidi: embed;">
<span style="color: black; mso-ascii-font-family: Calibri; mso-bidi-font-family: "Times New Roman"; mso-bidi-language: AR-SA; mso-fareast-font-family: "Times New Roman"; mso-hansi-font-family: Calibri;">34<o:p></o:p></span></div>
</td>
<td nowrap="" style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 15.0pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; padding: 0cm 5.4pt 0cm 5.4pt; width: 48.0pt;" valign="bottom" width="64"><div align="right" class="MsoNormal" style="direction: ltr; line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; text-align: right; unicode-bidi: embed;">
<span style="color: black; mso-ascii-font-family: Calibri; mso-bidi-font-family: "Times New Roman"; mso-bidi-language: AR-SA; mso-fareast-font-family: "Times New Roman"; mso-hansi-font-family: Calibri;">0.99<o:p></o:p></span></div>
</td>
<td nowrap="" style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 15.0pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; padding: 0cm 5.4pt 0cm 5.4pt; width: 48.0pt;" valign="bottom" width="64"><div align="right" class="MsoNormal" style="direction: ltr; line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; text-align: right; unicode-bidi: embed;">
<span style="color: black; mso-ascii-font-family: Calibri; mso-bidi-font-family: "Times New Roman"; mso-bidi-language: AR-SA; mso-fareast-font-family: "Times New Roman"; mso-hansi-font-family: Calibri;">-0.24333<o:p></o:p></span></div>
</td>
<td nowrap="" style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 15.0pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; padding: 0cm 5.4pt 0cm 5.4pt; width: 48.0pt;" valign="bottom" width="64"><div align="right" class="MsoNormal" style="direction: ltr; line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; text-align: right; unicode-bidi: embed;">
<span style="color: black; mso-ascii-font-family: Calibri; mso-bidi-font-family: "Times New Roman"; mso-bidi-language: AR-SA; mso-fareast-font-family: "Times New Roman"; mso-hansi-font-family: Calibri;">0.59<o:p></o:p></span></div>
</td>
</tr>
<tr style="height: 15.0pt; mso-yfti-irow: 5;">
<td nowrap="" style="border-top: none; border: solid windowtext 1.0pt; height: 15.0pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; padding: 0cm 5.4pt 0cm 5.4pt; width: 48.0pt;" valign="bottom" width="64"><div align="right" class="MsoNormal" style="direction: ltr; line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; text-align: right; unicode-bidi: embed;">
<span style="color: black; mso-ascii-font-family: Calibri; mso-bidi-font-family: "Times New Roman"; mso-bidi-language: AR-SA; mso-fareast-font-family: "Times New Roman"; mso-hansi-font-family: Calibri;">35<o:p></o:p></span></div>
</td>
<td nowrap="" style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 15.0pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; padding: 0cm 5.4pt 0cm 5.4pt; width: 48.0pt;" valign="bottom" width="64"><div align="right" class="MsoNormal" style="direction: ltr; line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; text-align: right; unicode-bidi: embed;">
<span style="color: black; mso-ascii-font-family: Calibri; mso-bidi-font-family: "Times New Roman"; mso-bidi-language: AR-SA; mso-fareast-font-family: "Times New Roman"; mso-hansi-font-family: Calibri;">0.99<o:p></o:p></span></div>
</td>
<td nowrap="" style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 15.0pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; padding: 0cm 5.4pt 0cm 5.4pt; width: 48.0pt;" valign="bottom" width="64"><div align="right" class="MsoNormal" style="direction: ltr; line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; text-align: right; unicode-bidi: embed;">
<span style="color: black; mso-ascii-font-family: Calibri; mso-bidi-font-family: "Times New Roman"; mso-bidi-language: AR-SA; mso-fareast-font-family: "Times New Roman"; mso-hansi-font-family: Calibri;">0.156667<o:p></o:p></span></div>
</td>
<td nowrap="" style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 15.0pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; padding: 0cm 5.4pt 0cm 5.4pt; width: 48.0pt;" valign="bottom" width="64"><div align="right" class="MsoNormal" style="direction: ltr; line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; text-align: right; unicode-bidi: embed;">
<span style="color: black; mso-ascii-font-family: Calibri; mso-bidi-font-family: "Times New Roman"; mso-bidi-language: AR-SA; mso-fareast-font-family: "Times New Roman"; mso-hansi-font-family: Calibri;">-0.24333<o:p></o:p></span></div>
</td>
</tr>
<tr style="height: 15.0pt; mso-yfti-irow: 6; mso-yfti-lastrow: yes;">
<td nowrap="" style="border-top: none; border: solid windowtext 1.0pt; height: 15.0pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; padding: 0cm 5.4pt 0cm 5.4pt; width: 48.0pt;" valign="bottom" width="64"><div align="right" class="MsoNormal" style="direction: ltr; line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; text-align: right; unicode-bidi: embed;">
<span style="color: black; mso-ascii-font-family: Calibri; mso-bidi-font-family: "Times New Roman"; mso-bidi-language: AR-SA; mso-fareast-font-family: "Times New Roman"; mso-hansi-font-family: Calibri;">36<o:p></o:p></span></div>
</td>
<td nowrap="" style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 15.0pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; padding: 0cm 5.4pt 0cm 5.4pt; width: 48.0pt;" valign="bottom" width="64"><div align="right" class="MsoNormal" style="direction: ltr; line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; text-align: right; unicode-bidi: embed;">
<span style="color: black; mso-ascii-font-family: Calibri; mso-bidi-font-family: "Times New Roman"; mso-bidi-language: AR-SA; mso-fareast-font-family: "Times New Roman"; mso-hansi-font-family: Calibri;">0.99<o:p></o:p></span></div>
</td>
<td nowrap="" style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 15.0pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; padding: 0cm 5.4pt 0cm 5.4pt; width: 48.0pt;" valign="bottom" width="64"><div align="right" class="MsoNormal" style="direction: ltr; line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; text-align: right; unicode-bidi: embed;">
<span style="color: black; mso-ascii-font-family: Calibri; mso-bidi-font-family: "Times New Roman"; mso-bidi-language: AR-SA; mso-fareast-font-family: "Times New Roman"; mso-hansi-font-family: Calibri;">0.59<o:p></o:p></span></div>
</td>
<td nowrap="" style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 15.0pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; padding: 0cm 5.4pt 0cm 5.4pt; width: 48.0pt;" valign="bottom" width="64"><div align="right" class="MsoNormal" style="direction: ltr; line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; text-align: right; unicode-bidi: embed;">
<span style="color: black; mso-ascii-font-family: Calibri; mso-bidi-font-family: "Times New Roman"; mso-bidi-language: AR-SA; mso-fareast-font-family: "Times New Roman"; mso-hansi-font-family: Calibri;">-0.24333<o:p></o:p></span></div>
</td>
</tr>
</tbody></table>
</div>
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<span style="font-family: "times new roman" , "serif"; font-size: 12.0pt; line-height: 107%;">In fact, we can find 252 systems of three particles which have the
same total gravity potential energy.<o:p></o:p></span></div>
<div class="MsoNormal" style="direction: ltr; text-align: left; unicode-bidi: embed;">
<span style="font-family: "times new roman" , "serif"; font-size: 12.0pt; line-height: 107%;">As you can see, when the distances increase, the work done on
systems will decrease.<o:p></o:p></span></div>
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Gholamreza Soleimanihttp://www.blogger.com/profile/03273527405719420253noreply@blogger.com0tag:blogger.com,1999:blog-392703582366288634.post-36484658540458517652018-04-04T13:37:00.000+04:302018-04-04T13:37:09.005+04:30A Model for Making Two Ways Stochastic Matrix<div dir="ltr" style="text-align: left;" trbidi="on">
<br />
<div class="MsoNormal">
<span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%; mso-ascii-theme-font: major-bidi; mso-bidi-theme-font: major-bidi; mso-hansi-theme-font: major-bidi;">Making a two ways stochastic matrix
can be very hard especially when you have many elements in matrix such as a
matrix 5*5 or 6*6 and more. But, what is two ways stochastic matrix? <span class="MsoHyperlink"><span style="color: black; mso-themecolor: text1; text-decoration: none; text-underline: none;">A two ways stochastic matrix is </span></span>when
the sum of all elements on each column and row are equal to 1. What is the
application of the two ways stochastic matrix? In the reference with article of
“Does this conjecture lead us toward an absolute justice in the world?” posted
on link:</span> <a href="http://www.emfps.org/2018/02/a-model-to-produce-magic-matrix.html"><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%; mso-ascii-theme-font: major-bidi; mso-bidi-theme-font: major-bidi; mso-hansi-theme-font: major-bidi;">http://www.emfps.org/2018/02/a-model-to-produce-magic-matrix.html</span></a><span class="MsoHyperlink"><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%; mso-ascii-theme-font: major-bidi; mso-bidi-theme-font: major-bidi; mso-hansi-theme-font: major-bidi;">, </span></span><span class="MsoHyperlink"><span style="color: black; font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%; mso-ascii-theme-font: major-bidi; mso-bidi-theme-font: major-bidi; mso-hansi-theme-font: major-bidi; mso-themecolor: text1; text-decoration: none; text-underline: none;">by using a two ways stochastic
matrix, we will be able to predict a subject by using the Markov process. <o:p></o:p></span></span></div>
<div class="MsoNormal">
<span class="MsoHyperlink"><span style="color: black; font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%; mso-ascii-theme-font: major-bidi; mso-bidi-theme-font: major-bidi; mso-hansi-theme-font: major-bidi; mso-themecolor: text1; text-decoration: none; text-underline: none;"><br /></span></span></div>
<div class="MsoNormal">
<span class="MsoHyperlink"><span style="color: black; font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%; mso-ascii-theme-font: major-bidi; mso-bidi-theme-font: major-bidi; mso-hansi-theme-font: major-bidi; mso-themecolor: text1; text-decoration: none; text-underline: none;">Suppose
company X has a delivery system, if this company wants to use the Markov chain
to forecast the probability of delivery on each station, it will have to
investigate the statistics during the period of a specific time to obtain many
probability numbers. <o:p></o:p></span></span></div>
<div class="MsoNormal">
<span class="MsoHyperlink"><span style="color: black; font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%; mso-ascii-theme-font: major-bidi; mso-bidi-theme-font: major-bidi; mso-hansi-theme-font: major-bidi; mso-themecolor: text1; text-decoration: none; text-underline: none;"><br /></span></span></div>
<div class="MsoNormal">
<span class="MsoHyperlink"><span style="color: black; font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%; mso-ascii-theme-font: major-bidi; mso-bidi-theme-font: major-bidi; mso-hansi-theme-font: major-bidi; mso-themecolor: text1; text-decoration: none; text-underline: none;">Assume,
the company has 5 stations and according to its statistics, it has gotten 10
probabilities. There are two questions:<o:p></o:p></span></span></div>
<div class="MsoNormal">
<span class="MsoHyperlink"><span style="color: black; font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%; mso-ascii-theme-font: major-bidi; mso-bidi-theme-font: major-bidi; mso-hansi-theme-font: major-bidi; mso-themecolor: text1; text-decoration: none; text-underline: none;"><br /></span></span></div>
<div class="MsoNormal">
<span class="MsoHyperlink"><span style="color: black; font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%; mso-ascii-theme-font: major-bidi; mso-bidi-theme-font: major-bidi; mso-hansi-theme-font: major-bidi; mso-themecolor: text1; text-decoration: none; text-underline: none;">1.
Can these 10 probabilities make a two ways stochastic matrix?<o:p></o:p></span></span></div>
<div class="MsoNormal">
<span class="MsoHyperlink"><span style="color: black; font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%; mso-ascii-theme-font: major-bidi; mso-bidi-theme-font: major-bidi; mso-hansi-theme-font: major-bidi; mso-themecolor: text1; text-decoration: none; text-underline: none;">2.
