Maple Document: New Applications
https://www.maplesoft.com/applications/category.aspx?cid=1337
en-us2019 Maplesoft, A Division of Waterloo Maple Inc.Maplesoft Document SystemTue, 15 Oct 2019 06:52:32 GMTTue, 15 Oct 2019 06:52:32 GMTNew applications in the Maple Document categoryhttps://www.maplesoft.com/images/Application_center_hp.jpgMaple Document: New Applications
https://www.maplesoft.com/applications/category.aspx?cid=1337
Quantum Electromagnetic Radiation Pressure Spectrum
https://www.maplesoft.com/applications/view.aspx?SID=154576&ref=Feed
Electromagnetic transverse wave energy density radiation pressure -Pa vs wavelength λ spectrum, wherein shorter λ are compressive of central cosmological constant vacuum energy density pressure Λ and longer λ rarefactive of Λ. The present quantum information analysis, of the computationally dualistic units total field energy density J m^-3 = -Pa = kg m^-3 mass density pascals, introduces a nonstandard basis for the missing quantum 3D volumetric information − missing in the zero-dimensional (0D) Dirac delta functional imaginary-invisible mathematical point particle QED-Standard Model representation of the photon.<img src="https://www.maplesoft.com/view.aspx?si=154576/EMtransverseRadPaSpectrumGIF.gif" alt="Quantum Electromagnetic Radiation Pressure Spectrum" style="max-width: 25%;" align="left"/>Electromagnetic transverse wave energy density radiation pressure -Pa vs wavelength λ spectrum, wherein shorter λ are compressive of central cosmological constant vacuum energy density pressure Λ and longer λ rarefactive of Λ. The present quantum information analysis, of the computationally dualistic units total field energy density J m^-3 = -Pa = kg m^-3 mass density pascals, introduces a nonstandard basis for the missing quantum 3D volumetric information − missing in the zero-dimensional (0D) Dirac delta functional imaginary-invisible mathematical point particle QED-Standard Model representation of the photon.https://www.maplesoft.com/applications/view.aspx?SID=154576&ref=FeedMon, 07 Oct 2019 04:00:00 ZDavid HarnessDavid HarnessCenter manifolds for two-dimensional systems of differential equations
https://www.maplesoft.com/applications/view.aspx?SID=154568&ref=Feed
This worksheet implements a reduction principle. It allows us to compute a polynomial approximation of center manifold with a specified maximal degree of the polynomial.<img src="https://www.maplesoft.com/view.aspx?si=154568/center.png" alt="Center manifolds for two-dimensional systems of differential equations" style="max-width: 25%;" align="left"/>This worksheet implements a reduction principle. It allows us to compute a polynomial approximation of center manifold with a specified maximal degree of the polynomial.https://www.maplesoft.com/applications/view.aspx?SID=154568&ref=FeedSun, 29 Sep 2019 04:00:00 ZVeronika HajnováVeronika HajnováCenter manifolds for three-dimensional systems of differential equations
https://www.maplesoft.com/applications/view.aspx?SID=154575&ref=Feed
This worksheet implements a reduction principle. It allows us to compute a polynomial approximation of center manifold with a specified maximal degree of the polynomial.<img src="https://www.maplesoft.com/view.aspx?si=154575/center2.png" alt="Center manifolds for three-dimensional systems of differential equations" style="max-width: 25%;" align="left"/>This worksheet implements a reduction principle. It allows us to compute a polynomial approximation of center manifold with a specified maximal degree of the polynomial.https://www.maplesoft.com/applications/view.aspx?SID=154575&ref=FeedSun, 29 Sep 2019 04:00:00 ZVeronika HajnováVeronika HajnováBialternate matrix products and its application in bifurcation theory
https://www.maplesoft.com/applications/view.aspx?SID=154567&ref=Feed
The central theorems in bifurcation theory are normal form theorems. The structure of all the theorems is the same. It claims, under certain assumptions, an arbitrary system of differential, resp, difference, equations is locally topologically equivalent to the normal form. One type of assumption can be formulated as equalities. For generic one-parameter bifurcations, there is always only one equality assumption. It stands as a condition for eigenvalues of the Jacobi matrix of the system. Those assumptions, so-called test functions, are formulated in section Bifurcation of this sheet. Bialternate product is a matrix product, which allows expressing test functions for Hopf and Neimark-Sacker bifurcations detection and continuation.