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RSS Feed for Wolfram Community showing any discussions in tag sorted by activeLoop of solving integrals constants doesn't work properly?
https://community.wolfram.com/groups/-/m/t/3290199
There are 6 steps whereby I use DSolve, then Update and evaluate the Mathematica package. Each step the output yields a function which contains obviously integration constants. For example Step 2 output yields a function with integration constants C1 , C2, C3 . Step 3 outputs yields a function with integration constants C1, C2 (instead of C4 , C5). Step 4 outputs a function with integration constants, C1, C2 (instead of C6 , C7). See attachment
&[Wolfram Notebook][1]
May you please assist with a way of achieving obtaining continuous integration constants.
[1]: https://www.wolframcloud.com/obj/74a5f355-4170-4017-850e-be93ed4557eeNomsa Ledwaba2024-10-03T08:47:11ZSolution for summation involving associated Laguerre polynomials
https://community.wolfram.com/groups/-/m/t/3263017
I want the expression for the following:
Sum[(1/Factorial[(l + p)])*(x y)^l*LaguerreL[p, l, x^2]*
LaguerreL[p, l, y^2], {l, 0, Infinity}]
When I write this in Mathematica, it just gives back the same thing written in mathematical form, not the solution.
If I specify the value of p, then I get closed form expression, but I am not getting for a general p.Radhika Prasad2024-09-02T11:33:59ZOptimizing Cloud Storage Solutions with Wolfram Language
https://community.wolfram.com/groups/-/m/t/3294681
Hello everyone,
I’m exploring ways to optimize [cloud storage][1] solutions using Wolfram Language and would love to hear your insights and experiences.
I’ve been working with large datasets and am particularly interested in:
1. Data Compression: Are there specific functions in Wolfram Language that can help efficiently compress data before storing it in the cloud?
2. Batch Processing: What strategies can I implement to process and upload large volumes of data in batches, minimizing API calls and maximizing efficiency?
3. Storage Management: How can I automate data organization and retrieval to ensure that I’m only storing necessary data, and how can I monitor storage usage effectively?
4. Cost Optimization: Any tips on minimizing costs associated with cloud storage while using Wolfram tools?
I’d appreciate any resources, code snippets, or personal experiences you can share! Looking forward to a fruitful discussion.
Thanks!
[1]: https://www.lenovo.com/ch/fr/servers-storage/solutions/cloud-computing/Arthur Leo2024-10-09T05:12:18ZHelp with definite integral solved analytically
https://community.wolfram.com/groups/-/m/t/3293804
&[Wolfram Notebook][1]
[1]: https://www.wolframcloud.com/obj/dd6e9384-baff-415f-b10f-dbf8a40eef25Anuj Malik2024-10-08T09:41:43ZHow to I permanently set default window margins upon Mathematica bootup?
https://community.wolfram.com/groups/-/m/t/470081
Hi,
Every time I open Mathematica and auto starts a new notebook it opens with non-ideal margins. I'd like to change this setting.
I'd like the default window margins to be something I choose. Can I do this in the option inspector? Or can I change the default stylesheet to accomplish this? Or can I programmatically make Mathematica do this upon bootup? If so... how?
Thanks in advance. Sorry for all the questions. I'm on spring break and am having some fun learning all that I can while I can. Thank you!
MikeMichael McCain2015-03-31T00:58:02Z[WSG24] Daily Study Group: Introduction to Calculus
https://community.wolfram.com/groups/-/m/t/3241186
A Wolfram U Daily Study Group on ["Introduction to Calculus"][1] begins on Monday, August 12, 2024.
Join a cohort of fellow mathematics enthusiasts to learn about the fundamentals of calculus from the recent [Introduction to Calculus][2] ebook by John Clark and myself. Our topics will include functions and limits, differential and integral calculus, and practical applications of calculus.
The study group will be led by expert Wolfram U instructor [Luke Titus][4], and I will stop by occasionally to check in with the group. It should be a lot of fun!
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**
August 12- September 6, 2024,
11am-12pm CT (4-5pm GMT)
> **[REGISTER HERE][5]**
![enter image description here][6]
[1]: https://www.bigmarker.com/series/introduction-to-calculus-wsg56/series_details?utm_bmcr_source=community
[2]: https://www.wolfram-media.com/products/introduction-to-calculus/
[3]: https://www.wolfram.com/wolfram-u/courses/mathematics/introduction-to-calculus/
[4]: https://community.wolfram.com/web/luket
[5]: https://www.bigmarker.com/series/introduction-to-calculus-wsg56/series_details?utm_bmcr_source=community
[6]: https://community.wolfram.com//c/portal/getImageAttachment?filename=wolframu-banner.png&userId=26786Devendra Kapadia2024-08-05T20:01:27ZMaking images into 3D cylindrical shape
https://community.wolfram.com/groups/-/m/t/3293037
![Making images into 3D cylindrical shape][1]
&[Wolfram Notebook][2]
[1]: https://community.wolfram.com//c/portal/getImageAttachment?filename=Main08102024.png&userId=20103
[2]: https://www.wolframcloud.com/obj/0ff1ba2b-0e88-4673-a998-eb1e6bc7e230Gilmer Gary2024-10-07T16:55:19ZHow to calculate the gradient of the arg of a complex exponential?
https://community.wolfram.com/groups/-/m/t/3294269
I am trying to find the gradient of the phase of complex exponential functions.
For example:
Grad[Arg[Exp[-I (x + z)]], {x, z}]
Should be {1,1} for all x,z (Reals). However, instead I get:
{-I E^(-I (x + z))
Derivative[1][Arg][E^(-I (x + z))], -I E^(-I (x + z))
Derivative[1][Arg][E^(-I (x + z))]}
I think it has to do with the fact that `Arg[Exp[-I (x + z)]]` doesn't return (x+z). I assumed that was because it doesn't know that x,z are Reals.
I also tried `Refine[Arg[Exp[-I (x + z)]],
x \[Element] Reals && z \[Element] Reals]` but that doesn't return (x+z) either.
Thanks!Brian M2024-10-08T16:13:46Z[WSG24] Daily Study Group: Elementary Introduction to Wolfram Language
https://community.wolfram.com/groups/-/m/t/3270548
![enter image description here][1]
A Wolfram U Daily Study Group on Elementary Introduction to Wolfram Language begins on Monday, September 16.
Join me and [Eryn Gillam][2] and a group of fellow learners to learn about programming in Wolfram Language. Our topics for the study group include list manipulation, using and making functions, using dynamic functionality, and working with images, sounds, shapes, and colors.
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 and Times:#
September 16th-October 4th,
11am-12pm CT (4-5pm GMT)
#[Register Here][3]#
[1]: https://community.wolfram.com//c/portal/getImageAttachment?filename=wolframubanner.jpeg&userId=1835305
[2]: https://community.wolfram.com/web/eryng
[3]: https://www.bigmarker.com/series/an-elementary-introduction-to-wl-wsg57/series_details?utm_bmcr_source=communityRory Foulger2024-09-09T17:24:27ZImporting TOML file type
https://community.wolfram.com/groups/-/m/t/2980289
Does Mathematica support importing of TOML files? If so, how?
Thanks,
JochenJochen Klinke2023-07-31T23:05:01ZURLDownload broken in v14?
https://community.wolfram.com/groups/-/m/t/3293268
I have a notebook that used to work using v13.3, that updates the data used with URLDownload:
URLDownload["https://mydomain/myfile.csv", "myfile.csv"]
This used to work in v13.3. Now I upgraded to v14.1 and instead it says: invalid request. I tried to get the http error code, by adding options as in the documentation, but it only returns this message (that btw is not seen as an error, so it is now shown when running commands with suppressed output...initially I didn't really understand what was going on...). I suspect the download is not even attempted as it does not like the format of the request.... any tips?Giorgio Busoni2024-10-07T22:48:42ZSolving computationally the "True Genius: Grecian Computer" puzzle
https://community.wolfram.com/groups/-/m/t/2308671
*Disclaimer: I'm not a mathematician. I'm merely a hobbyist that loves programming and puzzles. Professionally, I work in IT management.*
For my birthday this year, my young nephew (much aware of my love for puzzles) gifted me a wooden brainteaser called "Grecian Computer" from the brand [True Genius][1].