If the answer to question (1) is positive, what is two ways stochastic matrix?<o:p></o:p></span></span></div>
<div class="MsoNormal">
<span class="MsoHyperlink"><span style="color: black; font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%; mso-ascii-theme-font: major-bidi; mso-bidi-theme-font: major-bidi; mso-hansi-theme-font: major-bidi; mso-themecolor: text1; text-decoration: none; text-underline: none;"><br /></span></span></div>
<div class="MsoNormal">
<span class="MsoHyperlink"><span style="color: black; font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%; mso-ascii-theme-font: major-bidi; mso-bidi-theme-font: major-bidi; mso-hansi-theme-font: major-bidi; mso-themecolor: text1; text-decoration: none; text-underline: none;">Below
model is able to answer above questions:<o:p></o:p></span></span></div>
<div class="MsoNormal">
<span class="MsoHyperlink"><span style="color: black; font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%; mso-ascii-theme-font: major-bidi; mso-bidi-theme-font: major-bidi; mso-hansi-theme-font: major-bidi; mso-themecolor: text1; text-decoration: none; text-underline: none;"><br /></span></span></div>
<div class="MsoNormal">
<span class="MsoHyperlink"><span style="color: black; font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%; mso-ascii-theme-font: major-bidi; mso-bidi-theme-font: major-bidi; mso-hansi-theme-font: major-bidi; mso-themecolor: text1; text-decoration: none; text-underline: none;"><br /></span></span></div>
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhbpibQbqjUZ8cAjYwXollVZZOCVcCiHrRu3u3H-uARuFbiykeA18oWbO4GkyjpPhmwcg323zvKDDxcHIHmw9cNPrCvAp6Tgem8k_njtpmhuyHuHFDsh9ntkTSZhU7Es_DDHIFvaBRHV50/s1600/1.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="248" data-original-width="682" height="116" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhbpibQbqjUZ8cAjYwXollVZZOCVcCiHrRu3u3H-uARuFbiykeA18oWbO4GkyjpPhmwcg323zvKDDxcHIHmw9cNPrCvAp6Tgem8k_njtpmhuyHuHFDsh9ntkTSZhU7Es_DDHIFvaBRHV50/s320/1.png" width="320" /></a></div>
<div class="MsoNormal">
<span class="MsoHyperlink"><span style="color: black; font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%; mso-ascii-theme-font: major-bidi; mso-bidi-theme-font: major-bidi; mso-hansi-theme-font: major-bidi; mso-themecolor: text1; text-decoration: none; text-underline: none;"><br /></span></span></div>
<div class="MsoNormal">
<span class="MsoHyperlink"><span style="color: black; font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%; mso-ascii-theme-font: major-bidi; mso-bidi-theme-font: major-bidi; mso-hansi-theme-font: major-bidi; mso-themecolor: text1; text-decoration: none; text-underline: none;"><br /></span></span></div>
<div class="MsoNormal">
<span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%; mso-ascii-theme-font: major-bidi; mso-bidi-theme-font: major-bidi; mso-fareast-font-family: "Times New Roman"; mso-fareast-theme-font: minor-fareast; mso-hansi-theme-font: major-bidi;">Let me explain you about the
components of above model as follows:<o:p></o:p></span></div>
<div class="MsoNormal">
<span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%; mso-ascii-theme-font: major-bidi; mso-bidi-theme-font: major-bidi; mso-fareast-font-family: "Times New Roman"; mso-fareast-theme-font: minor-fareast; mso-hansi-theme-font: major-bidi;"><br /></span></div>
<div class="MsoNormal">
<span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%; mso-ascii-theme-font: major-bidi; mso-bidi-theme-font: major-bidi; mso-fareast-font-family: "Times New Roman"; mso-fareast-theme-font: minor-fareast; mso-hansi-theme-font: major-bidi;">1. On cells P3:Y3, we have inputs
including </span><span class="MsoHyperlink"><span style="color: black; font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%; mso-ascii-theme-font: major-bidi; mso-bidi-theme-font: major-bidi; mso-hansi-theme-font: major-bidi; mso-themecolor: text1; text-decoration: none; text-underline: none;">10
probability</span></span><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%; mso-ascii-theme-font: major-bidi; mso-bidi-theme-font: major-bidi; mso-fareast-font-family: "Times New Roman"; mso-fareast-theme-font: minor-fareast; mso-hansi-theme-font: major-bidi;"> <o:p></o:p></span></div>
<div class="MsoNormal">
<span class="MsoHyperlink"><span style="color: black; font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%; mso-ascii-theme-font: major-bidi; mso-bidi-theme-font: major-bidi; mso-hansi-theme-font: major-bidi; mso-themecolor: text1; text-decoration: none; text-underline: none;"><br /></span></span></div>
<div class="MsoNormal">
<span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%; mso-ascii-theme-font: major-bidi; mso-bidi-theme-font: major-bidi; mso-fareast-font-family: "Times New Roman"; mso-fareast-theme-font: minor-fareast; mso-hansi-theme-font: major-bidi;">2. On cells Q4:T4, there are the
errors. The error on the sum of rows is error.H and the error on the sum of
columns is error.V.<o:p></o:p></span></div>
<div class="MsoNormal">
<span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%; mso-ascii-theme-font: major-bidi; mso-bidi-theme-font: major-bidi; mso-fareast-font-family: "Times New Roman"; mso-fareast-theme-font: minor-fareast; mso-hansi-theme-font: major-bidi;"><br /></span></div>
<div class="MsoNormal">
<span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%; mso-ascii-theme-font: major-bidi; mso-bidi-theme-font: major-bidi; mso-fareast-font-family: "Times New Roman"; mso-fareast-theme-font: minor-fareast; mso-hansi-theme-font: major-bidi;">3. On cells Q6:U10, we have outputs
which give us a two ways stochastic matrix.<o:p></o:p></span></div>
<div class="MsoNormal">
<span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%; mso-ascii-theme-font: major-bidi; mso-bidi-theme-font: major-bidi; mso-fareast-font-family: "Times New Roman"; mso-fareast-theme-font: minor-fareast; mso-hansi-theme-font: major-bidi;"><br /></span></div>
<div class="MsoNormal">
<span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%; mso-ascii-theme-font: major-bidi; mso-bidi-theme-font: major-bidi; mso-hansi-theme-font: major-bidi;">You can see below captured movie as
the example for this model:<o:p></o:p></span></div>
<div class="MsoNormal">
<span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%; mso-ascii-theme-font: major-bidi; mso-bidi-theme-font: major-bidi; mso-hansi-theme-font: major-bidi;"><br /></span></div>
<div class="MsoNormal">
<span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%; mso-ascii-theme-font: major-bidi; mso-bidi-theme-font: major-bidi; mso-hansi-theme-font: major-bidi;"><br /></span></div>
<div class="separator" style="clear: both; text-align: center;">
<iframe allowfullscreen='allowfullscreen' webkitallowfullscreen='webkitallowfullscreen' mozallowfullscreen='mozallowfullscreen' width='320' height='266' src='https://www.blogger.com/video.g?token=AD6v5dzl-tBNkkzBkP05wsSs4oM6ksyDzaQx1bQvIYyQcU97X_p0-V_96NzQOcxkJT0n5cgSRxqKoEEpmseMgJDHNQ' class='b-hbp-video b-uploaded' frameborder='0'></iframe></div>
<div class="MsoNormal">
<span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%; mso-ascii-theme-font: major-bidi; mso-bidi-theme-font: major-bidi; mso-hansi-theme-font: major-bidi;"><br /></span></div>
<div class="MsoNormal">
<br /></div>
<div class="MsoNormal">
<br /></div>
<div class="MsoNormal">
<br /></div>
<div class="MsoNormal">
<span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%; mso-ascii-theme-font: major-bidi; mso-bidi-theme-font: major-bidi; mso-hansi-theme-font: major-bidi;">All researchers and individual
people, who are interested in having this model, don’t hesitate to send their
request to below addresses:<o:p></o:p></span></div>
<div class="MsoNormal">
<span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%; mso-ascii-theme-font: major-bidi; mso-bidi-theme-font: major-bidi; mso-hansi-theme-font: major-bidi;"><br /></span></div>
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhM8JWKo6U974Qb3RQMZRID6pjmNrQnN4k_CpCTcC177k3nNqoQjYTeYnR88Jb4Iy3697Ag4hdF2aMCT8OG7-p0yPxEycedVaZNdCqPtl1n14trUpJqwo4CtAgiM0dI5XswYwXt_eV1mdo/s1600/%25D8%25AF%25D8%25B1%25DB%258C%25D8%25A7%25D9%2581%25D8%25AA+%25D9%2581%25D8%25A7%25DB%258C%25D9%2584+%25D8%25A7%25DA%25A9%25D8%25B3%25D9%2584.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="240" data-original-width="592" height="129" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhM8JWKo6U974Qb3RQMZRID6pjmNrQnN4k_CpCTcC177k3nNqoQjYTeYnR88Jb4Iy3697Ag4hdF2aMCT8OG7-p0yPxEycedVaZNdCqPtl1n14trUpJqwo4CtAgiM0dI5XswYwXt_eV1mdo/s320/%25D8%25AF%25D8%25B1%25DB%258C%25D8%25A7%25D9%2581%25D8%25AA+%25D9%2581%25D8%25A7%25DB%258C%25D9%2584+%25D8%25A7%25DA%25A9%25D8%25B3%25D9%2584.png" width="320" /></a></div>
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<span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%; mso-ascii-theme-font: major-bidi; mso-bidi-theme-font: major-bidi; mso-hansi-theme-font: major-bidi;"></span></div>
<div align="center" class="MsoNormal" dir="RTL" style="text-align: center;">
<a href="https://t.me/Allisnumber"><b><span dir="LTR" style="font-family: "Times New Roman","serif"; font-size: 22.0pt; line-height: 107%; mso-ascii-theme-font: major-bidi; mso-bidi-theme-font: major-bidi; mso-hansi-theme-font: major-bidi;">https://t.me/Allisnumber</span></b></a><b><span dir="LTR" style="font-family: "Times New Roman","serif"; font-size: 22.0pt; line-height: 107%; mso-ascii-theme-font: major-bidi; mso-bidi-theme-font: major-bidi; mso-hansi-theme-font: major-bidi;"><o:p></o:p></span></b></div>
<br /></div>
Gholamreza Soleimanihttp://www.blogger.com/profile/03273527405719420253noreply@blogger.com0tag:blogger.com,1999:blog-392703582366288634.post-25716135197526774872018-03-07T13:57:00.000+03:302018-04-17T15:45:20.954+04:30A Specific Permutation And Applications (1)<div dir="ltr" style="text-align: left;" trbidi="on">
<br />
<div class="MsoNormal">
<span style="font-family: "times new roman" , "serif"; font-size: 12.0pt; line-height: 115%;">The base of the probability theory
is always referred to permutations and combinations in which a permutation is
an ordered combination. It means, if we have “n” events and choose “r” of them,
we will have the opportunity to make many groups and subsets which are “r” from
“n” where the repetition and the replacement will also give us new concepts. <o:p></o:p></span><br />
<span style="font-family: "times new roman" , "serif"; font-size: 12.0pt; line-height: 115%;"><br /></span>
<span style="font-family: "times new roman" , "serif"; font-size: 12.0pt; line-height: 115%;"><br /></span>
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh_XvQ29Wcib4-E0DaJRx5S9ooo8qDQUMYxfA-MeHC7vu0G_KWdJKhlKd9qYKqfW2Bg4aQQYsh5WayRwViNnms21bG_KI_psjABS3Lg1WhH3IOA0WmvI675wva2fq-C8zW0I2TeM79-iKs/s1600/Permut.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="503" data-original-width="430" height="320" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh_XvQ29Wcib4-E0DaJRx5S9ooo8qDQUMYxfA-MeHC7vu0G_KWdJKhlKd9qYKqfW2Bg4aQQYsh5WayRwViNnms21bG_KI_psjABS3Lg1WhH3IOA0WmvI675wva2fq-C8zW0I2TeM79-iKs/s320/Permut.png" width="273" /></a></div>
<span style="font-family: "times new roman" , "serif"; font-size: 12.0pt; line-height: 115%;"><br /></span>
<span style="font-family: "times new roman" , "serif"; font-size: 12.0pt; line-height: 115%;"><br /></span></div>
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<span style="font-family: "times new roman" , "serif"; font-size: 12.0pt; line-height: 115%;">As you know, basically we have two
types of permutations:<o:p></o:p></span></div>
<div class="MsoNormal">
<span style="font-family: "times new roman" , "serif"; font-size: 12.0pt; line-height: 115%;"><br /></span></div>
<div class="MsoListParagraphCxSpFirst" style="mso-list: l1 level1 lfo1; text-indent: -18.0pt;">
<!--[if !supportLists]--><span style="font-family: "times new roman" , "serif"; font-size: 12.0pt; line-height: 115%;"><span style="mso-list: Ignore;">1.<span style="font: 7.0pt "Times New Roman";">
</span></span></span><!--[endif]--><span dir="LTR"></span><span style="font-family: "times new roman" , "serif"; font-size: 12.0pt; line-height: 115%;">Permutations
with repetition which is calculated by below formula:<o:p></o:p></span></div>
<div class="MsoListParagraphCxSpMiddle">
<br /></div>
<div class="MsoListParagraphCxSpMiddle">
<span style="font-family: "times new roman" , "serif"; font-size: 12.0pt; line-height: 115%;">The number of
Permutations = n^r<o:p></o:p></span></div>
<div class="MsoListParagraphCxSpMiddle">
<br /></div>
<div class="MsoListParagraphCxSpLast" style="mso-list: l1 level1 lfo1; text-indent: -18.0pt;">
<!--[if !supportLists]--><span style="font-family: "times new roman" , "serif"; font-size: 12.0pt; line-height: 115%;"><span style="mso-list: Ignore;">2.<span style="font: 7.0pt "Times New Roman";">
</span></span></span><!--[endif]--><span dir="LTR"></span><span style="font-family: "times new roman" , "serif"; font-size: 12.0pt; line-height: 115%;">Permutations
without repetition which is obtained by below formula:<o:p></o:p></span></div>
<div class="MsoListParagraphCxSpLast" style="mso-list: l1 level1 lfo1; text-indent: -18.0pt;">
<span style="font-family: "times new roman" , "serif"; font-size: 12.0pt; line-height: 115%;"><br /></span></div>
<div class="MsoNormal">
<span style="font-family: "times new roman" , "serif"; font-size: 12.0pt; line-height: 115%;"><span style="mso-spacerun: yes;"> </span>The number of Permutations = n!/(n-r)!<o:p></o:p></span></div>
