Maple Document: New Applications
http://www.maplesoft.com/applications/category.aspx?cid=1337
en-us2014 Maplesoft, A Division of Waterloo Maple Inc.Maplesoft Document SystemMon, 24 Nov 2014 01:22:25 GMTMon, 24 Nov 2014 01:22:25 GMTNew applications in the Maple Document categoryhttp://www.mapleprimes.com/images/mapleapps.gifMaple Document: New Applications
http://www.maplesoft.com/applications/category.aspx?cid=1337
The Comet 67P/Churyumov-Gerasimenko, Rosetta & Philae
http://www.maplesoft.com/applications/view.aspx?SID=153706&ref=Feed
<p> Abstract<br /><br />The Rosetta space probe launched 10 years ago by the European Space Agency (ESA) arrived recently (November 12, 2014) at the site of the comet known as 67P/Churyumov-Gerasimenco after a trip of 4 billions miles from Earth. After circling the comet, Rosetta released its precious load : the lander Philae packed with 21 different scientific instruments for the study of the comet with the main purpose : the origin of our solar system and possibly the origin of life on our planet.<br /><br />Our plan is rather a modest one since all we want is to get , by calculations, specific data concerning the comet and its lander.<br />We shall take a simplified model and consider the comet as a perfect solid sphere to which we can apply Newton's laws.<br /><br />We want to find:<br /><br />I- the acceleration on the comet surface ,<br />II- its radius,<br />III- its density,<br />IV- the velocity of Philae just after the 1st bounce off the comet (it has bounced twice),<br />V- the time for Philae to reach altitude of 1000 m above the comet .<br /><br />We shall compare our findings with the already known data to see how close our simplified mathematical model findings are to the duck-shaped comet already known results.<br />It turned out that our calculations for a sphere shaped comet are very close to the already known data.<br /><br />Conclusion<br /><br />Even with a shape that defies the application of any mechanical laws we can always get very close to reality by adopting a simplified mathematical model in any preliminary study of a complicated problem.<br /><br /></p><img src="/applications/images/app_image_blank_lg.jpg" alt="The Comet 67P/Churyumov-Gerasimenko, Rosetta & Philae" align="left"/><p> Abstract<br /><br />The Rosetta space probe launched 10 years ago by the European Space Agency (ESA) arrived recently (November 12, 2014) at the site of the comet known as 67P/Churyumov-Gerasimenco after a trip of 4 billions miles from Earth. After circling the comet, Rosetta released its precious load : the lander Philae packed with 21 different scientific instruments for the study of the comet with the main purpose : the origin of our solar system and possibly the origin of life on our planet.<br /><br />Our plan is rather a modest one since all we want is to get , by calculations, specific data concerning the comet and its lander.<br />We shall take a simplified model and consider the comet as a perfect solid sphere to which we can apply Newton's laws.<br /><br />We want to find:<br /><br />I- the acceleration on the comet surface ,<br />II- its radius,<br />III- its density,<br />IV- the velocity of Philae just after the 1st bounce off the comet (it has bounced twice),<br />V- the time for Philae to reach altitude of 1000 m above the comet .<br /><br />We shall compare our findings with the already known data to see how close our simplified mathematical model findings are to the duck-shaped comet already known results.<br />It turned out that our calculations for a sphere shaped comet are very close to the already known data.<br /><br />Conclusion<br /><br />Even with a shape that defies the application of any mechanical laws we can always get very close to reality by adopting a simplified mathematical model in any preliminary study of a complicated problem.<br /><br /></p>153706Mon, 17 Nov 2014 05:00:00 ZDr. Ahmed BaroudyDr. Ahmed BaroudyClassroom Tips and Techniques: Branch Cuts for a Product of Two Square-Roots
http://www.maplesoft.com/applications/view.aspx?SID=153697&ref=Feed
Naive simplification of f(z) = sqrt(z - 1) sqrt(z + 1) to F(z) = sqrt(z<sup>2</sup> - 1) results in a pair of functions that agree on only part of the complex plane. The enhanced ability of Maple 18 to find and display branch cuts of composite functions is used in this article to explore the branch cuts and regions of agreement/disagreement of f and F.<img src="/view.aspx?si=153697/thumb.jpg" alt="Classroom Tips and Techniques: Branch Cuts for a Product of Two Square-Roots" align="left"/>Naive simplification of f(z) = sqrt(z - 1) sqrt(z + 1) to F(z) = sqrt(z<sup>2</sup> - 1) results in a pair of functions that agree on only part of the complex plane. The enhanced ability of Maple 18 to find and display branch cuts of composite functions is used in this article to explore the branch cuts and regions of agreement/disagreement of f and F.153697Tue, 11 Nov 2014 05:00:00 ZDr. Robert LopezDr. Robert LopezGroebner Bases: What are They and What are They Useful For?
