New Application Center Additions
https://www.maplesoft.com/applications
en-us2019 Maplesoft, A Division of Waterloo Maple Inc.Maplesoft Document SystemWed, 19 Jun 2019 19:41:03 GMTWed, 19 Jun 2019 19:41:03 GMTThe latest content added to the Application Centerhttps://www.maplesoft.com/images/Application_center_hp.jpgNew Application Center Additions
https://www.maplesoft.com/applications
Linear 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 PardoPositions of Two Objects Suspended and Connected by Ropes
https://www.maplesoft.com/applications/view.aspx?SID=154535&ref=Feed
Two objects are connected and suspended by a system of ropes, as illustrated in the diagram.
<BR><BR>
This application finds the position of the objects and the tension in the ropes with a horizontal and vertical force balance.<img src="https://www.maplesoft.com/view.aspx?si=154535/thumb.png" alt="Positions of Two Objects Suspended and Connected by Ropes" style="max-width: 25%;" align="left"/>Two objects are connected and suspended by a system of ropes, as illustrated in the diagram.
<BR><BR>
This application finds the position of the objects and the tension in the ropes with a horizontal and vertical force balance.https://www.maplesoft.com/applications/view.aspx?SID=154535&ref=FeedWed, 05 Jun 2019 04:00:00 ZSamir KhanSamir KhanWorst Case Circuit Analysis with Monte Carlo Simulation
https://www.maplesoft.com/applications/view.aspx?SID=154534&ref=Feed
Electrical components are manufactured in large quantities. Inconsistencies in the raw materials and the manufacturing process means that component parameters have a statistical distribution. That is, the resistance of a batch of resistors might be described by a normal distribution.
<BR><BR>
Given the components in a circuit their parameter distribution, the circuit may not perform as specified. This is a risk that must be identified and mitigated early in the design process.
<BR><BR>
Worst Case Circuit Analysis is a set of techniques used to analyze how variations in parameters influence circuit performance. One approach is Monte Carlo analysis, in which parameters are randomly selected from a distribution, and the circuit simulated, anywhere from 1000 to 100000 times.
<BR><BR>
This application performs a worst case circuit analysis of an electrical circuit using a Monte Carlo approach.<img src="https://www.maplesoft.com/view.aspx?si=154534/WCCA_MC.png" alt="Worst Case Circuit Analysis with Monte Carlo Simulation" style="max-width: 25%;" align="left"/>Electrical components are manufactured in large quantities. Inconsistencies in the raw materials and the manufacturing process means that component parameters have a statistical distribution. That is, the resistance of a batch of resistors might be described by a normal distribution.
<BR><BR>
Given the components in a circuit their parameter distribution, the circuit may not perform as specified. This is a risk that must be identified and mitigated early in the design process.
<BR><BR>
Worst Case Circuit Analysis is a set of techniques used to analyze how variations in parameters influence circuit performance. One approach is Monte Carlo analysis, in which parameters are randomly selected from a distribution, and the circuit simulated, anywhere from 1000 to 100000 times.
<BR><BR>
This application performs a worst case circuit analysis of an electrical circuit using a Monte Carlo approach.https://www.maplesoft.com/applications/view.aspx?SID=154534&ref=FeedWed, 29 May 2019 04:00:00 ZSamir KhanSamir KhanExtreme Value Analysis of an Electrical Circuit
https://www.maplesoft.com/applications/view.aspx?SID=154533&ref=Feed
An electrical component, such as a resistor or capacitor, is usually quantified with a nominal value and a tolerance. Given the number of components in a circuit and their compounded tolerances, the actual performance of a circuit may not necessarily match its desired performance.
<BR><BR>
Extreme Value Analysis (EVA) is a process in which the behavior of a circuit is simulated for every permutation of extreme component parameters in combination with every permutation of extreme values for all other components. This application performs an extreme value analysis of a circuit with a photodiode-generated current and an op-amp, though the principles can be extended to any circuit.<img src="https://www.maplesoft.com/view.aspx?si=154533/circuit.png" alt="Extreme Value Analysis of an Electrical Circuit" style="max-width: 25%;" align="left"/>An electrical component, such as a resistor or capacitor, is usually quantified with a nominal value and a tolerance. Given the number of components in a circuit and their compounded tolerances, the actual performance of a circuit may not necessarily match its desired performance.
