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<?xml version="1.0" encoding="UTF-8"?> <rdf:RDF xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#" xmlns="http://purl.org/rss/1.0/" xmlns:dc="http://purl.org/dc/elements/1.1/"> <channel rdf:about="https://community.wolfram.com"> <title>Community RSS Feed</title> <link>https://community.wolfram.com</link> <description>RSS Feed for Wolfram Community showing any discussions in tag sorted by active</description> <items> <rdf:Seq> <rdf:li rdf:resource="https://community.wolfram.com/groups/-/m/t/3332840" /> <rdf:li rdf:resource="https://community.wolfram.com/groups/-/m/t/3332178" /> <rdf:li rdf:resource="https://community.wolfram.com/groups/-/m/t/3315449" /> <rdf:li rdf:resource="https://community.wolfram.com/groups/-/m/t/3332704" /> <rdf:li rdf:resource="https://community.wolfram.com/groups/-/m/t/3331934" /> <rdf:li rdf:resource="https://community.wolfram.com/groups/-/m/t/3331904" /> <rdf:li rdf:resource="https://community.wolfram.com/groups/-/m/t/3326555" /> <rdf:li rdf:resource="https://community.wolfram.com/groups/-/m/t/3330872" /> <rdf:li rdf:resource="https://community.wolfram.com/groups/-/m/t/3331281" /> <rdf:li rdf:resource="https://community.wolfram.com/groups/-/m/t/3223670" /> <rdf:li rdf:resource="https://community.wolfram.com/groups/-/m/t/3331113" /> <rdf:li rdf:resource="https://community.wolfram.com/groups/-/m/t/142857" /> <rdf:li rdf:resource="https://community.wolfram.com/groups/-/m/t/3190877" /> <rdf:li rdf:resource="https://community.wolfram.com/groups/-/m/t/1052348" /> <rdf:li rdf:resource="https://community.wolfram.com/groups/-/m/t/1541234" /> <rdf:li rdf:resource="https://community.wolfram.com/groups/-/m/t/3331233" /> <rdf:li rdf:resource="https://community.wolfram.com/groups/-/m/t/3331019" /> <rdf:li rdf:resource="https://community.wolfram.com/groups/-/m/t/3330242" /> <rdf:li rdf:resource="https://community.wolfram.com/groups/-/m/t/3330289" /> <rdf:li rdf:resource="https://community.wolfram.com/groups/-/m/t/3330805" /> <rdf:li rdf:resource="https://community.wolfram.com/groups/-/m/t/3330200" /> <rdf:li rdf:resource="https://community.wolfram.com/groups/-/m/t/3328982" /> <rdf:li rdf:resource="https://community.wolfram.com/groups/-/m/t/3325627" /> <rdf:li rdf:resource="https://community.wolfram.com/groups/-/m/t/3329609" /> <rdf:li rdf:resource="https://community.wolfram.com/groups/-/m/t/3330117" /> <rdf:li rdf:resource="https://community.wolfram.com/groups/-/m/t/3329526" /> <rdf:li rdf:resource="https://community.wolfram.com/groups/-/m/t/3329673" /> <rdf:li rdf:resource="https://community.wolfram.com/groups/-/m/t/3329460" /> <rdf:li rdf:resource="https://community.wolfram.com/groups/-/m/t/3328657" /> <rdf:li rdf:resource="https://community.wolfram.com/groups/-/m/t/3329303" /> <rdf:li rdf:resource="https://community.wolfram.com/groups/-/m/t/3325521" /> <rdf:li rdf:resource="https://community.wolfram.com/groups/-/m/t/3328790" /> <rdf:li rdf:resource="https://community.wolfram.com/groups/-/m/t/3328759" /> <rdf:li rdf:resource="https://community.wolfram.com/groups/-/m/t/3329048" /> <rdf:li rdf:resource="https://community.wolfram.com/groups/-/m/t/3329030" /> <rdf:li rdf:resource="https://community.wolfram.com/groups/-/m/t/3325314" /> <rdf:li rdf:resource="https://community.wolfram.com/groups/-/m/t/3328280" /> <rdf:li rdf:resource="https://community.wolfram.com/groups/-/m/t/3328263" /> <rdf:li rdf:resource="https://community.wolfram.com/groups/-/m/t/3327934" /> <rdf:li rdf:resource="https://community.wolfram.com/groups/-/m/t/3328470" /> <rdf:li rdf:resource="https://community.wolfram.com/groups/-/m/t/3327619" /> <rdf:li rdf:resource="https://community.wolfram.com/groups/-/m/t/3327833" /> <rdf:li rdf:resource="https://community.wolfram.com/groups/-/m/t/3322984" /> <rdf:li rdf:resource="https://community.wolfram.com/groups/-/m/t/3327416" /> <rdf:li rdf:resource="https://community.wolfram.com/groups/-/m/t/366628" /> <rdf:li rdf:resource="https://community.wolfram.com/groups/-/m/t/3161100" /> <rdf:li rdf:resource="https://community.wolfram.com/groups/-/m/t/3326111" /> <rdf:li rdf:resource="https://community.wolfram.com/groups/-/m/t/3327284" /> <rdf:li rdf:resource="https://community.wolfram.com/groups/-/m/t/3323292" /> <rdf:li rdf:resource="https://community.wolfram.com/groups/-/m/t/3326943" /> </rdf:Seq> </items> </channel> <item rdf:about="https://community.wolfram.com/groups/-/m/t/3332840"> <title>Don't use Forsyth-Edwards notation to play chess with LLMs</title> <link>https://community.wolfram.com/groups/-/m/t/3332840</link> <description>&amp;[Wolfram Notebook][1]
 
 
 [1]: https://www.wolframcloud.com/obj/0135cc34-647d-41c7-8cc5-61a47b090d8f</description> <dc:creator>Anton Antonov</dc:creator> <dc:date>2024-12-04T03:14:23Z</dc:date> </item> <item rdf:about="https://community.wolfram.com/groups/-/m/t/3332178"> <title>Find the coordinates of the bending points of linear elements in an image</title> <link>https://community.wolfram.com/groups/-/m/t/3332178</link> <description>I would like to find the coordinates of the divergence points of the double helix in a temperature change electrophoresis image of a gene, that is, the coordinates of the position of the mark in the attached image.
 
 ![a marked temperature change electrophoresis image of a gene][1]
 
 I collected sample images and tried to find the coordinates of the bending points using the Predict function and NetChain &amp; NetTrain and NetChain &amp; NetTrain, but the accuracy was too poor. 
 I tried using ImageCorners but the accuracy was still an issue. Is there no other way than to resort to tedious programming?
 
 
 ## Predict function
 
 &amp;[Wolfram Notebook][2]
 
 ## NetChain &amp; NetTrain 
 
 &amp;[Wolfram Notebook][3], 
 
 ## ImageCorners 
 
 &amp;[Wolfram Notebook][4] 
 
 [1]: https://community.wolfram.com//c/portal/getImageAttachment?filename=T-%E2%91%A0-11538.jpg&amp;userId=3138533
 [2]: https://www.wolframcloud.com/obj/86b33500-6a12-4e4a-8d41-292ea94a40b3
 [3]: https://www.wolframcloud.com/obj/9ab60f34-0798-483a-93de-4aaa9d28b9fe
 [4]: https://www.wolframcloud.com/obj/302feeec-f17a-4aeb-85f7-16e0426b3408</description> <dc:creator>Ueta Tsuyoshi</dc:creator> <dc:date>2024-12-03T10:57:31Z</dc:date> </item> <item rdf:about="https://community.wolfram.com/groups/-/m/t/3315449"> <title>[WSG24] Daily Study Group: Introduction to Complex Analysis</title> <link>https://community.wolfram.com/groups/-/m/t/3315449</link> <description>A Wolfram U Daily Study Group on [&#034;Introduction to Complex Analysis&#034;][1] begins on November 11, 2024.
 
 Join me and a group of fellow learners to learn about the fundamentals of complex analysis using the powerful tools for symbolic computation and visualization in Wolfram Language. Our topics for the study group include elementary complex functions, the Cauchy-Riemann equations, complex integration, Cauchy&#039;s theorem and the residue theorem.
 
 No prior Wolfram Language experience is required.
 
 Please feel free to use this thread to collaborate and share ideas, materials and links to other resources with fellow learners.
 