[![enter image description here][2]][3]
As described on the box, the goal is to "Turn the dials until all 12 columns add up to 42." Rather than faffing about with trial and error, I figured it would be much more fun and educational to try my hand at writing a bit of Wolfram Language code to produce the solution.
My first step was to disassemble the puzzle to understand its structure: five "dials", the bottom of which remains fixed in place while the remaining four may rotate through twelve positions. Each dial effectively contains a 4x12 matrix comprised of numbers and "holes" where numbers from lower dials may show through.
[![enter image description here][4]][5]
[![enter image description here][6]][7]
[![enter image description here][8]][9]
[![enter image description here][10]][11]
[![enter image description here][12]][13]
Using the Wolfram Language's functions for handling lists of lists, the puzzle seems readily represented as a three dimensional array: five layers, each with four rows of twelve columns. Here, I represent "holes" as zeroes:
puzzle = {{{8, 3, 4, 12, 2, 5, 10, 7, 16, 8, 7, 8}, {4, 4, 6, 6, 3, 3,
14, 14, 21, 21, 9, 9}, {4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14,
15}, {11, 11, 14, 11, 14, 11, 14, 14, 11, 14, 11, 14}}, {{1, 0,
9, 0, 12, 0, 6, 0, 10, 0, 10, 0}, {3, 26, 6, 0, 2, 13, 9, 0, 17,
19, 3, 12}, {9, 20, 12, 3, 6, 0, 14, 12, 3, 8, 9, 0}, {7, 0, 9,
0, 7, 14, 11, 0, 8, 0, 16, 2}}, {{0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0}, {22, 0, 16, 0, 9, 0, 5, 0, 10, 0, 8, 0}, {11, 26, 14, 1,
12, 0, 21, 6, 15, 4, 9, 18}, {17, 4, 5, 0, 7, 8, 9, 13, 9, 7, 13,
21}}, {{0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0}, {14, 0, 9, 0, 12, 0, 4, 0, 7, 15, 0, 0}, {11,
6, 11, 0, 6, 17, 7, 3, 0, 6, 0, 11}}, {{0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0}, {7, 0, 15, 0, 8, 0, 3, 0, 6, 0, 10,
0}}};
Next, we need to create a table of all of the possible permutations, rotating each of the four moving dials through its twelve possible positions, like a clock. I calculated there should be 20,736 possible permutations: 1x12x12x12x12:
puzzlePermutations =
Flatten[
Table[{puzzle[[1]], RotateRight[puzzle[[2]], {0, a}],
RotateRight[puzzle[[3]], {0, b}],
RotateRight[puzzle[[4]], {0, c}],
RotateRight[puzzle[[5]], {0, d}]}, {a, 0, 11}, {b, 0, 11}, {c, 0,
11}, {d, 0, 11}], 3];
Length[puzzlePermutations]
The next step was to "lift" the numbers from the lower dials to fill in the "holes" represented as zeroes:
Do[puzzlePermutations[[x]][[i]] =
ReplacePart[puzzlePermutations[[x]][[i]],
AssociationThread[
Position[puzzlePermutations[[x]][[i]], 0] ->
Extract[puzzlePermutations[[x]][[i - 1]],
Position[puzzlePermutations[[x]][[i]], 0]]]], {x,
Length[puzzlePermutations]}, {i, 2, 5}];
From here, we just need to select the permutation(s) for which the columns in the top layer all add up to 42:
solution = Select[puzzlePermutations, ContainsExactly[Total@#[[5]], {42}] &];
This produces the sole solution to the puzzle, and we can see how we should turn each dial to solve it:
Array[MatrixForm[solution[[1]][[#]]] &, 5]
![Array representing the solution.][14]
Finally, thanks to a bit of Wolfram Language code, the solved puzzle:
[![enter image description here][16]][15]
I had fun working through this. I'm sure there are more efficient or elegant ways to write this code and solve the puzzle, and I'd love to hear your thoughts.
Thanks for reading!
Christopher
[1]: https://www.projectgeniusinc.com/true-genius-collection
[2]: https://community.wolfram.com//c/portal/getImageAttachment?filename=15291.jpg&userId=20103
[3]: https://community.wolfram.com//c/portal/getImageAttachment?filename=IMG_4078.png&userId=241091
[4]: https://community.wolfram.com//c/portal/getImageAttachment?filename=101442.jpg&userId=20103
[5]: https://community.wolfram.com//c/portal/getImageAttachment?filename=IMG_4071.png&userId=241091
[6]: https://community.wolfram.com//c/portal/getImageAttachment?filename=58813.jpg&userId=20103
[7]: https://community.wolfram.com//c/portal/getImageAttachment?filename=IMG_4072.png&userId=241091
[8]: https://community.wolfram.com//c/portal/getImageAttachment?filename=97954.jpg&userId=20103
[9]: https://community.wolfram.com//c/portal/getImageAttachment?filename=IMG_4073.png&userId=241091
[10]: https://community.wolfram.com//c/portal/getImageAttachment?filename=31935.jpg&userId=20103
[11]: https://community.wolfram.com//c/portal/getImageAttachment?filename=IMG_4074.png&userId=241091
[12]: https://community.wolfram.com//c/portal/getImageAttachment?filename=61306.jpg&userId=20103
[13]: https://community.wolfram.com//c/portal/getImageAttachment?filename=IMG_4076.png&userId=241091
[14]: https://community.wolfram.com//c/portal/getImageAttachment?filename=solutionarray.png&userId=241091
[15]: https://community.wolfram.com//c/portal/getImageAttachment?filename=IMG_4069.png&userId=241091
[16]: https://community.wolfram.com//c/portal/getImageAttachment?filename=64797.jpg&userId=20103Christopher Fox2021-07-09T15:02:30ZFindMaximum::nrnum: The function value is not a real number
https://community.wolfram.com/groups/-/m/t/3291798
Hi everyone,
I'm working on an optimization problem with three decision variables: n (shipment frequency), x (replenishment cycle in days), and g (preservation technology investment cost). To find the optimal values for these variables, I fix n at various values and use FindMaximum to solve for x and g. Then, I compare the total profit for different n values to determine the optimal solution.
However, I’m encountering the following error when I try to run my code :
> FindMaximum::nrnum: The function value -7.431150025641089*10^1001-2.427197794764971*10^1017 I is not a real number at {x,g} = {2.15602,-2.3412}.
Here is the code :
Clear["Global`*"]
L = 7;
w = 0.064;
ww = 2;
R = 250;
Kf = 50;
Km = 0.5;
cf = 0.1;
cg = 0.01;
m = 0.2;
ml = 0.01;
Kp = 30;
Kj = 0.3;
hp = 0.05;
ht = 0.2;
Kr = 10;
Ks = 1;
hr = 0.1;
hs = 0.07;
j = 0.001;
k = 6.87;
q = 0.1;
a = 80;
b = 0.2;
Pv = 1;
pw = 0.5;
pf = 0.7;
pp = 2;
pr = 10;
c = 0.8;
S = 2;
Sv = 3;
Sr = 1;
T = 0.5;
v = 0.15;
vp = 1;
y = 400;
z = 100;
f = 0.9;
l = 0.3;
Ik = 0.1;
M = 0.5;
bk = 1 - f;
n = 1;
Tf = - (Log[1/z (k/ww - 1)]/q);
TP[x_, g_] =
pr/x ((a (1 - b) (x^2))/(2 L) (1 - E^(-y g)))^(1/(1 - b)) - (
hr + c hs + g + c j)/
x (2 x (-((a (-1 + b) (1 - E^(-y g)) x^2)/L))^(1/(1 - b))) - (Kr +
c Ks)/x - (Kp + Kf + c Km + c Kj)/(
n x) - (c pp + c pf)/x ((a (1 - b) (x^2))/(2 L) (1 - E^(-y g)))^(
1/(1 - b)) - (S + c T)/
x^2 - (hp + c ht + g + c j)/(
2 R x) ((a (1 - b) (x^2))/(2 L) (1 - E^(-y g)))^(2/(
1 - b)) - ((hp + c ht + g + c j) (n - 1))/(
2 x) ((a (1 - b) (x^2))/(2 L) (1 - E^(-y g)))^(2/(
1 - b)) (x ((a (1 - b) (x^2))/(2 L) (1 - E^(-y g)))^1/(b - 1) - 1/
R) - (Sv + c Sr)/(n x)^2 - ((vp + c v)/(
n x)) ((a (1 - b) (x^2))/(2 L) (1 - E^(-y g)))^(1/(
1 - b)) - ((Pv + c pw) w)/(
x f ww) ((a (1 - b) (x^2))/(2 L) (1 - E^(-y g)))^(1/(
1 - b)) - (cf f + c cg f + m bk + c ml bk)/(
x f ww ) ((a (1 - b) (x^2))/(2 L) (1 - E^(-y g)))^(1/(
1 - b)) (k Tf + k/q (Log[1 + z E^(-q Tf)] - Log[1 + z])) +
pr/x l ((
a E^(-g y) (-1 + E^(g y)) x^3 ((a (1 - b) (1 - E^(-g y)) T^2)/
L)^(b/(1 - b)) (3 (-1 + 2^(1/(-1 + b))) (-1 + b) - 2 ))/(
3 L) + ((a (1 - b) (x^2))/(2 L) (1 - E^(-y g)))^(1/(
1 - b)) (M - x));
FindMaximum[{TP[x, g]}, {x, g}]
Any insights on why this might be happening and how I can solve this problem?Shafa Hananta2024-10-07T06:43:29ZHow to work with GRIB files?