<div class="MsoNormal">
<span style="font-family: "times new roman" , "serif"; font-size: 12.0pt; line-height: 115%;"><br /></span></div>
<div class="MsoNormal">
<span style="font-family: "times new roman" , "serif"; font-size: 12.0pt; line-height: 115%;">The purpose of this article is to
introduce a specific permutation.<o:p></o:p></span></div>
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<span style="font-family: "times new roman" , "serif"; font-size: 12.0pt; line-height: 115%;"><br /></span></div>
<div class="MsoNormal">
<b><span style="font-family: "times new roman" , "serif"; font-size: 14.0pt; line-height: 115%;">A specific
permutation<o:p></o:p></span></b></div>
<div class="MsoNormal">
<b><span style="font-family: "times new roman" , "serif"; font-size: 14.0pt; line-height: 115%;"><br /></span></b></div>
<div class="MsoNormal">
<span style="font-family: "times new roman" , "serif"; font-size: 12.0pt; line-height: 115%;">Suppose we have a number of
events “n” and we consider whole events as the pairs just like below set:<o:p></o:p></span></div>
<div class="MsoNormal">
<span style="font-family: "times new roman" , "serif"; font-size: 12.0pt; line-height: 115%;"><br /></span></div>
<div class="MsoNormal">
<span style="font-family: "times new roman" , "serif"; font-size: 12.0pt; line-height: 115%;">S = {(a1,a2), (b1,b2), (c1,c2),
(d1,d2)….}<o:p></o:p></span></div>
<div class="MsoNormal">
<span style="font-family: "times new roman" , "serif"; font-size: 12.0pt; line-height: 115%;"><br /></span></div>
<div class="MsoNormal">
<span style="font-family: "times new roman" , "serif"; font-size: 12.0pt; line-height: 115%;">Here "S" is our sample space.</span><br />
<span style="font-family: "times new roman" , "serif"; font-size: 12.0pt; line-height: 115%;">We are willing to make all
permutations without repetition with “r” members from “S” <b><i>where each set
of permutations is included only one of the pairs.</i></b> This is additional
restriction for these permutations. It is clear; “r” must be always smaller or
equal half of “n”.<o:p></o:p></span></div>
<div class="MsoNormal">
<span style="font-family: "times new roman" , "serif"; font-size: 12.0pt; line-height: 115%;"><br /></span></div>
<div class="MsoNormal">
<span style="font-family: "times new roman" , "serif"; font-size: 12.0pt; line-height: 115%;">Therefore, the characteristics of
this specific permutation are defined as follows:<o:p></o:p></span></div>
<div class="MsoNormal">
<span style="font-family: "times new roman" , "serif"; font-size: 12.0pt; line-height: 115%;"><br /></span></div>
<div class="MsoListParagraphCxSpFirst" style="mso-list: l0 level1 lfo2; text-indent: -18.0pt;">
<!--[if !supportLists]--><span style="font-family: "symbol"; font-size: 14.0pt; line-height: 115%;"><span style="mso-list: Ignore;">·<span style="font: 7.0pt "Times New Roman";">
</span></span></span><!--[endif]--><span dir="LTR"></span><b><span style="font-family: "times new roman" , "serif"; font-size: 14.0pt; line-height: 115%;">n =
2k<span style="mso-spacerun: yes;"> </span>and<span style="mso-spacerun: yes;">
</span>k ε N<o:p></o:p></span></b></div>
<div class="MsoListParagraphCxSpMiddle" style="mso-list: l0 level1 lfo2; text-indent: -18.0pt;">
<!--[if !supportLists]--><span style="font-family: "symbol"; font-size: 14.0pt; line-height: 115%;"><span style="mso-list: Ignore;">·<span style="font: 7.0pt "Times New Roman";">
</span></span></span><!--[endif]--><span dir="LTR"></span><b><span style="font-family: "times new roman" , "serif"; font-size: 14.0pt; line-height: 115%;">r ≤
n/2<o:p></o:p></span></b></div>
<div class="MsoListParagraphCxSpLast" style="mso-list: l0 level1 lfo2; text-indent: -18.0pt;">
<!--[if !supportLists]--><span style="font-family: "symbol"; font-size: 14.0pt; line-height: 115%;"><span style="mso-list: Ignore;">·<span style="font: 7.0pt "Times New Roman";">
</span></span></span><!--[endif]--><span dir="LTR"></span><b><span style="font-family: "times new roman" , "serif"; font-size: 12.0pt; line-height: 115%;">Each
set of permutations is included only one of the pairs</span></b><b><span style="font-family: "times new roman" , "serif"; font-size: 14.0pt; line-height: 115%;"><o:p></o:p></span></b></div>
<div class="MsoListParagraphCxSpLast" style="mso-list: l0 level1 lfo2; text-indent: -18.0pt;">
<b><span style="font-family: "times new roman" , "serif"; font-size: 12.0pt; line-height: 115%;"><br /></span></b></div>
<div class="MsoNormal">
<span style="font-family: "times new roman" , "serif"; font-size: 14.0pt; line-height: 115%;">The question is: <span style="mso-spacerun: yes;"> </span>How can we calculate the number of these
permutations?<o:p></o:p></span></div>
<div class="MsoNormal">
<span style="font-family: "times new roman" , "serif"; font-size: 14.0pt; line-height: 115%;">By using below formula, we will be
able to get the number of all permutations:<o:p></o:p></span></div>
<div class="MsoNormal">
<span style="font-family: "times new roman" , "serif"; font-size: 14.0pt; line-height: 115%;"><br /></span></div>
<div class="separator" style="clear: both; text-align: left;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhtK2c6tCdaTb4gZtoPc7x-2KEbN8L-td4aJTfk_yjD1FiOdSjZT9Ot6TO1NXTa6b34ypuFo_bTA9X9NufE1q6bdHO6Kwzq-NJH5HM0XXslQQNtEWJuIQkgjQRK7pG_7U3t6zRo_XcHieA/s1600/1.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="101" data-original-width="485" height="66" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhtK2c6tCdaTb4gZtoPc7x-2KEbN8L-td4aJTfk_yjD1FiOdSjZT9Ot6TO1NXTa6b34ypuFo_bTA9X9NufE1q6bdHO6Kwzq-NJH5HM0XXslQQNtEWJuIQkgjQRK7pG_7U3t6zRo_XcHieA/s320/1.png" width="320" /></a></div>
<div class="MsoNormal">
<span style="font-family: "times new roman" , "serif"; font-size: 12.0pt; line-height: 115%;">For instance, when we choose three
choices from six events, we will have 48 permutations or if we have three
choices from eight events, we will get 192 permutations.<o:p></o:p></span></div>
<br />
<div class="MsoNormal">
<span style="font-family: "times new roman" , "serif"; font-size: 12.0pt; line-height: 115%;">By using Microsoft excel, we can
generate all permutations on a spreadsheet of excel.<o:p></o:p></span></div>
<div class="MsoNormal">
<span style="font-family: "times new roman" , "serif"; font-size: 12.0pt; line-height: 115%;"><br /></span></div>
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<b><span style="font-family: "times new roman" , "serif"; font-size: 12.0pt; line-height: 115%;">Example:
Generating the Points on a Sphere<o:p></o:p></span></b></div>
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<b><span style="font-family: "times new roman" , "serif"; font-size: 12.0pt; line-height: 115%;"><br /></span></b></div>
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<span style="font-family: "times new roman" , "serif"; font-size: 12.0pt; line-height: 115%;">Suppose our sample space or events
are pairs of plus and minus as follows:<o:p></o:p></span></div>
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<span style="font-family: "times new roman" , "serif"; font-size: 12.0pt; line-height: 115%;"><br /></span></div>
<div class="MsoNormal">
<span style="font-family: "times new roman" , "serif"; font-size: 12.0pt; line-height: 115%;">S = {(-a, a), (-b, b), (-c, c)…}<o:p></o:p></span></div>
<div class="MsoNormal">
<span style="font-family: "times new roman" , "serif"; font-size: 12.0pt; line-height: 115%;"><br /></span></div>
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<span style="font-family: "times new roman" , "serif"; font-size: 12.0pt; line-height: 115%;">In this case, for n = 6 we will
have: 48 points which have been located on a sphere. <o:p></o:p></span><br />
<span style="font-family: "times new roman" , "serif"; font-size: 12.0pt; line-height: 115%;"><br /></span>
<br />
<div class="MsoNormal">
<span style="font-family: "times new roman" , "serif"; font-size: 12.0pt; line-height: 115%;">Assume we have the point P (2, 5,
24) in the 3D space in which the sample space will be below cited:<o:p></o:p></span></div>
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<span style="font-family: "times new roman" , "serif"; font-size: 12.0pt; line-height: 115%;"><br /></span></div>
<div class="MsoNormal">
<span style="font-family: "times new roman" , "serif"; font-size: 12.0pt; line-height: 115%;">S = {(-2, 2), (-5, 5), (-24, 24)}<o:p></o:p></span></div>
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<span style="font-family: "times new roman" , "serif"; font-size: 12.0pt; line-height: 115%;"><br /></span></div>
<span style="font-family: "times new roman" , "serif"; font-size: 12.0pt; line-height: 115%;">
</span><br />
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<span style="font-family: "times new roman" , "serif"; font-size: 12.0pt; line-height: 115%;">All below points are located on a
sphere or gives us a field in 3D space:<o:p></o:p></span></div>
</div>
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<br /></div>
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgT_BqWThbyrygpYY9LFNk2u3JAjHiWB8faNAlJp95vvphSJdUO-SLmOLL6tgM69HE3l79Lo-UhCEccjtXVmiMnKu7yLstemnWHs2bPfCLFc_PN1bekZlgtvC8J1CDyVPhFJsmZrpPZEjI/s1600/2.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="527" data-original-width="260" height="320" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgT_BqWThbyrygpYY9LFNk2u3JAjHiWB8faNAlJp95vvphSJdUO-SLmOLL6tgM69HE3l79Lo-UhCEccjtXVmiMnKu7yLstemnWHs2bPfCLFc_PN1bekZlgtvC8J1CDyVPhFJsmZrpPZEjI/s320/2.png" width="157" /></a></div>
<o:p></o:p><br />
<br />
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<span style="font-family: "times new roman" , "serif"; font-size: 12.0pt; line-height: 115%;">Below model gives us all 48 points
on a sphere when we have only coordination of one point:<o:p></o:p></span></div>
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<span style="font-family: "times new roman" , "serif"; font-size: 12.0pt; line-height: 115%;"><br /></span></div>
<div class="separator" style="clear: both; text-align: center;">
<br /></div>
<iframe allowfullscreen='allowfullscreen' webkitallowfullscreen='webkitallowfullscreen' mozallowfullscreen='mozallowfullscreen' width='320' height='266' src='https://www.blogger.com/video.g?token=AD6v5dw9yrzSOFA1WCIXpZgqs0rIaucROHiQk0lf4YnSF6wn9CPHe3Ow5r9vmaj-v0Q1Hli5lYFzWqY3Fnl8xFX2Hg' class='b-hbp-video b-uploaded' frameborder='0'></iframe><br />
<div class="MsoNormal">
<span style="font-family: "times new roman" , "serif"; font-size: 12.0pt; line-height: 115%;"><br /></span></div>
<div class="MsoNormal">
<span style="font-family: "times new roman" , "serif"; font-size: 12.0pt; line-height: 115%;">In above model, the inputs are the coordination
of one point P (x,y,z) and the outputs are the coordination of all 48 points on
a sphere. As you can see, the radius of sphere (r) always stays the constant.</span></div>
<div class="MsoNormal">
<span style="font-family: "times new roman" , "serif"; font-size: 12.0pt; line-height: 115%;"><br /></span></div>
<div class="MsoNormal">
<span style="font-family: "times new roman" , "serif"; font-size: 12.0pt; line-height: 115%;">In the reference with above
mentioned, below movie as well as shows an overall shape of this system when the
location of a point is changed:<o:p></o:p></span></div>
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<span style="font-family: "times new roman" , "serif"; font-size: 12.0pt; line-height: 115%;"><br /></span></div>
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<span style="font-family: "times new roman" , "serif"; font-size: 12.0pt; line-height: 115%;"><br /></span></div>
<div class="separator" style="clear: both; text-align: center;">
<iframe allowfullscreen='allowfullscreen' webkitallowfullscreen='webkitallowfullscreen' mozallowfullscreen='mozallowfullscreen' width='320' height='266' src='https://www.blogger.com/video.g?token=AD6v5dx7764d36-0Ltlz40z4mO-EPQWxLNi7PV2GyS9Ke2x45o_Imbg_Wakpszn8uzvc771In1V94j4MJOaQO3JGUQ' class='b-hbp-video b-uploaded' frameborder='0'></iframe></div>
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<br /></div>
Gholamreza Soleimanihttp://www.blogger.com/profile/03273527405719420253noreply@blogger.com0tag:blogger.com,1999:blog-392703582366288634.post-35704796179974498772018-02-25T16:33:00.002+03:302018-02-28T20:13:52.813+03:30 Does this conjecture lead us toward an absolute justice in the world?<div dir="ltr" style="text-align: left;" trbidi="on">
<div class="MsoNormal">
<br /></div>
<div class="MsoNormal">
<b><span style="font-family: "times new roman" , "serif"; font-size: 12.0pt; line-height: 115%;">Eigenvalue
equal to the sum of all elements on each column or row<o:p></o:p></span></b></div>
<div class="MsoNormal">
<b><span style="font-family: "times new roman" , "serif"; font-size: 12.0pt; line-height: 115%;"><br /></span></b></div>
<div class="MsoNormal">
<span style="font-family: "times new roman" , "serif"; font-size: 12.0pt; line-height: 115%;">One of the properties two ways
matrices which can be easily proved is, to obtain the Eigenvalue where the sum
of all elements on each column or row is equal to Eigenvalue of these matrices.<o:p></o:p></span></div>
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<br /></div>
<div class="MsoNormal">
<span style="font-family: "times new roman" , "serif"; font-size: 12.0pt; line-height: 115%;">Another interesting property of a