 **Dates:** November 11-22, 2024
 
 &gt; **Register here:** https://wolfr.am/1qGinMguv
 
 ![Wolfram U banner image][2]
 
 
 [1]: https://www.wolfram.com/wolfram-u/courses/mathematics/introduction-to-complex-analysis/
 [2]: https://community.wolfram.com//c/portal/getImageAttachment?filename=banner.png&amp;userId=3315421</description> <dc:creator>Marco Saragnese</dc:creator> <dc:date>2024-11-06T14:35:16Z</dc:date> </item> <item rdf:about="https://community.wolfram.com/groups/-/m/t/3332704"> <title>Quantum graph models for transport in filamentary switching</title> <link>https://community.wolfram.com/groups/-/m/t/3332704</link> <description>![Quantum graph models for transport in filamentary switching][1]
 
 &amp;[Wolfram Notebook][2]
 
 
 [1]: https://community.wolfram.com//c/portal/getImageAttachment?filename=7775Main2.gif&amp;userId=20103
 [2]: https://www.wolframcloud.com/obj/3da18cce-a00b-47ce-9477-a11d19778f61</description> <dc:creator>Alison Antunes da Silva</dc:creator> <dc:date>2024-12-03T18:17:24Z</dc:date> </item> <item rdf:about="https://community.wolfram.com/groups/-/m/t/3331934"> <title>CurrencyConvert in version 14.1</title> <link>https://community.wolfram.com/groups/-/m/t/3331934</link> <description>Hello! I just upgraded Mathematica from v. 12.1 to 14.1, and I have a quite basic problem with currency conversion! Formerly, the code hereunder 
 
 Clear[&#034;Global`*&#034;];
 
 port = {&#034;NASDAQ:COST&#034;, &#034;NASDAQ:NFLX&#034;, &#034;NYSE:LMT&#034;, &#034;PA:SU&#034;, 
 &#034;NASDAQ:AMZN&#034;, &#034;PA:AM&#034;};
 EnClair = Map[FinancialData[#, &#034;Name&#034;] &amp;, port]
 début = DayRound[DatePlus[{-18, &#034;Month&#034;}], &#034;BusinessDay&#034;]
 Prix = CurrencyConvert[
 FinancialData[#, &#034;Price&#034;, {début, Date[]}, &#034;DateValue&#034;], 
 &#034;USDollars&#034;] &amp; /@ port; 
 \[Eta] = 0.9;
 Fractiles = Map[QuantityMagnitude@Quantile[#, \[Eta]] &amp;, Prix];
 Print@MapThread[
 DateListPlot[#1, Frame -&gt; True, Filling -&gt; #2, PlotRange -&gt; All, 
 PlotLabel -&gt; #3 &lt;&gt; &#034; ; \[Eta]=&#034; &lt;&gt; ToString@\[Eta]] &amp;, {Prix, 
 Fractiles, EnClair}];
 
 resulted in a plot of time series, but this doesn&#039;t work in v14, because &#034;Prix&#034; cannot be computed anymore (this is endless). What should I do?
 
 
 Best regards, Claude.</description> <dc:creator>Claude Mante</dc:creator> <dc:date>2024-12-03T10:46:27Z</dc:date> </item> <item rdf:about="https://community.wolfram.com/groups/-/m/t/3331904"> <title>A chain of Lucas cubes in right triangle</title> <link>https://community.wolfram.com/groups/-/m/t/3331904</link> <description>![ani][1]
 
 &amp;[Wolfram Notebook][2]
 
 
 [1]: https://community.wolfram.com//c/portal/getImageAttachment?filename=5691test.gif&amp;userId=23928
 [2]: https://www.wolframcloud.com/obj/06e8b2e4-e692-4fc8-9faa-c82761f8551e</description> <dc:creator>Shenghui Yang</dc:creator> <dc:date>2024-12-03T08:26:44Z</dc:date> </item> <item rdf:about="https://community.wolfram.com/groups/-/m/t/3326555"> <title>Trying to understand WolframKernel processes licensing</title> <link>https://community.wolfram.com/groups/-/m/t/3326555</link> <description>I&#039;m trying to understand how the licensing works with Mathematica 14.1 -- I look at my account info and it says this license has 2 controlling and 4 computing processes maximum. 
 
 So when I start up Mathematica on a macOS 15.1.1 system (Mac mini M2 Pro with 6 high performance cores and 4 efficiency cores) I see there are now two WolframKernel processes started when looking at the Activity Monitor window showing all processes on the system. 
 
 So I then created two pre-defined kernels in the Evaluation/KernelConfigurationOptions menu and named the kernels - kernel1 and kernel2. 
 
 I then created a new notebook with one line 
 
 PerfectNumber[22]
 
 which I then assign kernel1 to and then run it. 
 
 I then look at Activity Monitor and see another WolframKernel process has now started and is using 100% of the cpu/core it&#039;s been assigned to. 
 
 So the first question is why didn&#039;t one of the already existing WolframKernel processes start handling this notebook?? Exactly what could I have done differently to prevent the third WolframKernel process to have started and instead one of the already existing WolframKernel processes to be using a CPU core to run? Is there some way to find out which WolframKernel process is being used on a particular running Notebook?? 
 
 But, if I then click on the &#034;About Mathematica&#034; menu, I see all the info about Mathetica as expected, and then try and click on the &#034;Copy&#034; button to copy the license number to the paste buffer, but I get a popup error window about the number of licenses has been exceeded. But I thought the number of WolframKernel processes limit was 4 - so why the error??
 
 Have I exceeded the Controlling limit of 2 or the computing limit of 4? Are WolframKernel processes able to be both a controlling process and a computing process?? From the Activity Monitor window how can you differentiate between the two?
 
 What exactly does Mathemitica consider a &#034;controlling&#034; process and what is considered a &#034;computing&#034; process???
 
 I was hoping to be able to have four notebooks able to be running at the same time and each of them being assigned to a different core cpu processor. Is this not how things are supposed to work??
 
 Thanks...
 
 -bob</description> <dc:creator>Bob Freeman</dc:creator> <dc:date>2024-11-21T17:40:08Z</dc:date> </item> <item rdf:about="https://community.wolfram.com/groups/-/m/t/3330872"> <title>Source code of a Wolfram Demo</title> <link>https://community.wolfram.com/groups/-/m/t/3330872</link> <description>Using version 12.3.1.0. Getting the source code used to be dead simple. But something&#039;s changed. In the images included, all options that I can see (including both under source code!) lead to places with no source code in sight. Invitation to copy to clipboard is unhelpful because I don&#039;t even understand what the clipboard is, nor where to find it. Maybe someone can solve this for me.![dem1![\]\[1\]][1]
 
 
 ![enter image description here][2]
 
 [1]: https://community.wolfram.com//c/portal/getImageAttachment?filename=dem2.png&amp;userId=2664748
 
 [2]: https://community.wolfram.com//c/portal/getImageAttachment?filename=dem1.png&amp;userId=2664748</description> <dc:creator>Eric Wiebe</dc:creator> <dc:date>2024-11-30T22:27:54Z</dc:date> </item> <item rdf:about="https://community.wolfram.com/groups/-/m/t/3331281"> <title>Quantum Wakes: Bose-Einstein condensate under time-dependent perturbations</title> <link>https://community.wolfram.com/groups/-/m/t/3331281</link> <description>![Quantum Wakes: Bose-Einstein condensate under time-dependent perturbations][1]
 
 &amp;[Wolfram Notebook][2]
 
 
 [1]: https://community.wolfram.com//c/portal/getImageAttachment?filename=collage_BowTie_Circle_Line_Spiral.gif&amp;userId=20103
 [2]: https://www.wolframcloud.com/obj/8f89d43c-0e30-426e-bc89-4f71599db990</description> <dc:creator>Mohammad Bahrami</dc:creator> <dc:date>2024-12-02T05:51:37Z</dc:date> </item> <item rdf:about="https://community.wolfram.com/groups/-/m/t/3223670"> <title>Can someone help me with accessing my certification?</title> <link>https://community.wolfram.com/groups/-/m/t/3223670</link> <description>I have been asking same question over 3 days, and no one gave no response. How to get access to my certification? I did all task what was required in track your progress 
 Please do not ignore me i did send message through email, and still no response</description> <dc:creator>Daniyal Kozybak</dc:creator> <dc:date>2024-07-17T10:34:02Z</dc:date> </item> <item rdf:about="https://community.wolfram.com/groups/-/m/t/3331113"> <title>Time to extract vertex coordinates from a gGraph</title> <link>https://community.wolfram.com/groups/-/m/t/3331113</link> <description>I am making large graphs (&gt;400000 vertices) of modest density (6% possible edges). I am embedding them in 2d with the spring-electric embedding and need the coordinates. It runs, what appears to me to be quite slowly. Any thoughts. Note I would have embedded the example notebook, but it was too large. Note this is my first post, so apologies for errors in protocol. Thank you.
 