<img src="https://www.maplesoft.com/view.aspx?si=154567/bif.PNG" alt="Bialternate matrix products and its application in bifurcation theory" style="max-width: 25%;" align="left"/>The central theorems in bifurcation theory are normal form theorems. The structure of all the theorems is the same. It claims, under certain assumptions, an arbitrary system of differential, resp, difference, equations is locally topologically equivalent to the normal form. One type of assumption can be formulated as equalities. For generic one-parameter bifurcations, there is always only one equality assumption. It stands as a condition for eigenvalues of the Jacobi matrix of the system. Those assumptions, so-called test functions, are formulated in section Bifurcation of this sheet. Bialternate product is a matrix product, which allows expressing test functions for Hopf and Neimark-Sacker bifurcations detection and continuation.https://www.maplesoft.com/applications/view.aspx?SID=154567&ref=FeedSat, 28 Sep 2019 04:00:00 ZVeronika HajnováVeronika HajnováGraph Theory and Pokémon
https://www.maplesoft.com/applications/view.aspx?SID=154565&ref=Feed
This application aims to illustrate the functionalities of graph theory in the Pokémon game: Pokémon Blue.<img src="https://www.maplesoft.com/view.aspx?si=154565/pokemon.png" alt="Graph Theory and Pokémon" style="max-width: 25%;" align="left"/>This application aims to illustrate the functionalities of graph theory in the Pokémon game: Pokémon Blue.https://www.maplesoft.com/applications/view.aspx?SID=154565&ref=FeedThu, 19 Sep 2019 04:00:00 ZValerie BustosValerie BustosThe LegendreSobolev Package and its Applications in Handwriting Recognition
https://www.maplesoft.com/applications/view.aspx?SID=154553&ref=Feed
The present applications are motivated by the problem of mathematical handwriting recognition where symbols are represented as parametric plane curves in a Legendre-Sobolev basis. An early work showed that approximating the coordinate functions as truncated series in a Legendre-Sobolev basis yields fast and effective recognition rates. Furthermore, this representation allows one to study the geometrical features of handwritten characters as a whole. These geometrical features are equivalent to baselines, bounding boxes, loops, and cusps appearing in handwritten characters. The study of these features becomes a crucial task when dealing with two-dimensional math formulas and the large set of math characters with different variations in style and size.
In an early paper, we proposed methods for computing the derivatives, roots, and gcds of polynomials in Legendre-Sobolev bases to find such features without needing to convert the approximations to the monomial
basis.Our findings in employing parametrized Legendre-Sobolev approximations for representing handwritten characters and studying the geometrical features of such representation has led us to develop two Maple packages called LegendreSobolev and HandwritingRecognitionTesting. The methods in these packages rely on Maple’s linear algebra routines.<img src="https://www.maplesoft.com/applications/images/app_image_blank_lg.jpg" alt="The LegendreSobolev Package and its Applications in Handwriting Recognition" style="max-width: 25%;" align="left"/>The present applications are motivated by the problem of mathematical handwriting recognition where symbols are represented as parametric plane curves in a Legendre-Sobolev basis. An early work showed that approximating the coordinate functions as truncated series in a Legendre-Sobolev basis yields fast and effective recognition rates. Furthermore, this representation allows one to study the geometrical features of handwritten characters as a whole. These geometrical features are equivalent to baselines, bounding boxes, loops, and cusps appearing in handwritten characters. The study of these features becomes a crucial task when dealing with two-dimensional math formulas and the large set of math characters with different variations in style and size.
In an early paper, we proposed methods for computing the derivatives, roots, and gcds of polynomials in Legendre-Sobolev bases to find such features without needing to convert the approximations to the monomial
basis.Our findings in employing parametrized Legendre-Sobolev approximations for representing handwritten characters and studying the geometrical features of such representation has led us to develop two Maple packages called LegendreSobolev and HandwritingRecognitionTesting. The methods in these packages rely on Maple’s linear algebra routines.https://www.maplesoft.com/applications/view.aspx?SID=154553&ref=FeedSun, 15 Sep 2019 04:00:00 ZStephen M. WattStephen M. WattCalculating the Latent Heats of Vaporization and Fusion of Water
https://www.maplesoft.com/applications/view.aspx?SID=154552&ref=Feed
This application demonstrates how you can calculate the latent heat of vaporization and the latent heat of fusion of water.
