New Application Center Additions
http://www.maplesoft.com/applications
en-us2014 Maplesoft, A Division of Waterloo Maple Inc.Maplesoft Document SystemWed, 27 Aug 2014 22:57:21 GMTWed, 27 Aug 2014 22:57:21 GMTThe latest content added to the Application Centerhttp://www.mapleprimes.com/images/mapleapps.gifNew Application Center Additions
http://www.maplesoft.com/applications
Generating 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 LinderCustom Plot Sizing and Shading
http://www.maplesoft.com/applications/view.aspx?SID=153607&ref=Feed
Many Maple users, no matter what they are working on, make use of Maple’s plotting abilities, and so this Tips and Techniques highlights some small but useful new plotting features introduced in Maple 18. Maple 18 give you the ability to set the size of your plots, giving you more control over your document’s use of space, as well as the ability to set the colour gradients used in 3-D plots. In this Tips and Techniques, you will find a variety of example that show you how to take advantage of these new plot options.<img src="/view.aspx?si=153607/thumb.jpg" alt="Custom Plot Sizing and Shading" align="left"/>Many Maple users, no matter what they are working on, make use of Maple’s plotting abilities, and so this Tips and Techniques highlights some small but useful new plotting features introduced in Maple 18. Maple 18 give you the ability to set the size of your plots, giving you more control over your document’s use of space, as well as the ability to set the colour gradients used in 3-D plots. In this Tips and Techniques, you will find a variety of example that show you how to take advantage of these new plot options.153607Mon, 16 Jun 2014 04:00:00 ZDave LinderDave LinderPacking Circles into a Triangle
http://www.maplesoft.com/applications/view.aspx?SID=153596&ref=Feed
<p>This application finds the best packing and largest radius of equal-sized circles, such that they fit in a pre-defined triangle. One solution, as visualized by this application, is given below.</p>
<p>This is a difficult global optimization problem and demands strong solvers. This application uses Maple's <a href="http://www.maplesoft.com/products/toolboxes/globaloptimization/">Global Optimization Toolbox</a>.</p>
<p>Circle packing (and packing optimization in general) is characterized by a large optimization space and many constraints; for this application, 20 circles generates 310 constraint equations.</p>
<p>The number of circles can be increased to create an increasingly complex problem; Maple automatically generates the symbolic constraint equations. The vertices of the triangle can also be modified</p>
<p>Applications like this are used to stress-test global optimizers.</p><img src="/view.aspx?si=153596/2ac6ca1378717b3d939f3d8107616b35.gif" alt="Packing Circles into a Triangle" align="left"/><p>This application finds the best packing and largest radius of equal-sized circles, such that they fit in a pre-defined triangle. One solution, as visualized by this application, is given below.</p>
<p>This is a difficult global optimization problem and demands strong solvers. This application uses Maple's <a href="http://www.maplesoft.com/products/toolboxes/globaloptimization/">Global Optimization Toolbox</a>.</p>
<p>Circle packing (and packing optimization in general) is characterized by a large optimization space and many constraints; for this application, 20 circles generates 310 constraint equations.</p>
<p>The number of circles can be increased to create an increasingly complex problem; Maple automatically generates the symbolic constraint equations. The vertices of the triangle can also be modified</p>
<p>Applications like this are used to stress-test global optimizers.</p>153596Wed, 04 Jun 2014 04:00:00 ZSamir KhanSamir KhanCircle Packing in an Ellipse
http://www.maplesoft.com/applications/view.aspx?SID=153598&ref=Feed
<p>This application optimizes the packing of circles in an ellipse, such that the area of the ellipse is minimized. A typical solution is visualized here.</p>
<p>This is a difficult global optimization problem and demands strong solvers. This application uses Maple's <a href="/products/toolboxes/globaloptimization/">Global Optimization Toolbox</a>.</p>
<p>Circle packing (and packing optimization in general) is characterized by a large optimization space and many constraints; for this application, 35 circles generates 666 constraint equations.</p>
<p>The number of circles can be increased to create an increasingly complex problem; Maple automatically generates the symbolic constraint equations.</p>
<p>Applications like this are used to stress-test global optimizers.</p>
<p>The constraints and ellipse parameterization are taken from "Packing circles within ellipses", Birgin et al., International Transactions in Operational Research , Volume 20, Issue 3, pages 365–389, May 2013.</p><img src="/view.aspx?si=153598/5f52383daddaeb53aec548d14ebd6ce0.gif" alt="Circle Packing in an Ellipse" align="left"/><p>This application optimizes the packing of circles in an ellipse, such that the area of the ellipse is minimized. A typical solution is visualized here.</p>
<p>This is a difficult global optimization problem and demands strong solvers. This application uses Maple's <a href="/products/toolboxes/globaloptimization/">Global Optimization Toolbox</a>.</p>
