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RSS Feed for Wolfram Community showing any discussions in tag sorted by activeIntegral de Ahmed.
https://community.wolfram.com/groups/-/m/t/3143222
¿ Porqué Mathematica no evalúa la conocida integral de Ahmed
Integrate[(ArcTan[Sqrt[q^2 + x^2]]/((1 + x^2) Sqrt[q^2 + x^2])), {x, 0, 1}]?
Tampoco evalúa ciertas generalizaciones de la integral de Ahmed, por ejemplo
Integrate[ArcTan[ Sqrt[4 + x^2]]/(
Sqrt[4 + x^2] (2 + x^2)), {x, 0, 1}] ,
Integrate[ArcTan[ Sqrt[2 + x^2]]/(
Sqrt[2 + x^2] (4 + x^2)), {x, 0, 1}], ......etc.José Luis Garrido2024-03-19T09:20:01ZHow to limit variables in solve[]?
https://community.wolfram.com/groups/-/m/t/3143472
Hello swarm intelligence,
I ran into an issue while trying to solve a problem.
Starting point is, that I have two 2D polar coordinate systems, that are offset to each other in x/y and are are turned by an unknown value and want to setup a calculation to find these three values.
Now I have two points of which I know the radial and and angular values for both systems. With these 4 values I did some trigonometry and came to the following equation, which I want to solve to x, with x being the angle difference between the two systems:
sin(a1 + x) s11)^2 + (s21 - cos(a1 + x) s11)^2 = (sin(a2 + x) s12)^2 + (s22 - cos(a2 + x) s12)^2
Which works with the command:
solve (sin(a1 + x) s11)^2 + (s21 - cos(a1 + x) s11)^2 = (sin(a2 + x) s12)^2 + (s22 - cos(a2 + x) s12)^2 for x
But gives a multitude of solutions, since without limiting the values there are a multitude of solutions.
Since I know that all my values are real numbers and my angles are within 0 to 2pi, I tried to limit the values through using assumptions.
https://reference.wolfram.com/language/ref/Solve.html
But switching through multiple types of syntax found there, it screwed up the solving that the calculation wasn't recognized anymore.
tldr: how do I limit my variables and values to reduce the amount of possible solutions?Reinhard Müller2024-03-19T09:14:47ZDifficulty with PointProcess
https://community.wolfram.com/groups/-/m/t/2151051
When I use PoissonPointProcess with my data, it is OK
ClearAll["Global`*"]
villes = Entity["Country", "France"]["LargestCities"];
data = SpatialPointData[villes]
proc = EstimatedPointProcess[data, PoissonPointProcess[\[Lambda], 2]]
ListPlot[{RipleyK[data, Range[0, 200, 10]],
RipleyK[proc, Range[0, 200, 10]]},
PlotLegends -> {"original process", "estimated model"}]
But if I work with an other PointProcess, I can't have a result. Why ?
see for example :
proc4 = EstimatedPointProcess[data, StraussPointProcess[a, b, c, 2]]
ListPlot[{RipleyK[data, Range[0, 200, 10]],
RipleyK[proc4, Range[0, 200, 1]]},
PlotLegends -> {"original process", "estimated model"}]André Dauphiné2020-12-30T13:42:23ZHow to earn money online?