<BR><BR>
Extreme Value Analysis (EVA) is a process in which the behavior of a circuit is simulated for every permutation of extreme component parameters in combination with every permutation of extreme values for all other components. This application performs an extreme value analysis of a circuit with a photodiode-generated current and an op-amp, though the principles can be extended to any circuit.https://www.maplesoft.com/applications/view.aspx?SID=154533&ref=FeedTue, 28 May 2019 04:00:00 ZSamir KhanSamir KhanPhysical Properties of Natural Gas
https://www.maplesoft.com/applications/view.aspx?SID=154532&ref=Feed
Oil and gas engineers need accurate values of the transport and thermodynamic properties of natural gas, over a broad range of temperatures, pressures, and compositions.
<BR><BR>
This data is needed to size pipes, pumps, valves, heat exchangers, compressors and other items of a process plant.
<BR><BR>
Inaccurate data compounded over the many items of process equipment can amplify risk, both to cost and safety.
<BR><BR>
Maple lets you calculate the transport properties of several standard natural gas mixtures (Gulf Coast, Amarillo, Ekofisk, High N2 and High N2/O2), and your own custom mixtures. The functionality is available in the ThermophysicalData package, powered by the open source <A HREF="http://www.coolprop.org" TARGET="_blank">CoolProp</A> project.
<BR><BR>
Properties are calculated with a Helmholtz energy approach, and includes density, viscosity, specific heat capacity, compressibility factor, Joule-Thomson coefficient and more.
<BR><BR>
This data is instantly accessible in Maple's interactive computing environment - this means you can use all of Maple's plotting, solving and optimization routines, and employ units as a dimensionality check.<img src="https://www.maplesoft.com/view.aspx?si=154532/thumb.png" alt="Physical Properties of Natural Gas" style="max-width: 25%;" align="left"/>Oil and gas engineers need accurate values of the transport and thermodynamic properties of natural gas, over a broad range of temperatures, pressures, and compositions.
<BR><BR>
This data is needed to size pipes, pumps, valves, heat exchangers, compressors and other items of a process plant.
<BR><BR>
Inaccurate data compounded over the many items of process equipment can amplify risk, both to cost and safety.
<BR><BR>
Maple lets you calculate the transport properties of several standard natural gas mixtures (Gulf Coast, Amarillo, Ekofisk, High N2 and High N2/O2), and your own custom mixtures. The functionality is available in the ThermophysicalData package, powered by the open source <A HREF="http://www.coolprop.org" TARGET="_blank">CoolProp</A> project.
<BR><BR>
Properties are calculated with a Helmholtz energy approach, and includes density, viscosity, specific heat capacity, compressibility factor, Joule-Thomson coefficient and more.
<BR><BR>
This data is instantly accessible in Maple's interactive computing environment - this means you can use all of Maple's plotting, solving and optimization routines, and employ units as a dimensionality check.https://www.maplesoft.com/applications/view.aspx?SID=154532&ref=FeedThu, 23 May 2019 04:00:00 ZSamir KhanSamir KhanRobot Arm Writing "Maplesoft" in Handwritten Cursive Script
https://www.maplesoft.com/applications/view.aspx?SID=154531&ref=Feed
This application models a 3 DoF robot arm, with the motion of the tip writing "Maplesoft" in handwritten cursive script.
<BR><BR>
To model the arm, the worksheet:
<UL>
<LI>Analytically derives the Denavit & Hartenberg transformation matrix for each of the three joints
<LI>Lets the user specify a parametric path for the tip of the robot to follow. The default equations in the worksheet writes "Maplesoft" in cursive script
<LI>Animates the robot arm following the specified path
</UL><img src="https://www.maplesoft.com/view.aspx?si=154531/thumb.png" alt="Robot Arm Writing "Maplesoft" in Handwritten Cursive Script" style="max-width: 25%;" align="left"/>This application models a 3 DoF robot arm, with the motion of the tip writing "Maplesoft" in handwritten cursive script.