 ClearSystemCache[]
 
 Timing[g=RandomGraph[{400000,24000000}]]
 
 Timing[g=Graph[g, GraphLayout-&gt;&#034;SpringElectricalEmbedding&#034;];]
 
 Timing[vertexLocations=ResourceFunction[&#034;VertexCoordinateList&#034;][g];]
 
 Out[6]= {1.95313,Graph[Vertex count: 400000, Edge count: 24000000]}
 
 Out[7]= {0.,Null}
 
 Out[8]= {67.6563,Null}</description> <dc:creator>Robert Lipshutz</dc:creator> <dc:date>2024-11-30T16:45:54Z</dc:date> </item> <item rdf:about="https://community.wolfram.com/groups/-/m/t/142857"> <title>How to use tensors in Mathematica?</title> <link>https://community.wolfram.com/groups/-/m/t/142857</link> <description>Hello everybody, I am beginner in Mathematica. I would like to know how to use tensors in Mathematica in general relativity, i.e. when i have defined metric tensor, how to compute tensors that appear in Einstein and Maxwell equations and get exact form of both sides; lowering/uppering four-vectors, covariant derivate etc. Is it built in or is some package needed? Thank you for any answer.</description> <dc:creator>Ji?í Ryzner</dc:creator> <dc:date>2013-10-22T21:44:31Z</dc:date> </item> <item rdf:about="https://community.wolfram.com/groups/-/m/t/3190877"> <title>Cannot create an App ID in Wolfram Alpha</title> <link>https://community.wolfram.com/groups/-/m/t/3190877</link> <description>I am taking a tutorial that uses Wolframalpha&#039;s API. I created an account, and after creating the account, I went to the New App ID page, filled out the name and description and then selected the Simple API.
 
 Nothing happens. Any clue to what I am doing wrong?</description> <dc:creator>Edward Cheadle</dc:creator> <dc:date>2024-06-11T16:22:25Z</dc:date> </item> <item rdf:about="https://community.wolfram.com/groups/-/m/t/1052348"> <title>Calculating NMR-spectra with Wolfram Language</title> <link>https://community.wolfram.com/groups/-/m/t/1052348</link> <description>#Introduction
 
 Perhaps there are already Mma-Procedures to calculate NMR-spectra, but I did not do a literature research.
 
 I post a notebook to calculate NMR-Spectra of simple spin I = 1/2 systems.
 
 The notebook comes in two parts. 
 
 Part one uses a spin-product function approach, where the spin-product function a, a ,...b is used as e.g. phi [ 1, 1, ,...., -1 ]. 
 The Hamiltonian is constructed according to different mT-values and the spectrum is calculated.
 
 Part two uses the &#034;brute force&#034; approach where all operators are mapped unto matrices (Kronecker-Products of individual matrix-operators) in the total spin-space. So here products of operators are matrix-products (in part 1 they are functions of functions) .Having the Hamiltonian and its Eigensystem the spectrum is calculated.
 
 Note that the number of lines of even small systems are growing rapidly. So it may well be that there is not enough memory to cope with a system you would like to consider.
 
 If you omit giving numbers to frequencies and coupling-constants you may get pure theoretical results. That works fine for two spins, but already for three spins - although here you will still get the Hamiltonian - very large outputs are generated, especially in the Eigensystems, So you should avoid that.
 
 It seems to be not too complicated to modify the approach in part two to include spins with I &gt; 1/2.
 
 And certainly it is well possible to modify the code as to get an iterative procedure to fit data to spectra.
 
 I am aware that there are &#034;professional&#034; systems to do all this, but I just wanted to see how it could be done in Mathematica.
 #Part 1#
 Number of Spins
 
 nsp = 3;
 Input of Parameters
 
 freqs = {372.2, 364.4, 342, 6.083, 5.8};
 JJ = ( {
 {0, .91, 17.9, 1, 1, 1},
 {0, 0, 11.75, 1, 1, 1},
 {0, 0, 0, 1, 1, 1},
 {0, 0, 0, 0, 1, 1},
 {0, 0, 0, 0, 0, 1},
 {0, 0, 0, 0, 0, 0}
 } );
 Do[\[Nu][i] = freqs[[i]], {i, 1, nsp}];
 Do[J[i, k] = JJ[[i, k]], {i, 1, nsp - 1}, {k, i + 1, nsp}];
 
 Basevectors
 
 base = Apply[\[CurlyPhi], 
 IntegerDigits[#, 2, nsp] + 1 &amp; /@ Table[j, {j, 0, 2^nsp - 1}] /. 
 2 -&gt; -1, {1}]
 ![enter image description here][1]
 
 mT - Values
 
 mT = Table[-nsp/2 + j, {j, 0, nsp}]
 
 ![enter image description here][2]
 
 Number of lines in the spectrum ( = Sum[Binomial[nsp, k] Binomial[nsp, k + 1], {k, 0, nsp - 1}], because only transitions between states of different mT&#039;s give lines on non-zero intensity )
 
 numberoflines = Binomial[2 nsp, nsp - 1]
 
 &gt; 15
 
 Rule for scalar products
 
 rscp = {\[CurlyPhi][x__]^2 -&gt; 1, \[CurlyPhi][x__] \[CurlyPhi][y__] -&gt; 0}
 ![enter image description here][3]
 
 SpinOperators
 
 cs[a_, j_] := Module[{t}, t = a; b = t[[j]]; t[[j]] = -b; t]
 Ix[v_, j_] := v/2 /. \[CurlyPhi][x___] :&gt; \[CurlyPhi] @@ cs[{x}, j]
 Iy[v_, j_] := 
 I v/2 /. \[CurlyPhi][x___] :&gt; {x}[[j]] \[CurlyPhi] @@ cs[{x}, j]
 Iz[v_, j_] := v/2 /. \[CurlyPhi][x___] :&gt; {x}[[j]] \[CurlyPhi][x]
 
 Example
 
 {Ix[\[CurlyPhi][4], 1], Ix[\[CurlyPhi][-1], 1], Iy[\[CurlyPhi][5], 1],
 Iy[\[CurlyPhi][-1], 1], Iz[\[CurlyPhi][6], 1], 
 Iz[\[CurlyPhi][-1], 1]}
 ![enter image description here][7]
 
 Hamiltonian - Matrixelements Subscript[H, i,j] for (sub-)base b
 
 HH[b_, i_, j_] := (Sum[\[Nu][m] b[[j]] Iz[b[[i]], m], {m, 1, nsp}] + 
 Sum[J[m, k] b[[
 j]] (Ix[Ix[b[[i]], k], m] + Iy[Iy[b[[i]], k], m] + 
 Iz[Iz[b[[i]], k], m]), {m, 1, nsp - 1}, {k, m + 1, nsp}] // 
 Expand) /. rscp
 Example
 
 HH[base, 1, 1]
 
 &gt; 546.94
 
 HH[base, 1, 2]
 
 &gt; 0
 
 HH[base, 3, 5]
 
 &gt; 0.455
 
 Spinfunctions according to mT - value 
 
 wf = Function[x, Select[base, Total[List @@ #] == 2 x &amp;]] /@ mT
 ![enter image description here][8]
 
 Hamilton - Submatrices
 
 HSM[j_] := (nn = Length[wf[[j]]]; 
 Table[HH[wf[[j]], m, n], {m, 1, nn}, {n, 1, nn}])
 HSM[2];
 % // MatrixForm
 ![enter image description here][9]
 
 HSM[2] /. {\[Nu][10] -&gt; -\[Nu], \[Nu][11] -&gt; 0, \[Nu][12] -&gt; \[Nu], 
 J[1, 2] -&gt; J, J[1, 3] -&gt; J, J[2, 3] -&gt; J};
 % // MatrixForm
 ![enter image description here][13]
 
 Get Eigenstates \[Congruent] all sets { freq, eigenvector } for different spin-states (mT values)
 
 frevec[n_] := Module[{es},
 es = Eigensystem[HSM[n]];
 {#[[1]], #[[2]].wf[[n]]} &amp; /@ Transpose[es]
 ]
 eigenstates = frevec /@ Range[nsp + 1]
 
 ![enter image description here][14]
 
 Operator for calculating relative intensities
 
 IOP[x_] := Sum[Ix[x, n], {n, 1, nsp}]
 Calculating a spectral line = difference of eigenvalues and intensity
 
 line[a_, b_] := Module[{},
 freq = Abs[a[[1]] - b[[1]]];
 m2 = (Expand[a[[2]] IOP[b[[2]]]] /. rscp)^2;
 {freq, Sqrt[m2]}]
 Lorentzfunction
 
 LF[x_, x0_, a_, h_] := Module[{},
 If[h == 0, h = 1];
 1/Sqrt[Pi] (a h/2)/(h^2/4 + Pi (x - x0)^2)]
 Calculating the spectrum
 
 spec = Table[0, {numberoflines}];
 nL = 0;
 Do[
 lk = Length[eigenstates[[i]]];
 lk1 = Length[eigenstates[[i + 1]]];
 Do[
 Do[
 nL = nL + 1;
 spec[[nL]] = line[eigenstates[[i, m]], eigenstates[[i + 1, n ]]],
 {n, 1, lk1}
 ],
 {m, 1, lk}
 ],
 {i, 1, Length[eigenstates] - 1}];
 normalizer = Max[Transpose[spec][[2]]];
 bb = {.95 Min[Transpose[spec][[1]]], 1.05 Max[Transpose[spec][[1]]]};
 spec = {#[[1]], #[[2]]/normalizer} &amp; /@ spec;
 spec
 pl1 = ListPlot[spec, Filling -&gt; Axis]
 ![enter image description here][15]
 