two way matrix is, to have a special eigenvector that all elements of it are
the same. It means, if “M” is a two ways matrix, vector “V” will be eigenvector
of matrix “M” where we have:<o:p></o:p></span></div>
<div class="MsoNormal">
<span style="font-family: "times new roman" , "serif"; font-size: 12.0pt; line-height: 115%;"><br /></span></div>
<br />
<div class="MsoNormal">
<b><span style="font-family: "times new roman" , "serif"; font-size: 12.0pt; line-height: 115%;">V = (x, x, x,
x, ….) and λ = the sum of all elements on each column or row<o:p></o:p></span></b></div>
<div class="MsoNormal">
<b><span style="font-family: "times new roman" , "serif"; font-size: 12.0pt; line-height: 115%;"><br /></span></b></div>
<div class="MsoNormal">
<span style="font-family: "times new roman" , "serif"; font-size: 12.0pt; line-height: 115%;">This property can be easily proved. <o:p></o:p></span></div>
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<span style="font-family: "times new roman" , "serif"; font-size: 12.0pt; line-height: 115%;"><br /></span></div>
<div class="separator" style="clear: both; text-align: left;">
<span style="font-family: "times new roman" , "serif"; font-size: 12.0pt; line-height: 115%;">Following
to article of <b>“The Impact of Stochastic Matrix on Any Vector”</b> posted on
link: <b></b></span><a href="http://www.emfps.org/2018/02/the-impact-of-stochastic-matrix-on-any.html"><span style="font-family: "times new roman" , "serif"; font-size: 12.0pt; line-height: 115%;">http://www.emfps.org/2018/02/the-impact-of-stochastic-matrix-on-any.html</span></a><span class="MsoHyperlink"><span style="font-family: "times new roman" , serif; font-size: 12pt; line-height: 115%;">, let me tell you about another conjecture as
follows:</span></span></div>
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<span class="MsoHyperlink"><span style="font-family: "times new roman" , serif; font-size: 12pt; line-height: 115%;"><br /></span></span></div>
<div class="MsoNormal">
<b><i><span style="font-family: "times new roman" , "serif"; font-size: 12.0pt; line-height: 115%;">Conjecture (2):
The final result of Markov Process including the impact of a two ways
stochastic matrix on any vector will be a vector with the same elements where
each element will be equal to average all elements of initial vector.<o:p></o:p></span></i></b></div>
<div class="MsoNormal">
<b><i><span style="font-family: "times new roman" , "serif"; font-size: 12.0pt; line-height: 115%;"><br /></span></i></b></div>
<div class="separator" style="clear: both;">
<span class="MsoHyperlink"><span style="font-family: "times new roman" , serif; font-size: 12pt; line-height: 115%;">
</span></span></div>
<div class="MsoNormal">
<b><i><span style="font-family: "times new roman" , "serif"; font-size: 12.0pt; line-height: 115%;">Initial Vector:
V0 = (a, b, c, d,….) and M = two ways stochastic matrix<o:p></o:p></span></i></b></div>
<div class="MsoNormal">
<b><i><span style="font-family: "times new roman" , "serif"; font-size: 12.0pt; line-height: 115%;"><br /></span></i></b></div>
<div class="separator" style="clear: both; text-align: left;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjIN_TDKIvpFwXXUK4guQxs_Xbu0qgKwgDKefmfJ_15zdT83SIfR-lVbq63IYYLWgZWo71rfjLTRgH8O7kv7RIY9udAGBtsNWdwtCGa6NzNB3AlPcyH-AIc7vOslMZcPGQbHum_CoVuaXw/s1600/2.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="282" data-original-width="530" height="170" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjIN_TDKIvpFwXXUK4guQxs_Xbu0qgKwgDKefmfJ_15zdT83SIfR-lVbq63IYYLWgZWo71rfjLTRgH8O7kv7RIY9udAGBtsNWdwtCGa6NzNB3AlPcyH-AIc7vOslMZcPGQbHum_CoVuaXw/s320/2.png" width="320" /></a></div>
<div class="MsoNormal">
<span class="MsoHyperlink"><span style="font-family: "times new roman" , serif; font-size: 12pt; line-height: 115%;">Example:<o:p></o:p></span></span></div>
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<span class="MsoHyperlink"><span style="font-family: "times new roman" , serif; font-size: 12pt; line-height: 115%;"><br /></span></span></div>
<div class="separator" style="clear: both; text-align: left;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhnwcketAlGq7ooc9WM9oxYUPIDQ2BYbjlSwAae6F6sJFbWPALL9i9tBDp20BIY4AQg98gdTBl2GTu-gdbTc2znHkz1ULshUzVvfXJ-aB55NatbZwUaWlI9lYeg3liG9nCp1al990VqTm0/s1600/3.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="760" data-original-width="1280" height="190" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhnwcketAlGq7ooc9WM9oxYUPIDQ2BYbjlSwAae6F6sJFbWPALL9i9tBDp20BIY4AQg98gdTBl2GTu-gdbTc2znHkz1ULshUzVvfXJ-aB55NatbZwUaWlI9lYeg3liG9nCp1al990VqTm0/s320/3.png" width="320" /></a></div>
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<span class="MsoHyperlink"><span style="font-family: "times new roman" , serif; font-size: 12pt; line-height: 115%;"><br /></span></span></div>
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<span class="MsoHyperlink"><span style="font-family: "times new roman" , serif; font-size: 12pt; line-height: 115%;"></span></span></div>
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<b><i><span style="font-family: "times new roman" , "serif"; font-size: 12.0pt; line-height: 115%;">Does this
conjecture lead us toward an absolute justice in the world?<o:p></o:p></span></i></b></div>
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<b><i><span style="font-family: "times new roman" , "serif"; font-size: 12.0pt; line-height: 115%;"><br /></span></i></b></div>
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<span class="MsoHyperlink"><span style="font-family: "times new roman" , serif; font-size: 12pt; line-height: 115%;"><o:p></o:p></span></span></div>
<br />
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<span style="font-family: "times new roman" , "serif"; font-size: 12.0pt; line-height: 115%;"><br /></span></div>
<b style="font-family: Calibri, sans-serif; font-size: 11pt;"><i></i></b></div>
Gholamreza Soleimanihttp://www.blogger.com/profile/03273527405719420253noreply@blogger.com0tag:blogger.com,1999:blog-392703582366288634.post-31532008887710219082018-02-19T14:14:00.000+03:302018-02-19T14:14:36.024+03:30A Model for Analysis of Work Done by a Special Force<div dir="ltr" style="text-align: left;" trbidi="on">
<span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%; mso-ansi-language: EN-US; mso-ascii-theme-font: major-bidi; mso-bidi-language: AR-SA; mso-bidi-theme-font: major-bidi; mso-fareast-font-family: Calibri; mso-fareast-language: EN-US; mso-fareast-theme-font: minor-latin; mso-hansi-theme-font: major-bidi;">This model is an example as application one of
theorems mentioned in article of “The Change Depends on the Direction of the
Motion: The Symmetric Group Action (2)” posted on link:</span><br />
<br />
<div class="MsoNormal">
<span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%; mso-ascii-theme-font: major-bidi; mso-bidi-theme-font: major-bidi; mso-hansi-theme-font: major-bidi;"><a href="http://www.emfps.org/2017/08/the-change-depends-on-direction-of_9.html?m=1">http://www.emfps.org/2017/08/the-change-depends-on-direction-of_9.html?m=1</a></span><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%; mso-ascii-theme-font: major-bidi; mso-bidi-theme-font: major-bidi; mso-hansi-theme-font: major-bidi;"><o:p></o:p></span></div>
<div class="MsoNormal">
<br /></div>
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</div>
<div class="MsoNormal">
<b><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%; mso-ascii-theme-font: major-bidi; mso-bidi-theme-font: major-bidi; mso-hansi-theme-font: major-bidi;">Work Done by
Force<o:p></o:p></span></b></div>
<div class="MsoNormal">
<b><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%; mso-ascii-theme-font: major-bidi; mso-bidi-theme-font: major-bidi; mso-hansi-theme-font: major-bidi;"><br /></span></b></div>
<div class="MsoNormal">
<span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%; mso-ascii-theme-font: major-bidi; mso-bidi-theme-font: major-bidi; mso-hansi-theme-font: major-bidi;">When we are speaking about the work
done by a force, we have usually two options:<o:p></o:p></span></div>
<div class="MsoNormal">
<span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%; mso-ascii-theme-font: major-bidi; mso-bidi-theme-font: major-bidi; mso-hansi-theme-font: major-bidi;"><br /></span></div>
<div class="MsoNormal">
<span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%; mso-ascii-theme-font: major-bidi; mso-bidi-theme-font: major-bidi; mso-hansi-theme-font: major-bidi;">1. The work done on a particle by a
constant force in magnitude and direction which is calculated by below
equation:<o:p></o:p></span></div>
<br /><br />
<div class="separator" style="clear: both; text-align: left;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjxWqlISQJ6VqqK-uQSoaO7u8K-gkwU6pHns6yyLcu8ZWj-R7ZwJrBaiaL_aVI3xS7KTtT6gWF0S2PIW51dcNqTdl61GzFJOjnaQyizMzmnm-PTooCo6rSU37d41WUeMlRrEO94Am_d8hs/s1600/1.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="42" data-original-width="216" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjxWqlISQJ6VqqK-uQSoaO7u8K-gkwU6pHns6yyLcu8ZWj-R7ZwJrBaiaL_aVI3xS7KTtT6gWF0S2PIW51dcNqTdl61GzFJOjnaQyizMzmnm-PTooCo6rSU37d41WUeMlRrEO94Am_d8hs/s1600/1.png" /></a></div>
<div class="MsoNormal">
</div>
<div class="MsoNormal">
<span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%; mso-ascii-theme-font: major-bidi; mso-bidi-theme-font: major-bidi; mso-hansi-theme-font: major-bidi;">2. The work done on a particle by a
varying force in magnitude and direction in which we should use the line
integral to calculate it as follows:<o:p></o:p></span></div>
<br /><br />
<div class="separator" style="clear: both; text-align: left;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhYQUVTSm_5UmIX1_G_06HXARi4ebs1uD0AA07MlhcCbIstflbGQZletT36mdqN1jQG3d6ONxdUGR_TUE9co8B5HB2R2fDgg5Y2jUNoedyo-qkcfqBMIH_VE9LlCO6Ny6tbS3WBCadk3FE/s1600/2.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="121" data-original-width="684" height="56" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhYQUVTSm_5UmIX1_G_06HXARi4ebs1uD0AA07MlhcCbIstflbGQZletT36mdqN1jQG3d6ONxdUGR_TUE9co8B5HB2R2fDgg5Y2jUNoedyo-qkcfqBMIH_VE9LlCO6Ny6tbS3WBCadk3FE/s320/2.png" width="320" /></a></div>
<div class="MsoNormal">
</div>
<div class="MsoNormal">
<span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%; mso-ascii-theme-font: major-bidi; mso-bidi-theme-font: major-bidi; mso-hansi-theme-font: major-bidi;">But, in this article, I am willing
to introduce you a special force which has the constant magnitude but varying in
direction. In this case, I have made a model that it is able to show us the
location of the particle after being displaced by this special force.<o:p></o:p></span></div>
<div class="MsoNormal">
<span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%; mso-ascii-theme-font: major-bidi; mso-bidi-theme-font: major-bidi; mso-hansi-theme-font: major-bidi;"><br /></span></div>
<div class="MsoNormal">
<span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%; mso-ascii-theme-font: major-bidi; mso-bidi-theme-font: major-bidi; mso-hansi-theme-font: major-bidi;">Suppose a particle P (0, 0, 0) just
like below figure being displaced by a force F:<o:p></o:p></span></div>
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<span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%; mso-ascii-theme-font: major-bidi; mso-bidi-theme-font: major-bidi; mso-hansi-theme-font: major-bidi;"><br /></span></div>
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjIYlPqtdnkWl88TzjzOrRkPO5xfFHLmdaH5OXyjfUFbz7-Cb1ouSsEl-8U9-t8RrHMf7jAPjPfTX8aRA3-tqm9CGVAkgNIcDj69exgsyXiQFdX6Q8LSzHKffFtHECgCt6a5cgc-wwJlRs/s1600/3.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="455" data-original-width="571" height="254" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjIYlPqtdnkWl88TzjzOrRkPO5xfFHLmdaH5OXyjfUFbz7-Cb1ouSsEl-8U9-t8RrHMf7jAPjPfTX8aRA3-tqm9CGVAkgNIcDj69exgsyXiQFdX6Q8LSzHKffFtHECgCt6a5cgc-wwJlRs/s320/3.png" width="320" /></a></div>
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<span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%; mso-ascii-theme-font: major-bidi; mso-bidi-theme-font: major-bidi; mso-hansi-theme-font: major-bidi;"></span></div>
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<i><span style="line-height: 115%;"><span style="font-family: Times New Roman, serif;"><span style="font-size: 14pt;"><b>Theorem: The force with below vector has the constant </b></span><span style="font-size: 18.6667px;"><b>magnitude</b></span><span style="font-size: 14pt;"><b> equal to </b></span></span><u style="font-family: "Times New Roman", serif; font-size: 14pt; font-weight: bold;">1.22474487139159</u><span style="font-family: Times New Roman, serif;"><span style="font-size: 14pt;"><b>
but varying in direction:<o:p></o:p></b></span></span></span></i></div>
<div class="MsoNormal">
<i><span style="line-height: 115%;"><span style="font-family: Times New Roman, serif;"><span style="font-size: 14pt;"><b><br /></b></span></span></span></i></div>
<div class="separator" style="clear: both; text-align: left;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEg-shxtxvGT1xd0qWQXo_lF4T19xlx_75pyJs0_uaVD6jW7pTOmOjnYeteK_Hw9xHZHYNeFxD2hlWX5z5ql_rtjYqQpxo8UhSPcaLbQ7UQojIYoVyVkP-wMThBp8KS-QUOMChPS2KhpAAQ/s1600/4.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="160" data-original-width="516" height="99" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEg-shxtxvGT1xd0qWQXo_lF4T19xlx_75pyJs0_uaVD6jW7pTOmOjnYeteK_Hw9xHZHYNeFxD2hlWX5z5ql_rtjYqQpxo8UhSPcaLbQ7UQojIYoVyVkP-wMThBp8KS-QUOMChPS2KhpAAQ/s320/4.png" width="320" /></a></div>