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The application uses empirical data from the <A HREF="/products/maple/features/thermophysicaldata.aspx">ThermophysicalData package</A><img src="https://www.maplesoft.com/applications/images/app_image_blank_lg.jpg" alt="Calculating the Latent Heats of Vaporization and Fusion of Water" style="max-width: 25%;" align="left"/>This application demonstrates how you can calculate the latent heat of vaporization and the latent heat of fusion of water.
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The application uses empirical data from the <A HREF="/products/maple/features/thermophysicaldata.aspx">ThermophysicalData package</A>https://www.maplesoft.com/applications/view.aspx?SID=154552&ref=FeedThu, 12 Sep 2019 04:00:00 ZSamir KhanSamir KhanSudoku Maplet
https://www.maplesoft.com/applications/view.aspx?SID=154551&ref=Feed
Cette Maplet compatible avec Maple2019 permet de générer,de résoudre et de jouer au sudoku.
La durée pour que la maplet soit chargée est plus petite que pour GSudoku10 surtout pour les sudoku de grandes tailles et la maplet peut etre petite pour les afficher à l'écran.
On peut sauvegarder les grilles,leur solution ,et leur variante couleur en fichier .gif
On peut sauvegarder en fichier .txt sous differentes formes pour charger les grilles dans d'autres logiciels:Isanaki,Hodoku,pour pc.
Peter Stancel Sudoku,SudokuWiki,Vokware pour Android
Puzzerax Sudoku,Sudoktor sur Apple<img src="https://www.maplesoft.com/view.aspx?si=154551/Captsud.JPG" alt="Sudoku Maplet" style="max-width: 25%;" align="left"/>Cette Maplet compatible avec Maple2019 permet de générer,de résoudre et de jouer au sudoku.
La durée pour que la maplet soit chargée est plus petite que pour GSudoku10 surtout pour les sudoku de grandes tailles et la maplet peut etre petite pour les afficher à l'écran.
On peut sauvegarder les grilles,leur solution ,et leur variante couleur en fichier .gif
On peut sauvegarder en fichier .txt sous differentes formes pour charger les grilles dans d'autres logiciels:Isanaki,Hodoku,pour pc.
Peter Stancel Sudoku,SudokuWiki,Vokware pour Android
Puzzerax Sudoku,Sudoktor sur Applehttps://www.maplesoft.com/applications/view.aspx?SID=154551&ref=FeedWed, 11 Sep 2019 04:00:00 Zxavier cormierxavier cormierGraph Colouring with SAT
https://www.maplesoft.com/applications/view.aspx?SID=154550&ref=Feed
A colouring of a graph is an assignment of colours to its vertices such that every two adjacent vertices are coloured differently. Finding a colouring of a given graph using the fewest number of colours is a difficult problem in general. In this worksheet we demonstrate how to solve the graph colouring problem by translating it into Boolean logic and using Maple's built-in efficient SAT solver. This approach is now available as an option to Maple’s ChromaticNumber function, which also solves the graph colouring problem. Using SAT can dramatically improve the performance of this function in some cases, including the “queen graphs” problem shown in this application.<img src="https://www.maplesoft.com/view.aspx?si=154550/queens_colouring.png" alt="Graph Colouring with SAT" style="max-width: 25%;" align="left"/>A colouring of a graph is an assignment of colours to its vertices such that every two adjacent vertices are coloured differently. Finding a colouring of a given graph using the fewest number of colours is a difficult problem in general. In this worksheet we demonstrate how to solve the graph colouring problem by translating it into Boolean logic and using Maple's built-in efficient SAT solver. This approach is now available as an option to Maple’s ChromaticNumber function, which also solves the graph colouring problem. Using SAT can dramatically improve the performance of this function in some cases, including the “queen graphs” problem shown in this application.https://www.maplesoft.com/applications/view.aspx?SID=154550&ref=FeedMon, 09 Sep 2019 04:00:00 ZCurtis BrightCurtis BrightMaplet pour creer des forteresses en Etoile
https://www.maplesoft.com/applications/view.aspx?SID=154513&ref=Feed
Cette maplet permet de rajouter sur chaque étoile imbriquée des "pointes" entre deux branches pour former des sortes de forteresses.