http://www.maplesoft.com/applications/view.aspx?SID=153693&ref=Feed
Since they were first introduced in 1965, Groebner bases have proven to be an invaluable contribution to mathematics and computer science. All general purpose computer algebra systems like Maple have Groebner basis implementations. But what is a Groebner basis? And what applications do Groebner bases have? In this Tips and Techniques article, I’ll give some examples of the main application of Groebner bases, which is to solve systems of polynomial equations.<img src="/view.aspx?si=153693/thumb.jpg" alt="Groebner Bases: What are They and What are They Useful For?" align="left"/>Since they were first introduced in 1965, Groebner bases have proven to be an invaluable contribution to mathematics and computer science. All general purpose computer algebra systems like Maple have Groebner basis implementations. But what is a Groebner basis? And what applications do Groebner bases have? In this Tips and Techniques article, I’ll give some examples of the main application of Groebner bases, which is to solve systems of polynomial equations.153693Fri, 17 Oct 2014 04:00:00 ZProf. Michael MonaganProf. Michael MonaganStrong Cryptographic File Protection Using Base 32 Encoding Scheme
http://www.maplesoft.com/applications/view.aspx?SID=153686&ref=Feed
<p>It has been shown how to implement user-friendly tool for strong cryptographic protection of e-mail enclosures.</p><img src="/view.aspx?si=153686/Patio.jpg" alt="Strong Cryptographic File Protection Using Base 32 Encoding Scheme" align="left"/><p>It has been shown how to implement user-friendly tool for strong cryptographic protection of e-mail enclosures.</p>153686Fri, 10 Oct 2014 04:00:00 ZCzeslaw KoscielnyCzeslaw KoscielnyPhoton Exposure
http://www.maplesoft.com/applications/view.aspx?SID=153684&ref=Feed
<p>This application uses a blackbody model of the sun to calculate the number of photons reaching a cameras sensor. It demonstrates the "Sunny 16" model of exposure.</p><img src="/view.aspx?si=153684/e771d3d2526673d4a8bc8221b6d228ee.gif" alt="Photon Exposure" align="left"/><p>This application uses a blackbody model of the sun to calculate the number of photons reaching a cameras sensor. It demonstrates the "Sunny 16" model of exposure.</p>153684Mon, 29 Sep 2014 04:00:00 ZJohn DoleseJohn DoleseComputational Performance with evalhf and Compile: A Newton Fractal Case Study
http://www.maplesoft.com/applications/view.aspx?SID=153683&ref=Feed
<p>This Tips and Techniques article focuses on the relative performance of Maple's various modes for floating-point computations. The example used here is the computation of a particular Newton fractal, which is easily parallelizable. We compute an image representation for this fractal under several computational modes, using both serial and multithreaded computation schemes.</p>
<p>This article is a follow up to a previous Tips and Techniques, <a href="http://www.maplesoft.com/applications/view.aspx?SID=153645">evalhf, Compile, hfloat and all that</a>, which discusses functionality differences amongst Maple's the different floating-point computation modes available in Maple.</p><img src="/view.aspx?si=153683/thumb.jpg" alt="Computational Performance with evalhf and Compile: A Newton Fractal Case Study" align="left"/><p>This Tips and Techniques article focuses on the relative performance of Maple's various modes for floating-point computations. The example used here is the computation of a particular Newton fractal, which is easily parallelizable. We compute an image representation for this fractal under several computational modes, using both serial and multithreaded computation schemes.</p>
<p>This article is a follow up to a previous Tips and Techniques, <a href="http://www.maplesoft.com/applications/view.aspx?SID=153645">evalhf, Compile, hfloat and all that</a>, which discusses functionality differences amongst Maple's the different floating-point computation modes available in Maple.</p>153683Fri, 26 Sep 2014 04:00:00 ZDave LinderDave LinderCounting quadratic residues