<p>Circle packing (and packing optimization in general) is characterized by a large optimization space and many constraints; for this application, 35 circles generates 666 constraint equations.</p>
<p>The number of circles can be increased to create an increasingly complex problem; Maple automatically generates the symbolic constraint equations.</p>
<p>Applications like this are used to stress-test global optimizers.</p>
<p>The constraints and ellipse parameterization are taken from "Packing circles within ellipses", Birgin et al., International Transactions in Operational Research , Volume 20, Issue 3, pages 365–389, May 2013.</p>153598Wed, 04 Jun 2014 04:00:00 ZSamir KhanSamir KhanCircle Packing in a Square
http://www.maplesoft.com/applications/view.aspx?SID=153599&ref=Feed
<p>This application optimizes the packing of circles (of varying radii) in a square, such that the side-length of the square is minimized. One solution for 20 circles (with integer radii of 1 to 20) is visualized here.</p>
<p>This is a difficult global optimization problem and demands strong solvers. This application uses Maple's <a href="/products/toolboxes/globaloptimization/">Global Optimization Toolbox</a>.</p>
<p>Circle packing (and packing optimization in general) is characterized by a large optimization space and many constraints; for this application, 20 circles generates 230 constraint equations.</p>
<p>The number of circles can be increased to create an increasingly complex problem; Maple automatically generates the symbolic constraint equations.</p>
<p>Applications like this are used to stress-test global optimizers.</p><img src="/view.aspx?si=153599/071f7b81258c5cad651a5030370d824f.gif" alt="Circle Packing in a Square" align="left"/><p>This application optimizes the packing of circles (of varying radii) in a square, such that the side-length of the square is minimized. One solution for 20 circles (with integer radii of 1 to 20) is visualized here.</p>
<p>This is a difficult global optimization problem and demands strong solvers. This application uses Maple's <a href="/products/toolboxes/globaloptimization/">Global Optimization Toolbox</a>.</p>
<p>Circle packing (and packing optimization in general) is characterized by a large optimization space and many constraints; for this application, 20 circles generates 230 constraint equations.</p>
<p>The number of circles can be increased to create an increasingly complex problem; Maple automatically generates the symbolic constraint equations.</p>
<p>Applications like this are used to stress-test global optimizers.</p>153599Wed, 04 Jun 2014 04:00:00 ZSamir KhanSamir KhanPacking Disks into a Circle
http://www.maplesoft.com/applications/view.aspx?SID=153600&ref=Feed
<p>This application finds the best packing of unequal non-overlapping disks in a circular container, such that the radius of the container is minimized. This is a tough global optimization problem that demands strong solvers; this application uses Maple's <a href="/products/toolboxes/globaloptimization/">Global Optimization Toolbox</a>. You must have the Global Optimization Toolbox installed to use this application.</p>
<p>One solution for the packing of 50 disks with the integer radii 1 to 50 (as found by this application) is visualized here.</p>
<p>Other solutions for similar packing problems are documented at <a href="http://www.packomania.com">http://www.packomania.com</a>.</p>
<p>Packing optimization is industrially important, with applications in pallet loading, the arrangement of fiber optic cables in a tube, or the placing of components on a circuit board.</p><img src="/view.aspx?si=153600/32183b61c1bca332d0c71924ae09f73a.gif" alt="Packing Disks into a Circle" align="left"/><p>This application finds the best packing of unequal non-overlapping disks in a circular container, such that the radius of the container is minimized. This is a tough global optimization problem that demands strong solvers; this application uses Maple's <a href="/products/toolboxes/globaloptimization/">Global Optimization Toolbox</a>. You must have the Global Optimization Toolbox installed to use this application.</p>
<p>One solution for the packing of 50 disks with the integer radii 1 to 50 (as found by this application) is visualized here.</p>
<p>Other solutions for similar packing problems are documented at <a href="http://www.packomania.com">http://www.packomania.com</a>.</p>
<p>Packing optimization is industrially important, with applications in pallet loading, the arrangement of fiber optic cables in a tube, or the placing of components on a circuit board.</p>153600Wed, 04 Jun 2014 04:00:00 ZSamir KhanSamir KhanGuia de estudio para integrales dobles
http://www.maplesoft.com/applications/view.aspx?SID=153595&ref=Feed