<BR><BR>
To model the arm, the worksheet:
<UL>
<LI>Analytically derives the Denavit & Hartenberg transformation matrix for each of the three joints
<LI>Lets the user specify a parametric path for the tip of the robot to follow. The default equations in the worksheet writes "Maplesoft" in cursive script
<LI>Animates the robot arm following the specified path
</UL>https://www.maplesoft.com/applications/view.aspx?SID=154531&ref=FeedMon, 06 May 2019 04:00:00 ZBryon ThurBryon ThurGame of Thrones and Graph Theory
https://www.maplesoft.com/applications/view.aspx?SID=154529&ref=Feed
Graph theory can help you understand the social landscape of the television series Game of Thrones, based upon the A Song of Ice and Fire books. With the judicious use of Maple, you can ask yourself really pressing questions like
<UL>
<LI>Who is the most influential person in Westeros? How has their influence changed over each season?</LI>
<LI>How are Eddard Stark and Randyll Tarly connected?</LI>
<LI>What do eigenvectors have to do with the battle for the Iron Throne, anyway?</LI>
</UL>
This application uses data from the television series. See <A HREF="https://www.maplesoft.com/applications/view.aspx?SID=154530">A Song of Ice and Fire and Graph Theory</A> to ask these types of questions using data for the books.<img src="https://www.maplesoft.com/view.aspx?si=154529/thumb.png" alt="Game of Thrones and Graph Theory" style="max-width: 25%;" align="left"/>Graph theory can help you understand the social landscape of the television series Game of Thrones, based upon the A Song of Ice and Fire books. With the judicious use of Maple, you can ask yourself really pressing questions like
<UL>
<LI>Who is the most influential person in Westeros? How has their influence changed over each season?</LI>
<LI>How are Eddard Stark and Randyll Tarly connected?</LI>
<LI>What do eigenvectors have to do with the battle for the Iron Throne, anyway?</LI>
</UL>
This application uses data from the television series. See <A HREF="https://www.maplesoft.com/applications/view.aspx?SID=154530">A Song of Ice and Fire and Graph Theory</A> to ask these types of questions using data for the books.https://www.maplesoft.com/applications/view.aspx?SID=154529&ref=FeedWed, 27 Mar 2019 04:00:00 ZSamir KhanSamir KhanA Song of Ice and Fire and Graph Theory
https://www.maplesoft.com/applications/view.aspx?SID=154530&ref=Feed
Graph theory can help you understand the social landscape of the books in the series A Song of Ice and Fire by G. R. R. Martin. With the judicious use of Maple, you can ask yourself <i>really</i> pressing questions like
<UL>
<LI>Who is the most influential person in Westeros? How has their influence changed over the five books?</LI>
<LI>How are Eddard Stark and Randyll Tarly connected?</LI>
<LI>What do eigenvectors have to do with the battle for the Iron Throne, anyway?</LI>
</UL>
This application uses data from the books. See <A HREF="https://www.maplesoft.com/applications/view.aspx?SID=154529">A Game of Thrones and Graph Theory</A> to ask these types of questions using data for the television series.<img src="https://www.maplesoft.com/view.aspx?si=154530/thumb.png" alt="A Song of Ice and Fire and Graph Theory" style="max-width: 25%;" align="left"/>Graph theory can help you understand the social landscape of the books in the series A Song of Ice and Fire by G. R. R. Martin. With the judicious use of Maple, you can ask yourself <i>really</i> pressing questions like
<UL>
<LI>Who is the most influential person in Westeros? How has their influence changed over the five books?</LI>
<LI>How are Eddard Stark and Randyll Tarly connected?</LI>
<LI>What do eigenvectors have to do with the battle for the Iron Throne, anyway?</LI>
</UL>
This application uses data from the books. See <A HREF="https://www.maplesoft.com/applications/view.aspx?SID=154529">A Game of Thrones and Graph Theory</A> to ask these types of questions using data for the television series.https://www.maplesoft.com/applications/view.aspx?SID=154530&ref=FeedWed, 27 Mar 2019 04:00:00 ZSamir KhanSamir KhanSystem of Equations 2x2 and 3x3
https://www.maplesoft.com/applications/view.aspx?SID=154520&ref=Feed
This application solves a set of compatible equations of two or three variables. For two variables, it also graphs the intersection point of the variable "x" and "y". If we want to observe the intersection point closer we will use the zoom button that is activated when manipulating the graph. If we want to change the variable ("x" and "y") we enter the code of the button that solves and graphs. For three variables, the intersecting planes are shown.