http://www.maplesoft.com/applications/view.aspx?SID=153678&ref=Feed
<p>After an introductory overview of a property of the symmetry in the ordered sequence of the quadratic residues modulo n, a formula to count them is provided, as well as to count only those coprime to n. The related Maple procedures are also provided. They are tested with infinite loops of random integers.</p><img src="/view.aspx?si=153678/qres_detail.PNG" alt="Counting quadratic residues" align="left"/><p>After an introductory overview of a property of the symmetry in the ordered sequence of the quadratic residues modulo n, a formula to count them is provided, as well as to count only those coprime to n. The related Maple procedures are also provided. They are tested with infinite loops of random integers.</p>153678Tue, 23 Sep 2014 04:00:00 ZGiulio BonfissutoGiulio BonfissutoHollywood Math 2
http://www.maplesoft.com/applications/view.aspx?SID=153681&ref=Feed
<p>Over the years, Hollywood has entertained us with many mathematical moments in film and television, often in unexpected places. In this application, you’ll find several examples of Hollywood Math, including Fermat’s Last Theorem and <em>The Simpsons</em>, the Monty Hall problem in <em>21</em>, and a discussion of just how long that runway actually was in <em>The Fast and the Furious</em>. These examples are also presented in <a href="/webinars/recorded/featured.aspx?id=782">Hollywood Math 2: The Recorded Webinar</a>.</p>
<p>For even more examples, see <a href="/applications/view.aspx?SID=6611">Hollywood Math: The Original Episode</a>.</p><img src="/view.aspx?si=153681/HollywoodMath2.jpg" alt="Hollywood Math 2" align="left"/><p>Over the years, Hollywood has entertained us with many mathematical moments in film and television, often in unexpected places. In this application, you’ll find several examples of Hollywood Math, including Fermat’s Last Theorem and <em>The Simpsons</em>, the Monty Hall problem in <em>21</em>, and a discussion of just how long that runway actually was in <em>The Fast and the Furious</em>. These examples are also presented in <a href="/webinars/recorded/featured.aspx?id=782">Hollywood Math 2: The Recorded Webinar</a>.</p>
<p>For even more examples, see <a href="/applications/view.aspx?SID=6611">Hollywood Math: The Original Episode</a>.</p>153681Tue, 23 Sep 2014 04:00:00 ZMaplesoftMaplesoftSpeed-up calculation of nextprime
http://www.maplesoft.com/applications/view.aspx?SID=5729&ref=Feed
<p>A speed-up calculation of the functions nextprime and prevprime is intended. In some distributions used it was observed similarities to "Prime Number Races" (primes of the form qn+a).</p><img src="/view.aspx?si=5729/nextprime_19_sm.gif" alt="Speed-up calculation of nextprime" align="left"/><p>A speed-up calculation of the functions nextprime and prevprime is intended. In some distributions used it was observed similarities to "Prime Number Races" (primes of the form qn+a).</p>5729Thu, 18 Sep 2014 04:00:00 ZGiulio BonfissutoGiulio BonfissutoSudoku tactile généralisé (version finale)
http://www.maplesoft.com/applications/view.aspx?SID=124424&ref=Feed
<p>Mes 2 maplets de sudoku (à régions n*m) en version finale.</p>
<p>(une interface avec radiobutton,une autre interface avec popupmenu).</p><img src="/view.aspx?si=124424/capsud.PNG" alt="Sudoku tactile généralisé (version finale)" align="left"/><p>Mes 2 maplets de sudoku (à régions n*m) en version finale.</p>
<p>(une interface avec radiobutton,une autre interface avec popupmenu).</p>124424Thu, 11 Sep 2014 04:00:00 Zxavier cormierxavier cormierGenerating random numbers efficiently
http://www.maplesoft.com/applications/view.aspx?SID=153662&ref=Feed