https://community.wolfram.com/groups/-/m/t/3143357
India’s Best Online Earning App. Solve captchas Anytime, Anywhere & Earn Unlimited Cash! Now earn money online is easier than ever before. Start your online earning journey with the [Earneasy24 app][1] and earn INR 20, 000 per month by just solving captchas. How to Earn Money Online With Earneasy24? Solve the captchas one by one and earn coins for every correct captcha entry & Repeat! Receive payments directly to your Bank Account. Start Earning In Three Simple Steps: 1. Download & Register - Download the app and Register. 2. Select a Plan and Pay security Deposit (Refundable). 3. Solve Captchas - Click to start button and solve the captchas correctly. . There is no penalty for incorrect or skipped entries. Solve as much as you can and there is no limitation on earning. 3. Get Payments - Get paid for solving correct captchas & receive payments directly to your Bank Account. Why Is [Earneasy24][2] The Best Online Earning App In India? 1. Easy to use The user interface of the application has been designed to provide a smooth and hassle free user hassle-free. 2. No skills required Earning on [Earneasy24][3] is very simple and using it needs no skill set. Just Solve the Captchas visible on the screen & get paid for each solved case. 3. Easy and on Time Payments You can redeem the earned coins easily via options like Paytm, Phonepe, Gray, and IMPS/NEFT in just 4-7 working days. 4. Unlimited Earning There is no limitation on earning in Earneasy24. Work anytime from anywhere and earn unlimited cash. 5. The Finest Customer Support Want to resolve any query about Subscribing to a plan, service, refund, or anything related to earneasy24, just email us at support@earneasy24.in
[1]: https://play.google.com/store/apps/details?id=com.techaircraft.techaircraft
[2]: https://www.earneasy24.com/
[3]: https://earneasy24.in/Vashu Pandat2024-03-19T09:06:25ZHow to access a private paclet server
https://community.wolfram.com/groups/-/m/t/3143427
As far as I spleunked, neither PacletSiteRegister nor PacletSiteUpdate accept Authentication or "Headers" options, which are required to access a private remote server. Furthermore, neither of them actually accept HTTPRequest instead of an url as first argument. A paclet server set up in a private GitHub repository requires the following code to access the PacletSite.mz
Assuming that the user has access to the pre-set myToken (in this case, a Personal Authentication Token), this works. Howeverm, I have no way to pass on authentication details to PacletSiteRegister or PacletSiteUpdate. I understand that a private repo goes somewhat against the idea of a public paclet server, but due to legal considerations
xem thêm dịch vụ [thu mua ipad cũ giá cao][1] [cho thuê ipad hcm][2]
[1]: https://thumuaipadcu.com/thu-mua-ipad-cu-gia-cao-tphcm/
[2]: https://techservice.vn/san-pham/cho-thue-ipad-gia-re-tai-tphcm/cadiva jack2024-03-19T08:12:04ZLiquid Chromatography with Linear Adsorption Equilibrium and Transfer Rate Model
https://community.wolfram.com/groups/-/m/t/3143304
&[Wolfram Notebook][1]
[1]: https://www.wolframcloud.com/obj/fa2a641f-9eb5-42d4-92fc-230f6eefc6feHousam Binous2024-03-19T06:45:15ZFitting Solution of a DE to a function
https://community.wolfram.com/groups/-/m/t/3142858
I am trying to solve the following system of differential equations, which depend on three parameters, namely lambda, sigma0, sigma a. The final goal is to find a parameter triple, which fits the function sqrt[0.3166*(1+z)^3+0.6847] on the interval z=(0,3).
So far, I managed to plot the solution of the system of differential equations via Manipulate. But finding a parameter triple, for which the solution fits, seems quite tedious. Is there a way to do this systematically, or only trial and error? I attach what I have so far.
&[Wolfram Notebook][1]
[1]: https://www.wolframcloud.com/obj/f055ea80-d619-426c-bac6-8e541ce37505Lehel Csillag2024-03-18T19:51:49Z[WSG24] Daily Study Group: Topics in Artisanal Calculus
https://community.wolfram.com/groups/-/m/t/3139584
Don't forget to join us this week for our ongoing study group covering topics in calculus from new angles. Bell polynomials, the Euler-Maclaurin formula, and fractional calculus are among the topics you will see how to explore with Wolfram Language. Also see how these ideas find applications in the study of dynamical systems, minimal surfaces, and number theory. Each day's session is self-contained if your schedule causes you to miss one.