https://community.wolfram.com/groups/-/m/t/3293403
Does anyone have any kind of tutorial on how to work with GRIB/GRIB2 files (extracting and mapping the data with `GeoGraphics`), for example, https://tgftp.nws.noaa.gov/SL.us008001/ST.opnl/DF.gr2/DC.ndfd/AR.oceanic/VP.004-007/ds.wspd.bin ?
The online documentation is insanely vague.Steven Buehler2024-10-08T00:49:12ZExample of solving the Cahn-Hilliard equation with NDSolve
https://community.wolfram.com/groups/-/m/t/3291843
&[Wolfram Notebook][1]
[1]: https://www.wolframcloud.com/obj/d7b3e58f-bc39-4d23-8d1b-162b2e0127cdDavid Moore2024-10-06T14:18:41ZTracking hurricane Milton advisories, the fastest storm to go from category 1 to 5 in Atlantic Basin
https://community.wolfram.com/groups/-/m/t/3292663
![Tracking hurricane Milton advisories, the fastest storm to go from category 1 to 5 in Atlantic Basin][1]
&[Wolfram Notebook][2]
[1]: https://community.wolfram.com//c/portal/getImageAttachment?filename=Main07102024.png&userId=20103
[2]: https://www.wolframcloud.com/obj/323ab07a-bdb5-4853-86b1-8df24eb670d4Arnoud Buzing2024-10-07T16:01:24ZGalois groups and the symmetries of polynomials
https://community.wolfram.com/groups/-/m/t/3292345
&[Wolfram Notebook][1]
[1]: https://www.wolframcloud.com/obj/16d8ca1c-110f-4ae6-94be-d99caa87d903Paul Abbott2024-10-07T07:59:00ZNDSolve - Can anyone see what's wrong in my thinking?
https://community.wolfram.com/groups/-/m/t/389584
Here is a simple differential-algebraic equation. I think that since d[t] has a delta at t=10, s[t] should step up at that point. But it steps down.
eqs1 = {
s'[t] == d[t] - s[t]/10,
s[0] == 0,
d[t] == DiracDelta[t - 10]
};
ss1 = NDSolveValue[eqs1, s, {t, 0, 100}];
p1 = Plot[ss1[t], {t, 0, 100}, PlotRange -> All]
![enter image description here][1]
This did not seem right, but to check I made the sign in front of d[t] in the first equation negative:
(* note the - sign in front of d[t] *)
eqs2 = {
s'[t] == -d[t] - s[t]/10,
s[0] == 0,
d[t] == DiracDelta[t - 10]
};
ss2 = NDSolveValue[eqs2, s, {t, 0, 100}];
p2 = Plot[ss2[t], {t, 0, 100}, PlotRange -> All]
![enter image description here][2]
But it does not seem to matter!
[1]: /c/portal/getImageAttachment?filename=5909p1.png&userId=98179
[2]: /c/portal/getImageAttachment?filename=6412p2.png&userId=98179David Keith2014-11-15T02:07:22ZNumerical instability in simulation
https://community.wolfram.com/groups/-/m/t/3292107
Hello. when I run the code below, i get the error NDSolveValue::reinitfail: Unable to reinitialize the system at t = 11.692137665979317` within specified tolerances. which i think is due to numerical instability in the calculations. any help on how to solve this issue would be greatly appreciated.
ClearAll["Global`*"]
m[n_] := Piecewise[{{0.1, n == 40}}, 0.0001];
l[n_] := 0.02;
\[Zeta][t_] := 0.1 Cos[7 t]
r[n_, t_] := \[Zeta][t] UnitVector[3, 3] +
Sum[UnitVector[3, 1]*l[i] Sin[\[Theta][i, t]] -
UnitVector[3, 3]*l[i] Cos[\[Theta][i, t]], {i, n}];
rdot[n_, t_] := D[r[n, t], t];
tt[nn_] := 1/2 Sum[m[n]*Total[rdot[n, t]^2], {n, nn}];
vv[nn_] := g*Sum[m[n]*r[n, t][[3]], {n, nn}];
ll[nn_] := tt[nn] - vv[nn];
rr[nn_] := 1/2 cd*Sum[Total[rdot[n, t]^2], {n, nn}];
eqLag[k_, nn_] :=
D[D[ll[nn], D[\[Theta][k, t], t]], t] -
D[ll[nn], \[Theta][k, t]] == -D[rr[nn], D[\[Theta][k, t], t]];
Block[{nn = 40,(*m=Function[1],l=Function[1],\[Zeta]=Function[1],*)
cd = 0.00005, g = 9.81},
eqs = Table[eqLag[n, nn], {n, nn}](*//Simplify*);
initialData =
Flatten[Table[{\[Theta][k, 0] == 0.05,
Derivative[0, 1][\[Theta]][k, 0] == 0}, {k, nn}]];
sols = NDSolveValue[
Flatten@{eqs, initialData,
WhenEvent[
0.02 (Sin[\[Theta][1, t]] + Sin[\[Theta][2, t]] +
Sin[\[Theta][3, t]] + Sin[\[Theta][4, t]] +
Sin[\[Theta][5, t]] + Sin[\[Theta][6, t]] +
Sin[\[Theta][7, t]] + Sin[\[Theta][8, t]] +
Sin[\[Theta][9, t]] + Sin[\[Theta][10, t]] +
Sin[\[Theta][11, t]] + Sin[\[Theta][12, t]] +
Sin[\[Theta][13, t]] + Sin[\[Theta][14, t]] +
Sin[\[Theta][15, t]] + Sin[\[Theta][16, t]] +
Sin[\[Theta][17, t]] + Sin[\[Theta][18, t]] +
Sin[\[Theta][19, t]] + Sin[\[Theta][20, t]] +
Sin[\[Theta][21, t]] + Sin[\[Theta][22, t]] +
Sin[\[Theta][23, t]] + Sin[\[Theta][24, t]] +
Sin[\[Theta][25, t]] + Sin[\[Theta][26, t]] +
Sin[\[Theta][27, t]] + Sin[\[Theta][28, t]] +
Sin[\[Theta][29, t]] + Sin[\[Theta][30, t]] +
Sin[\[Theta][31, t]] + Sin[\[Theta][32, t]] +
Sin[\[Theta][33, t]] + Sin[\[Theta][34, t]] +
Sin[\[Theta][35, t]] + Sin[\[Theta][36, t]] +
Sin[\[Theta][37, t]] + Sin[\[Theta][38, t]] +
Sin[\[Theta][39, t]] + Sin[\[Theta][40, t]])
<= 0,
Derivative[0, 1][\[Theta]][40, t] -> -0.8*
Derivative[0, 1][\[Theta]][40, t]]},
Table[\[Theta][k, t], {k, nn}], {t, 0, 20},
Method -> {"EquationSimplification" -> "Residual"}]]Ee Kin Chan2024-10-07T02:06:00ZSolving system of equations gives empty output, but gives result when reduced
https://community.wolfram.com/groups/-/m/t/522486
I want solve equation group below, but you can see the result return a {},
but when i reduce the equation group like this , it can give a solution(Seeing in the image),
why is this ? ![enter image description here][1]
[1]: /c/portal/getImageAttachment?filename=mathematica.png&userId=522471Panron Ryan2015-07-04T16:27:22ZInterpolating a sampled signal with sinc
https://community.wolfram.com/groups/-/m/t/3291440
&[Wolfram Notebook][1]
[1]: https://www.wolframcloud.com/obj/5f2caf8e-8d77-4cf2-8973-da157062f0d5Tom Lieber2024-10-05T23:43:17Z[WSS24] Modeling of interactions in aqueous electrolyte with peptide additive
https://community.wolfram.com/groups/-/m/t/3210091
&[Wolfram Notebook][1]
[1]: https://www.wolframcloud.com/obj/158c2618-22ea-4c32-aada-f997d1d9cbdfXuelian Liu2024-07-10T02:19:19ZWhat does TrapezoidalRule at NIntegrate really do?
https://community.wolfram.com/groups/-/m/t/3290658
Hello everybody,
I have a question as regards the TrapezoidalRule at the implemented NIntegrate function of Mathematica.