Generating (pseudo-)random values is a frequent task in simulations and other programs. For some situations, you want to generate some combinatorial or algebraic values, such as a list or a polynomial; in other situations, you need random numbers, from a distribution that is uniform or more complicated. In this article I'll talk about all of these situations.<img src="/view.aspx?si=153662/thumb.jpg" alt="Generating random numbers efficiently" align="left"/>Generating (pseudo-)random values is a frequent task in simulations and other programs. For some situations, you want to generate some combinatorial or algebraic values, such as a list or a polynomial; in other situations, you need random numbers, from a distribution that is uniform or more complicated. In this article I'll talk about all of these situations.153662Mon, 18 Aug 2014 04:00:00 ZDr. Erik PostmaDr. Erik PostmaEconomic Pipe Sizer for Process Plants
http://www.maplesoft.com/applications/view.aspx?SID=153659&ref=Feed
<p>Pipework is a large part of the cost of a process plant. Plant designers need to minimize the total cost of this pipework across the lifetime of the plant. The total overall cost is a combination of individual costs related to the:</p>
<ul>
<li>pipe material,</li>
<li>installation, </li>
<li>maintenance, </li>
<li>depreciation, </li>
<li>energy costs for pumping, </li>
<li>liquid parameters, </li>
<li>required flowrate,</li>
<li>pumping efficiencies,</li>
<li>taxes,</li>
<li>and more.</li>
</ul>
<p>The total cost is not a simple linear sum of the individual costs; a more complex relationship is needed.</p>
<p>This application uses the approach described in [1] to find the pipe diameter that minimizes the total lifetime cost. The method involves the iterative solution of an empirical equation using <a href="/support/help/Maple/view.aspx?path=fsolve">Maple’s fsolve function</a> (the code for the application is in the Startup code region).</p>
<p>Users can choose the pipe material (carbon steel, stainless steel, aluminum or brass), and specify the desired fluid flowrate, fluid viscosity and density. The application then solves the empirical equation (using Maple’s fsolve() function) and returns the economically optimal pipe diameter.</p>
<p>Bear in mind that the empirical parameters used in the application vary as economic conditions change. Those used in this application are correct for 1998 and 2008.</p>
<p><em>[1]: "Updating the Rules for Pipe Sizing", Durand et al., Chemical Engineering, January 2010</em></p><img src="/applications/images/app_image_blank_lg.jpg" alt="Economic Pipe Sizer for Process Plants" align="left"/><p>Pipework is a large part of the cost of a process plant. Plant designers need to minimize the total cost of this pipework across the lifetime of the plant. The total overall cost is a combination of individual costs related to the:</p>
<ul>
<li>pipe material,</li>
<li>installation, </li>
<li>maintenance, </li>
<li>depreciation, </li>
<li>energy costs for pumping, </li>
<li>liquid parameters, </li>
<li>required flowrate,</li>
<li>pumping efficiencies,</li>
<li>taxes,</li>
<li>and more.</li>
</ul>
<p>The total cost is not a simple linear sum of the individual costs; a more complex relationship is needed.</p>
<p>This application uses the approach described in [1] to find the pipe diameter that minimizes the total lifetime cost. The method involves the iterative solution of an empirical equation using <a href="/support/help/Maple/view.aspx?path=fsolve">Maple’s fsolve function</a> (the code for the application is in the Startup code region).</p>
<p>Users can choose the pipe material (carbon steel, stainless steel, aluminum or brass), and specify the desired fluid flowrate, fluid viscosity and density. The application then solves the empirical equation (using Maple’s fsolve() function) and returns the economically optimal pipe diameter.</p>
<p>Bear in mind that the empirical parameters used in the application vary as economic conditions change. Those used in this application are correct for 1998 and 2008.</p>