Whether you are new to Calculus or an instructor looking for cool new examples, learn how Wolfram|Alpha developers bring computation to the study of mathematics. Ask questions in the study group sessions, answer polls to check your understanding, and receive a certificate of attendance. If you follow the registration link after the study group concludes, you will find video recordings of the sessions.
> [**REGISTER HERE**][1]
Use this thread to collaborate and to share ideas, materials and links to other resources with fellow learners.
![enter image description here][2]
[1]: https://www.bigmarker.com/series/wsg49-artisanal-calculus/series_details?utm_bmcr_source=community
[2]: https://community.wolfram.com//c/portal/getImageAttachment?filename=WolframUbanner.png&userId=2643831John McNally2024-03-12T16:55:28ZMathmatica pefromance and CPU usage
https://community.wolfram.com/groups/-/m/t/3143033
I have a general question that may have been addressed previously, albeit not directly. I utilize Mathematica to solve a set of non-linear equations and achieve successful results. However, the computation time is considerably long despite the minimal CPU and memory usage. Additionally, the computer I am using is a high-performance PC, yet the execution speed of this code resembles that of my laptop. Am I overlooking something? Why isn't Mathematica utilizing more resources? For instance, the CPU usage remains around 7% max.Nima Moini2024-03-18T23:02:58ZStationary dynamics in DNA: a nonlinear Klein-Gordon approach
https://community.wolfram.com/groups/-/m/t/3137876
&[Wolfram Notebook][1]
[1]: https://www.wolframcloud.com/obj/24692edf-0555-4097-80ce-1958ebe919fdAthanasios Paraskevopoulos2024-03-08T23:25:24ZColloquium event - numerical methods for partial differential equations and their applications
https://community.wolfram.com/groups/-/m/t/3132386
![enter image description here][1]
In this special online colloquium, we have invited researchers from around the world to share their recent exciting work. The topic of the inaugural event in this series is "Numerical Methods for Partial Differential Equations and Their Applications". The works shown range from new quantitative methods, to new real-world applications, to novel ways of modeling. The event also begins with a very brief introduction to [PDE Models][2] in the Wolfram Language that introduces functionality new to Version 14.
The (estimated) start time for each presenter can be found in the cloud notebook here: [Link][3].
To register for the event please follow the link to the BigMarker platform found below.
> [**Register Here**][4]
Please feel free to use this thread to collaborate and share ideas. Also let us know what colloquium topics interest you for future events in this series!
![enter image description here][5]
[1]: https://community.wolfram.com//c/portal/getImageAttachment?filename=fem-promo.png&userId=2643831
[2]: https://reference.wolfram.com/language/PDEModels/tutorial/PDEModelsOverview.html
[3]: https://www.wolframcloud.com/obj/jmcnally0/Published/Feb29Colloqium-Schedule.nb
[4]: https://www.bigmarker.com/wolfram-u/numerical-methods-for-pde-and-applications?utm_bmcr_source=community
[5]: https://community.wolfram.com//c/portal/getImageAttachment?filename=WolframUbanner.png&userId=2643831John McNally2024-02-28T21:41:17ZInOrder tree traversal option?
https://community.wolfram.com/groups/-/m/t/3142141
What code is used to traverse a binary tree inorder?Tony Van Haagen2024-03-17T05:06:48ZAll languages text-to-Speech with ElevenLabs
https://community.wolfram.com/groups/-/m/t/3142293
&[Wolfram Notebook][1]
[1]: https://www.wolframcloud.com/obj/4f49480b-e15f-4b05-af29-31bc656655b9Marco Thiel2024-03-17T19:44:16ZPassing Wolfram language to other teams?
https://community.wolfram.com/groups/-/m/t/3142709
I'm intrigued by coding but lack proficiency in any language beyond GUI Object, such as Grasshopper. However, I excel in logic, abstraction, and problem-solving.
Though I've never developed software before, I have an exciting idea I'd like to explore.