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<i><span style="line-height: 115%;"><span style="font-family: Times New Roman, serif;"><span style="font-size: 14pt;"><b><br /></b></span></span></span></i></div>
<div class="MsoNormal">
<span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%; mso-ascii-theme-font: major-bidi; mso-bidi-font-style: italic; mso-bidi-theme-font: major-bidi; mso-hansi-theme-font: major-bidi; mso-no-proof: yes;">In this case, we can still use option (1) and below equation
to calculate the work done:<o:p></o:p></span></div>
<br /><br />
<div class="MsoNormal">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjxWqlISQJ6VqqK-uQSoaO7u8K-gkwU6pHns6yyLcu8ZWj-R7ZwJrBaiaL_aVI3xS7KTtT6gWF0S2PIW51dcNqTdl61GzFJOjnaQyizMzmnm-PTooCo6rSU37d41WUeMlRrEO94Am_d8hs/s1600/1.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="42" data-original-width="216" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjxWqlISQJ6VqqK-uQSoaO7u8K-gkwU6pHns6yyLcu8ZWj-R7ZwJrBaiaL_aVI3xS7KTtT6gWF0S2PIW51dcNqTdl61GzFJOjnaQyizMzmnm-PTooCo6rSU37d41WUeMlRrEO94Am_d8hs/s1600/1.png" /></a></div>
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</div>
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<span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%; mso-ascii-theme-font: major-bidi; mso-bidi-theme-font: major-bidi; mso-hansi-theme-font: major-bidi;">Below figure shows the components of
this model:<o:p></o:p></span></div>
<br /><br />
<div class="separator" style="clear: both; text-align: left;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEib4hC_Yf_azwH944fzcHU-pnRnuGcMpWC7qv11B_osHw0HDCUkOKmGj602DCv3ZuesFNlbMzCK4pzpfscwrkCE_G5Vq7W1gJuI3bKsvzJ57IjKr9BvN_laKIbINM6goor6LF7Ix1ZEHwc/s1600/5.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="215" data-original-width="755" height="91" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEib4hC_Yf_azwH944fzcHU-pnRnuGcMpWC7qv11B_osHw0HDCUkOKmGj602DCv3ZuesFNlbMzCK4pzpfscwrkCE_G5Vq7W1gJuI3bKsvzJ57IjKr9BvN_laKIbINM6goor6LF7Ix1ZEHwc/s320/5.png" width="320" /></a></div>
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<br /></div>
<div class="MsoNormal">
</div>
<div class="MsoNormal">
<span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%; mso-ascii-theme-font: major-bidi; mso-bidi-theme-font: major-bidi; mso-fareast-font-family: "Times New Roman"; mso-fareast-theme-font: minor-fareast; mso-hansi-theme-font: major-bidi;">Let me explain you about the
components of above model as follows:<o:p></o:p></span></div>
<div class="MsoNormal">
<span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%; mso-ascii-theme-font: major-bidi; mso-bidi-theme-font: major-bidi; mso-fareast-font-family: "Times New Roman"; mso-fareast-theme-font: minor-fareast; mso-hansi-theme-font: major-bidi;"><br /></span></div>
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1. <span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%; mso-ascii-theme-font: major-bidi; mso-bidi-theme-font: major-bidi; mso-fareast-font-family: "Times New Roman"; mso-fareast-theme-font: minor-fareast; mso-hansi-theme-font: major-bidi;">In left side on
cells C2:D3, we have inputs including the angle φ (degree) of force vector and
amount of displacement of particle “P” which is “r”.<o:p></o:p></span></div>
<div class="MsoNormal">
<span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%; mso-ascii-theme-font: major-bidi; mso-bidi-theme-font: major-bidi; mso-fareast-font-family: "Times New Roman"; mso-fareast-theme-font: minor-fareast; mso-hansi-theme-font: major-bidi;"><br /></span></div>
<div class="MsoNormal">
<span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%; mso-ascii-theme-font: major-bidi; mso-bidi-theme-font: major-bidi; mso-fareast-font-family: "Times New Roman"; mso-fareast-theme-font: minor-fareast; mso-hansi-theme-font: major-bidi;">2. In right side on cells F3:J8, we
have outputs including:<o:p></o:p></span></div>
<div class="MsoNormal">
<span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%; mso-ascii-theme-font: major-bidi; mso-bidi-theme-font: major-bidi; mso-fareast-font-family: "Times New Roman"; mso-fareast-theme-font: minor-fareast; mso-hansi-theme-font: major-bidi;"><br /></span></div>
<div class="MsoNormal">
<span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%; mso-ascii-theme-font: major-bidi; mso-bidi-theme-font: major-bidi; mso-fareast-font-family: "Times New Roman"; mso-fareast-theme-font: minor-fareast; mso-hansi-theme-font: major-bidi;"><span style="mso-spacerun: yes;">
</span>2-1) on cells G3:I3, a special force vector can be calculated by using
above theorem.<o:p></o:p></span></div>
<div class="MsoNormal">
<span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%; mso-ascii-theme-font: major-bidi; mso-bidi-theme-font: major-bidi; mso-fareast-font-family: "Times New Roman"; mso-fareast-theme-font: minor-fareast; mso-hansi-theme-font: major-bidi;"><br /></span></div>
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<span style="mso-spacerun: yes;"> </span><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%; mso-ascii-theme-font: major-bidi; mso-bidi-theme-font: major-bidi; mso-fareast-font-family: "Times New Roman"; mso-fareast-theme-font: minor-fareast; mso-hansi-theme-font: major-bidi;"><span style="mso-spacerun: yes;"> </span>2-2) on
cells G4:I4, the direction of special force can be obtained by using below
formula:<o:p></o:p></span></div>
<div class="MsoNormal">
<span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%; mso-ascii-theme-font: major-bidi; mso-bidi-theme-font: major-bidi; mso-fareast-font-family: "Times New Roman"; mso-fareast-theme-font: minor-fareast; mso-hansi-theme-font: major-bidi;"><br /></span></div>
<div class="separator" style="clear: both; text-align: left;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgWkMWCo7RoiH35F1XlXb1xZgic9eYiVh_IFnklHGyiLqenZNtjG4_t0n8NPAn0RmnhZ8PCa5bejPx4zL9QEq6-AC1_xt03D1Jobne7N3pXHNPWhO0OZE8P1cXp9ulCceXQJtNJ0UZSWPM/s1600/6.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="89" data-original-width="639" height="44" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgWkMWCo7RoiH35F1XlXb1xZgic9eYiVh_IFnklHGyiLqenZNtjG4_t0n8NPAn0RmnhZ8PCa5bejPx4zL9QEq6-AC1_xt03D1Jobne7N3pXHNPWhO0OZE8P1cXp9ulCceXQJtNJ0UZSWPM/s320/6.png" width="320" /></a></div>
<div class="MsoNormal">
<span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%; mso-ascii-theme-font: major-bidi; mso-bidi-theme-font: major-bidi; mso-fareast-font-family: "Times New Roman"; mso-fareast-theme-font: minor-fareast; mso-hansi-theme-font: major-bidi;"><br /></span></div>
<div class="MsoNormal">
<span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%; mso-ascii-theme-font: major-bidi; mso-bidi-theme-font: major-bidi; mso-fareast-font-family: "Times New Roman"; mso-fareast-theme-font: minor-fareast; mso-hansi-theme-font: major-bidi;">The magnitude of this force is the
constant and equal to </span><span style="font-family: "Times New Roman","serif"; font-size: 14.0pt; line-height: 115%; mso-ascii-theme-font: major-bidi; mso-bidi-theme-font: major-bidi; mso-hansi-theme-font: major-bidi; mso-no-proof: yes;">1.22474487139159.<b><i><u><o:p></o:p></u></i></b></span></div>
<div class="MsoNormal">
<span style="font-family: "Times New Roman","serif"; font-size: 14.0pt; line-height: 115%; mso-ascii-theme-font: major-bidi; mso-bidi-theme-font: major-bidi; mso-hansi-theme-font: major-bidi; mso-no-proof: yes;"><br /></span></div>
<div class="MsoNormal">
<span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%; mso-ascii-theme-font: major-bidi; mso-bidi-theme-font: major-bidi; mso-fareast-font-family: "Times New Roman"; mso-fareast-theme-font: minor-fareast; mso-hansi-theme-font: major-bidi;"><span style="mso-spacerun: yes;"> </span>2-3) on cell G5, we have the work done which
is calculated by below formulas:<o:p></o:p></span></div>
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<span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%; mso-ascii-theme-font: major-bidi; mso-bidi-theme-font: major-bidi; mso-fareast-font-family: "Times New Roman"; mso-fareast-theme-font: minor-fareast; mso-hansi-theme-font: major-bidi;"><br /></span></div>
<div class="separator" style="clear: both; text-align: left;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhA6VvyyHqpoxesaoaw8pB6tL5uAaEEnfr3VKLhMlI6OXDo2vUBWtGIGuxZS2zgDzBZ0Tb72knOi4cje5Iv7vbDyTIHzILgkWEgGjZu_ArC5zkUSDsgy7rpthGFyDRIbiR0Zb0hshAdPbo/s1600/7.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="243" data-original-width="628" height="123" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhA6VvyyHqpoxesaoaw8pB6tL5uAaEEnfr3VKLhMlI6OXDo2vUBWtGIGuxZS2zgDzBZ0Tb72knOi4cje5Iv7vbDyTIHzILgkWEgGjZu_ArC5zkUSDsgy7rpthGFyDRIbiR0Zb0hshAdPbo/s320/7.png" width="320" /></a></div>
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<span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%; mso-ascii-theme-font: major-bidi; mso-bidi-theme-font: major-bidi; mso-fareast-font-family: "Times New Roman"; mso-fareast-theme-font: minor-fareast; mso-hansi-theme-font: major-bidi;"><br /></span></div>
<div class="MsoNormal">
<span style="mso-spacerun: yes;"> </span><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%; mso-ascii-theme-font: major-bidi; mso-bidi-theme-font: major-bidi; mso-fareast-font-family: "Times New Roman"; mso-fareast-theme-font: minor-fareast; mso-hansi-theme-font: major-bidi;">2-4) on cells G7:I7, we have the location
particle P (x, y, z) which is derived by this model.<o:p></o:p></span></div>
<div class="MsoNormal">
<span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%; mso-ascii-theme-font: major-bidi; mso-bidi-theme-font: major-bidi; mso-fareast-font-family: "Times New Roman"; mso-fareast-theme-font: minor-fareast; mso-hansi-theme-font: major-bidi;"><br /></span></div>
<div class="MsoNormal">
<span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%; mso-ascii-theme-font: major-bidi; mso-bidi-theme-font: major-bidi; mso-fareast-font-family: "Times New Roman"; mso-fareast-theme-font: minor-fareast; mso-hansi-theme-font: major-bidi;"><span style="mso-spacerun: yes;"> </span></span><span style="mso-spacerun: yes;"> </span><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%; mso-ascii-theme-font: major-bidi; mso-bidi-theme-font: major-bidi; mso-fareast-font-family: "Times New Roman"; mso-fareast-theme-font: minor-fareast; mso-hansi-theme-font: major-bidi;">2-5) on cells G8:I8,</span> <span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%; mso-ascii-theme-font: major-bidi; mso-bidi-theme-font: major-bidi; mso-fareast-font-family: "Times New Roman"; mso-fareast-theme-font: minor-fareast; mso-hansi-theme-font: major-bidi;">the direction of motion particle P can be
calculated by using below formula:<o:p></o:p></span></div>
<div class="MsoNormal">
<span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%; mso-ascii-theme-font: major-bidi; mso-bidi-theme-font: major-bidi; mso-fareast-font-family: "Times New Roman"; mso-fareast-theme-font: minor-fareast; mso-hansi-theme-font: major-bidi;"><br /></span></div>
<div class="separator" style="clear: both; text-align: left;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh3nzQomSFyw9-OMIt2QN5-Kz2UIKudBK2Uh47J9fLFYAxVFgv3yVK-28enoPwz4RjBSu8vQi9YCGpidxOJygoaEjqAIJMYTNiu7tXYJhw8SYcPg5rTYyac_t4GCkfHqsxWzklVRR2Fquk/s1600/8.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="68" data-original-width="388" height="56" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh3nzQomSFyw9-OMIt2QN5-Kz2UIKudBK2Uh47J9fLFYAxVFgv3yVK-28enoPwz4RjBSu8vQi9YCGpidxOJygoaEjqAIJMYTNiu7tXYJhw8SYcPg5rTYyac_t4GCkfHqsxWzklVRR2Fquk/s320/8.png" width="320" /></a></div>
<div class="MsoNormal">
<span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%; mso-ascii-theme-font: major-bidi; mso-bidi-theme-font: major-bidi; mso-fareast-font-family: "Times New Roman"; mso-fareast-theme-font: minor-fareast; mso-hansi-theme-font: major-bidi;"><br /></span></div>
<div class="MsoNormal">
<span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%; mso-ascii-theme-font: major-bidi; mso-bidi-theme-font: major-bidi; mso-hansi-theme-font: major-bidi;"><span style="mso-spacerun: yes;"> </span>2-6) The change of direction particle P will
be done by click on cell A1 and also this change will again go back by click on
cell B1 (Go & Back).</span><span style="mso-spacerun: yes;"> </span><o:p></o:p></div>
<div class="MsoNormal">
<span style="mso-spacerun: yes;"><br /></span></div>
<div align="right" class="MsoNormal" dir="RTL" style="direction: rtl; text-align: left; unicode-bidi: embed;">
<span dir="LTR" style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%; mso-ascii-theme-font: major-bidi; mso-bidi-theme-font: major-bidi; mso-hansi-theme-font: major-bidi;">You can see
below screenshot as the examples for this model:<o:p></o:p></span></div>
<div align="right" class="MsoNormal" dir="RTL" style="direction: rtl; text-align: left; unicode-bidi: embed;">
<span dir="LTR" style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%; mso-ascii-theme-font: major-bidi; mso-bidi-theme-font: major-bidi; mso-hansi-theme-font: major-bidi;"><br /></span></div>
<div class="separator" style="clear: both; text-align: center;">