<p><em>[1]: "Updating the Rules for Pipe Sizing", Durand et al., Chemical Engineering, January 2010</em></p>153659Fri, 15 Aug 2014 04:00:00 ZSamir KhanSamir KhanCreating Quizzes in Descriptive Statistics
http://www.maplesoft.com/applications/view.aspx?SID=153646&ref=Feed
<p>This application features the code used in the Statistics tutorial video: <a title="https://www.youtube.com/watch?v=Xc4D17rjDxo" href="https://www.youtube.com/watch?v=Xc4D17rjDxo">Creating Quizzes</a> . Examples include building procedures for grading entered text and plots as well as generating random data samples.</p><img src="/view.aspx?si=153646/Capture.PNG" alt="Creating Quizzes in Descriptive Statistics" align="left"/><p>This application features the code used in the Statistics tutorial video: <a title="https://www.youtube.com/watch?v=Xc4D17rjDxo" href="https://www.youtube.com/watch?v=Xc4D17rjDxo">Creating Quizzes</a> . Examples include building procedures for grading entered text and plots as well as generating random data samples.</p>153646Thu, 24 Jul 2014 04:00:00 ZDaniel SkoogDaniel Skoogevalhf, Compile, hfloat and all that
http://www.maplesoft.com/applications/view.aspx?SID=153645&ref=Feed
Users sometimes ask how to make their floating-point (numeric) computations perform faster in Maple. The answers often include references to special terms such as evalhf, the Compiler, and option hfloat. A difficulty for the non-expert lies in knowing which of these can be used, and when. This Tips and Techniques attempts to clear up some of the mystery of these terms, by discussion and functionality comparison.<img src="/applications/images/app_image_blank_lg.jpg" alt="evalhf, Compile, hfloat and all that" align="left"/>Users sometimes ask how to make their floating-point (numeric) computations perform faster in Maple. The answers often include references to special terms such as evalhf, the Compiler, and option hfloat. A difficulty for the non-expert lies in knowing which of these can be used, and when. This Tips and Techniques attempts to clear up some of the mystery of these terms, by discussion and functionality comparison.153645Tue, 22 Jul 2014 04:00:00 ZDave LinderDave LinderThe Extremal and Non-Trivial Minimal Topologies by Definitions
http://www.maplesoft.com/applications/view.aspx?SID=153625&ref=Feed
<p> by </p>
<p> <br /> MS.C Taha Guma el turki </p>
<p> Benghazi University department of Mathematics</p>
<p> email: taha 1978_2002@yahoo.com </p>
<p> <strong><em>Definition </em>[1]:-</strong> </p>
<p>Let X be any set, τ is not a discrete topology on X then τ is said to be an extremal topology if every topology strictly finer than τ is discrete.<br /> <br />A non-trivial minimal topology is a topology which is not Indiscrete and does not contain any other topology over X .<br /><br /><em>References</em><br /><br />[1] http://www.damascusuniversity.edu.sy/mag/asasy/images/stories/e19.pdf .</p>
<p>[2] http://www.maplesoft.com/applications/view.aspx?SID=153617 .</p><img src="/applications/images/app_image_blank_lg.jpg" alt="The Extremal and Non-Trivial Minimal Topologies by Definitions" align="left"/><p> by </p>
<p> <br /> MS.C Taha Guma el turki </p>
<p> Benghazi University department of Mathematics</p>
<p> email: taha 1978_2002@yahoo.com </p>
<p> <strong><em>Definition </em>[1]:-</strong> </p>
<p>Let X be any set, τ is not a discrete topology on X then τ is said to be an extremal topology if every topology strictly finer than τ is discrete.<br /> <br />A non-trivial minimal topology is a topology which is not Indiscrete and does not contain any other topology over X .<br /><br /><em>References</em><br /><br />[1] http://www.damascusuniversity.edu.sy/mag/asasy/images/stories/e19.pdf .</p>
<p>[2] http://www.maplesoft.com/applications/view.aspx?SID=153617 .</p>153625Thu, 17 Jul 2014 04:00:00 ZTaha Guma el turkiTaha Guma el turkiDrawdown of Historical Stock Prices