Le i eme "rapport1" x le rayon "interne" de la i eme etoile est egale a la distance et l'extremité d'une de ses pointes.
Le i eme "rapport2" x la longueur du coté d'une branche de la i eme etoile est egale à la longueur entre un point de base de la branche et le point de base de la "pointe".
"rapport-distance entre les etoiles" x le rayon "interne" de la i ème etoile est egale au rayon "externe" de la (i+1) ème etoile imbriquée.
"rapport1" et "rapport2" sont des sequences comme pour "angle des branches de l'étoiles".<img src="https://www.maplesoft.com/view.aspx?si=154513/forteresse-etoile.gif" alt="Maplet pour creer des forteresses en Etoile" style="max-width: 25%;" align="left"/>Cette maplet permet de rajouter sur chaque étoile imbriquée des "pointes" entre deux branches pour former des sortes de forteresses.
Le i eme "rapport1" x le rayon "interne" de la i eme etoile est egale a la distance et l'extremité d'une de ses pointes.
Le i eme "rapport2" x la longueur du coté d'une branche de la i eme etoile est egale à la longueur entre un point de base de la branche et le point de base de la "pointe".
"rapport-distance entre les etoiles" x le rayon "interne" de la i ème etoile est egale au rayon "externe" de la (i+1) ème etoile imbriquée.
"rapport1" et "rapport2" sont des sequences comme pour "angle des branches de l'étoiles".https://www.maplesoft.com/applications/view.aspx?SID=154513&ref=FeedThu, 29 Aug 2019 04:00:00 Zxavier cormierxavier cormierGenerating Parametric Curves from 2-D Data using Discrete Fourier Transforms
https://www.maplesoft.com/applications/view.aspx?SID=154546&ref=Feed
This application will generate parametric equations for a set of 2-D points. When plotted, the parametric equations resemble the shape of the points.
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This application has an interactive plot that lets you draw a curve. Maple will generate discrete points on this curve as it is drawn. Maple will then
<UL>
<LI>compute the discrete Fourier transforms (DFT) of the X and Y coordinates.
<LI>generate two parametric equations that consist of a sum of sines. The frequency and amplitude of each sine term are extracted from the DFT.
<LI>assign the equations to two variables
</UL><img src="https://www.maplesoft.com/view.aspx?si=154546/maple.png" alt="Generating Parametric Curves from 2-D Data using Discrete Fourier Transforms" style="max-width: 25%;" align="left"/>This application will generate parametric equations for a set of 2-D points. When plotted, the parametric equations resemble the shape of the points.
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This application has an interactive plot that lets you draw a curve. Maple will generate discrete points on this curve as it is drawn. Maple will then
<UL>
<LI>compute the discrete Fourier transforms (DFT) of the X and Y coordinates.
<LI>generate two parametric equations that consist of a sum of sines. The frequency and amplitude of each sine term are extracted from the DFT.
<LI>assign the equations to two variables
</UL>https://www.maplesoft.com/applications/view.aspx?SID=154546&ref=FeedMon, 12 Aug 2019 04:00:00 ZSamir KhanSamir KhanFinding the Sutherland Equation Coefficients with Least-Squares Curve Fitting
https://www.maplesoft.com/applications/view.aspx?SID=154547&ref=Feed
The Sutherland equation is commonly used to describe the variation of gas viscosity with temperature.
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There are two constants in the equation. These are typically found by fitting experimental data for viscosity to the equation.
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This application finds the Sutherland coefficients for Helium.
<UL>
<LI>Frist, data for the viscosity of Helium at several temperatures is generated with the ThermophysicalData:-Property command.
<LI>Then, the Statistics:-NonlinearFit command is used to find the value of the two constants.
</UL>
This gives us the constants in the equation. The principles can be extended to any gas.<img src="https://www.maplesoft.com/view.aspx?si=154547/sutherland.png" alt="Finding the Sutherland Equation Coefficients with Least-Squares Curve Fitting" style="max-width: 25%;" align="left"/>The Sutherland equation is commonly used to describe the variation of gas viscosity with temperature.