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In Spanish.<img src="https://www.maplesoft.com/view.aspx?si=154520/sis_eq_dpd.png" alt="System of Equations 2x2 and 3x3" style="max-width: 25%;" align="left"/>This application solves a set of compatible equations of two or three variables. For two variables, it also graphs the intersection point of the variable "x" and "y". If we want to observe the intersection point closer we will use the zoom button that is activated when manipulating the graph. If we want to change the variable ("x" and "y") we enter the code of the button that solves and graphs. For three variables, the intersecting planes are shown.
<BR><BR>
In Spanish.https://www.maplesoft.com/applications/view.aspx?SID=154520&ref=FeedTue, 19 Mar 2019 04:00:00 ZLenin Araujo CastilloLenin Araujo CastilloLomb-Scargle Spectral Analysis of Irregularly Sampled Data
https://www.maplesoft.com/applications/view.aspx?SID=154521&ref=Feed
This application
<UL>
<LI>generates an irregularly sampled signal of a sum of two sinusoids (i.e. a time vector at irregular intervals, and a signal vector containing a value at each of those times)
<LI>and then generates a Lomb-Scargle periodogram of that data.
</UL>
The periodogram correctly identifies the frequencies used to generate the irregularly sampled signal.<img src="https://www.maplesoft.com/view.aspx?si=154521/lomb-thumbnailbnail.jpg" alt="Lomb-Scargle Spectral Analysis of Irregularly Sampled Data" style="max-width: 25%;" align="left"/>This application
<UL>
<LI>generates an irregularly sampled signal of a sum of two sinusoids (i.e. a time vector at irregular intervals, and a signal vector containing a value at each of those times)
<LI>and then generates a Lomb-Scargle periodogram of that data.
</UL>
The periodogram correctly identifies the frequencies used to generate the irregularly sampled signal.https://www.maplesoft.com/applications/view.aspx?SID=154521&ref=FeedTue, 19 Mar 2019 04:00:00 ZSamir KhanSamir KhanBlurring an Image in the Spatial Frequency Domain
https://www.maplesoft.com/applications/view.aspx?SID=154522&ref=Feed
ere, we will blur in an image with a Gaussian Filter (effectively a low-pass filter) applied in the spatial frequency domain.
<UL>
<LI>First an image is imported
<LI>The fourier transform of the image is then computed, and the image periodogram plotted.
<LI>The fourier transform is multiplied by a Gaussian filter (this attenuates higher spatial frequencies - i.e. the finer detail is removed, leaving only the broad outline).
<LI>The resulted is inverted to the image domain, giving a blurry image
</UL>
This application uses the new Maple 2019 FFTShift function to swap data in a matrix or a vector into a different position. The Fourier transform of an image places lower frequency data near all four corners, with higher frequency data near the center. In this instance, FFTShift is typically applied to move the lowest frequencies to the center and the highest frequencies to the corners.
<BR><BR>
This results in a more meaningful visualization of the power spectrum where the lowest frequency data is contiguous, and simplifies the manipulation of image frequency data.<img src="https://www.maplesoft.com/view.aspx?si=154522/blurimage.jpg" alt="Blurring an Image in the Spatial Frequency Domain" style="max-width: 25%;" align="left"/>ere, we will blur in an image with a Gaussian Filter (effectively a low-pass filter) applied in the spatial frequency domain.
<UL>
<LI>First an image is imported
<LI>The fourier transform of the image is then computed, and the image periodogram plotted.
<LI>The fourier transform is multiplied by a Gaussian filter (this attenuates higher spatial frequencies - i.e. the finer detail is removed, leaving only the broad outline).