http://www.maplesoft.com/applications/view.aspx?SID=153624&ref=Feed
<p>The drawdown of a stock indicates how much time it's spent "underwater" - it's essentially the percentage drop of its price from a peak to a trough, with the drawdown resetting to zero if a previous high is reached. The drawdown of a stock is a valuable risk measure and is employed by traders to gauge volatility.</p>
<p>This application:</p>
<ul>
<li>downloads historical stock prices from Yahoo Finance for a chosen ticker symbol (this requires a connection to the Internet),</li>
<li>defines a procedure that calculates the drawdown of the historical stock price</li>
<li>and plots the drawdown against the adjusted close price of the asset</li>
</ul>
<p>By changing the ticker symbol and the two dates, you can examine drawdown of any stock between any period.</p>
<p>The application uses Maple 18's improved Internet connectivity; you can now download data from a URL into a matrix using <span><a href="/support/help/Maple/view.aspx?path=ImportMatrix">ImportMatrix()</a></span>.</p><img src="/view.aspx?si=153624/2def9a8f2111f9b47d0bee568aed6035.gif" alt="Drawdown of Historical Stock Prices" align="left"/><p>The drawdown of a stock indicates how much time it's spent "underwater" - it's essentially the percentage drop of its price from a peak to a trough, with the drawdown resetting to zero if a previous high is reached. The drawdown of a stock is a valuable risk measure and is employed by traders to gauge volatility.</p>
<p>This application:</p>
<ul>
<li>downloads historical stock prices from Yahoo Finance for a chosen ticker symbol (this requires a connection to the Internet),</li>
<li>defines a procedure that calculates the drawdown of the historical stock price</li>
<li>and plots the drawdown against the adjusted close price of the asset</li>
</ul>
<p>By changing the ticker symbol and the two dates, you can examine drawdown of any stock between any period.</p>
<p>The application uses Maple 18's improved Internet connectivity; you can now download data from a URL into a matrix using <span><a href="/support/help/Maple/view.aspx?path=ImportMatrix">ImportMatrix()</a></span>.</p>153624Mon, 07 Jul 2014 04:00:00 ZSamir KhanSamir KhanSpectral k-statistics
http://www.maplesoft.com/applications/view.aspx?SID=153618&ref=Feed
<p>The algorithm constructs natural statistics of a spectral sample, by using convolutions on the symmetric group and the Weingarten function. These statistics are unbiased estimators of cumulants of traces.</p><img src="/view.aspx?si=153618/39882f96bb55a4970488a9bcf94fd60d.gif" alt="Spectral k-statistics" align="left"/><p>The algorithm constructs natural statistics of a spectral sample, by using convolutions on the symmetric group and the Weingarten function. These statistics are unbiased estimators of cumulants of traces.</p>153618Thu, 03 Jul 2014 04:00:00 ZDr. Giuseppe GuarinoDr. Giuseppe GuarinoThe Extremal and Non-Trivial Minimal Topologies Over a Finite Set with Maple
http://www.maplesoft.com/applications/view.aspx?SID=153617&ref=Feed
<p><strong> <br /> M.Sc .Taha Guma el turki , Prof. Al mabrouk Ali sola</strong><strong> </strong><br /><br /><br />There was a beautiful mathematical work done by Kherie Mohamed mera & Prof.Al mabrouk Ali sola .Related to extremal topologies and how to extract the extremal topologies and their numbers by a formula .<strong> </strong></p>
<p><strong>Definition :-</strong></p>
<p>Let X be a set and ,T is not a discreet topology on X then T is said to be an extremal topology if every topology strictly finer than T is discreet.</p>
<p><strong>Theorem 1-2 of [1] :-</strong> <br /><br /> If X is any set with more than one element , x , y ∈ X , x ≠y , and<br />T<sub>{x,y}</sub>= P(X\{x}) U {{x} U A , A ∈P(X\{x}),y ∈ A} ,then T<sub>{x,y}</sub> is <br />an extremal topology on X [1] .<br /><br /><strong>Remark<br /></strong><br />i-Notice that if X is a set x,y ∈ X , x≠ y , then T<sub>{x,y} ≠</sub>T<sub>{y,x}</sub> [1].</p>