If I calculate the numeric(!) integral of f(x)=x^2 from 0 to 3 with 5 trapezoids by hand, I get a result of 9.18. If I use the implemented method "TrapezoidalRule" with the option "Points" -> 5 it gives me exactly 9.0.
So I doubt, that I do not fully understand what Mathematica does when using this Rule. I have tried a lot of (changing the WorkingPrecision, setting the MaxRecursions to 0 etc...), but it always comes up with the "real" (analytical) result.
Can anyone please explain what's going on?
Thanks a lot,
JJJ
f[x_] := x^2;
a = 0; b = 3;
\[CapitalDelta]x[n_] := (b - a)/n;
left[n_] := \!\(
\*UnderoverscriptBox[\(\[Sum]\), \(i = 0\), \(n - 1\)]\(f[
a + i*\[CapitalDelta]x[n]]*\[CapitalDelta]x[n]\)\);
right[n_] := \!\(
\*UnderoverscriptBox[\(\[Sum]\), \(i = 1\), \(n\)]\(f[
a + i*\[CapitalDelta]x[n]]*\[CapitalDelta]x[n]\)\);
trap[n_] := (left[n] + right[n])/2;
trap2[n_] := \[CapitalDelta]x[n]/2 (f[a] + 2 \!\(
\*UnderoverscriptBox[\(\[Sum]\), \(i = 1\), \(n - 1\)]\(f[
a + i*\[CapitalDelta]x[n]]\)\) + f[b]);
{left[5.], right[5.], trap[5.], trap2[5.]}
NIntegrate[f[x], {x, a, b},
Method -> {"TrapezoidalRule", "Points" -> 3}, WorkingPrecision -> 10,
MaxRecursion -> 0]Joachim Janezic2024-10-04T13:08:10ZCompiling from a Turing machine to a cyclic tag system
https://community.wolfram.com/groups/-/m/t/3290282
&[Wolfram Notebook][1]
[1]: https://www.wolframcloud.com/obj/c9ceb30d-1ded-4cf8-bb8b-1e06aa47ecf2Eric Parfitt2024-10-03T21:09:08Z3*5/3*5 versus 3*5:3*5 in Wolfram Alpha
https://community.wolfram.com/groups/-/m/t/3290739
Hello fellows :-)
Why WolframAlpha give the answer 25 (correct) for 3x5/3x5 but 1 for 3x5:3x5 ?
Thanks.Sergio da Silva2024-10-04T10:13:54ZIs the atlas 2 add-on no longer supported by anyone?
https://community.wolfram.com/groups/-/m/t/1303742
Is `atlas 2` add-on to *Mathematica* supported by anybody now? Links to it at wolfram.com have gone dead, and the website of the publisher, digi-area.com, also has vanished.Murray Eisenberg2018-03-17T20:12:04ZTrouble using Wolfram notebooks with a screen reader on Windows
https://community.wolfram.com/groups/-/m/t/3057413
Hello,
I'm using screen reading software packages such as JAWS For Windows or NVDA. For that reason, I have to do everything via my PC keyboard, without using the mouse. This means that I can only read text, not graphics, and that graphics are only accessible to me if they have a meaningful "alt" tag attached to them.
Even though Wolfram Alpha's accessibility has improved over the past couple of years and I can use it to some extent, I think Wolfram notebooks must either be totally inaccessible for people who use a screen reader or I have no idea how I'm supposed to work with them when I can't use the mouse and when I can't read graphics.
I have set up a basic account on Wolfram Cloud.
I want to evaluate the entire contents of the file downloaded from a particular webpage (I can post the link later if someone's interested). It's a file with an ".m" extension.
This means that when I open a new notebook, I'm supposed to copy the contents of the whole file into my new notebook and then choose "Evaluate all cells".
I logged into my Wolfram Cloud account and I chose the button labeled "New computational notebook".
I thought I was supposed to reach an edit field where I would paste the contents of the "main.m" file. But I did not find any such thing on the webpage. And if it's something other than a conventional edit field of the kind that I would fill in on a web form, then I don't know where I'm supposed to paste the contents of the ".m" file.
I had a very long conversation with someone from the Wolfram support. The support person told me that they could only suggest me to read the Wolfram tutorial webpage called "Keyboard shortcut listing".
But on that webpage, I'm unable to find anything that would help me to reach the field I'm looking for. And if I'm supposed to paste the text into something other than an edit field, then I have no idea what that would be.
My question is simple:
Is there anyone here who might be able to describe to me what I should be trying to find, avoiding phrases like "click the red button" or "click the blue icon" or similar? Those won't help me. I'm currently absolutely stuck.
Thank you in advance.
- PetrPetr Pařízek2023-10-28T22:26:55ZSpectroGAN soundMap
https://community.wolfram.com/groups/-/m/t/2829436
My goal:
With great interest in GANs, a series of AI-generated spectrograms are created for further analysis and manipulation. Spectrograms are visual representations of audio signals, and GANs are machine-learning models used to generate synthetic data that resembles real data. By creating AI-generated spectrograms using GANs, I aim to study and manipulate these visual and sound representations of synthetic audio data. This could potentially have applications in fields such as audio processing and music synthesis. I created an exploratory workflow with a fundamental question in mind: what is music?
Description and process:
As an artist or musician, one begins by learning the rules and techniques of their craft. However, as one gains more experience and becomes more confident in their abilities, their own personal emotions and intuition begin to play a larger role in their creations. The unique experiences and perspectives that each individual brings to their art form the basis of their own unique voice and style. This blending of technical skill with personal emotion and intuition leads to a creation that is not just technically sound but also reflects the artist's view of the world and its place within it. In this way, art and music become a reflection not just of technical proficiency, but also of the human experience and emotion. Further research and exploration in this field will shed light on the potential of AI to augment or even change the way we experience and create art and music.
This raises the question of what happens when trained machine-learning models generate music and art. How do these AI-generated pieces evoke human emotions and experiences, if at all?
Exploratory Workflow:
1: Create GANs models
![enter image description here][1]
2: Feed spectrograms into GANs models to produce AI-generated spectrograms.
![enter image description here][2]
3: Select 20 samples of the GANs-generated spectrograms by listening to 120 random samples.
![enter image description here][3]
4. Combine the 20 samples
![enter image description here][4]
5. Denoise the combined sample
![enter image description here][5]
6. Further manipulations upon the denoise sample (Fisheye effect and etc)
![enter image description here][6]
[1]: https://community.wolfram.com//c/portal/getImageAttachment?filename=image%289%29.png&userId=2829000
[2]: https://community.wolfram.com//c/portal/getImageAttachment?filename=image%2810%29.png&userId=2829000
[3]: https://community.wolfram.com//c/portal/getImageAttachment?filename=image%2811%29.png&userId=2829000
[4]: https://community.wolfram.com//c/portal/getImageAttachment?filename=Screenshot2023-02-12201850.jpg&userId=2829000
[5]: https://community.wolfram.com//c/portal/getImageAttachment?filename=image%2812%29.png&userId=2829000
[6]: https://community.wolfram.com//c/portal/getImageAttachment?filename=image%2813%29.png&userId=2829000Yingxuan Ma2023-02-13T01:20:51Z[WSS17] Music Genre Classifier
https://community.wolfram.com/groups/-/m/t/1136863
We aim to create a music genre classifier which allows the detection of the genre of audio/music files. The dataset used for training the model is the GTZAN dataset, it consists of 1000 audio tracks each 30 seconds long. It contains 10 genres, each of them have 100 tracks. For feature extraction, we will be extracting the MFCC values of the audio file. MFCC's are commonly used as features in speech recognition and music information retrieval systems.