<LI>The resulted is inverted to the image domain, giving a blurry image
</UL>
This application uses the new Maple 2019 FFTShift function to swap data in a matrix or a vector into a different position. The Fourier transform of an image places lower frequency data near all four corners, with higher frequency data near the center. In this instance, FFTShift is typically applied to move the lowest frequencies to the center and the highest frequencies to the corners.
<BR><BR>
This results in a more meaningful visualization of the power spectrum where the lowest frequency data is contiguous, and simplifies the manipulation of image frequency data.https://www.maplesoft.com/applications/view.aspx?SID=154522&ref=FeedTue, 19 Mar 2019 04:00:00 ZSamir KhanSamir KhanLocate a Signal in Audio in the Presence of Noise
https://www.maplesoft.com/applications/view.aspx?SID=154523&ref=Feed
This application demonstrates how you can estimate the location of a signal that might exist in a larger (perhaps noisy) measurement. In this instance, we find the location of a small segment of audio in a larger audio file.
<UL>
<LI>First, an audio file is first loaded, a small segment is extracted, and random Gaussian noise is added to both.
<LI>The cross-correlation of the full audio and the extract is computed, and the maximum lag computed.
</UL>
The maximum lag is the index at which the extract is predicted to exist in the audio.<img src="https://www.maplesoft.com/view.aspx?si=154523/thumbnail.jpg" alt="Locate a Signal in Audio in the Presence of Noise" style="max-width: 25%;" align="left"/>This application demonstrates how you can estimate the location of a signal that might exist in a larger (perhaps noisy) measurement. In this instance, we find the location of a small segment of audio in a larger audio file.
<UL>
<LI>First, an audio file is first loaded, a small segment is extracted, and random Gaussian noise is added to both.
<LI>The cross-correlation of the full audio and the extract is computed, and the maximum lag computed.
</UL>
The maximum lag is the index at which the extract is predicted to exist in the audio.https://www.maplesoft.com/applications/view.aspx?SID=154523&ref=FeedTue, 19 Mar 2019 04:00:00 ZSamir KhanSamir KhanFundamental Frequency and Harmonics of a Violin Note
https://www.maplesoft.com/applications/view.aspx?SID=154524&ref=Feed
This application finds the fundamental frequency and harmonics of a violin using information from the amplitude spectrum. Then, we generate a sinusoidal signal with the same frequency-amplitude characteristics of the violin note, and play the resulting sound.
The analysis uses the new Maple 2019 command for finding the peaks and valleys of a 1D data set - FindPeaks. This command offers several options that let you filter out peaks or valleys that are too close, what defines a peak or valley, and more.<img src="https://www.maplesoft.com/view.aspx?si=154524/thumnbail.jpg" alt="Fundamental Frequency and Harmonics of a Violin Note" style="max-width: 25%;" align="left"/>This application finds the fundamental frequency and harmonics of a violin using information from the amplitude spectrum. Then, we generate a sinusoidal signal with the same frequency-amplitude characteristics of the violin note, and play the resulting sound.
The analysis uses the new Maple 2019 command for finding the peaks and valleys of a 1D data set - FindPeaks. This command offers several options that let you filter out peaks or valleys that are too close, what defines a peak or valley, and more.https://www.maplesoft.com/applications/view.aspx?SID=154524&ref=FeedTue, 19 Mar 2019 04:00:00 ZSamir KhanSamir KhanFundamental Frequency of a Human Voice
https://www.maplesoft.com/applications/view.aspx?SID=154525&ref=Feed
This application predicts the fundamental frequency of a human voice using the ComplexCepstrum command.
<BR><BR>
After converting a small window of the audio to the cepstral domain, we find the pitch by noting the maximum "quefrency" in a carefully selected range.<img src="https://www.maplesoft.com/view.aspx?si=154525/thumbnail.jpg" alt="Fundamental Frequency of a Human Voice" style="max-width: 25%;" align="left"/>This application predicts the fundamental frequency of a human voice using the ComplexCepstrum command.