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There are two constants in the equation. These are typically found by fitting experimental data for viscosity to the equation.
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This application finds the Sutherland coefficients for Helium.
<UL>
<LI>Frist, data for the viscosity of Helium at several temperatures is generated with the ThermophysicalData:-Property command.
<LI>Then, the Statistics:-NonlinearFit command is used to find the value of the two constants.
</UL>
This gives us the constants in the equation. The principles can be extended to any gas.https://www.maplesoft.com/applications/view.aspx?SID=154547&ref=FeedMon, 12 Aug 2019 04:00:00 ZSamir KhanSamir KhanCompressor Power for a Supersonic Wind Tunnel at Steady-state and Start-up
https://www.maplesoft.com/applications/view.aspx?SID=154548&ref=Feed
This application calculates the compressor power (at steady-state and at start-up) for a fixed geometry supersonic wind tunnel. The test section will operate at Mach 2.5, simulate an altitude of 21 km and has a circular cross-sectional area with a diameter of 30 cm. A supersonic fixed-area diffuser follows the test section.
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A cooler between the compressor and the nozzle ensures that the air at the compressor inlet and in the test section have the same stagnation temperature.
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The air entering the compressor and in the test section has the same stagnation temperature. The compressor is isentropic, and friction and boundary layer effects are not considered.<img src="https://www.maplesoft.com/view.aspx?si=154548/wind_tunnel.png" alt="Compressor Power for a Supersonic Wind Tunnel at Steady-state and Start-up" style="max-width: 25%;" align="left"/>This application calculates the compressor power (at steady-state and at start-up) for a fixed geometry supersonic wind tunnel. The test section will operate at Mach 2.5, simulate an altitude of 21 km and has a circular cross-sectional area with a diameter of 30 cm. A supersonic fixed-area diffuser follows the test section.
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A cooler between the compressor and the nozzle ensures that the air at the compressor inlet and in the test section have the same stagnation temperature.
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The air entering the compressor and in the test section has the same stagnation temperature. The compressor is isentropic, and friction and boundary layer effects are not considered.https://www.maplesoft.com/applications/view.aspx?SID=154548&ref=FeedMon, 12 Aug 2019 04:00:00 ZSamir KhanSamir KhanUnpowered Glide Analysis of a Baron 58 Light Aircraft
https://www.maplesoft.com/applications/view.aspx?SID=154544&ref=Feed
This application presents an unpowered glide analysis of a Baron 58 aircraft.
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An aircraft with no engine power will glide to the ground. The best glide angle is the flight angle at which the airplane will travel the greatest distance, and occurs at the maximum lift-to-drag ratio.
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For the parameters used in this application, a Baron 58 aircraft has a maximum lift-to-drag ratio of about 12.2. This means an unpowered Baron will fall 1 m for every 12.2 m of travel. This application also calculates the best glide velocity, drag and lift coefficients, and the dynamic pressure.<img src="https://www.maplesoft.com/view.aspx?si=154544/Drag_force.png" alt="Unpowered Glide Analysis of a Baron 58 Light Aircraft" style="max-width: 25%;" align="left"/>This application presents an unpowered glide analysis of a Baron 58 aircraft.
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An aircraft with no engine power will glide to the ground. The best glide angle is the flight angle at which the airplane will travel the greatest distance, and occurs at the maximum lift-to-drag ratio.
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For the parameters used in this application, a Baron 58 aircraft has a maximum lift-to-drag ratio of about 12.2. This means an unpowered Baron will fall 1 m for every 12.2 m of travel. This application also calculates the best glide velocity, drag and lift coefficients, and the dynamic pressure.https://www.maplesoft.com/applications/view.aspx?SID=154544&ref=FeedThu, 18 Jul 2019 04:00:00 ZSamir KhanSamir KhanUS Standard Atmosphere 1976
https://www.maplesoft.com/applications/view.aspx?SID=154545&ref=Feed
Standard atmospheric models describe how the properties of air change with altitude. The properties reflect conditions typically expected at that altitude, and do not vary with current climatic conditions. The results are typically used for flight studies, rocketry and ballistics.