 Show the spectrum with lines
 
 pl2 = Plot[
 Plus @@ (LF[x, #[[1]], #[[2]], 1.5] &amp; /@ spec), {x, bb[[1]], 
 bb[[2]]}, PlotRange -&gt; All, AxesOrigin -&gt; {320, 0}]
 ![enter image description here][16]
 
 For some physical reason spectra are recorded so that frequencies grow from right to left. So the plot is reversed and compared to the experimental spectrum ( see http://www.users.csbsju.edu/~frioux/nmr/Speclab4.htm ) which is given below the plot.
 
 pl3 = Plot[
 Plus @@ (LF[-x, #[[1]], #[[2]], 1.5] &amp; /@ spec), {x, -bb[[2]], -bb[[
 1]]}, PlotRange -&gt; All]
 ![enter image description here][17]
 #Part 2#
 
 nsp = 3;
 Input of Parameters
 
 freqs = {372.2, 364.4, 342, 6.083, 5.8};
 JJ = ( {
 {0, .91, 17.9, 1, 1, 1},
 {0, 0, 11.75, 1, 1, 1},
 {0, 0, 0, 1, 1, 1},
 {0, 0, 0, 0, 1, 1},
 {0, 0, 0, 0, 0, 1},
 {0, 0, 0, 0, 0, 0}
 } );
 Do[\[Nu][i] = freqs[[i]], {i, 1, nsp}];
 Do[J[i, k] = JJ[[i, k]], {i, 1, nsp - 1}, {k, i + 1, nsp}];
 number of lines to be expected and dimension ot (total) spin - space (at least for spin 1/2 )
 
 numberoflines = Binomial[2 nsp, nsp - 1]
 dimspsp = 2^nsp
 
 &gt; 15
 
 &gt; 8
 
 spin operators for spin I = 1/2
 
 ix = ( { {0, 1}, {1, 0} } )/2;
 iy = ( { {0, -I}, {I, 0} } )/2;
 iz = ( {{1, 0}, {0, -1} } )/2;
 
 this function constructs the spin operator of particle j as matrix in the spin space of n particles 
 
 Op[op_, n_, j_] := Module[{x, m},
 x = Join[Table[{{1, 0}, {0, 1}}, {j - 1}], {op}, 
 Table[{{1, 0}, {0, 1}}, {n - j}]];
 m = SparseArray[KroneckerProduct[Sequence @@ x]]
 ]
 oIx[j_] := Op[ix, nsp, j]
 oIy[j_] := Op[iy, nsp, j]
 oIz[j_] := Op[iz, nsp, j]
 
 Hamiltonian
 
 HH = \!\(
 \*UnderoverscriptBox[\(\[Sum]\), \(i = 1\), \(nsp\)]\(\[Nu][i] oIz[
 i]\)\) + \!\(
 \*UnderoverscriptBox[\(\[Sum]\), \(i = 1\), \(nsp - 1\)]\(
 \*UnderoverscriptBox[\(\[Sum]\), \(j = i + 1\), \(nsp\)]J[i, 
 j] \((oIx[i] . oIx[j] + oIy[i] . oIy[j] + oIz[i] . oIz[j])\)\)\)
 
 &gt; SparseArray[SequenceForm[&#034;&lt;&#034;, 32, &#034;&gt;&#034;], {8, 8}]
 
 Eigensystem for the Hamilton - Operator
 
 est = Transpose[Eigensystem[HH]]
 ![enter image description here][18]
 
 Intensity operator
 
 IOP1 = \!\(
 \*UnderoverscriptBox[\(\[Sum]\), \(j = 1\), \(nsp\)]\(oIx[j]\)\)
 
 &gt; SparseArray[SequenceForm[&#034;&lt;&#034;, 24, &#034;&gt;&#034;], {8, 8}]
 
 line1[a_, b_] := Module[{},
 freq = Abs[a[[1]] - b[[1]]];
 m2 = (a[[2]].IOP1.b[[2]])^2;
 {freq, Sqrt[m2]}]
 
 Calculate spectrum, show it and display result from part 1
 
 spec1 = Table[0, {Binomial[dimspsp, 2]}];
 nL = 0;
 Do[
 Do[
 nL = nL + 1;
 spec1[[nL]] = line1[est[[u]], est[[v]]],
 {u, v + 1, dimspsp}
 ],
 {v, 1, dimspsp - 1}
 ]
 spec1 = Select[spec1, #[[2]] &gt; 0. &amp;];
 normalizer = Max[Transpose[spec1][[2]]];
 bb = {.95 Min[Transpose[spec][[1]]], 1.05 Max[Transpose[spec][[1]]]};
 spec1 = {#[[1]], #[[2]]/normalizer} &amp; /@ spec1;
 spec1
 ListPlot[spec1, Filling -&gt; Axis, FillingStyle -&gt; Directive[Red, Thick]]
 Show[pl1]
 ![enter image description here][19]
 
 Plot the spectrum and compare with the result of the 1 st part
 
 pl4 = Plot[
 Plus @@ (LF[x, #[[1]], #[[2]], 1.5] &amp; /@ spec1), {x, bb[[1]], 
 bb[[2]]}, PlotRange -&gt; All, PlotStyle -&gt; Red]
 Show[pl2]
 ![enter image description here][20]
 
 
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 [20]: http://community.wolfram.com//c/portal/getImageAttachment?filename=ScreenShot2017-04-25at16.55.25.png&amp;userId=95400</description> <dc:creator>Hans Dolhaine</dc:creator> <dc:date>2017-04-04T08:36:27Z</dc:date> </item> <item rdf:about="https://community.wolfram.com/groups/-/m/t/1541234"> <title>Any trial for RBF-FD method? (A method for PDE on irregular region)</title> <link>https://community.wolfram.com/groups/-/m/t/1541234</link> <description>Today I come across the homepage of 
 [Bengt Fornberg](http://amath.colorado.edu/faculty/fornberg/) (A guy who is frequently mentioned in the [document of method of lines](https://reference.wolfram.com/language/tutorial/NDSolveMethodOfLines.html)) and notice he seems to have been promoting a _radial basis function generated finite differences (RBF-FD) method_ for quite a while. The method, which is said to be suitable for irregular region and strongly related to finite difference method, looks interesting to me. So I wonder if there&#039;s any ready-made package or trial for this method using _Mathematica_? A quick search doesn&#039;t show anything interesting.</description> <dc:creator>xzczd </dc:creator> <dc:date>2018-11-02T01:59:24Z</dc:date> </item> <item rdf:about="https://community.wolfram.com/groups/-/m/t/3331233"> <title>Step-by-step using API</title> <link>https://community.wolfram.com/groups/-/m/t/3331233</link> <description>Hello everyone, 
 Thanks for taking your time to read my post.
 
 I&#039;m using the following API, but it no longer provides a step-by-step solution as it did previously. A few days ago, the step-by-step breakdown stopped appearing in the response.
 
 Here is the API query I&#039;m using: https://api.wolframalpha.com/v2/query?appid=MYAPI_ID&amp;input=(3x-5)(6x+16)&amp;podstate=Step-by-step+solution&amp;output=json&amp;mag=2
 
 I always include &#034;podstate=Step-by-step solution&#034; so that i get the step by stem solution for my math question. However, recently, the step by step solution stopped showing in the api output result.
 
 Could you help me understand why this is happening and how i can resolve it?</description> <dc:creator>Ahmed Ahmed</dc:creator> <dc:date>2024-12-01T06:19:29Z</dc:date> </item> <item rdf:about="https://community.wolfram.com/groups/-/m/t/3331019"> <title>Define two lists with a correlation of -1</title> <link>https://community.wolfram.com/groups/-/m/t/3331019</link> <description>Hi,
 
 How do I define two lists with a correlation of -1 (r=-1)?
 Many thanks for your time.
 Alex
 
 In[19]:= data = {4, 10, 50}
 
 Out[19]= {4, 10, 50}
 
 In[24]:= data1 = 1/data
 
 Out[24]= {1/4, 1/10, 1/50}
 
 In[23]:= Correlation[data, data1]
 
 Out[23]= -0.83795</description> <dc:creator>Alex Teymouri</dc:creator> <dc:date>2024-11-30T13:19:21Z</dc:date> </item> <item rdf:about="https://community.wolfram.com/groups/-/m/t/3330242"> <title>Jacobian matrix of two functions</title> <link>https://community.wolfram.com/groups/-/m/t/3330242</link> <description>Greetings -- 
 
 Apologies if this is posted to the wrong forum. Have been using Maple and Maxima for 20+ years, and have only recently started using Mathematica (v. 14). Having a heck of a time getting Mathematica to do what is trivial in either Maple or Maxima (not a slam on Mathematica - just an honest statement of where I am on the learning curve). Simple example: 2 equations in 2 unknowns (say, x1 and x2). Want to derive the Jacobian of these equations wrt x1 and x2, and print said Jacobian in matrix form. This is basically 3-4 lines in Maple or Maxima. But in Mathematica? Here is what I&#039;ve tried. 
 