My question is: If I begin learning Wolfram and create a prototype, is the language widely embraced enough that I can confidently hand off my work to a distributed team of professionals?Alf Schiller2024-03-18T13:57:27ZDowngrading for dragon year Pi day
https://community.wolfram.com/groups/-/m/t/3140560
&[Wolfram Notebook][1]
[1]: https://www.wolframcloud.com/obj/f8c1cc1b-f366-4bb5-bda3-dd5bfb4c07c6Brad Klee2024-03-14T01:07:00ZFinding critical points with NMaximize[] and Solve[] yielding different results query
https://community.wolfram.com/groups/-/m/t/3142452
I have two codes which carry out the same task, that is finding the maxima of a function. The function I am considering is a log-likelihood function. Since I am modelling a quantum process, I am using a random number generator to generate to measurement outcomes {m1,m1,m2} which then defines the log-likelihood function. The codes follow identical mathematical approaches, but In Code 1 I use the Mathematica built-in function NMaximize[] to find the critical points (which maximize the function) directly from the log-likelihood function, and in Code 2 I first take the derivative of the function and analytically solve for the points which yield the a zero derivative using the built-in Mathematica Solve[] function. I would expect these two approaches to yield identical results (or very similar results) for large iteration counts. But Code 1 does not converge to the expected value of 1.5, but instead maintains a negative bias by converging to about 1.475 (regardless of the number of trials). Code 2 converges to 1.5 as expected. Could anyone advise on the cause of the discrepancy. Many thanks for any assistance.
&[Wolfram Notebook][1]
[1]: https://www.wolframcloud.com/obj/b6ae5ce0-c597-4764-853e-788ca73b2e4d
**Note**: I have tried setting different Methods in the NMaximum function but still get a negative bias. There also does not seem to be an appreciable difference when considering the built-in Maximum function as opposed to NMaximum, one still gets a negative bias.Byron Alexander2024-03-18T11:49:37ZConverting a function of two variables into a matrix
https://community.wolfram.com/groups/-/m/t/3142572
Hi I hope you all doing well, I have an equation (G(A)=g(A,r)*L(r)) wish I want to solve in matrix form by turning the function "g(A,r)" into a matrix where "r" varies by column and "A" varies by row, and in the end I want to plot L(r) but I dont know how to construct this matrix, If any of you have an idea It will help me a lot, Thank you all in advance
&[Wolfram Notebook][1]
[1]: https://www.wolframcloud.com/obj/fd7e1d81-59a0-42b9-a9ce-939c65f38bc4Ali Moukhtari2024-03-18T12:16:25ZNew volcano discovered on Mars hidden in plain sight
https://community.wolfram.com/groups/-/m/t/3142811
![enter image description here][1]
&[Wolfram Notebook][2]
[1]: https://community.wolfram.com//c/portal/getImageAttachment?filename=435wg54qg.jpg&userId=11733
[2]: https://www.wolframcloud.com/obj/d7970f5e-ccd6-4048-b300-debe32b1bb56Jeffrey Bryant2024-03-18T16:23:11ZAPI access to Claude 3 and use cases: image processing, conversation and programming
https://community.wolfram.com/groups/-/m/t/3142280
![enter image description here][1]
&[Wolfram Notebook][2]
[1]: https://community.wolfram.com//c/portal/getImageAttachment?filename=1917Main.png&userId=20103
[2]: https://www.wolframcloud.com/obj/42516f06-2e9d-4dc9-8974-2be640577d3bMarco Thiel2024-03-17T18:00:41ZUsing "ToExpression" inside a Module creates Global symbols. How to force localized ones?
https://community.wolfram.com/groups/-/m/t/3142270
Converting text to useful expressions is a nice feature. In the exemple (first part) one can see that the symbols created in the "ToExpression" function are global. But I want these created symbols localized in a defined function. Logical solution is using a Module. But this went wrong, see exemple (second part). I tried a lot of other solutions in vain. So I'am missing something and asking for some help.