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This application implements the US Standard Atmosphere model for the lower atmosphere, published by the US Committee on Extension to the Standard Atmosphere (COESA) in 1976.
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The model gives the pressure, temperature, density and viscosity of air as a function of geopotential altitude, and is valid from a geopotential altitude of 0 m to 84852 m.
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Reference: <A HREF="https://ntrs.nasa.gov/search.jsp?R=19770009539" TARGET="_blank">US Standard Atmosphere 1976</A><img src="https://www.maplesoft.com/view.aspx?si=154545/US_Standard_Atmosphere_1976.png" alt="US Standard Atmosphere 1976" style="max-width: 25%;" align="left"/>Standard atmospheric models describe how the properties of air change with altitude. The properties reflect conditions typically expected at that altitude, and do not vary with current climatic conditions. The results are typically used for flight studies, rocketry and ballistics.
<BR><BR>
This application implements the US Standard Atmosphere model for the lower atmosphere, published by the US Committee on Extension to the Standard Atmosphere (COESA) in 1976.
<BR><BR>
The model gives the pressure, temperature, density and viscosity of air as a function of geopotential altitude, and is valid from a geopotential altitude of 0 m to 84852 m.
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Reference: <A HREF="https://ntrs.nasa.gov/search.jsp?R=19770009539" TARGET="_blank">US Standard Atmosphere 1976</A>https://www.maplesoft.com/applications/view.aspx?SID=154545&ref=FeedThu, 18 Jul 2019 04:00:00 ZSamir KhanSamir KhanMUSIC Method for Spectral Estimation
https://www.maplesoft.com/applications/view.aspx?SID=154543&ref=Feed
The <A HREF="https://en.wikipedia.org/wiki/MUSIC_(algorithm)">MUtiple SIgnal Classifier (MUSIC)</A> method is an approach for spectral estimation that is particularly appropriate for signals that consists of multiple sinusoids polluted with white (i.e. Gaussian) noise.
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Since the power estimate offered by the MUSIC method can be evaluated at any frequency, the MUSIC method offers a form of superesolution - that is, frequencies smaller than one sample (i.e. smaller than one DFT bin).
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This application generates a noisy sinusoidal signal, and then applies the MUSIC method to identify the frequencies used to generate the signal.<img src="https://www.maplesoft.com/view.aspx?si=154543/music.png" alt="MUSIC Method for Spectral Estimation" style="max-width: 25%;" align="left"/>The <A HREF="https://en.wikipedia.org/wiki/MUSIC_(algorithm)">MUtiple SIgnal Classifier (MUSIC)</A> method is an approach for spectral estimation that is particularly appropriate for signals that consists of multiple sinusoids polluted with white (i.e. Gaussian) noise.
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Since the power estimate offered by the MUSIC method can be evaluated at any frequency, the MUSIC method offers a form of superesolution - that is, frequencies smaller than one sample (i.e. smaller than one DFT bin).
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This application generates a noisy sinusoidal signal, and then applies the MUSIC method to identify the frequencies used to generate the signal.https://www.maplesoft.com/applications/view.aspx?SID=154543&ref=FeedWed, 10 Jul 2019 04:00:00 ZSamir KhanSamir KhanKinematic Analysis of a Quick Return Device
https://www.maplesoft.com/applications/view.aspx?SID=154541&ref=Feed
This is a quick return device.
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This application will:
<UL>
<LI>determine the range of motion of this device
<li>and its behavior if the crank driven at (i) a constant angular velocity, and (ii) a constant angular acceleration
</UL>
The latter involves numerically solving differential equations. These are symbolically derived by differentiating the geometric relationships with respect to time. The resulting equations contain the first and second derivative of the crank angle with respect to time; these will be set to constant values to reveal the behavior of the system.<img src="https://www.maplesoft.com/view.aspx?si=154541/kinematic.png" alt="Kinematic Analysis of a Quick Return Device" style="max-width: 25%;" align="left"/>This is a quick return device.