![enter image description here][1]
We divided each song into two parts of 15 seconds each, this way we get more data and our dataset increases to 2000 songs. We will be extracting the MFCC values of all the audio files by partitioning the song into 15 seconds each.
In[25]:= rockdata =
Import["/Users/aishwaryapraveen/Desktop/Summer School \
Project/genres/rock/*.au"];
rockdata1 = Flatten[AudioSplit[#, 15] & /@ rockdata];
countrydata =
Import["/Users/aishwaryapraveen/Desktop/Summer School \
Project/genres/country/*.au"];
In[29]:= countrydata1 = Flatten[AudioSplit[#, 15] & /@ countrydata];
In[30]:= bluesdata =
Import["/Users/aishwaryapraveen/Desktop/Summer School \
Project/genres/blues/*.au"];
bluesdata1 = Flatten[AudioSplit[#, 15] & /@ bluesdata];
In[33]:= classicaldata =
Import["/Users/aishwaryapraveen/Desktop/Summer School \
Project/genres/classical/*.au"];
In[34]:= classicaldata1 =
Flatten[AudioSplit[#, 15] & /@ classicaldata];
In[10]:= discodata =
Import["/Users/aishwaryapraveen/Desktop/Summer School \
Project/genres/disco/*.au"];
In[35]:= discodata1 = Flatten[AudioSplit[#, 15] & /@ discodata];
In[36]:= Length@discodata1
Out[36]= 200
In[39]:= hiphopdata =
Import["/Users/aishwaryapraveen/Desktop/Summer School \
Project/genres/hiphop/*.au"];
In[38]:= hiphopdata1 = Flatten[AudioSplit[#, 15] & /@ hiphopdata];
In[40]:= jazzdata =
Import["/Users/aishwaryapraveen/Desktop/Summer School \
Project/genres/jazz/*.au"];
jazzdata1 = Flatten[AudioSplit[#, 15] & /@ jazzdata];
In[42]:= metaldata =
Import["/Users/aishwaryapraveen/Desktop/Summer School \
Project/genres/metal/*.au"];
metaldata1 = Flatten[AudioSplit[#, 15] & /@ metaldata];
In[130]:=
popdata =
Import["/Users/aishwaryapraveen/Desktop/Summer School \
Project/genres/pop/*.au"];
In[131]:= popdata1 = Flatten[AudioSplit[#, 15] & /@ popdata];
In[46]:= reggaedata =
Import["/Users/aishwaryapraveen/Desktop/Summer School \
Project/genres/reggae/*.au"];
In[47]:= reggaedata1 = Flatten[AudioSplit[#, 15] & /@ reggaedata];
MFCC Extraction
mFCCFeaturesreggaedata = (Values@
AudioLocalMeasurements[#, "MFCC",
PartitionGranularity -> {1., 1.}]) & /@ reggaedata1;
mFCCFeaturesClassReggae = Thread[mFCCFeaturesreggaedata -> "reggae"];
mFCCFeaturespopdata = (Values@
AudioLocalMeasurements[#, "MFCC",
PartitionGranularity -> {1., 1.}]) & /@ popdata1;
mFCCFeaturesClassPop = Thread[mFCCFeaturespopdata -> "pop"];
mFCCFeaturesmetaldata = (Values@
AudioLocalMeasurements[#, "MFCC",
PartitionGranularity -> {1., 1.}]) & /@ metaldata1;
mFCCFeaturesClassMetal = Thread[mFCCFeaturesmetaldata -> "metal"];
mFCCFeaturesjazzdata = (Values@
AudioLocalMeasurements[#, "MFCC",
PartitionGranularity -> {1., 1.}]) & /@ jazzdata1;
mFCCFeaturesClassJazz = Thread[mFCCFeaturesjazzdata -> "jazz"];
mFCCFeatureshiphopdata = (Values@
AudioLocalMeasurements[#, "MFCC",
PartitionGranularity -> {1., 1.}]) & /@ hiphopdata1;
mFCCFeaturesClasshiphop = Thread[mFCCFeatureshiphopdata -> "hiphop"];
mFCCFeaturesdiscodata = (Values@
AudioLocalMeasurements[#, "MFCC",
PartitionGranularity -> {1., 1.}]) & /@ discodata1;
mFCCFeaturesClassdisco = Thread[mFCCFeaturesdiscodata -> "disco"];
mFCCFeaturesbluesdata = (Values@
AudioLocalMeasurements[#, "MFCC",
PartitionGranularity -> {1., 1.}]) & /@ bluesdata1;
mFCCFeaturesClassblues = Thread[mFCCFeaturesbluesdata -> "blues"];
mFCCFeaturesclassicaldata = (Values@
AudioLocalMeasurements[#, "MFCC",
PartitionGranularity -> {1., 1.}]) & /@ classicaldata1;
mFCCFeaturesClassclassical =
Thread[mFCCFeaturesclassicaldata -> "classical"];
mFCCFeaturesrockdata = (Values@
AudioLocalMeasurements[#, "MFCC",
PartitionGranularity -> {1., 1.}]) & /@ rockdata1;
mFCCFeaturesClassrock = Thread[mFCCFeaturesrockdata -> "rock"];
mFCCFeaturescountrydata = (Values@
AudioLocalMeasurements[#, "MFCC",
PartitionGranularity -> {1., 1.}]) & /@ countrydata1;
mFCCFeaturesClasscountry =
Thread[mFCCFeaturescountrydata -> "country"];
First we will be implementing a neural network only on the first three genres to see how it performs, our training set consists of 540 songs and the validation set consists of 60 songs.
net = NetChain[{
GatedRecurrentLayer[128],
GatedRecurrentLayer[128],
SequenceLastLayer[],
LinearLayer[],
SoftmaxLayer[]},
"Input" -> {"Varying", 13},
"Output" -> NetDecoder[{"Class", {"metal", "pop", "reggae"}}]]
data = RandomSample[
Join[mFCCFeaturesClassPop, mFCCFeaturesClassReggae,
mFCCFeaturesClassMetal]];
trainSet1 = data[[1 ;; 540]];
validationSet1 = data[[541 ;;]];
trainedNet =
NetTrain[net, trainSet1, ValidationSet -> validationSet1,
MaxTrainingRounds -> 100]
cl5 = ClassifierMeasurements[trainedNet, validationSet1]
In[582]:= cl5["Accuracy"]
Out[582]= 0.733333
Confusion Matrix Plot
![enter image description here][2]
We implement a different architecture of the recurrent neural network for all the 10 genres, this time our training set is 1900 songs and validation set is 100 songs.
net4 = NetChain[{
GatedRecurrentLayer[256],
GatedRecurrentLayer[256],
GatedRecurrentLayer[256],
SequenceLastLayer[],
LinearLayer[],
SoftmaxLayer[]},
"Input" -> {"Varying", 13},
"Output" ->
NetDecoder[{"Class", {"country", "blues", "disco", "hiphop",
"jazz", "metal", "pop", "reggae", "rock", "classical"}}]
]
data = RandomSample[
Join[mFCCFeaturesClassPop, mFCCFeaturesClassReggae,
mFCCFeaturesClassMetal, mFCCFeaturesClassJazz,
mFCCFeaturesClassblues, mFCCFeaturesClassclassical,
mFCCFeaturesClasscountry, mFCCFeaturesClassdisco,
mFCCFeaturesClassrock, mFCCFeaturesClasshiphop]];
trainSet = data[[1 ;; 1900]];
validationSet = data[[1901 ;;]];
trainednet4 =
NetTrain[net4, trainSet, ValidationSet -> validationSet,
MaxTrainingRounds -> 100]
cl = ClassifierMeasurements[trainednet4, validationSet]
In[620]:= cl["Accuracy"]
Out[620]= 0.75
![enter image description here][3] Confusion Matrix Plot
We achieve an accuracy of 75% for classifying the genres of the audio files.