<p><strong>Theorem 2-1 of [1] :-</strong></p>
<p> Any extremal topology on a finite set with more than one element is in the form T<sub>{x,y}</sub> for some x,y ∈ X , x ≠y [1] .<br /><br /><strong>Theorem 2-2 of [1] :-<br /><br /></strong>If X is a set has n elements then the number of extremal topologies defined on X is n(n-1) [1].</p>
<p><strong>Theorem 2-3 of [1] :-</strong><br /><br />If X is a set with n elements then any extremal topology has 3(2<sup>n-2</sup>) elements [1] .<br /><br />Also we compute in this application the Non-trivial minimal topologies and there number which is equal to 2<sup>n</sup>-2 ;<br /><br /><strong>Notes </strong>:-<br /><br />1- The Author of the procedures: Taha Guma el turki uses low speed computer with 1.7 GH processor.<br /><br />2- If you use such or lower portable then replace ; by : at the end of procedure calling To compute issues for n>10.<br /><br />3- The users can easily remove #Example(2) and #Example(3) and use the application for arbitrary n depending on their computer options .</p>
<p> <strong>References<br /></strong><br />[1] A lmabrouk Ali Sola , Extremal Topologies ,Damascus University Journal of BASIC SCIENCES,2005,Vol.21,No 1,19-25 . </p><img src="/applications/images/app_image_blank_lg.jpg" alt="The Extremal and Non-Trivial Minimal Topologies Over a Finite Set with Maple" align="left"/><p><strong> <br /> M.Sc .Taha Guma el turki , Prof. Al mabrouk Ali sola</strong><strong> </strong><br /><br /><br />There was a beautiful mathematical work done by Kherie Mohamed mera & Prof.Al mabrouk Ali sola .Related to extremal topologies and how to extract the extremal topologies and their numbers by a formula .<strong> </strong></p>
<p><strong>Definition :-</strong></p>
<p>Let X be a set and ,T is not a discreet topology on X then T is said to be an extremal topology if every topology strictly finer than T is discreet.</p>
<p><strong>Theorem 1-2 of [1] :-</strong> <br /><br /> If X is any set with more than one element , x , y ∈ X , x ≠y , and<br />T<sub>{x,y}</sub>= P(X\{x}) U {{x} U A , A ∈P(X\{x}),y ∈ A} ,then T<sub>{x,y}</sub> is <br />an extremal topology on X [1] .<br /><br /><strong>Remark<br /></strong><br />i-Notice that if X is a set x,y ∈ X , x≠ y , then T<sub>{x,y} ≠</sub>T<sub>{y,x}</sub> [1].</p>
<p><strong>Theorem 2-1 of [1] :-</strong></p>
<p> Any extremal topology on a finite set with more than one element is in the form T<sub>{x,y}</sub> for some x,y ∈ X , x ≠y [1] .<br /><br /><strong>Theorem 2-2 of [1] :-<br /><br /></strong>If X is a set has n elements then the number of extremal topologies defined on X is n(n-1) [1].</p>
<p><strong>Theorem 2-3 of [1] :-</strong><br /><br />If X is a set with n elements then any extremal topology has 3(2<sup>n-2</sup>) elements [1] .<br /><br />Also we compute in this application the Non-trivial minimal topologies and there number which is equal to 2<sup>n</sup>-2 ;<br /><br /><strong>Notes </strong>:-<br /><br />1- The Author of the procedures: Taha Guma el turki uses low speed computer with 1.7 GH processor.<br /><br />2- If you use such or lower portable then replace ; by : at the end of procedure calling To compute issues for n>10.<br /><br />3- The users can easily remove #Example(2) and #Example(3) and use the application for arbitrary n depending on their computer options .</p>
<p> <strong>References<br /></strong><br />[1] A lmabrouk Ali Sola , Extremal Topologies ,Damascus University Journal of BASIC SCIENCES,2005,Vol.21,No 1,19-25 . </p>153617Wed, 02 Jul 2014 04:00:00 ZProf.Al mabrouk Ali solaProf.Al mabrouk Ali solaOptimizing the Design of a Coil Spring
http://www.maplesoft.com/applications/view.aspx?SID=153608&ref=Feed