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This application will:
<UL>
<LI>determine the range of motion of this device
<li>and its behavior if the crank driven at (i) a constant angular velocity, and (ii) a constant angular acceleration
</UL>
The latter involves numerically solving differential equations. These are symbolically derived by differentiating the geometric relationships with respect to time. The resulting equations contain the first and second derivative of the crank angle with respect to time; these will be set to constant values to reveal the behavior of the system.https://www.maplesoft.com/applications/view.aspx?SID=154541&ref=FeedMon, 08 Jul 2019 04:00:00 ZSamir KhanSamir KhanForces in a 4 Member Frame
https://www.maplesoft.com/applications/view.aspx?SID=154542&ref=Feed
This frame is subject to a load P at point G. This application will determine the forces at the supports and in members BE and CF.
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Since the frame is in equilibrium, the sum of horizontal forces, sum of vertical forces, and sum of momentum about a point is zero. This allows us to identify the unknown forces in a system.<img src="https://www.maplesoft.com/view.aspx?si=154542/frame.png" alt="Forces in a 4 Member Frame" style="max-width: 25%;" align="left"/>This frame is subject to a load P at point G. This application will determine the forces at the supports and in members BE and CF.
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Since the frame is in equilibrium, the sum of horizontal forces, sum of vertical forces, and sum of momentum about a point is zero. This allows us to identify the unknown forces in a system.https://www.maplesoft.com/applications/view.aspx?SID=154542&ref=FeedMon, 08 Jul 2019 04:00:00 ZSamir KhanSamir KhanComplex Nonlinear Least Squares Fitting of Immittance Data
https://www.maplesoft.com/applications/view.aspx?SID=154540&ref=Feed
This worksheet provides a procedure immfit that carries out complex nonlinear least squares fitting of experimental data to an arbitrary function of s = Iω. This can be used to fit impedance, admittance or other similar data, in which real and imaginary parts are measured as a function of frequency, to theoretical expressions such as expressions for the impedance of an electrical circuit.<img src="https://www.maplesoft.com/view.aspx?si=154540/Immfit.png" alt="Complex Nonlinear Least Squares Fitting of Immittance Data" style="max-width: 25%;" align="left"/>This worksheet provides a procedure immfit that carries out complex nonlinear least squares fitting of experimental data to an arbitrary function of s = Iω. This can be used to fit impedance, admittance or other similar data, in which real and imaginary parts are measured as a function of frequency, to theoretical expressions such as expressions for the impedance of an electrical circuit.https://www.maplesoft.com/applications/view.aspx?SID=154540&ref=FeedSat, 22 Jun 2019 04:00:00 ZDr. David HarringtonDr. David HarringtonLinear Codes and Syndrome Decoding
https://www.maplesoft.com/applications/view.aspx?SID=154536&ref=Feed
Implementation of the encoding and decoding algorithms associated to an error-correcting linear code. Such a code can be characterized by a generator matrix or by a parity-check matrix and we introduce, as examples, the [7, 4, 2] binary Hamming code, the [24, 12, 8] and [23, 12, 7] binary Golay codes and the [12, 6, 6] and [11, 6, 5] ternary Golay codes. We give procedures to compute the minimum distance of a linear code and we use them with the Hamming and Golay codes. We show how to build the standard array and the syndrome array of a linear code and we give an implementation of syndrome decoding. Finally, we simulate a noisy channel and use the Hamming and Golay codes to show how syndrome decoding allows error correction on text messages.<img src="https://www.maplesoft.com/view.aspx?si=154536/Golay3.jpg" alt="Linear Codes and Syndrome Decoding" style="max-width: 25%;" align="left"/>Implementation of the encoding and decoding algorithms associated to an error-correcting linear code. Such a code can be characterized by a generator matrix or by a parity-check matrix and we introduce, as examples, the [7, 4, 2] binary Hamming code, the [24, 12, 8] and [23, 12, 7] binary Golay codes and the [12, 6, 6] and [11, 6, 5] ternary Golay codes. We give procedures to compute the minimum distance of a linear code and we use them with the Hamming and Golay codes. We show how to build the standard array and the syndrome array of a linear code and we give an implementation of syndrome decoding. Finally, we simulate a noisy channel and use the Hamming and Golay codes to show how syndrome decoding allows error correction on text messages.https://www.maplesoft.com/applications/view.aspx?SID=154536&ref=FeedThu, 06 Jun 2019 04:00:00 ZJosé Luis Gómez PardoJosé Luis Gómez Pardo