<iframe allowfullscreen='allowfullscreen' webkitallowfullscreen='webkitallowfullscreen' mozallowfullscreen='mozallowfullscreen' width='320' height='266' src='https://www.blogger.com/video.g?token=AD6v5dy1qtXPhH1VSmWV4bjoN-GYx46Ss9wT__6Td9ONa8eNYYSS-gNqSlgeAnHTtWwJ0LatjcPlohIvQQtVIMJ1dg' class='b-hbp-video b-uploaded' frameborder='0'></iframe></div>
<div align="right" class="MsoNormal" dir="RTL" style="direction: rtl; text-align: left; unicode-bidi: embed;">
<span dir="LTR" style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%; mso-ascii-theme-font: major-bidi; mso-bidi-theme-font: major-bidi; mso-hansi-theme-font: major-bidi;"><br /></span></div>
<div align="right" class="MsoNormal" dir="RTL" style="direction: rtl; text-align: left; unicode-bidi: embed;">
<span dir="LTR" style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%; mso-ascii-theme-font: major-bidi; mso-bidi-theme-font: major-bidi; mso-hansi-theme-font: major-bidi;">All researchers
and individual people, who are interested in having this model, don’t hesitate
to send their request to below addresses:<o:p></o:p></span></div>
<br /><br />
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhOXIFdl1O2_jAVni-RUuj6UywGL7j8ybGmAS4t_l0hiZUAgT12vdI7pTR732ilAWaDUiEV1XdSXGvuyrxFqwDBKE-eiuI5vvwrS8BjBU923Ov53T4Z5M_JXRefGLBwqPh9ke0v8sREFJk/s1600/%25D8%25AF%25D8%25B1%25DB%258C%25D8%25A7%25D9%2581%25D8%25AA+%25D9%2581%25D8%25A7%25DB%258C%25D9%2584+%25D8%25A7%25DA%25A9%25D8%25B3%25D9%2584.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="240" data-original-width="592" height="129" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhOXIFdl1O2_jAVni-RUuj6UywGL7j8ybGmAS4t_l0hiZUAgT12vdI7pTR732ilAWaDUiEV1XdSXGvuyrxFqwDBKE-eiuI5vvwrS8BjBU923Ov53T4Z5M_JXRefGLBwqPh9ke0v8sREFJk/s320/%25D8%25AF%25D8%25B1%25DB%258C%25D8%25A7%25D9%2581%25D8%25AA+%25D9%2581%25D8%25A7%25DB%258C%25D9%2584+%25D8%25A7%25DA%25A9%25D8%25B3%25D9%2584.png" width="320" /></a></div>
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Gholamreza Soleimanihttp://www.blogger.com/profile/03273527405719420253noreply@blogger.com0tag:blogger.com,1999:blog-392703582366288634.post-52461451581052004302018-02-09T13:41:00.003+03:302024-02-14T23:33:52.917+03:30A Model to Solve a System of Nonlinear Equations by Using Microsoft Excel<div dir="ltr" style="text-align: left;" trbidi="on">
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<span style="font-family: "times new roman" , serif; font-size: 12pt; line-height: 107%;">This is an example for solving a system of nonlinear
equations by using the Big Data Science Analysis with Microsoft excel plus VBA.<o:p></o:p></span><br />
<span style="font-family: "times new roman" , serif; font-size: 12pt; line-height: 107%;"><br /></span>
<span style="font-family: "times new roman" , serif; font-size: 12pt; line-height: 107%;"><br /></span>
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjLJJF6_dkVf13GUznADhuYJbp3YdyeLtt2AYSifnBnzWUM5-4diL7rdXI5NG1iKBf-9D4u6LIbvyQZaeZ2Y03Twoid32Yv3WMil-GighcrQJu99MYQXw7o-q8sygmjrTkRUIxdcDdXxDw/s1600/nonlinear.png" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="500" data-original-width="796" height="201" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjLJJF6_dkVf13GUznADhuYJbp3YdyeLtt2AYSifnBnzWUM5-4diL7rdXI5NG1iKBf-9D4u6LIbvyQZaeZ2Y03Twoid32Yv3WMil-GighcrQJu99MYQXw7o-q8sygmjrTkRUIxdcDdXxDw/s320/nonlinear.png" width="320" /></a></div>
<span style="font-family: "times new roman" , serif; font-size: 12pt; line-height: 107%;"><br /></span></div>
<div class="MsoNormal" style="direction: ltr; unicode-bidi: embed;"><br /></div><div class="MsoNormal" style="direction: ltr; text-align: justify; unicode-bidi: embed;"><p class="MsoNormal">Definitely, there are many complicated problems that can be
solved by using this analytic model. For instance, one of the applications of
this model is to solve problems related to optimization, such as<b><i> Hill
Climbing.</i></b><o:p></o:p></p>
<p class="MsoNormal">For example, what is the maximum area of a rectangle
inscribed in a circle with a radius of 2 units?<o:p></o:p></p>
<p class="MsoNormal">You can find the answers for “x” and “y” in this rectangle
in the below data analysis:<o:p></o:p></p><p class="MsoNormal"><br /></p></div><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEi3__ZnS4YuIZboU3WlOZvMNlKx8QXjEemnL05fBrjEByYnmkkHpvK7g29XBcW7rmg79rl1xSns3oev33bS82HTF0ZBg3lMZm0J6-yKzSHjKYED1xD2jLtZ_zjBIa6T_jepHVRPhjTqJpjl_JjnE-clFtKGQZCUkXIIx8JWA6sMk8nfnCQ1U2DiV4Nb-Uw/s586/04.01.2024_01.51.31_REC.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="501" data-original-width="586" height="274" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEi3__ZnS4YuIZboU3WlOZvMNlKx8QXjEemnL05fBrjEByYnmkkHpvK7g29XBcW7rmg79rl1xSns3oev33bS82HTF0ZBg3lMZm0J6-yKzSHjKYED1xD2jLtZ_zjBIa6T_jepHVRPhjTqJpjl_JjnE-clFtKGQZCUkXIIx8JWA6sMk8nfnCQ1U2DiV4Nb-Uw/s320/04.01.2024_01.51.31_REC.png" width="320" /></a></div><br /><div class="MsoNormal" style="direction: ltr; unicode-bidi: embed;"><br /></div><div class="MsoNormal" style="direction: ltr; unicode-bidi: embed;"><br /></div><div class="MsoNormal" style="direction: ltr; unicode-bidi: embed;"><br /></div><div class="MsoNormal" style="direction: ltr; unicode-bidi: embed;">
<span style="background: white; color: #333333; font-family: "times new roman" , "serif"; font-size: 12pt; line-height: 107%;">I would like to inform you that this
model is able to solve all linear and nonlinear system of equations in which it gives us less error than traditional methods such as
Newton – Raphson , Gauss – Seidel, Jacobian and so on. Don't worry, if you have
not any knowledge about traditional methods. Dive into new technology.</span><span style="font-family: "times new roman" , "serif"; font-size: 12pt; line-height: 107%;"><o:p></o:p></span></div>
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<b><u>Example: A
Model to Track the Location of a Particle in the Space</u></b></div>
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<o:p></o:p></div>
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One of the most important needs for many projects is, quickly to track the motion of a particle when</div>
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<span dir="LTR">it is tripping between two points in the space. For
instance, suppose particle P is moving by velocity “V” with accelerate equal to
zero from point A (x1, y1, z1) to point B (x2, y2, z2). We want to know the
coordination of P (x, y, z) at the moment of “t” when it is moving in direction
of A to B. This model gives us the opportunity to obtain the coordination P (x,
y, z) only by click. In fact, if we have the coordination P (x, y, z), it will
be as an index for us that other particles which are moving from A to B such as
P1, P2, …. are not tripping in the exact direction of A to B. In this case, we
have to solve a system of two nonlinear equations as follows:<o:p></o:p></span></div>
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjfi7Afq7SHtE_ZHka-13Ac4SDwjDLXKNc1pWjzOsgoB1wVKrjxuPu-Gi9_BHHQLhLrKoDlsTrf7A2iLnxgUUCqRgFADv9RFyEHr46s8REQkTunYpx_CSpTqTtc8qtPkkpnBhBjpSi8I1A/s1600/1.png" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="120" data-original-width="433" height="88" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjfi7Afq7SHtE_ZHka-13Ac4SDwjDLXKNc1pWjzOsgoB1wVKrjxuPu-Gi9_BHHQLhLrKoDlsTrf7A2iLnxgUUCqRgFADv9RFyEHr46s8REQkTunYpx_CSpTqTtc8qtPkkpnBhBjpSi8I1A/s320/1.png" width="320" /></a></div>
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<span dir="LTR"> First of all, we should define amount of “a”
and “b” as follows:<o:p></o:p></span></div>
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<span dir="LTR"><br /></span></div>
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<span dir="LTR">
</span></div>
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<span dir="LTR">The
distance of point A to point B is calculated by using below formula and also
“X” is the distance that particle P will travel after time “t” in direction of
A to B:<o:p></o:p></span></div>
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<span dir="LTR"><br /></span></div>
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgrQmO0UqxIN2aXFjA4Ke4o7jEUUHNkj-ColOb3QmTdBWLzNlGE0pAU5lgqa5B-Y6pNNZAfX4-c53LShKFsSOANlWJKAz2N40O0cEuS_9CvvNQGXOmEMunAG5YIIjogF5oQ4C_tm0uWoFs/s1600/2.png" style="clear: left; float: left; margin-bottom: 1em; margin-left: 1em;"><img border="0" data-original-height="188" data-original-width="488" height="123" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgrQmO0UqxIN2aXFjA4Ke4o7jEUUHNkj-ColOb3QmTdBWLzNlGE0pAU5lgqa5B-Y6pNNZAfX4-c53LShKFsSOANlWJKAz2N40O0cEuS_9CvvNQGXOmEMunAG5YIIjogF5oQ4C_tm0uWoFs/s320/2.png" width="320" /></a></div>
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<span dir="LTR"><br /></span></div>
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<span dir="LTR"><br /></span></div>
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<span dir="LTR"><br /></span></div>
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<span dir="LTR"><br /></span></div>
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<span dir="LTR"></span></div>
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<span style="font-family: "times new roman" , "serif"; font-size: 12pt; line-height: 107%;">Therefore, we should
solve below </span><span style="font-family: "times new roman" , "serif"; font-size: 12pt; line-height: 107%;">system of two nonlinear equations</span></div>
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<span style="font-family: "times new roman" , "serif"; font-size: 12pt; line-height: 107%;"><br /></span></div>
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhfaNobgIR8-8b9sRq2XRv3W44ljN2fsS0kmd5Dh7Eb45Km_K96ALNljyXR9DJgz0x40aTB7Q1Nlb4a7fbcYEO3kn_RQegmqTjqpOq0CJ39X_pW8l4mUQmSY2BHYY3D5FICkfsYcQ2_lWQ/s1600/3.png" style="clear: left; float: left; margin-bottom: 1em; margin-left: 1em;"><img border="0" data-original-height="94" data-original-width="533" height="56" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhfaNobgIR8-8b9sRq2XRv3W44ljN2fsS0kmd5Dh7Eb45Km_K96ALNljyXR9DJgz0x40aTB7Q1Nlb4a7fbcYEO3kn_RQegmqTjqpOq0CJ39X_pW8l4mUQmSY2BHYY3D5FICkfsYcQ2_lWQ/s320/3.png" width="320" /></a></div>
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<span style="line-height: 107%;"><span style="font-family: "times new roman" , serif;">Below figure as well as shows you the components of this model</span></span></div>
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<span style="line-height: 107%;"><span style="font-family: "times new roman" , serif;"><br /></span></span></div>
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<span style="line-height: 107%;"><span style="font-family: "times new roman" , serif;"><br /></span></span></div>
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjygavSsvgBu_lP4vMUCxGJcJrV2seg2n2VWqoZ8Ec5IGS1BgDAxGHDEQC2U-UPjEree2AF8j3SUXBbnF0witSYabkx0ipbvG_TusX68CP_EaTB9azvqtxU8d04X_-3fSmm0d3uK3H-3k8/s1600/4.png" style="clear: left; float: left; margin-bottom: 1em; margin-left: 1em;"><img border="0" data-original-height="451" data-original-width="1124" height="128" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjygavSsvgBu_lP4vMUCxGJcJrV2seg2n2VWqoZ8Ec5IGS1BgDAxGHDEQC2U-UPjEree2AF8j3SUXBbnF0witSYabkx0ipbvG_TusX68CP_EaTB9azvqtxU8d04X_-3fSmm0d3uK3H-3k8/s320/4.png" width="320" /></a></div>
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<span style="line-height: 107%;"><span style="font-family: "times new roman" , serif;"><br /></span></span></div>
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<span style="font-family: "times new roman" , "serif"; font-size: 12pt; line-height: 107%;"><br /></span></div>
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<span style="font-family: "times new roman" , "serif"; font-size: 12pt; line-height: 107%;"><br /></span></div>
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<span style="font-family: "times new roman" , "serif"; font-size: 12pt; line-height: 107%;"><br /></span></div>
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<span style="font-family: "times new roman" , "serif"; font-size: 12pt; line-height: 107%;"><br /></span></div>
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<span style="font-family: "times new roman" , "serif"; font-size: 12pt; line-height: 107%;"><br /></span></div>
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<span style="font-family: "times new roman" , "serif"; font-size: 12pt; line-height: 107%;"><br /></span></div>
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<span style="font-family: "times new roman" , "serif"; font-size: 12pt; line-height: 107%;"><br /></span></div>
<div class="MsoNormal" dir="RTL" style="text-align: left;">
<span style="font-family: "times new roman" , "serif"; font-size: 12pt; line-height: 107%;"><br /></span></div>
<div class="MsoNormal" dir="RTL" style="text-align: left;">
<span style="font-family: "times new roman" , "serif"; font-size: 12pt; line-height: 107%;"></span></div>
<div class="MsoNormal" dir="RTL" style="text-align: left;">
<span dir="LTR" style="font-family: "times new roman" , "serif"; font-size: 12pt; line-height: 107%;">Let me explain you about the components of
above model as follows:<o:p></o:p></span></div>
<div class="MsoNormal" dir="RTL" style="text-align: left;">
<span dir="LTR" style="font-family: "times new roman" , "serif"; font-size: 12pt; line-height: 107%;"><br /></span></div>
<div class="MsoNormal" dir="RTL" style="text-align: left;">