 (*Define the functions*)
 f1[x1_, x2_] := x1^2 + x2^2
 f2[x1_, x2_] := x1 x2
 
 (*Compute the Jacobian matrix with respect to x1 and x2*)
 jacobian = JacobianMatrix[{f1[x1, x2], f2[x1, x2]}, {x1, x2}]
 
 (*Display the Jacobian matrix*) 
 MatrixForm[jacobian]
 
 But, the final command to display the Jacobian returns nada of any use. It simply returns the following:
 
 JacobianMatrix[{x1^2+x2^2,x1x2},{x1,x2}]
 
 So, how the heck do I get Mathematica to output what Maple (for example - same code more or less in Maxima) outputs in one command, looking like what I expect (i.e., the formatted Jacobian matrix, below):
 
 ![enter image description here][1]
 
 [1]: https://community.wolfram.com//c/portal/getImageAttachment?filename=Screenshot2024-11-28135520.jpg&amp;userId=3330227
 
 Many thanks in advance. I was warned the learning curve for Mathematica was appreciably steeper than (say) Maple, but I wasn&#039;t expected even something this simple to stump me quite so soon.</description> <dc:creator>Evan Cooch</dc:creator> <dc:date>2024-11-28T18:58:23Z</dc:date> </item> <item rdf:about="https://community.wolfram.com/groups/-/m/t/3330289"> <title>Opening & displaying the contents of a notebook within a notebook</title> <link>https://community.wolfram.com/groups/-/m/t/3330289</link> <description>Hi;
 
 In the code sample below, I am trying to open and display the contents of a notebook named &#034;StereographicProjection&#034; from within an open notebook with both notebooks being in the same directory. My thinking is that with the exact same code in an existing notebook, I should be able to access that information without needing to duplicate or copy it into another notebook.
 
 In[1]:= NotebookOpen[&#034;StereographicProjection&#034;]
 
 Out[1]= $Failed
 
 Thanks,
 
 Mitch Sandlin</description> <dc:creator>Mitchell Sandlin</dc:creator> <dc:date>2024-11-29T18:38:19Z</dc:date> </item> <item rdf:about="https://community.wolfram.com/groups/-/m/t/3330805"> <title>Mean-field elastic moduli of a three-dimensional, cell-based vertex model</title> <link>https://community.wolfram.com/groups/-/m/t/3330805</link> <description>![Mean-field elastic moduli of a three-dimensional, cell-based vertex model][1]
 
 &amp;[Wolfram Notebook][2]
 
 
 [1]: https://community.wolfram.com//c/portal/getImageAttachment?filename=Main29112024.png&amp;userId=20103
 [2]: https://www.wolframcloud.com/obj/a34c6a9d-97c1-427b-a52f-4f37112632f6</description> <dc:creator>Kyung Eun Kim</dc:creator> <dc:date>2024-11-29T20:06:58Z</dc:date> </item> <item rdf:about="https://community.wolfram.com/groups/-/m/t/3330200"> <title>Errors in code for fission yield analysis across different patterns</title> <link>https://community.wolfram.com/groups/-/m/t/3330200</link> <description>I am working on a Mathematica program to analyze fission yield data of U-235. The program calculates results for 5 different patterns based on neutron incident energies. While the calculation works correctly for pattern = 3, it produces errors for other patterns such as pattern = 1.
 
 Key errors include:
 
 Union::normal: Nonatomic expression expected at position 1 in Union[vars12]. 
 Part::take: Cannot take positions 6 through 42 in datax2. 
 FindMinimum::vloc: The variable Union[vars12] cannot be localized so that it can be assigned to numerical values.
 
 The result Reff becomes undefined (Indeterminate) or infinite. 
 What might be causing these issues, and how can I modify the code to ensure correct calculations for all patterns?
 
 
 Note: 
 
 When running the program on Mathematica version 11.3 or later, changes in the `FindMinimum` function result in errors even for the previously working pattern. Therefore, I kindly request that this issue be evaluated on Mathematica version 11.2.</description> <dc:creator>Hirokazu Maruyama</dc:creator> <dc:date>2024-11-28T14:32:27Z</dc:date> </item> <item rdf:about="https://community.wolfram.com/groups/-/m/t/3328982"> <title>Abort dynamic evaluation error when I open a txt by Mathematica</title> <link>https://community.wolfram.com/groups/-/m/t/3328982</link> <description>&amp;[Wolfram Notebook][1]
 
 
 [1]: https://www.wolframcloud.com/obj/c36643fa-2c60-4b55-8c2b-080e6e90b5d1</description> <dc:creator>Martin Xia</dc:creator> <dc:date>2024-11-27T05:51:48Z</dc:date> </item> <item rdf:about="https://community.wolfram.com/groups/-/m/t/3325627"> <title>How to specify incremental constraint in LongestOrderedSequence?</title> <link>https://community.wolfram.com/groups/-/m/t/3325627</link> <description>I&#039;m looking for the longest ordered subsequences of integer pairs with specific incremental constraints. In these examples, I&#039;d like the last value of each pair to be 1 less than the first value of the next pair. So far I&#039;ve not discovered what pattern to specify.
 
 Example 1.
 
 LongestOrderedSequence[{{4, 5}, {7, 8}, {11, 12}, {13, 14}, {15, 16},
 {65, 66}}, (#2[[1]] - #1[[2]] == 1) &amp;]
 
 {{4, 5}}
 I was hoping for
 
 {{11, 12}, {13, 14}, {15, 16}}
 
 Example 2.
 
 LongestOrderedSequence[{{2, 4}, {6, 8}, {9, 11}, {12, 14},
 {98, 100}}, (#2[[1]] - #1[[2]] == 1) &amp;]
 
 {{2, 4}}
 I was hoping for
 
 {{6, 8}, {9, 11}, {12, 14}}</description> <dc:creator>Richard Frost</dc:creator> <dc:date>2024-11-21T00:43:42Z</dc:date> </item> <item rdf:about="https://community.wolfram.com/groups/-/m/t/3329609"> <title>Changing how EngineeringForm output is being displayed</title> <link>https://community.wolfram.com/groups/-/m/t/3329609</link> <description>&amp;[Wolfram Notebook][1]
 
 
 [1]: https://www.wolframcloud.com/obj/811b53c8-932f-4322-bf3f-51e6d2b18c54</description> <dc:creator>Martin Xia</dc:creator> <dc:date>2024-11-27T08:34:02Z</dc:date> </item> <item rdf:about="https://community.wolfram.com/groups/-/m/t/3330117"> <title>Wolfram Alpha step-by-step using API</title> <link>https://community.wolfram.com/groups/-/m/t/3330117</link> <description>Hello all, 
 
 Thank you for taking the time to read my post, I have wasted hours and hours trying to figure this out!
 
 If anybody can possibly tell me **how in the world I can call the API as well as have it return the &#034;step-by-step&#034; instructions for each query** (if available of course) I would be beyond grateful!!! I hope I didn&#039;t just waste 60 bucks for nothing! 
 
 I have been messing around with it for probably over 30-40 hours and cannot get any of the useful info returned, such as: podstate, step-by-step solution, etc. I can get the result returned, but have messed with many of the various &#034;Parameters&#034; to return what I need or want it to, and have had no luck. I can get it to return most items, but not the pod that has access to, or can see, the &#034;step-by-step&#034; solution. Please help!!
 
 I am a pro member, I actually got the pro membership specifically for this reason. I use wolfram in OpenAI and I love it, and now I want to integrate it into my &#034;tutor&#034; workflow to study for various math exams, tests, among many other mathematics applied use cases. 
 
 If mathmatica can call the API for step by step, why wouldn&#039;t the standard WolframAlpha API? I have tried many of the API&#039;s, and the only two that do somewhat well are the &#034;converstaional&#034; and the &#034;full results&#034; but neither is returning anything that has to do with the &#034;step-by-step&#034; solution, nor any pods that can see or return any info regarding these pods/subpods.
 
 Just so you can all see, this is an example of one of the **many** http get requests I have made and sent to the API. Dont be too critical on it, as I am merely trying to tinker to get it to return the output that I am in desperate need of! 
 