&[Wolfram Notebook][1]
[1]: https://www.wolframcloud.com/obj/4a40228f-1ce6-4613-981f-1f58a3bb4749Chris Van Damme2024-03-17T16:26:29ZFinding roots of multivariable function
https://community.wolfram.com/groups/-/m/t/3137899
I have a real-valued function of four variables, namely $L[\phi, m0, m1, m2]$. I am interested in taking the partial derivative $\partial_{\phi}L$ thereof and setting the partial derivative to zero, that is $\partial_{\phi}L = 0$. Then solving for $\phi \in [0,2\pi]$ in terms of $m0, m1, m2 \in
\mathbb{N}_{0}$. I have reached the point in the attached code where I have generated the partial derivative $\partial_{\phi}L$, but I am having difficulty setting the partial derivative to zero and getting an analytic expression for $\phi$ in terms of the other variables $m0,~m1$ and $m2$. Please advise if there is a clear way of doing this analytically and numerically.
&[Wolfram Notebook][1]
Just a note that the function $L[\phi, m0, m1, m2]$ is defined in terms of probabilities $P1, P2$ and $P3$, hence it has a real-valued output for any $\phi \in \mathbb{R}$. Link to [related Mathematica SE post][2].
[1]: https://www.wolframcloud.com/obj/8a8e8c5b-b040-4954-bc13-f6fd943d5026
[2]: https://mathematica.stackexchange.com/questions/300241/solving-multivariable-equation-after-setting-partial-derivative-to-zero?noredirect=1#comment739470_300241Byron Alexander2024-03-09T14:21:21ZDefine the domain of symbolic variables for a matrix when solving a system of linear equations?
https://community.wolfram.com/groups/-/m/t/3141135
Hi! I have a problem about solving a system of linear equations with 8 equations and 8 unknowns in the form A*X = 0. I solved Det[A] =2*(b^2 - 1)*c^3*(x - 2)^2*Sin[Pi*x]^3*(b*f*Sin[Pi*x] + Cos[Pi*x]), but this matrix has parameters c > 0, -0.5 < b < 0.5, f ≠ 0, and 0 < x < 1. So there is only one solution for x: x=ArcTan[1/b/f]/Pi. But I brought this solution into A using the NullSpace to solve gives me the output { }. I guess it could be that the matrix does not define the domains of the parameters a,b,c,f. Is that something that I should specify in the code? I want to get the solution to the system of equations when x = ArcTan[1/b/f]/Pi.
Here is my code:
&[Wolfram Notebook][1]
[1]: https://www.wolframcloud.com/obj/10142db1-7d88-423c-9d70-7bad0c4f47f9Russell Michael2024-03-15T10:07:27ZA two-factor model of stock returns and its application in Pairs trading
https://community.wolfram.com/groups/-/m/t/3142605
&[Wolfram Notebook][1]
[1]: https://www.wolframcloud.com/obj/733c8c1f-9e4e-4ab7-8775-8f2653cf8c2eJonathan Kinlay2024-03-18T07:58:56ZDifference between / and : in Wolfram Alpha
https://community.wolfram.com/groups/-/m/t/3142231
Hello all, I'm "new" on this.
It may sound a stupid question but... I want to know why this two formulas give different results. I read both in the name way.
[6:2(2+1)=1][1]
[6/2(2+1)=9][2]
What is the difference between / symbol and : symbol?