<BR><BR>
After converting a small window of the audio to the cepstral domain, we find the pitch by noting the maximum "quefrency" in a carefully selected range.https://www.maplesoft.com/applications/view.aspx?SID=154525&ref=FeedTue, 19 Mar 2019 04:00:00 ZSamir KhanSamir KhanCompressing Audio with the Discrete Cosine Transform
https://www.maplesoft.com/applications/view.aspx?SID=154526&ref=Feed
This application demonstrates how you can compress a signal by discarding low-energy parts of its discrete cosine transform. Specifically, we only retain those coefficients that cumulatively sum to a large part of the signal energy.
<BR><BR>
Here, the signal is an audio file, where only 13% of the DCT coefficients are needed to represent 97% of the signal energy. After compression, the resulting audio is hissy but still legible.<img src="https://www.maplesoft.com/view.aspx?si=154526/thumbnail.jpg" alt="Compressing Audio with the Discrete Cosine Transform" style="max-width: 25%;" align="left"/>This application demonstrates how you can compress a signal by discarding low-energy parts of its discrete cosine transform. Specifically, we only retain those coefficients that cumulatively sum to a large part of the signal energy.
<BR><BR>
Here, the signal is an audio file, where only 13% of the DCT coefficients are needed to represent 97% of the signal energy. After compression, the resulting audio is hissy but still legible.https://www.maplesoft.com/applications/view.aspx?SID=154526&ref=FeedTue, 19 Mar 2019 04:00:00 ZSamir KhanSamir KhanEcho Cancellation using Cepstrum Analysis
https://www.maplesoft.com/applications/view.aspx?SID=154527&ref=Feed
This application will
<UL>
<LI>import an audio file that has an echo
<LI>identify the start of the echo in the cepstral domain (using the RealCepstrum function)
<LI>use this information to generate and apply an IIR filter to remove the echo'
<LI>and write the de-echoed audio back to a sound file
</UL><img src="https://www.maplesoft.com/view.aspx?si=154527/thumbnail.jpg" alt="Echo Cancellation using Cepstrum Analysis" style="max-width: 25%;" align="left"/>This application will
<UL>
<LI>import an audio file that has an echo
<LI>identify the start of the echo in the cepstral domain (using the RealCepstrum function)
<LI>use this information to generate and apply an IIR filter to remove the echo'
<LI>and write the de-echoed audio back to a sound file
</UL>https://www.maplesoft.com/applications/view.aspx?SID=154527&ref=FeedTue, 19 Mar 2019 04:00:00 ZSamir KhanSamir KhanPredicting the Orbital Period of Exoplanets by Analyzing the Wobble of Stars
https://www.maplesoft.com/applications/view.aspx?SID=154528&ref=Feed
Stars are pulled in a circle or ellipse in reponse to the gravity of orbiting planets. By analyzing the "wobble" (or radial velocity) of a star, astronomers can predict the presence and orbital period of exoplanets.
<BR><BR>
Radial velocity is recorded, often over months or years, with a spectrograph connected to a telescope. This data is used to generate a periodogram, in which a peak is evidence of an exoplanet; the orbital period of the exoplanet is given by the location of the peak.
<BR><BR>
However cloud cover, scheduling conflicts and other issues can often disrupt observations, so data is generally not regularly sampled. This means that standard Fourier techniques cannot be used to generate a periodogram, and other approaches are needed. A common method for the frequency analysis of irregularly sampled data is the Lomb-Scargle technique.
<BR><BR>
Fischer (2003) recorded the radial velocity of the star HD 3561 (also known as 54 Piscium), and generated a periodogram to show evidence of an exoplanet (now known as 54 Piscium b).
<BR><BR>
This application uses Maple 2019's new Lomb-Scargle tools to reproduce the analysis; the periodogram shows a periodicity of 62.2 days, agreeing with value given by Fischer (2003).
<BR><BR>
References:
<UL>
<LI>A Sub-Saturn Mass Planet Orbiting HD 3651, Fischer D.A. et al., The Astrophysical Journal, 590:1081–1087, 2003 June 20
<LI>Orbital velocity data found at http://astrostatistics.psu.edu/datasets/exoplanet_Doppler.html
</UL><img src="https://www.maplesoft.com/view.aspx?si=154528/thumbnail.jpg" alt="Predicting the Orbital Period of Exoplanets by Analyzing the Wobble of Stars" style="max-width: 25%;" align="left"/>Stars are pulled in a circle or ellipse in reponse to the gravity of orbiting planets. By analyzing the "wobble" (or radial velocity) of a star, astronomers can predict the presence and orbital period of exoplanets.