We will now construct a function which takes in an audio and classifies it into a genre.
In[571]:=
findGenre[sound_] :=
With[{audio =
Values@AudioLocalMeasurements[AudioResample[sound, 22050], "MFCC",
PartitionGranularity -> {1., 1.}]},
trainednet4[audio]
]
In[577]:= findGenre[rockdata[[-3]]]
Out[577]= "rock"
In[587]:= findGenre[countrydata[[-2]]]
Out[587]= "country"
[1]: http://community.wolfram.com//c/portal/getImageAttachment?filename=ScreenShot2017-07-05at4.02.54AM.png&userId=1082206
[2]: http://community.wolfram.com//c/portal/getImageAttachment?filename=ScreenShot2017-07-05at4.31.13PM.png&userId=1082206
[3]: http://community.wolfram.com//c/portal/getImageAttachment?filename=ScreenShot2017-07-05at4.42.33PM.png&userId=1082206Aishwarya Praveen2017-07-05T20:50:50ZCommutative avatars of representations of semisimple Lie groups
https://community.wolfram.com/groups/-/m/t/3290514
![Commutative avatars of representations of semisimple Lie groups math printed with J850 Digital Anatomy 3D Printer ][1]
&[Wolfram Notebook][2]
[back-up]: https://community.wolfram.com//c/portal/getImageAttachment?filename=Main03102024.png&userId=20103
[1]: https://community.wolfram.com//c/portal/getImageAttachment?filename=2435qtegdsb.jpg&userId=11733
[2]: https://www.wolframcloud.com/obj/06872339-7181-493f-9079-759464171944Tamas Hausel2024-10-03T20:40:45ZFinding missing gems amidst chaos
https://community.wolfram.com/groups/-/m/t/3289552
![enter image description here][1]
&[Wolfram Notebook][2]
[1]: https://community.wolfram.com//c/portal/getImageAttachment?filename=4418hero.png&userId=20103
[2]: https://www.wolframcloud.com/obj/5a57cc41-0643-46b1-872a-2605ee2f03baBrad Klee2024-10-03T01:23:58ZWhat is the substitution or replacement method for multiple functions and their derivatives?
https://community.wolfram.com/groups/-/m/t/3290412
I want to substitute functions and their derivatives in this:
{LXi = x*D[Xi[2][t], t] + Sqrt[x] h[t],
Xi[2][t]}; LPhi = { (p[t] + f[x, t]) u + g[x, t]};
f[x, t] =
C[1][t] + ((-((4 k \[Theta] h[t])/Sqrt[x]) +
6 Sqrt[x] (k h[t] + 2 Derivative[1][h][t]) +
6 x (k Derivative[1][Xi[2]][t] + (Xi[2]^\[Prime]\[Prime])[t]))/(
8 k \[Theta]))
Is this correct?
{LXi, LPhi} =
ReplaceAll[{LXi = {x*D[Xi[2][t], t] + Sqrt[x] h[t], Xi[2][t]},
LPhi = { (p[t] +
1/(8 k \[Theta]) (-(1/Sqrt[x]) 4 k \[Theta] h[t] +
6 Sqrt[x] (k (*h[t]*)+ 2 D[h[t], t]) +
6 x (k D[Xi[2][t], t] + D[Xi[2][t], {t, 2}]))) u +
g[x, t]}}, {h[t] ->
E^((Sqrt[k] t Sqrt[3 k + 8 \[Theta]])/(2 Sqrt[3])) C[1] +
E^(-((Sqrt[k] t Sqrt[3 k + 8 \[Theta]])/(2 Sqrt[3]))) C[2],
p[t] -> C[3] - (
3 E^(-((t Sqrt[k (3 k + 8 \[Theta])])/Sqrt[
3])) (-1 + E^((t Sqrt[k (3 k + 8 \[Theta])])/Sqrt[
3])) (-3 k +
3 E^((t Sqrt[k (3 k + 8 \[Theta])])/Sqrt[3]) k - 8 \[Theta] +
8 E^((t Sqrt[k (3 k + 8 \[Theta])])/Sqrt[3]) \[Theta] +
Sqrt[3] Sqrt[k (3 k + 8 \[Theta])] +
Sqrt[3] E^((t Sqrt[k (3 k + 8 \[Theta])])/Sqrt[3]) Sqrt[
k (3 k + 8 \[Theta])]) C[5])/(8 (3 k + 8 \[Theta])) - (
3 E^(-((t Sqrt[k (3 k + 8 \[Theta])])/Sqrt[
3])) (-1 + E^((t Sqrt[k (3 k + 8 \[Theta])])/Sqrt[
3])) (3 Sqrt[3] k +
3 Sqrt[3] E^((t Sqrt[k (3 k + 8 \[Theta])])/Sqrt[3]) k +
8 Sqrt[3] \[Theta] +
8 Sqrt[3] E^((t Sqrt[k (3 k + 8 \[Theta])])/Sqrt[
3]) \[Theta] - 3 Sqrt[k (3 k + 8 \[Theta])] +
3 E^((t Sqrt[k (3 k + 8 \[Theta])])/Sqrt[3]) Sqrt[
k (3 k + 8 \[Theta])]) C[6])/(
8 (3 k + 8 \[Theta]) Sqrt[k (3 k + 8 \[Theta])]),
Xi[2][t] ->
C[4] + (Sqrt[3]
E^(-((t Sqrt[k (3 k + 8 \[Theta])])/Sqrt[
3])) (-1 + E^((2 t Sqrt[k (3 k + 8 \[Theta])])/Sqrt[3])) C[
5])/(2 Sqrt[k (3 k + 8 \[Theta])]) + (
3 E^(-((t Sqrt[k (3 k + 8 \[Theta])])/Sqrt[
3])) (-1 + E^((t Sqrt[k (3 k + 8 \[Theta])])/Sqrt[3]))^2 C[
6])/(2 k (3 k + 8 \[Theta])),
D[h[t], t] -> (
E^((Sqrt[k] t Sqrt[3 k + 8 \[Theta]])/(2 Sqrt[3])) Sqrt[k]
Sqrt[3 k + 8 \[Theta]] C[1])/(2 Sqrt[3]) - (
E^(-((Sqrt[k] t Sqrt[3 k + 8 \[Theta]])/(2 Sqrt[3]))) Sqrt[k]
Sqrt[3 k + 8 \[Theta]] C[2])/(2 Sqrt[3]) ,
D[Xi[2][t], t] ->
E^((t Sqrt[k (3 k + 8 \[Theta])])/Sqrt[3]) C[5] -
1/2 E^(-((t Sqrt[k (3 k + 8 \[Theta])])/Sqrt[
3])) (-1 + E^((2 t Sqrt[k (3 k + 8 \[Theta])])/Sqrt[3])) C[
5] + (
Sqrt[3] (-1 + E^((t Sqrt[k (3 k + 8 \[Theta])])/Sqrt[3])) Sqrt[
k (3 k + 8 \[Theta])] C[6])/(k (3 k + 8 \[Theta])) - (
Sqrt[3] E^(-((t Sqrt[k (3 k + 8 \[Theta])])/Sqrt[
3])) (-1 + E^((t Sqrt[k (3 k + 8 \[Theta])])/Sqrt[
3]))^2 Sqrt[k (3 k + 8 \[Theta])] C[6])/(
2 k (3 k + 8 \[Theta])),
D[Xi[2][t], {t, 2}] -> (
2 E^((t Sqrt[k (3 k + 8 \[Theta])])/Sqrt[3])
k (3 k + 8 \[Theta]) C[5])/(
Sqrt[3] Sqrt[k (3 k + 8 \[Theta])]) + (
E^(-((t Sqrt[k (3 k + 8 \[Theta])])/Sqrt[
3])) (-1 + E^((2 t Sqrt[k (3 k + 8 \[Theta])])/Sqrt[
3])) k (3 k + 8 \[Theta]) C[5])/(
2 Sqrt[3] Sqrt[k (3 k + 8 \[Theta])]) - (
2 E^((t Sqrt[k (3 k + 8 \[Theta])])/Sqrt[3]) Sqrt[
k (3 k + 8 \[Theta])] C[5])/Sqrt[
3] + ((-2 (-1 + E^((t Sqrt[k (3 k + 8 \[Theta])])/Sqrt[
3])) k (3 k + 8 \[Theta]) +
1/2 E^(-((t Sqrt[k (3 k + 8 \[Theta])])/Sqrt[
3])) (-1 + E^((t Sqrt[k (3 k + 8 \[Theta])])/Sqrt[
3]))^2 k (3 k + 8 \[Theta]) +
3/2 E^(-((t Sqrt[k (3 k + 8 \[Theta])])/Sqrt[
3])) (2/3 E^((2 t Sqrt[k (3 k + 8 \[Theta])])/Sqrt[3])
k (3 k + 8 \[Theta]) +
2/3 E^((t Sqrt[k (3 k + 8 \[Theta])])/Sqrt[
3]) (-1 + E^((t Sqrt[k (3 k + 8 \[Theta])])/Sqrt[
3])) k (3 k + 8 \[Theta]))) C[6])/(
k (3 k + 8 \[Theta]))
Please show a generic way of substitution if possible, without having to manually find their derivatives first before substitution.Nomsa Ledwaba2024-10-03T10:03:23ZVirus production in shallow groundwater at the bank of the Danube River
https://community.wolfram.com/groups/-/m/t/3289943
![Virus production in shallow groundwater at the bank of the Danube River][1]