 Thank you all again for your time and I look very very forward to reading any responses I may get. **I am very eager to put this project to rest!**
 
 
 HTTP Request Example:
 
 // Define the API endpoint and parameters
 const apiUrl = &#039;http://api.wolframalpha.com/v2/query&#039;;
 const appid = &#039;MY_APP_ID&#039;;
 const input = `${$json.message.content.equation} step-by-step`;
 const format = &#039;plaintext,mathml&#039;;
 const output = &#039;JSON&#039;;
 
 // Construct the full URL with query parameters
 const url = `${apiUrl}?appid=${appid}&amp;input=${encodeURIComponent(input)}&amp;format=${format}&amp;output=${output}`;
 
 try {
 // Perform the HTTP GET request
 const response = await this.helpers.httpRequest({
 method: &#039;GET&#039;,
 url: url,
 json: true,
 });
 
 return [
 {
 json: response,
 },
 ];
 } catch (error) {
 // Handle any errors that occur during the request
 throw new Error(`HTTP Request failed: ${error.message}`);
 }</description> <dc:creator>Christropher Chausse</dc:creator> <dc:date>2024-11-28T03:37:01Z</dc:date> </item> <item rdf:about="https://community.wolfram.com/groups/-/m/t/3329526"> <title>Dataset output is not as expected</title> <link>https://community.wolfram.com/groups/-/m/t/3329526</link> <description>Hi Folks, Not sure if this will format correctly, but. Mathematica newbie here. Given :
 
 data = &lt;|&#034;on&#034; -&gt; &lt;|&#034;A&#034; -&gt; &lt;|Length -&gt; 19, Total -&gt; 8|&gt;, 
 &#034;B&#034; -&gt; &lt;|Length -&gt; 19, Total -&gt; 8|&gt;, 
 &#034;C&#034; -&gt; &lt;|Length -&gt; 7, Total -&gt; 0|&gt;|&gt;, 
 &#034;off&#034; -&gt; &lt;|&#034;A&#034; -&gt; &lt;|Length -&gt; 9, Total -&gt; 42|&gt;, 
 &#034;B&#034; -&gt; &lt;|Length -&gt; 7, Total -&gt; 11|&gt;, 
 &#034;C&#034; -&gt; &lt;|Length -&gt; 9, Total -&gt; 27|&gt;|&gt;|&gt;;
 
 (*Extract the columns (A,B,C,...)*)
 columns = Keys[data[&#034;on&#034;]];
 
 (*Extract the data for &#034;on&#034; and &#034;off&#034;*)
 extractRowData[status_] := 
 Map[Function[
 column, {data[status][column][Length], 
 data[status][column][Total]}], columns];
 
 (*Construct the dataset with hierarchical columns*)
 finalDataset = Dataset[
 Association[
 &#034;on&#034; -&gt;
 AssociationThread[columns, extractRowData[&#034;on&#034;]],
 &#034;off&#034; -&gt;
 AssociationThread[columns, extractRowData[&#034;off&#034;]]]][All,
 AssociationThread[&#034;group&#034;,
 Map[Function[column,
 Association[&#034;Length&#034; -&gt; #[[1]], 
 &#034;Total&#034; -&gt; #[[2]]]], #1] &amp; /@ # &amp;]]
 
 The finalDataset duplicates the Length, Total values row such that there are two row for on/off where there should be only one row for on/off. Looking at the finalDataset via //Normal show that the Length,Total element bit is being duplicated, but I cannot track where this happens though I suspect something in my &#034;&amp;/@#&amp;&#034; bit but its confusing me presently. Any help much appreciated. Thanks</description> <dc:creator>Karl Fraser</dc:creator> <dc:date>2024-11-27T20:33:11Z</dc:date> </item> <item rdf:about="https://community.wolfram.com/groups/-/m/t/3329673"> <title>3D printing of solar coronal flux tubes: Wang-Sheeley-Arge model</title> <link>https://community.wolfram.com/groups/-/m/t/3329673</link> <description>![3D printing of solar coronal flux tubes: Wang-Sheeley-Arge model][1]
 
 &amp;[Wolfram Notebook][2]
 
 
 [1]: https://community.wolfram.com//c/portal/getImageAttachment?filename=SolarCoronaFluxTubesMoviess.gif&amp;userId=20103
 [2]: https://www.wolframcloud.com/obj/24d6c65c-35e5-4c0d-a5aa-fcefe1d7cac2</description> <dc:creator>Gilmer Allen Gary</dc:creator> <dc:date>2024-11-27T18:57:32Z</dc:date> </item> <item rdf:about="https://community.wolfram.com/groups/-/m/t/3329460"> <title>Considerations for numerically solving a set of differential equation</title> <link>https://community.wolfram.com/groups/-/m/t/3329460</link> <description>Hi Guys
 
 Please refer the below differential equations which I have derived.
 Each equation presents acceleration terms of the other equation.
 Would one go about solving such a system?
 ![Set of differential equations][1]
 
 
 [1]: https://community.wolfram.com//c/portal/getImageAttachment?filename=7003Capture.JPG&amp;userId=2379780</description> <dc:creator>Mishal Mohanlal</dc:creator> <dc:date>2024-11-27T13:46:09Z</dc:date> </item> <item rdf:about="https://community.wolfram.com/groups/-/m/t/3328657"> <title>2500 double pendulums. Varying initial angles: domains of chaos and order.</title> <link>https://community.wolfram.com/groups/-/m/t/3328657</link> <description>![2500 double pendulums. Varying initial angles: domains of chaos and order.][1]
 
 &amp;[Wolfram Notebook][2]
 
 
 [1]: https://community.wolfram.com//c/portal/getImageAttachment?filename=ezS.gif&amp;userId=11733
 [2]: https://www.wolframcloud.com/obj/1fd57106-8c90-4e68-9418-fb72649f8225</description> <dc:creator>Vitaliy Kaurov</dc:creator> <dc:date>2024-11-26T05:41:17Z</dc:date> </item> <item rdf:about="https://community.wolfram.com/groups/-/m/t/3329303"> <title>Assigning data lists to variables from Python output</title> <link>https://community.wolfram.com/groups/-/m/t/3329303</link> <description>this is the python output in my wolfram notebook after i applied Normal[data]:
 
 &lt;|0 -&gt; &lt;|&#034;x&#034; -&gt; 0., &#034;y&#034; -&gt; 0.|&gt;, 
 1 -&gt; &lt;|&#034;x&#034; -&gt; 0.526316, &#034;y&#034; -&gt; 0.277008|&gt;, 
 2 -&gt; &lt;|&#034;x&#034; -&gt; 1.05263, &#034;y&#034; -&gt; 1.10803|&gt;, 
 3 -&gt; &lt;|&#034;x&#034; -&gt; 1.57895, &#034;y&#034; -&gt; 2.49307|&gt;, 
 4 -&gt; &lt;|&#034;x&#034; -&gt; 2.10526, &#034;y&#034; -&gt; 4.43213|&gt;, 
 5 -&gt; &lt;|&#034;x&#034; -&gt; 2.63158, &#034;y&#034; -&gt; 6.92521|&gt;, 
 6 -&gt; &lt;|&#034;x&#034; -&gt; 3.15789, &#034;y&#034; -&gt; 9.9723|&gt;, 
 7 -&gt; &lt;|&#034;x&#034; -&gt; 3.68421, &#034;y&#034; -&gt; 13.5734|&gt;, 
 8 -&gt; &lt;|&#034;x&#034; -&gt; 4.21053, &#034;y&#034; -&gt; 17.7285|&gt;, 
 9 -&gt; &lt;|&#034;x&#034; -&gt; 4.73684, &#034;y&#034; -&gt; 22.4377|&gt;, 
 10 -&gt; &lt;|&#034;x&#034; -&gt; 5.26316, &#034;y&#034; -&gt; 27.7008|&gt;, 
 11 -&gt; &lt;|&#034;x&#034; -&gt; 5.78947, &#034;y&#034; -&gt; 33.518|&gt;, 
 12 -&gt; &lt;|&#034;x&#034; -&gt; 6.31579, &#034;y&#034; -&gt; 39.8892|&gt;, 
 13 -&gt; &lt;|&#034;x&#034; -&gt; 6.84211, &#034;y&#034; -&gt; 46.8144|&gt;, 
 14 -&gt; &lt;|&#034;x&#034; -&gt; 7.36842, &#034;y&#034; -&gt; 54.2936|&gt;, 
 15 -&gt; &lt;|&#034;x&#034; -&gt; 7.89474, &#034;y&#034; -&gt; 62.3269|&gt;, 
 16 -&gt; &lt;|&#034;x&#034; -&gt; 8.42105, &#034;y&#034; -&gt; 70.9141|&gt;, 
 17 -&gt; &lt;|&#034;x&#034; -&gt; 8.94737, &#034;y&#034; -&gt; 80.0554|&gt;, 
 18 -&gt; &lt;|&#034;x&#034; -&gt; 9.47368, &#034;y&#034; -&gt; 89.7507|&gt;, 
 19 -&gt; &lt;|&#034;x&#034; -&gt; 10., &#034;y&#034; -&gt; 100.|&gt;|&gt;
 
 how can i store x and y values?</description> <dc:creator>JE π</dc:creator> <dc:date>2024-11-26T21:59:54Z</dc:date> </item> <item rdf:about="https://community.wolfram.com/groups/-/m/t/3325521"> <title>Discover More from our Wolfram Technology Conference 2024</title> <link>https://community.wolfram.com/groups/-/m/t/3325521</link> <description>New series on the [Wolfram R&amp;D YouTube channel][1]! 
 