<BR><BR>
Radial velocity is recorded, often over months or years, with a spectrograph connected to a telescope. This data is used to generate a periodogram, in which a peak is evidence of an exoplanet; the orbital period of the exoplanet is given by the location of the peak.
<BR><BR>
However cloud cover, scheduling conflicts and other issues can often disrupt observations, so data is generally not regularly sampled. This means that standard Fourier techniques cannot be used to generate a periodogram, and other approaches are needed. A common method for the frequency analysis of irregularly sampled data is the Lomb-Scargle technique.
<BR><BR>
Fischer (2003) recorded the radial velocity of the star HD 3561 (also known as 54 Piscium), and generated a periodogram to show evidence of an exoplanet (now known as 54 Piscium b).
<BR><BR>
This application uses Maple 2019's new Lomb-Scargle tools to reproduce the analysis; the periodogram shows a periodicity of 62.2 days, agreeing with value given by Fischer (2003).
<BR><BR>
References:
<UL>
<LI>A Sub-Saturn Mass Planet Orbiting HD 3651, Fischer D.A. et al., The Astrophysical Journal, 590:1081–1087, 2003 June 20
<LI>Orbital velocity data found at http://astrostatistics.psu.edu/datasets/exoplanet_Doppler.html
</UL>https://www.maplesoft.com/applications/view.aspx?SID=154528&ref=FeedTue, 19 Mar 2019 04:00:00 ZSamir KhanSamir KhanMaplet 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=FeedSun, 03 Mar 2019 05:00:00 Zxavier cormierxavier cormierLinear Optimization Examples
https://www.maplesoft.com/applications/view.aspx?SID=154517&ref=Feed
So, this was introduced into my son's high school Precalculus I class, and he really didn't understand it. After reading his textbook, I could understand why, the explanation was terrible. So, I decided to do a few examples for him, to show him how it would work. While I used Maple to do the computational pieces, I didn't use any built-in functions, I kept it as simple as possible.<img src="https://www.maplesoft.com/view.aspx?si=154517/b0e3e02e0b878253dcb11a11a2b75fce.gif" alt="Linear Optimization Examples" style="max-width: 25%;" align="left"/>So, this was introduced into my son's high school Precalculus I class, and he really didn't understand it. After reading his textbook, I could understand why, the explanation was terrible. So, I decided to do a few examples for him, to show him how it would work. While I used Maple to do the computational pieces, I didn't use any built-in functions, I kept it as simple as possible.https://www.maplesoft.com/applications/view.aspx?SID=154517&ref=FeedTue, 19 Feb 2019 05:00:00 ZProf. Peter SchochProf. Peter SchochPlane flying through a thundercloud, calculating the E field
https://www.maplesoft.com/applications/view.aspx?SID=154519&ref=Feed
This problem models a thundercloud by a +40C charge at 10km height, -40C charge at 5km height and a 10C charge at a 2km height. It then has an airplane flying at 8km through the cloud. The crux of the problem is to calculate the Electric field on the plane beginning at the left of the cloud through to the right of the coud.
I placed the y axis along the charges within the cloud. his means the airplane has a fixed y value and just changes in x. I also numbered the charges from bottom to the top.<img src="https://www.maplesoft.com/view.aspx?si=154519/b9715d1a184de2946329d1d396866539.gif" alt="Plane flying through a thundercloud, calculating the E field" style="max-width: 25%;" align="left"/>This problem models a thundercloud by a +40C charge at 10km height, -40C charge at 5km height and a 10C charge at a 2km height. It then has an airplane flying at 8km through the cloud. The crux of the problem is to calculate the Electric field on the plane beginning at the left of the cloud through to the right of the coud.
I placed the y axis along the charges within the cloud. his means the airplane has a fixed y value and just changes in x. I also numbered the charges from bottom to the top.https://www.maplesoft.com/applications/view.aspx?SID=154519&ref=FeedTue, 19 Feb 2019 05:00:00 ZProf. Peter SchochProf. Peter Schoch