&[Wolfram Notebook][2]
[1]: https://community.wolfram.com//c/portal/getImageAttachment?filename=5336Main02102024.png&userId=20103
[2]: https://www.wolframcloud.com/obj/f80a61a0-6ca0-4da8-8e21-a76f61e7fcefChristian Winter2024-10-02T18:29:52Z[WSA24] Simulation of a geometrical racing line
https://community.wolfram.com/groups/-/m/t/3289389
![enter image description here][1]
&[Wolfram Notebook][2]
[1]: https://community.wolfram.com//c/portal/getImageAttachment?filename=5678hero.png&userId=20103
[2]: https://www.wolframcloud.com/obj/f8b81ede-6fdd-4fd8-bc5d-05423dd7b4cbVladimir Shirkhanyan2024-10-02T10:33:47ZGauss-Bonnet for form curvatures
https://community.wolfram.com/groups/-/m/t/3289909
![enter image description here][1]
&[Wolfram Notebook][2]
[1]: https://community.wolfram.com//c/portal/getImageAttachment?filename=8628Main02102024.png&userId=20103
[2]: https://www.wolframcloud.com/obj/743858fd-433c-4c2c-8b52-6779d10de985Oliver Knill2024-10-02T15:21:49ZAnnular solar eclipse of Oct 2, 2024
https://community.wolfram.com/groups/-/m/t/3289692
![enter image description here][1]
&[Wolfram Notebook][2]
[1]: https://community.wolfram.com//c/portal/getImageAttachment?filename=Main02102024.png&userId=20103
[2]: https://www.wolframcloud.com/obj/8d24d13d-07e7-466c-933c-443ee8cd954dJeffrey Bryant2024-10-02T14:27:18ZUsing recurrent layer in neural network
https://community.wolfram.com/groups/-/m/t/3289669
Hello
I am new to machine learning models
I use the Classify and other instructions quite well
But I have difficulties with neural networks
I have a training set of 36 examples that is presented in the following form
training={{0.105, 0.92, -1.5} -> 2.69, {-0.04, 0.4, -1.3} ->
7.2, {-0.112, -0.36, -1.2} -> 8.18, {-0.137, 0.73, -1.2} ->
9.02, {-0.065, -0.59, -1.1} -> 15.29, {-0.049, -0.06, -0.9} ->
19.85, {-0.062, -1.26, -0.5} -> 20.97, {0.014, -0.05, -0.4} ->
19.07, {0.003, 0.25, -0.4} -> 14.94, {-0.097, 0.85, -0.4} ->
11.28, {0.073, -1.26, -0.6} -> 7.78, {0.082, -1.02, -0.8} ->
0.75, {0.096, 0.08, -0.8} -> 5.14, {-0.008, 0.7, -0.5} ->
5.22, {0.006, -1.02, -0.2} -> 6.34, {0.162, -0.22, 0.2} ->
9.97, {0.166, -0.59, 0.4} -> 12.19, {0.283, -1.64, 0.6} ->
16.34, {0.415, 1.37, 0.7} -> 18.77, {0.297, -0.22, 0.9} ->
17.58, {0.243, -1.36, 1.} -> 16.87, {0.252, 1.87, 1.2} ->
10.4, {0.168, -0.39, 1.} -> 8.98, {0.168, 1.32, 0.8} ->
4.76, {0.165, 0.93, 0.5} -> 2.5, {0.176, -0.83, 0.4} ->
2.4, {0.224, -1.49, 0.3} -> 9.03, {0.184, 1.01, 0.3} ->
12.3, {0.174, -1.12, 0.2} -> 15.07, {0.376, -0.4, 0.} ->
18.43, {0.366, -0.09, -0.1} -> 21.26, {0.397, -0.28, 0.} ->
19.59, {0.355, -0.54, 0.2} -> 12.83, {0.348, -0.73, 0.1} ->
11.01, {0.244, -1.13, 0.} -> 5.27, {0.334, -0.43, 0.1} -> 3.44}
When I use a LinearLayer[] with the following instructions everything is OK
model = NetTrain[LinearLayer[], trainingset]
And now I have a good result on a test set
model[oscil12[[3]]]
The result is : 10.07
But if I use a recurrent layer, for example BasicRecurrentLayer, and I initialize it,
netL = NetInitialize[BasicRecurrentLayer[1, "Input" -> {"Varying", 3}]]
model = NetTrain[netL, trainingset]
I do not have the right result
Question 1 : Why?, my netL is incomplete? What layer I must add? SigmoidLayer or other active or output layer?
Question 2 : What is the simpler solution?
Question 3 : When I agree with my model, can I include this model in Predict[] instruction if I choose NeuralNetwork method
Thanks for your attentionAndré Dauphiné2024-10-02T12:30:14ZMatrixSymbol simplifications
https://community.wolfram.com/groups/-/m/t/3288833
I'm exploring the new 14.1 MatrixSymbol functionality, hoping to eventually simplify complex and lengthy matrix expressions. But I'm running into limitations even with simple expressions. For example:
A = MatrixSymbol["A", {n, n}];
FullSimplify[A + Transpose[A], Assumptions -> A == Transpose[A]]
Out[18]= 2 Transpose[(MatrixSymbol["A", {n, n}])]
(** OK !! **)
FullSimplify[A - Transpose[A], Assumptions -> A == Transpose[A]]
Out[19]= 0
(** should we not see O_n,n ? **)
FullSimplify[Inverse[A] . Transpose[A], Assumptions -> A == Transpose[A]]
Out[20]= Inverse[(MatrixSymbol[
"A", {n, n}])] . Transpose[(MatrixSymbol["A", {n, n}])]
(**I was hoping to see an identity matrix **)
What am I missing?Eric Michielssen2024-09-30T23:57:43ZCalculate present value of cashflow with irregular intervals
https://community.wolfram.com/groups/-/m/t/3093128
How do I calculate the present value of a cashflow with irregular intervals and amounts. I didn't find anything about this in TimeValue[] documentation. Say, the cashflow is...
cf = {{{2024, 1, 16}, 324.67`}, {{2024, 2, 6}, 634.09`}, {{2024, 11, 20}, 356.27`}, {{2023,12,31}, 0};
What functions would return the present value on 1/1/2023 assuming a 5 percent discount?Jay Gourley2023-12-29T22:32:00ZEmpowering mathematics education through programming with Wolfram AI and chat-enabled notebooks
https://community.wolfram.com/groups/-/m/t/3288988
&[Wolfram Notebook][1]
[1]: https://www.wolframcloud.com/obj/390b3f6c-6c28-477b-9f08-d74f7f24ea7dPaul Abbott2024-10-01T17:36:50ZIs Opacity in Graphics3D flinky on your (Linux) system (Mathematica 4.1.0)?
https://community.wolfram.com/groups/-/m/t/3285996
After several years of using Windows, I recently returned to using Linux, so I can't say how long this has been an issue. I don't even know if it is a generic Linux problem, or specific to my setup. Under Linux, Graphics3D with opacity has "clipping" issues. **I would like to know if others are experiencing a similar result.** I note that the image generated by the server hosting this forum is not problematic.