 Missed the Wolfram Technology Conference? This series features videos that bring the best of WTC 2024! This week, the featured videos will be focusing on System Modeler. 
 
 Check out the first video on [Electric Circuits here][2]. 
 
 
 Stay tuned for the latest updates and exciting content -- subscribe now and become a part of our community!
 
 
 [![enter image description here][3]][2]
 
 
 [1]: https://www.youtube.com/playlist?list=PLdIcYTEZ4S8RnaOQl8h16Vg6RnQ0KiYsE
 [2]: https://youtu.be/EnWBVz9pQrM
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 &amp;[Wolfram Notebook][2]
 
 
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 [1]: https://community.wolfram.com//c/portal/getImageAttachment?filename=Screenshot%28376%29.png&amp;userId=3324898</description> <dc:creator>Antam Gill</dc:creator> <dc:date>2024-11-20T15:40:07Z</dc:date> </item> <item rdf:about="https://community.wolfram.com/groups/-/m/t/3328280"> <title>Circular reference in differential equations</title> <link>https://community.wolfram.com/groups/-/m/t/3328280</link> <description>Hi Guys
 
 Please refer to the below code. Each differential equation presents acceleration terms from the other 2 differential equations, I assume that this would be a circular reference. I cannot get the system to solve, can anyone please guide me as to what is wrong?
 
 from wolframclient.evaluation import WolframLanguageSession
 from wolframclient.language import wl, wlexpr
 import matplotlib.pyplot as plt
 import numpy as np
 
 session = WolframLanguageSession()
 
 wolfram_code = &#034;&#034;&#034;
 
 IC = {x[0] == 0, theta[0] == 0, phi[0] == 0, x&#039;[0] == 0, theta&#039;[0] == 0, phi&#039;[0] == 0};
 
 
 
 
 
 l = 1;
 m = 1000;
 r = 0.1;
 g = 9.81;
 
 Kt = 1000;
 Kb = 10000;
 Ib = 1000;
 It = 1000;
 
 C1 = 0;
 C2 = 0;
 C3 = 0;
 
 
 
 one = -0.5*m*(2*l*theta&#039;&#039;[t]*Cos[theta[t]]-2*l*theta&#039;[t]*Sin[theta[t]]+2*r*phi&#039;&#039;[t]*Sin[phi[t]]+2*r*phi&#039;[t]^2*Cos[theta[t]])-C1*x&#039;[t];
 
 
 two_part_one = -0.5*m*(2*l*x&#039;&#039;[t]*Cos[theta[t]]-2*l*x&#039;[t]*theta&#039;[t]*Sin[theta[t]]+2*r*phi&#039;&#039;[t]*Cos[theta[t]]*Sin[theta[t]]+2*r*l*theta&#039;[t]*phi&#039;[t]*Cos[2*theta[t]]);
 two_part_two = 0.5*m*(-2*l*theta&#039;[t]*x&#039;[t]*Sin[theta[t]]+2*r*l*theta&#039;[t]*phi&#039;[t]*Cos[2*theta[t]])+Kb*theta[t]+m*g*l*Sin[theta[t]]-C2*theta&#039;[t];
 two = two_part_one+two_part_two;
 
 three_part_one = -0.5*m*(m*r*x&#039;&#039;[t]*Sin[theta[t]]+2*r*x&#039;[t]*theta&#039;[t]*Cos[theta[t]]+2*r*l*theta&#039;&#039;[t]*Cos[theta[t]]*Sin[theta[t]]+2*r*l*theta&#039;[t]^2*Cos[theta[t]]);
 three_part_two = 0.5*m*(-2*r*phi&#039;[t]*x&#039;[t]*Cos[phi[t]])-Kt*phi[t]-C3*phi&#039;[t];
 three = three_part_one+three_part_two; 
 
 S = NDSolve[{x&#039;&#039;[t] == one/m, theta&#039;&#039;[t] == two/(m*l^2+2*Ib), phi&#039;&#039;[t] == three/(m*r+2*It),IC},{x,theta,phi},{t,0,10}]
 
 
 
 &#034;&#034;&#034;
 
 # Evaluate the Wolfram code
 result = session.evaluate(wlexpr(wolfram_code))
 
 # Terminate the Wolfram session
 session.terminate()</description> <dc:creator>Mishal Mohanlal</dc:creator> <dc:date>2024-11-26T12:22:08Z</dc:date> </item> <item rdf:about="https://community.wolfram.com/groups/-/m/t/3328263"> <title>A problem of nested custom functions</title> <link>https://community.wolfram.com/groups/-/m/t/3328263</link> <description>&amp;[Wolfram Notebook][1]
 
 
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 &amp;[Wolfram Notebook][2]
 
 
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 [2]: https://www.wolframcloud.com/obj/6f5b2224-0792-4d8d-84a1-8bce5125c0f4</description> <dc:creator>Catalin Popescu</dc:creator> <dc:date>2024-11-24T23:40:07Z</dc:date> </item> <item rdf:about="https://community.wolfram.com/groups/-/m/t/3328470"> <title>Curvatura: a library for tensor calculus and dynamical evolution in general relativity</title> <link>https://community.wolfram.com/groups/-/m/t/3328470</link> <description>&amp;[Wolfram Notebook][1]
 
 
 [1]: https://www.wolframcloud.com/obj/6081d395-4306-45f3-94de-bc2f11de272a</description> <dc:creator>Andrea Palessandro</dc:creator> <dc:date>2024-11-25T20:13:51Z</dc:date> </item> <item rdf:about="https://community.wolfram.com/groups/-/m/t/3327619"> <title>Interfacing with SmilesDB in Wolfram</title> <link>https://community.wolfram.com/groups/-/m/t/3327619</link> <description>![enter image description here][1]
 
 &amp;[Wolfram Notebook][2]
 
 
 [1]: https://community.wolfram.com//c/portal/getImageAttachment?filename=68747470733a2f2f692e696d6775722e636f6d2f5a6d73345648732e706e67.png&amp;userId=3211209
 [2]: https://www.wolframcloud.com/obj/bef2437b-84a1-47cd-8075-1398b9de8be1</description> <dc:creator>William Choi-Kim</dc:creator> <dc:date>2024-11-24T21:06:24Z</dc:date> </item> <item rdf:about="https://community.wolfram.com/groups/-/m/t/3327833"> <title>Magnetochiral charge pumping due to charge trapping and skin effects in CISS</title> <link>https://community.wolfram.com/groups/-/m/t/3327833</link> <description>![Magnetochiral Charge Pumping due to Charge Trapping and Skin Effects in Chirality-Induced Spin Selectivity][1]
 
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 x&#039;&#039;[t] + t x&#039;[t] + x[t] = z[t], y&#039;&#039;[t] + y&#039;[t] + y[t] = 0
 
 and z&#039;&#039;[t] + z&#039;[t] +z[t] = 0 analytically using Mathematica?</description> <dc:creator>Tapas Ray Mahapatra</dc:creator> <dc:date>2024-11-18T12:56:07Z</dc:date> </item> <item rdf:about="https://community.wolfram.com/groups/-/m/t/3327416"> <title>Outer region of a polygon</title> <link>https://community.wolfram.com/groups/-/m/t/3327416</link> <description>&amp;[Wolfram Notebook][1]
 
 
 [1]: https://www.wolframcloud.com/obj/353c8f88-ca72-4702-a109-dc68b27bb196</description> <dc:creator>Frank Kampas</dc:creator> <dc:date>2024-11-23T21:42:30Z</dc:date> </item> <item rdf:about="https://community.wolfram.com/groups/-/m/t/366628"> <title>Try to beat these MRB constant records!</title> <link>https://community.wolfram.com/groups/-/m/t/366628</link> <description>POSTED BY:
 ========
 
 ever curious, ever learning Marvin Ray Burns and collaborators.
 ===========================
 
 ![aboutme1][1]
 ![aboutme2][2]
 
 
 
 ----------
 
 
 ----------
 
 
 ----------
 
 ![If you see this instead of an image, reload the page][3]
 ![enter image description here][4]
 
 is the MRB constant.
 ====================
 
 Weisstein, Eric W. &#034;MRB Constant.&#034; From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/MRBConstant.html
 
 ----------
 
 
 ----------
 
 
 ----------
 
 Understanding the Intersection of Critical Thinking and Mathematical Discovery Within You
 ------------------------------------------------------------------------
 
 Mark Twain’s apocryphal quote, “I’m in favor of progress; it’s change I don’t like,” encapsulates a profound human sentiment that echoes through the corridors of intellectual history. At its heart, this statement reflects the delicate balance between embracing new ideas and the inherent discomfort of moving beyond the familiar. (Educational humility is essential to mathematical maturity.) This tension is a driving force behind critical thinking, a process that has evolved and refined over centuries. The innate innocence of a young pupil, who accepts lessons at face value, contrasts sharply with this. While the pupil&#039;s unquestioning acceptance lays the foundation for learning, critical thinking&#x2014;embodied by the pupil&#039;s never-ending imagination, religious figures like prophets, as well as discoverers and inventors of scientific ideas&#x2014;represents the evolution towards questioning established norms and advocating for transformative progress.
 