<span dir="LTR" style="font-family: "times new roman" , "serif"; font-size: 12pt; line-height: 107%;">1. In right side on cells G4:J10, we have
inputs including the coordination points A and B, velocity of particle P (v),
the time after staring to travel particle P (t) and Error which is the
difference between the results. So, X = v.t, d = distance between point A and B
and on cell G10, I have included a logic formula (=if (H8 >= H9, H8, 0)). It
means, if X = 0 then the particle has passed point B<o:p></o:p></span></div>
<div class="MsoNormal" dir="RTL" style="text-align: left;">
<span dir="LTR" style="font-family: "times new roman" , "serif"; font-size: 12pt; line-height: 107%;"><br /></span>
<span dir="LTR" style="font-family: "times new roman" , "serif"; font-size: 12pt; line-height: 107%;"><span style="font-family: "times new roman" , serif; font-size: 12pt; line-height: 107%;">2. In left side on cells
C5:E6, we have other inputs including the ranges to reach to the answer for coordination particle P (x, y, z) which is the solution for </span><span style="font-family: "times new roman" , serif; font-size: 12pt; line-height: 107%;">system
of two nonlinear equations. </span></span><br />
<span dir="LTR" style="font-family: "times new roman" , "serif"; font-size: 12pt; line-height: 107%;"><span style="font-family: "times new roman" , "serif"; font-size: 12pt; line-height: 107%;"> Here, there are lower and upper ranges which are
changed by click on cell A2 and also this change will again go back by click on
cell B2 (Go & Back).</span></span><br />
<span dir="LTR" style="font-family: "times new roman" , "serif"; font-size: 12pt; line-height: 107%;"><span style="font-family: "times new roman" , "serif"; font-size: 12pt; line-height: 107%;"><br /></span></span>
<span dir="LTR" style="font-family: "times new roman" , "serif"; font-size: 12pt; line-height: 107%;"><span style="font-family: "times new roman" , "serif"; font-size: 12pt; line-height: 107%;"><span style="font-family: "times new roman" , serif; font-size: 12pt;">This part has been utilized </span><span style="background: white; color: #181818; font-family: "times new roman" , serif; font-size: 12pt;">by the method stated in article of “Can We Solve a
Nonlinear Equation with Many Variables?” posted on link:</span></span></span><br />
<span dir="LTR" style="font-family: "times new roman" , "serif"; font-size: 12pt; line-height: 107%;"><span style="font-family: "times new roman" , "serif"; font-size: 12pt; line-height: 107%;"><a href="http://emfps.org/2016/10/can-we-solve-nonlinear-equation-with.html" style="font-family: Calibri, sans-serif; font-size: 11pt;"><span dir="LTR" style="background: white; font-family: "times new roman" , "serif"; font-size: 12pt; line-height: 107%;">http://emfps.org/2016/10/can-we-solve-nonlinear-equation-with.html</span></a> </span></span><br />
<div style="text-align: right;">
<br /></div>
</div>
<div class="MsoNormal" dir="RTL" style="text-align: left;">
<span dir="LTR" style="background: white; font-family: "times new roman" , "serif"; font-size: 12pt; line-height: 107%;">3. On cells C9:E9, we have outputs which are the
answer to above </span></div>
<div class="MsoNormal" dir="RTL" style="text-align: left;">
<span dir="LTR" style="font-family: "times new roman" , "serif"; font-size: 12pt; line-height: 107%;">system of two
nonlinear equations.<o:p></o:p></span></div>
<div class="MsoNormal" dir="RTL" style="text-align: left;">
<span dir="LTR" style="font-family: "times new roman" , "serif"; font-size: 12pt; line-height: 107%;"><br /></span></div>
<div class="MsoNormal" dir="RTL" style="text-align: left;">
<span dir="LTR" style="font-family: "times new roman" , "serif"; font-size: 12pt; line-height: 107%;">4. On cells C12:E13, we have Control (1) where first equation is
solved by using the coordination A </span></div>
<div class="MsoNormal" dir="RTL" style="text-align: left;">
<span dir="LTR" style="font-family: "times new roman" , "serif"; font-size: 12pt; line-height: 107%;">and P and it is compared with amount of
“X^2” on cell C14. So, second equation is solved by using the coordination B
and P and it is also compared with amount of “(d-X)^2”on cell C15. The differences
have been mentioned on cell G12 and G13 as the errors.<o:p></o:p></span></div>
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</span></div>
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<span dir="LTR" style="font-family: "times new roman" , "serif"; font-size: 12pt; line-height: 107%;">5. On cells E15:G17, we have Control (2) which is referred to track
the directions in which we are willing to know if the motion of particle P is in
direction from point A to point B. In this case, a control can be conducted by
using below formulas:<o:p></o:p></span></div>
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<span dir="LTR" style="font-family: "times new roman" , "serif"; font-size: 12pt; line-height: 107%;">You can see below screenshot as the examples for this model:<o:p></o:p></span></div>
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<div class="separator" style="clear: both; text-align: center;">
<iframe allowfullscreen='allowfullscreen' webkitallowfullscreen='webkitallowfullscreen' mozallowfullscreen='mozallowfullscreen' width='320' height='266' src='https://www.blogger.com/video.g?token=AD6v5dwVMkVu-1s-HgOKoY8Pnh71RBIRmzCqDO7fFuQseGZwK8GQerZxDYBXWl6wAu4dM7OMFWCZrVhiD7zotAVm8w' class='b-hbp-video b-uploaded' frameborder='0'></iframe></div>
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<br /></div>
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<b><span dir="LTR" style="font-family: "times new roman" , "serif"; font-size: 12pt; line-height: 107%;">Conclusion<o:p></o:p></span></b></div>
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<br /></div>
<div class="MsoNormal" dir="RTL" style="text-align: left;">
<span style="font-family: "times new roman" , "serif"; font-size: 12pt; line-height: 107%;">.Above article gives you
a simple example</span></div>
<div class="MsoNormal" style="text-align: left;">
<span style="font-family: "times new roman" , "serif"; font-size: 12pt; line-height: 107%;"><span style="font-size: 12pt; line-height: 107%;">In fact, I am willing to
tell you that this model is able to solve all </span><span style="font-size: 12pt; line-height: 107%;">system of two or three
nonlinear </span></span></div>
<div class="MsoNormal" style="text-align: left;">
<span style="font-family: "times new roman" , serif; font-size: 12pt;">equations.</span></div>
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<span style="font-family: "times new roman" , serif; font-size: 12pt;"><br /></span></div>
<div class="MsoNormal" dir="RTL" style="text-align: left;">
<span dir="LTR" style="font-family: "times new roman" , "serif"; font-size: 12pt; line-height: 107%;">All researchers and individual people, who are interested in having
this model, don’t hesitate to send </span><br />
<span dir="LTR" style="font-family: "times new roman" , "serif"; font-size: 12pt; line-height: 107%;">their request to below addresses:<o:p></o:p></span><br />
<span dir="LTR" style="font-family: "times new roman" , "serif"; font-size: 12pt; line-height: 107%;"><br /></span>
<br />
<div class="separator" style="clear: both; text-align: center;">
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<span dir="LTR" style="font-family: "times new roman" , "serif"; font-size: 12pt; line-height: 107%;"></span><br />
<div align="center" class="MsoNormal" dir="RTL" style="text-align: center;">
<a href="https://t.me/Allisnumber"><b><span dir="LTR" style="font-family: "times new roman" , "serif"; font-size: 22pt; line-height: 107%;">https://t.me/Allisnumber</span></b></a><b><span dir="LTR" style="font-family: "times new roman" , "serif"; font-size: 22pt; line-height: 107%;"><o:p></o:p></span></b></div>
</div>
</div>
Gholamreza Soleimanihttp://www.blogger.com/profile/03273527405719420253noreply@blogger.com0tag:blogger.com,1999:blog-392703582366288634.post-5863581826748322072018-02-05T13:28:00.003+03:302018-02-13T09:33:14.032+03:30The Impact of Stochastic Matrix on Any Vector<div dir="ltr" style="text-align: left;" trbidi="on">
<div class="MsoNormal">
<span style="font-family: "times new roman" , "serif"; font-size: 12.0pt; line-height: 115%;">A stochastic matrix shows us that
the sum all elements on each column (or each row) is equal one or we can say
that each column (or each row) of a stochastic matrix is just a probability
vector. <o:p></o:p></span><br />
<br /></div>
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<span style="font-family: "times new roman" , "serif"; font-size: 12.0pt; line-height: 115%;"><br /></span></div>
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<b><i><span style="font-family: "times new roman" , "serif"; font-size: 12.0pt; line-height: 115%;">Theorem (1):
The sequence of operations a stochastic matrix on any vector will be finally
obtained the constant vector. (The elements of vector are the members of Real Number)</span></i></b></div>
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<b><i><span style="font-family: "times new roman" , "serif"; font-size: 12.0pt; line-height: 115%;"><br /></span></i></b></div>
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<b><i><span style="font-family: "times new roman" , "serif"; font-size: 12.0pt; line-height: 115%;">V1 = V0 * M^1 ,
V2 = V1*M^2, V3 = V2*M^3, …. Vn+1 = V n*
M^k<o:p></o:p></span></i></b></div>
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<b><i><span style="font-family: "times new roman" , "serif"; font-size: 12.0pt; line-height: 115%;">Where vector
Vn+1 always will be the constant.<o:p></o:p></span></i></b></div>
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<b><i><span style="font-family: "times new roman" , "serif"; font-size: 12.0pt; line-height: 115%;"><br /></span></i></b></div>
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<b><i><u>A special state is when the vector is a probability
vector which is named Markov Chain or Markov Process<o:p></o:p></u></i></b></div>
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<b><i><u><br /></u></i></b></div>
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<b><span style="font-family: "times new roman" , "serif"; font-size: 12.0pt; line-height: 115%;">Example (1):<o:p></o:p></span></b></div>
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<b><span style="font-family: "times new roman" , "serif"; font-size: 12.0pt; line-height: 115%;"><br /></span></b></div>
<br />
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<span style="font-family: "times new roman" , "serif"; font-size: 12.0pt; line-height: 115%;">The sample of our vector (1*4) is:<o:p></o:p></span></div>
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<span style="font-family: "times new roman" , serif; font-size: 12pt;">V0 =</span></div>
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<span style="font-family: "times new roman" , serif; font-size: 12pt;"> </span></div>
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<span style="font-family: "times new roman" , "serif"; font-size: 12.0pt; line-height: 115%;"></span></div>
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjmb1_9KLu3gzToaaNNzedwVardmMcQV9apn8wORImwxYwfLNxrqvploiPKrlQMtMoDiXAljKj3amohw0whsMf-NfHv_SNqWeaNfG4mFJWGo3XosHVll7iqjwjoSHd73RBxFSRDhZpWuUo/s1600/1.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="29" data-original-width="376" height="24" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjmb1_9KLu3gzToaaNNzedwVardmMcQV9apn8wORImwxYwfLNxrqvploiPKrlQMtMoDiXAljKj3amohw0whsMf-NfHv_SNqWeaNfG4mFJWGo3XosHVll7iqjwjoSHd73RBxFSRDhZpWuUo/s320/1.png" width="320" /></a></div>
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<span style="font-size: 12pt; line-height: 115%;">Suppose we have below stochastic
matrix M (4*4):<o:p></o:p></span></div>
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M =<o:p></o:p></div>
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjTu8hC3meJi1y5CZOKGXXT5CmMC59MyfvJSkteKbNRT7rCpRzv8uQHjos22THwU3yOhsBFNlLz1LvmVMU9m9NqP7839i0NmSev8LJG8wBswZVyUZT678hyf6SH_V9uTx0nuOhfixJmK1g/s1600/2.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="111" data-original-width="361" height="98" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjTu8hC3meJi1y5CZOKGXXT5CmMC59MyfvJSkteKbNRT7rCpRzv8uQHjos22THwU3yOhsBFNlLz1LvmVMU9m9NqP7839i0NmSev8LJG8wBswZVyUZT678hyf6SH_V9uTx0nuOhfixJmK1g/s320/2.png" width="320" /></a></div>
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<span style="font-family: "times new roman" , "serif"; font-size: 12.0pt; line-height: 115%;">The results of the sequences (V0 * M) are as
follows:<o:p></o:p></span></div>
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<span style="font-family: "times new roman" , "serif"; font-size: 12.0pt; line-height: 115%;"><br /></span></div>
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<span style="font-family: "times new roman" , "serif"; font-size: 12.0pt; line-height: 115%;">As we can see, the vectors of V5 and
V6 are approximately the same.<o:p></o:p></span></div>
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<span style="font-family: "times new roman" , "serif"; font-size: 12.0pt; line-height: 115%;"><br /></span></div>
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<b><u><span style="font-family: "times new roman" , "serif"; font-size: 12.0pt; line-height: 115%;">Example (2):<o:p></o:p></span></u></b></div>