After I originally posted, I noticed that if I "grab" the image with my mouse to move it around, the clipping vanishes until it is released.
Also, there is an errant comma in the graphics object list of the code I posted, but it appears to benign.
Without more resources, it is difficult to determine the source of this problem. It could be hardware, drivers, display server (X vs Windows), configuration (screen resolution, etc.), etc. Knowing if others are experiencing this problem, and under what circumstances, will help determine its source.
<h3>A notebook exhibiting the problem under Linux:</h3>
&[Example notebook producing the problem][1]
<h3>A screen-scrape of the problem taken from my Linux system:</h3>
![Example of the problem under Linux][2]
<h3>A screen-scrape of the preferred result taken from my Windows 11 system:</h3>
![enter image description here][3]
<h3>My Linux system's information:</h3>
Operating System: openSUSE Leap 15.6
KDE Plasma Version: 5.27.11
KDE Frameworks Version: 5.115.0
Qt Version: 5.15.12
Kernel Version: 6.4.0-150600.23.22-default (64-bit)
Graphics Platform: X11
Processors: 32 × Intel® Core™ i9-14900KS
Memory: 94.0 GiB of RAM
Graphics Processor: Mesa Intel® Graphics
Manufacturer: ASUS
[1]: https://www.wolframcloud.com/obj/bdaaa26f-248a-420a-b08d-994ad9861834
[2]: https://community.wolfram.com//c/portal/getImageAttachment?filename=flinky-opacity-linux.png&userId=3269649
[3]: https://community.wolfram.com//c/portal/getImageAttachment?filename=flinky-opacity-windows.png&userId=3269649Steven Hatton2024-09-28T15:10:18ZTopological minibands and quantum anomalous hall state in Moiré insulators
https://community.wolfram.com/groups/-/m/t/3288963
![enter image description here][1]
&[Wolfram Notebook][2]
[1]: https://community.wolfram.com//c/portal/getImageAttachment?filename=Main01102024.png&userId=20103
[2]: https://www.wolframcloud.com/obj/7f959940-163f-40c4-a122-e86781741ed1Kaijie Yang2024-10-01T15:33:12ZAppend a column to a nested dataset
https://community.wolfram.com/groups/-/m/t/3288108
I have the following nested dataset:
![enter image description here][1]
ds = Dataset[
<|"x" ->
{<|"col1" -> 4.2, "col2" -> 2.5|>, <|"col1" -> 1.6,
"col2" -> 7.4|>, <|"col1" -> 7.1, "col2" -> 3.6|>}
,
"y" ->
{<|"col1" -> 9.1, "col2" -> 2.8|>, <|"col1" -> 2.7,
"col2" -> 5.4|>, <|"col1" -> 5.3, "col2" -> 0.6|>}
|>
]
How can I append a column `col3` to the `x` sub-dataset, so that `col3=f[col1]`, as below:
![enter image description here][2]
Doing
ds = ds["x", All, <|#, "new" -> f[#col1]|> &]
adds the column but removes information about the "y" key.
[1]: https://community.wolfram.com//c/portal/getImageAttachment?filename=6227Untitled.png&userId=1344988
[2]: https://community.wolfram.com//c/portal/getImageAttachment?filename=Untitled2.png&userId=1344988Ehud Behar2024-09-30T11:10:57ZCreative generative design with mathematical marbling
https://community.wolfram.com/groups/-/m/t/3258063
[![Generative design with mathematical marbling][1]][2]
&[Wolfram Notebook][3]
[1]: https://community.wolfram.com//c/portal/getImageAttachment?filename=MathematicalMarblingBanner.jpg&userId=20103
[2]: https://community.wolfram.com//c/portal/getImageAttachment?filename=MathematicalMarblingBanner.png&userId=20103
[3]: https://www.wolframcloud.com/obj/18517ffb-0f53-4ab0-a2c9-a989b51c6268Phileas Dazeley-Gaist2024-08-27T14:59:23Z[WSRP24] Study of Hash Probing on a Graph
https://community.wolfram.com/groups/-/m/t/3215183
![Torus graph with grid probing performed on it][1]
&[Wolfram Notebook][2]
[1]: https://community.wolfram.com//c/portal/getImageAttachment?filename=CoverImage.png&userId=3214738
[2]: https://www.wolframcloud.com/obj/9f5f3991-4070-4937-98e2-6e4a2218775fDavid Wang2024-07-11T18:47:11ZIs it possible to publish to the cloud using custom packages and custom stylesheets?
https://community.wolfram.com/groups/-/m/t/3288246
I have 100+ notebooks which all depend on on a custom style sheet and one or more custom packages. Is it possible to share these on the cloud so that they have access to the packages and stylesheet?Steven Hatton2024-09-30T20:19:01ZThe limit space of self-similar groups and Schreier graphs
https://community.wolfram.com/groups/-/m/t/3288175
![enter image description here][1]
&[Wolfram Notebook][2]
[1]: https://community.wolfram.com//c/portal/getImageAttachment?filename=Main30092024.png&userId=20103
[2]: https://www.wolframcloud.com/obj/e4496ce7-2068-4b18-99e9-c9dcb1bb765dBozorgmehr vaziri2024-09-30T19:18:56ZDo LLM's learn transferable skills?
https://community.wolfram.com/groups/-/m/t/3288389
![Correlation matrix of evals from the HuggingFace dataset. Do LLM's learn transferable skills?][1]
&[Wolfram Notebook][2]
[1]: https://community.wolfram.com//c/portal/getImageAttachment?filename=2837Main07102024.png&userId=20103
[2]: https://www.wolframcloud.com/obj/e6afe122-ec83-4afe-8270-cbe0c03d607aChristopher Wolfram2024-09-30T16:27:30ZImplement 'curl' command with URLRead, HTTPRequest, etc.
https://community.wolfram.com/groups/-/m/t/3282552
I am attempting to access the list of projects from a private/internal GitLab host with ML's URLRead function. I have been successful accessing the data via a browser as well as from the following command in a terminal:
curl --cert /path/to/certs.pem:its_password --header "Authorization: Bearer users_personal_access_token" https://private.gitlab.com/api/v4/projects
(with the proper values of 'its\_password', 'users\_personal\_access\_token', and 'private.gitlab.com' private git lab host). Unfortunately in WL I am unable to replicate the query with various iterations of the following:
URLRead[
HTTPRequest[
"Scheme"->"https",
"Domain"->"private.gitlab.com",
"Path"->"/api/v4/projects"
],
All,
Authentication-><|
"Headers"-><|"Authorization"->"Bearer users_personal_access_token"|>,
"PEMFile"->"/path/to/certs.pem",
"PEMFilePassword"->"its_password"
|>
]
The URLRead returns errors "400 No required SSL certificate was sent." The various iterations are moving things around, such as removing the "Authentication->..." and moving the "Header"->... inside the HTTPRequest above it; also replacing "PEMFile" (etc.) with "ClientCertificate", "CertificateFile", depending on how Mathematica Stack Exchange, Microsoft Copilot, and Claude feel that day. Even took Wireshark traces of "curl" and "URLRead"; that was overwhelming and did not manage to get any useful comparison due to my lack of experience.
Have you been successful querying services that require authentication (particularly GitLab)? How did you do it? Any assistance would be great, and thank you for your time.Ed Estrella2024-09-24T20:28:32ZSolving differential equation depending on radial and time parameter
https://community.wolfram.com/groups/-/m/t/3285392
Hi, I hope you are all doing well so I am trying to solve this differential equations which depends on radial and a time parameter to find the velocity, as an initial condition i took the value of the stationary condition which I solved separately. So when i tried to solve the final equations i got these errors which I don't know what causes it, is it the initial conditions or the method in which i want to solve it. So if any one of you have an idea it would help me a lot Thank you all in advance
&[Wolfram Notebook][1]
[1]: https://www.wolframcloud.com/obj/c772837f-00e0-42a3-9c1d-4a33cc33c6daLeo Murphy2024-09-27T09:53:55Z