 
 
 
 Mathematics include:
 ====================
 
 ![1][5]
 ![2][6]
 
 
 **Examples of further research done by me and many better scholars unveiling the inexhaustible utility of the MRB constant are in the following reply.**
 
 
 ----------
 
 
 
 Published at
 
 https://mathworld.wolfram.com/MRBConstant.html,
 
 ![enter image description here][7]
 
 **created by an amateur, serves as a potential catalyst for the field of mathematics by generating new questions, prompting re-evaluation of existing concepts, and encouraging broader participation in research -- a gateway to a world of intellectual exploration, collaboration, and potential breakthroughs! -- is a testament to the power of curiosity, collaboration, and the relentless pursuit of knowledge.**
 
 
 
 
 
 
 
 
 ----------
 
 ----------
 
 
 
 
 
 
 
 Explored here:
 
 
 
 &amp;[LambertM][8]
 
 
 
 
 
 
 
 
 
 ----------
 
 
 Now, let m=the MRB constant which relates to the divergent series
 
 
 ![DNE][9]
 
 The divergent sequence of its partial sums has two accumulation points with an upper limiting value or limsup, m,and a liminf , m-1: 
 
 &amp;[plot sup and inf][10]
 
 
 &amp;[Close][11]
 
 
 
 
 Further, out of the many series for CMRB=m, first analyze the sum prototype or prototypical series, i.e., the conditionally convergent summation, the sum of two divergent ones:
 
 
 ![two series][12]
 
 
 
 
 
 
 
 
 
 
 However, a conditionally convergent series was not satisfying to me, as the Riemann series theorem states, &#034;By a suitable rearrangement of terms, a conditionally convergent series may be made to converge to any desired value, or to diverge.&#034; I soon noticed that grouping its terms gave a convergent series:
 
 ![enter image description here][13]
 
 In[405]:= test = (2 k)^(1/(2 k)) - (2 k + 1)^(1/(2 k + 1));
 
 In[406]:= SumConvergence[Abs[test], k]
 
 Out[406]= True
 
 An equivalent absolutely convergent one.is
 
 ![enter image description here][14] 
 
 
 
 
 \was simply proven by Gottfried Helms 
 
 ![Gottfried Helms][15]
 
 
 
 
 
 ----------
 
 
 ----------
 
 
 
 In Mathematics in the Stack Exchange Network, an internet scholar going by the moniker Dark Malthorp presented a beautiful integral for the MRB constant: the integral of Im[(1 + I t)^(1/(1 + I t))]/Sinh[Pi t] for t&gt;0.
 
 ![enter image description here][16]
 ![enter image description here][17]
 
 
 ----------
 
 
 ----------
 
 
 If the header and the words
 
 Reply | Flag
 
 are shown at the same time in any of the following replies, refresh the page to see them.
 
 
 
 
 
 
 [1]: https://community.wolfram.com//c/portal/getImageAttachment?filename=Screenshot2024-11-26113455.png&amp;userId=366611
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 [7]: https://community.wolfram.com//c/portal/getImageAttachment?filename=Screenshot2024-07-18201721.png&amp;userId=366611
 [8]: https://www.wolframcloud.com/obj/1d839276-f629-4a8e-a234-0b1c4147bd34
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 [12]: https://community.wolfram.com//c/portal/getImageAttachment?filename=Screenshot2024-10-28134824.png&amp;userId=366611
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 [17]: https://community.wolfram.com//c/portal/getImageAttachment?filename=Screenshot2024-11-27142915.png&amp;userId=366611</description> <dc:creator>Marvin Ray Burns</dc:creator> <dc:date>2014-10-09T18:08:49Z</dc:date> </item> <item rdf:about="https://community.wolfram.com/groups/-/m/t/3161100"> <title>Simple equations that approximate semiPrime factors. Lots of them. Graphing to find estimate.</title> <link>https://community.wolfram.com/groups/-/m/t/3161100</link> <description>The middle equation crosses the x-axis at zero where x is 41227 the smaller Prime factor of pnp.
 
 These equations approximate x and y where pnp = x*y.
 
 The larger the pop however the more factors to test. But the graph gives a starting point.
 
 &amp;[Wolfram Notebook][1]
 
 
 [1]: https://www.wolframcloud.com/obj/df083bc4-c1fe-4cf0-99ac-83c97cfb00f2</description> <dc:creator>Bobby Joe Snyder</dc:creator> <dc:date>2024-04-19T21:20:30Z</dc:date> </item> <item rdf:about="https://community.wolfram.com/groups/-/m/t/3326111"> <title>Combining Graphics3D with MaterialShading and Opacity</title> <link>https://community.wolfram.com/groups/-/m/t/3326111</link> <description>Im trying to render two objects together, one with MaterialShading and one with Opacity.
 However, when combining these objects my computer becomes very slow and for large objects the frontend even crashes. 
 
 I managed to get a toy example running that shows the issue.
 By combining these two objects the graphics rendering time goes from a fraction of a second to over 4s.
 does anyone know what is going on here or has any solutions?
 
 dat = Table[
 x^2 + y^2 - z^2 + RandomReal[0.1], {x, -2, 2, 0.2}, {y, -2, 2, 
 0.2}, {z, -2, 2, 0.2}];
 g1 = First@
 ListContourPlot3D[dat, Contours -&gt; {0}, Mesh -&gt; None, 
 ContourStyle -&gt; Directive[{Blue, Opacity[0.5]}]];
 g2 = {MaterialShading[&#034;Gold&#034;], Tube[RandomReal[20, {10, 10, 3}]]};
 
 gr1 = Graphics3D[{g1}];
 gr2 = Graphics3D[{g2}];
 gr3 = Graphics3D[{g1, g2}];
 gr4 = Show[gr1, gr2];
 
 {gr1, gr2, gr3, gr4}
 Graphics`RenderTiming /@ {gr1, gr2, gr3, gr4}
 
 ![enter image description here][1]
 
 I&#039;m on Mathematica 14.1 with Windows 10.
 
 As a indication what needs to be rendered see below, the left does not has surface volumes rendered, the right does. The render times are already quite large so the times 100 as in the example wont work. 
 
 ![enter image description here][2]
 
 
 [1]: https://community.wolfram.com//c/portal/getImageAttachment?filename=Screenshot2024-11-21132505.png&amp;userId=1332602
 [2]: https://community.wolfram.com//c/portal/getImageAttachment?filename=Screenshot2024-11-21141250.png&amp;userId=1332602</description> <dc:creator>Martijn Froeling</dc:creator> <dc:date>2024-11-21T12:26:15Z</dc:date> </item> <item rdf:about="https://community.wolfram.com/groups/-/m/t/3327284"> <title>Plotting level curves for orthogonal analytic functions u, and v</title> <link>https://community.wolfram.com/groups/-/m/t/3327284</link> <description>I&#039;m the Wolfram-U Complex Analysis lecture series. In the example 3 of the section on Harmonic functions we are asked to plot some level curves for the real and imaginary parts of a complex function.
 Given f(z) = z^2 
 I&#039;m trying to plot the level curves for 
 
 u[x_,y_]:= x^2-y^2
 
 and
 
 v[x_,y_]:= 2*x*y
 
 I have tried ContourPlot and ComplexContourPlot what am I missing?</description> <dc:creator>Matthew Mawson</dc:creator> <dc:date>2024-11-23T16:40:20Z</dc:date> </item> <item rdf:about="https://community.wolfram.com/groups/-/m/t/3323292"> <title>Most popular county names in the U.S.</title> <link>https://community.wolfram.com/groups/-/m/t/3323292</link> <description>![Most popular county names in the U.S.][1]
 
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 [1]: https://community.wolfram.com//c/portal/getImageAttachment?filename=Main18112024.png&amp;userId=20103
 [2]: https://www.wolframcloud.com/obj/cb54bb64-3822-4528-a284-e12ba3698e2a</description> <dc:creator>Gosia Konwerska</dc:creator> <dc:date>2024-11-18T17:55:26Z</dc:date> </item> <item rdf:about="https://community.wolfram.com/groups/-/m/t/3326943"> <title>Mathematical Games: anagrams, letter banks and other wordplay</title> <link>https://community.wolfram.com/groups/-/m/t/3326943</link> <description>&amp;[Wolfram Notebook][1]
 
 
 [1]: https://www.wolframcloud.com/obj/9da76742-0573-4fe8-a49a-0af7904043ae</description> <dc:creator>Ed Pegg</dc:creator> <dc:date>2024-11-22T16:33:22Z</dc:date> </item> </rdf:RDF>