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<b><u><span style="font-family: "times new roman" , "serif"; font-size: 12.0pt; line-height: 115%;"><br /></span></u></b></div>
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</div>
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<span style="font-family: "times new roman" , "serif"; font-size: 12.0pt; line-height: 115%;">The sample of our vector (1*4) is:<o:p></o:p></span></div>
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<span style="font-family: "times new roman" , "serif"; font-size: 12.0pt; line-height: 115%;"><br /></span></div>
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<span style="font-family: "times new roman" , "serif"; font-size: 12.0pt; line-height: 115%;">V0 = </span></div>
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<span style="font-family: "times new roman" , "serif"; font-size: 12.0pt; line-height: 115%;"><br /></span></div>
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<span style="font-family: "times new roman" , "serif"; font-size: 12.0pt; line-height: 115%;"><br /></span></div>
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<span style="font-family: "times new roman" , "serif"; font-size: 12.0pt; line-height: 115%;"></span></div>
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<span style="font-family: "times new roman" , "serif"; font-size: 12.0pt; line-height: 115%;">The results of the sequences are as
follows:<o:p></o:p></span></div>
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<span style="font-family: "times new roman" , "serif"; font-size: 12.0pt; line-height: 115%;"><br /></span></div>
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<span style="font-family: "times new roman" , "serif"; font-size: 12.0pt; line-height: 115%;"><br /></span></div>
<div class="MsoNormal">
<span style="font-family: "times new roman" , "serif"; font-size: 12.0pt; line-height: 115%;">As we can see, the vectors of V5 and
V6 are approximately the same.<o:p></o:p></span></div>
<div class="MsoNormal">
<br /></div>
<div class="MsoNormal">
<b><u><span style="font-family: "times new roman" , "serif"; font-size: 12.0pt; line-height: 115%;">An example for
Markov Chain: <o:p></o:p></span></u></b></div>
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<b><u><span style="font-family: "times new roman" , "serif"; font-size: 12.0pt; line-height: 115%;"><br /></span></u></b></div>
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<span style="font-family: "times new roman" , "serif"; font-size: 12.0pt; line-height: 115%;">
</span></div>
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<span style="font-family: "times new roman" , "serif"; font-size: 12.0pt; line-height: 115%;">The sample of our probability vector
(1*4) is:<o:p></o:p></span></div>
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<span style="font-family: "times new roman" , "serif"; font-size: 12.0pt; line-height: 115%;"><br /></span></div>
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<span style="font-family: "times new roman" , "serif"; font-size: 12.0pt; line-height: 115%;">V0 = </span></div>
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgVQGpkCiRTwqZfFTUG2pcBHTCTZJfAQi4y260m6F3HXgN5cL_68cV1DXh07zsa5FDOK_GHCtEtJz-PRdSc0TWaDhKDQZ-yvVlkUVuYsMDZDwbupD8iwTXJvMuCupwlSDkqTkgWcIOhC0o/s1600/5_1.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="27" data-original-width="382" height="22" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgVQGpkCiRTwqZfFTUG2pcBHTCTZJfAQi4y260m6F3HXgN5cL_68cV1DXh07zsa5FDOK_GHCtEtJz-PRdSc0TWaDhKDQZ-yvVlkUVuYsMDZDwbupD8iwTXJvMuCupwlSDkqTkgWcIOhC0o/s320/5_1.png" width="320" /></a></div>
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<span style="font-family: "times new roman" , "serif"; font-size: 12.0pt; line-height: 115%;">I consider above stochastic matrix M
(4*4). <o:p></o:p></span></div>
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</div>
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<span style="font-family: "times new roman" , "serif"; font-size: 12.0pt; line-height: 115%;">Then, we will have below results:<o:p></o:p></span></div>
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<span style="font-family: "times new roman" , "serif"; font-size: 12.0pt; line-height: 115%;">As we can see, the vectors of V5 and
V6 are approximately the same.<o:p></o:p></span><br />
<span style="font-family: "times new roman" , "serif"; font-size: 12.0pt; line-height: 115%;"><b><i><br /></i></b></span>
<br />
<div style="text-align: left;">
<span style="font-family: "times new roman" , "serif"; font-size: 12.0pt; line-height: 115%;"><b><i>Is below conjecture is a theorem?</i></b></span></div>
</div>
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<b><i><span style="font-family: "times new roman" , "serif"; font-size: 12.0pt; line-height: 115%;">Conjecture (1):
The sequence of operations for transpose of a stochastic matrix (n*n) with non - zero elements on any vector
will be finally obtained a vector with the same elements. <o:p></o:p></span></i></b><b><i><span style="font-family: "times new roman" , "serif"; font-size: 12pt; line-height: 18.4px;">(The elements of vector are the members of Real Number)</span></i></b></div>
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEitq1jyGnjV6tssHg7EgmTN00bxrKsCMD0xCIVJt9OKC8iwBRoh7kkC5P2gMMM81c8LNlpkDr3YR0SDoxzMj2S2yJ2EG7C8nrBswJXfvOtSghz-yTPE0CnUyiu-u57njlJsIaW55K1R9q0/s1600/6_0.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="89" data-original-width="475" height="59" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEitq1jyGnjV6tssHg7EgmTN00bxrKsCMD0xCIVJt9OKC8iwBRoh7kkC5P2gMMM81c8LNlpkDr3YR0SDoxzMj2S2yJ2EG7C8nrBswJXfvOtSghz-yTPE0CnUyiu-u57njlJsIaW55K1R9q0/s320/6_0.png" width="320" /></a></div>
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEg25Dc0VEMvBsDf9b5mPsccEYniuEbFWzWtQQ0cC-FZkigFjpH29HtE1qcKmCeHtB6OVdWWFlsfAcLV65BnEs9XzC8sn6eXjrOYdkYW298w_Gwl1YVlZAnyZZDkxIxDAt0ZUGEI-OxYV7c/s1600/Untitled.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="490" data-original-width="1129" height="138" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEg25Dc0VEMvBsDf9b5mPsccEYniuEbFWzWtQQ0cC-FZkigFjpH29HtE1qcKmCeHtB6OVdWWFlsfAcLV65BnEs9XzC8sn6eXjrOYdkYW298w_Gwl1YVlZAnyZZDkxIxDAt0ZUGEI-OxYV7c/s320/Untitled.png" width="320" /></a></div>
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<b><span style="font-family: "times new roman" , "serif"; font-size: 12.0pt; line-height: 115%;"><br /></span></b>
<b><span style="font-family: "times new roman" , "serif"; font-size: 12.0pt; line-height: 115%;">Example (1):<o:p></o:p></span></b></div>
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<b><span style="font-family: "times new roman" , "serif"; font-size: 12.0pt; line-height: 115%;"><br /></span></b></div>
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<span style="font-family: "times new roman" , "serif"; font-size: 12.0pt; line-height: 115%;">Consider above stochastic matrix M
(4*4):<o:p></o:p></span></div>
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<span style="font-family: "times new roman" , "serif"; font-size: 12.0pt; line-height: 115%;">M =<o:p></o:p></span></div>
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEj5VPbItRP7EVZx8YkFYgHJPVs7nvLGqLlRuKm5d11-vaLHzMYPIMzok5c1rlr3Y8gTxIESoOyBJvbWrbVgUgkzA8mLr0smKxz248WcWEKorLwwUkWPbMZaoLTeyRT7Db6mBH2n687fOts/s1600/6_1.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="111" data-original-width="361" height="98" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEj5VPbItRP7EVZx8YkFYgHJPVs7nvLGqLlRuKm5d11-vaLHzMYPIMzok5c1rlr3Y8gTxIESoOyBJvbWrbVgUgkzA8mLr0smKxz248WcWEKorLwwUkWPbMZaoLTeyRT7Db6mBH2n687fOts/s320/6_1.png" width="320" /></a></div>
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<span style="font-family: "times new roman" , "serif"; font-size: 12.0pt; line-height: 115%;"><br /></span></div>
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<span style="font-family: "times new roman" , "serif"; font-size: 12.0pt; line-height: 115%;"><br /></span></div>
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<span style="font-family: "times new roman" , "serif"; font-size: 12.0pt; line-height: 115%;">The transpose of matrix M is:<o:p></o:p></span></div>
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<sup><span style="font-family: "times new roman" , "serif"; font-size: 12.0pt; line-height: 115%;">M</span><span style="font-family: "times new roman" , serif; line-height: 115%;"><span style="font-size: x-small;">T</span></span></sup><sup><span style="font-family: "times new roman" , "serif"; font-size: 12.0pt; line-height: 115%;"> =</span></sup></div>
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEguMmNO0v5OObaB3fOHCd4Nw5EwYOcGqWvsh0IPz5UuJYfE2aQsa86FVGFALwWtG_dgPyoM_HnPSC4cERNNljsHtRalQZkA0MgZfTw-4tyUUSKamesnG4ihsSSnwdU8Ry1ooEBc2wDYzJ8/s1600/6_2.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="111" data-original-width="361" height="98" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEguMmNO0v5OObaB3fOHCd4Nw5EwYOcGqWvsh0IPz5UuJYfE2aQsa86FVGFALwWtG_dgPyoM_HnPSC4cERNNljsHtRalQZkA0MgZfTw-4tyUUSKamesnG4ihsSSnwdU8Ry1ooEBc2wDYzJ8/s320/6_2.png" width="320" /></a></div>
<o:p></o:p><br />
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<sup><span style="font-family: "times new roman" , "serif"; font-size: 12.0pt; line-height: 115%;"><br /></span></sup></div>
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<span style="font-family: "times new roman" , "serif"; font-size: 12.0pt; line-height: 115%;">The sample of vector is:<o:p></o:p></span></div>
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<span style="font-family: "times new roman" , "serif"; font-size: 12.0pt; line-height: 115%;"><br /></span></div>
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<span style="font-family: "times new roman" , "serif"; font-size: 12.0pt; line-height: 115%;">V0 = </span></div>
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgRfXh6f4lxnvulhyphenhyphen1-DsUTptWDuJbtQsv5-HayTZnXzBx-cVpoV46vnEOGL2zr8BYgeLNycy4BpWqyVU5N2gr1pNvVX9flSdjMzHb37vh0m7b4rlXjfyKraU9OFDKqJ_5zEPXJQLYMV5M/s1600/7.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="26" data-original-width="381" height="21" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgRfXh6f4lxnvulhyphenhyphen1-DsUTptWDuJbtQsv5-HayTZnXzBx-cVpoV46vnEOGL2zr8BYgeLNycy4BpWqyVU5N2gr1pNvVX9flSdjMzHb37vh0m7b4rlXjfyKraU9OFDKqJ_5zEPXJQLYMV5M/s320/7.png" width="320" /></a></div>
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<span style="font-family: "times new roman" , "serif"; font-size: 12.0pt; line-height: 115%;"><br /></span></div>
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<span style="font-family: "times new roman" , "serif"; font-size: 12.0pt; line-height: 115%;">The results of the sequences are as
follows:<o:p></o:p></span></div>
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEi2WO57lLLC2io-3ZKYBDp7sxKRBjOZs9Upv4ygD0eaNEKEOIYJ-c6ftNphdavUibxRWWVebscOPhVGlD4u2jwG_yf2C3gGVyxDguNaccs5Ycx11mWQ25jEqpo3cFdBQmLIiaMxnpbFaII/s1600/8.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="222" data-original-width="648" height="109" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEi2WO57lLLC2io-3ZKYBDp7sxKRBjOZs9Upv4ygD0eaNEKEOIYJ-c6ftNphdavUibxRWWVebscOPhVGlD4u2jwG_yf2C3gGVyxDguNaccs5Ycx11mWQ25jEqpo3cFdBQmLIiaMxnpbFaII/s320/8.png" width="320" /></a></div>
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As we can see, the elements of vector V7 are the same.<o:p></o:p></div>
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<b><span style="font-family: "times new roman" , "serif"; font-size: 12.0pt; line-height: 115%;">Example (2):<o:p></o:p></span></b></div>
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<span style="font-family: "times new roman" , "serif"; font-size: 12.0pt; line-height: 115%;">The sample of vector is:<o:p></o:p></span></div>
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<span style="font-family: "times new roman" , "serif"; font-size: 12.0pt; line-height: 115%;">V0 =</span></div>
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh8X-j05hmI2ZegvH3F_UmebJRqiDe2xi_DZxR8rqoj9hxa7Mx7skNUjogSb0fzLYZCt19PUc9aJc_9SEWTYt4OaMkH0L9Y0LInKfU8ZyNMmJSkkSv4Gi0G66s5NQ1JciYSv5Gfd1TgT5U/s1600/9.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="25" data-original-width="386" height="20" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh8X-j05hmI2ZegvH3F_UmebJRqiDe2xi_DZxR8rqoj9hxa7Mx7skNUjogSb0fzLYZCt19PUc9aJc_9SEWTYt4OaMkH0L9Y0LInKfU8ZyNMmJSkkSv4Gi0G66s5NQ1JciYSv5Gfd1TgT5U/s320/9.png" width="320" /></a></div>
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<span style="font-family: "times new roman" , "serif"; font-size: 12.0pt; line-height: 115%;"><br /></span></div>
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<span style="font-family: "times new roman" , "serif"; font-size: 12.0pt; line-height: 115%;"></span></div>
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<span style="font-family: "times new roman" , "serif"; font-size: 12.0pt; line-height: 115%;">The results of the sequences are as
follows:<o:p></o:p></span></div>
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As we can see, the elements of vector V7 are the same.<o:p></o:p></div>
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Gholamreza Soleimanihttp://www.blogger.com/profile/03273527405719420253noreply@blogger.com0