<p>Esta guía de estudio tiene como objetivo aprovechar las capacidades de Maple para generar gráficas interactivas y lograr con ellas que el estudiante comprenda el problema geométrico que da origen a la integral doble, la interpretación geométrica de una integral doble cuando el integrando es positivo, y la interpretación geométrica del cálculo de integrales iteradas en una integral doble.</p><img src="/view.aspx?si=153595/Preview_figure.png" alt="Guia de estudio para integrales dobles" align="left"/><p>Esta guía de estudio tiene como objetivo aprovechar las capacidades de Maple para generar gráficas interactivas y lograr con ellas que el estudiante comprenda el problema geométrico que da origen a la integral doble, la interpretación geométrica de una integral doble cuando el integrando es positivo, y la interpretación geométrica del cálculo de integrales iteradas en una integral doble.</p>153595Tue, 03 Jun 2014 04:00:00 ZDr. Ranferi GutierrezDr. Ranferi GutierrezWelded Beam Design Optimization
http://www.maplesoft.com/applications/view.aspx?SID=153592&ref=Feed
<p>A rigid member is welded onto a beam, with a load applied to the end of the member. The total cost of production is equal to the labor costs (a function of the weld dimensions) plus the cost of the weld and beam material.</p>
<p>The design of the beam is optimized to minimize the production costs by varying the weld and member dimensions.</p>
<p>The constraints include limits on the shear stress, bending stress, buckling load and end deflection, and several size constraints.</p>
<p>The application uses Maple’s non-linear optimizers</p><img src="/view.aspx?si=153592/0621a9aba622112f66506495e21f68d9.gif" alt="Welded Beam Design Optimization" align="left"/><p>A rigid member is welded onto a beam, with a load applied to the end of the member. The total cost of production is equal to the labor costs (a function of the weld dimensions) plus the cost of the weld and beam material.</p>
<p>The design of the beam is optimized to minimize the production costs by varying the weld and member dimensions.</p>
<p>The constraints include limits on the shear stress, bending stress, buckling load and end deflection, and several size constraints.</p>
<p>The application uses Maple’s non-linear optimizers</p>153592Fri, 30 May 2014 04:00:00 ZSamir KhanSamir KhanPrincipal Component Analysis
http://www.maplesoft.com/applications/view.aspx?SID=153591&ref=Feed
<p>Principal Component Analysis transforms a multi-dimensional data set to a new set of perpendicular axes (or components) that describe decreasing amounts of variance. </p>
<p>This worksheet reduces the complexity of a data set using principal component analysis. Those components that have the least impact on the variance are discarded, and the simplified data reconstructed from the remaining components.</p><img src="/view.aspx?si=153591/PrincipalComponentAn.jpg" alt="Principal Component Analysis" align="left"/><p>Principal Component Analysis transforms a multi-dimensional data set to a new set of perpendicular axes (or components) that describe decreasing amounts of variance. </p>
<p>This worksheet reduces the complexity of a data set using principal component analysis. Those components that have the least impact on the variance are discarded, and the simplified data reconstructed from the remaining components.</p>153591Mon, 26 May 2014 04:00:00 ZSamir KhanSamir KhanGuia electronica de estudio sobre Multiplicadores de Lagrange
http://www.maplesoft.com/applications/view.aspx?SID=153587&ref=Feed
<p>El objetivo principal de la presente guia electronica de estudio es que el estudiante adquiera una comprension geometrica de lo que significa buscar valores extremos de una funcion de varias variables, la cual esta sujeta a una restriccion. El objetivo principal de esta guia se logra aprovechando las capacidades de Maple para generar graficos en 3D y manipularlos a traves del uso de componentes.</p><img src="/view.aspx?si=153587/multiplicadores.png" alt="Guia electronica de estudio sobre Multiplicadores de Lagrange" align="left"/><p>El objetivo principal de la presente guia electronica de estudio es que el estudiante adquiera una comprension geometrica de lo que significa buscar valores extremos de una funcion de varias variables, la cual esta sujeta a una restriccion. El objetivo principal de esta guia se logra aprovechando las capacidades de Maple para generar graficos en 3D y manipularlos a traves del uso de componentes.</p>153587Tue, 20 May 2014 04:00:00 ZDr. Ranferi GutierrezDr. Ranferi GutierrezComparison between LAGRANGE and Spline Interpolation
http://www.maplesoft.com/applications/view.aspx?SID=153574&ref=Feed
<p>In this worksheet a comparison between the <em>LAGRANGE </em>and the <em>Spline Interpolation </em>has been discused based upon eleven interpolating points. In order to arrive at a <em><strong>smooth </strong></em>interpolation a <strong>cubic spline </strong>has been utilized. High-degree splines are similar to LAGRANGE polynomials. A spline of degree = infinity is identical to the LAGRANGE approximation.</p><img src="/view.aspx?si=153574/4eafecf1baae01f83c8a823ac067d4fc.gif" alt="Comparison between LAGRANGE and Spline Interpolation" align="left"/><p>In this worksheet a comparison between the <em>LAGRANGE </em>and the <em>Spline Interpolation </em>has been discused based upon eleven interpolating points. In order to arrive at a <em><strong>smooth </strong></em>interpolation a <strong>cubic spline </strong>has been utilized. High-degree splines are similar to LAGRANGE polynomials. A spline of degree = infinity is identical to the LAGRANGE approximation.</p>153574Mon, 12 May 2014 04:00:00 ZProf. Josef BettenProf. Josef Betten