<p>The design optimization of helical springs is of considerable engineering interest, and demands strong solvers. While the number of constraints is small, the coil and wire diameters are raised to higher powers; this makes the optimization difficult for gradient-based solvers working in standard floating-point precision; a larger number of working digits is needed.</p>
<p>Maple lets you increase the number of digits used in calculations; hence numerically difficult problems, like this, can be solved.</p>
<p>This application minimizes the mass of a helical spring. The constraints include the minimum deflection, the minimum surge wave frequency and the maximum stress, and a loading condition.</p>
<ul>
<li>the minimum deflection, </li>
<li>the minimum surge wave frequency, </li>
<li>the maximum stress, </li>
<li>and a loading condition.</li>
</ul>
<p>The design variables are the</p>
<ul>
<li>diameter of the wire, </li>
<li>the outside diameter of the spring,</li>
<li>and the number of coils</li>
</ul>
<p> Reference: "Introduction to Optimum Design", Jasbir S. Arora, 3<sup>rd</sup> Edition 2012.</p><img src="/view.aspx?si=153608/695d991fff8fb4975d1e1dcd90bb771d.gif" alt="Optimizing the Design of a Coil Spring" align="left"/><p>The design optimization of helical springs is of considerable engineering interest, and demands strong solvers. While the number of constraints is small, the coil and wire diameters are raised to higher powers; this makes the optimization difficult for gradient-based solvers working in standard floating-point precision; a larger number of working digits is needed.</p>
<p>Maple lets you increase the number of digits used in calculations; hence numerically difficult problems, like this, can be solved.</p>
<p>This application minimizes the mass of a helical spring. The constraints include the minimum deflection, the minimum surge wave frequency and the maximum stress, and a loading condition.</p>
<ul>
<li>the minimum deflection, </li>
<li>the minimum surge wave frequency, </li>
<li>the maximum stress, </li>
<li>and a loading condition.</li>
</ul>
<p>The design variables are the</p>
<ul>
<li>diameter of the wire, </li>
<li>the outside diameter of the spring,</li>
<li>and the number of coils</li>
</ul>
<p> Reference: "Introduction to Optimum Design", Jasbir S. Arora, 3<sup>rd</sup> Edition 2012.</p>153608Tue, 17 Jun 2014 04:00:00 ZSamir KhanSamir KhanCustom Plot Sizing and Shading
http://www.maplesoft.com/applications/view.aspx?SID=153606&ref=Feed
<p>If the number of Online Help queries per topic or the number of click-throughs on errors for a particular area of functionality is anything to go by, then plotting is hands down the most significant functionality in Maple. I saw some data on those recently, and what leapt out was just how much plotting dominated.</p>
<p>When functionality is introduced that affects most kinds of 2D or 3D plots, then it likely affects a great many Maple users in important ways. While there are help pages on the new 2D plot sizing and 3D plot shading options in Maple 18, I find myself using these new options so often I feel that its important to mention them as tips for visualization techniques.</p><img src="/applications/images/app_image_blank_lg.jpg" alt="Custom Plot Sizing and Shading" align="left"/><p>If the number of Online Help queries per topic or the number of click-throughs on errors for a particular area of functionality is anything to go by, then plotting is hands down the most significant functionality in Maple. I saw some data on those recently, and what leapt out was just how much plotting dominated.</p>
<p>When functionality is introduced that affects most kinds of 2D or 3D plots, then it likely affects a great many Maple users in important ways. While there are help pages on the new 2D plot sizing and 3D plot shading options in Maple 18, I find myself using these new options so often I feel that its important to mention them as tips for visualization techniques.</p>153606Mon, 16 Jun 2014 04:00:00 ZDave LinderDave Linder