I know one is for division and he other one may be for ratio, but here I am wrong assuming they are the same
[1]: https://www.wolframalpha.com/input?i=6:2%282%2b1%29&lang=es
[2]: https://www.wolframalpha.com/input?i=6/2%282%2b1%29Victor Quintana2024-03-17T05:55:56ZMass balance in the Haber process
https://community.wolfram.com/groups/-/m/t/3142176
&[Wolfram Notebook][1]
[1]: https://www.wolframcloud.com/obj/031941d2-a9a1-4f92-b231-b88aa98b3580Housam Binous2024-03-17T16:25:52ZWhere half of the world lives: 69 of top 100 cities in Valeriepieris circle
https://community.wolfram.com/groups/-/m/t/3142243
[![enter image description here][1]][2]
&[Wolfram Notebook][3]
[1]: https://community.wolfram.com//c/portal/getImageAttachment?filename=VC691002.jpg&userId=11733
[2]: https://community.wolfram.com//c/portal/getImageAttachment?filename=VC691002.jpg&userId=11733
[3]: https://www.wolframcloud.com/obj/9ac23d46-7d76-4298-be53-3f28e77338efVitaliy Kaurov2024-03-17T08:06:37ZHow to make repeated notebook evaluations possible without restarting ?
https://community.wolfram.com/groups/-/m/t/3141750
Hello,
I am trying to use a notebook written by someone else, and I observe that in order to correctly repeat
the notebook evaluation I have to exit the notebook, re-load the MATHEMATICA, and read the notebook again. Otherwise the calculations are not reproduced. I presume this behaviour may be caused by un-cleared variables. I made a search for how to use Clear[] and ClearAll[] but I don't feel any wiser. I certainly don't want to put all numerous symbols present in the notebook into a Clear command, but I also don't want to unconsciously Clear something important that is defined outside the notebook. Is there no single command that would make all my runs of the notebook identically prepared, with no left-overs from previous runs?
LesławLeslaw Bieniasz2024-03-16T16:12:20ZConfidence regions with nuisance parameters
https://community.wolfram.com/groups/-/m/t/3141897
&[Wolfram Notebook][1]
[1]: https://www.wolframcloud.com/obj/c78dfa86-f81a-4e43-80ce-cc2e2b7b6976Jan Vrbik2024-03-17T02:29:58ZSupposed "antenna null" isn't?
https://community.wolfram.com/groups/-/m/t/3141376
UPDATE: This turned out to be a trivial error on my part. See the response.
I thought that [in the far field of a Hertzian dipole the reason there is no E field because the scalar and vector potential contributions to the E field cancel in the far field][1].
The following notebook *seems* to indicate that the E field of an antenna "null" isn't null at all -- it doesn't fall off as 1/r^3 nor even off as 1/r^2. It falls off as 1/r! What's going on with this ultra-simple calculation based not on an antenna but a simple point charge moving back and forth in a line?
&[Wolfram Notebook][2]
PS: The comments are a bit off. They should have said the numerator goes as the cube of z and denominator as the fourth power of z.
[1]: https://physics.stackexchange.com/questions/206631/vector-potential-oscillating-e-field-of-the-null-field-of-a-hertzian-dipole
[2]: https://www.wolframcloud.com/obj/24042a98-6003-4c02-b6b0-7214d84b07f7James Bowery2024-03-16T02:32:07ZShowing histogram and PDF of normal distribution in a plot?
https://community.wolfram.com/groups/-/m/t/2225208
Hi,
How do I show complete normal distribution over its histogram?
list = {0.014952084292167656`, -0.0011142109478073092`, \
-0.03200699329376222`, 0.02610873317718504`, -0.007922259316024804`,
0.02329423863175964`,
0.0034785055449905455`, -0.007747760345867161`,
0.003986198148096087`,
0.031948672158741004`, -0.01922689853585434`, 0.0232439658404808`,
0.009156392455101026`, 0.05302010750555419`, 0.025142071231658958`,
0.0116075829784546`, -0.001449418525741597`,
0.029618730201622007`,
0.005921508633949274`, -0.0180861548626976`, -0.00510255607675171`,
0.018578990326231004`, 0.017420623630748748`,
0.003315652924846646`,
0.005526839598472583`, -0.023282105739082348`, 0.0474595471466141`,
0.000629691585357639`, 0.005254308208282488`,
0.0323716812689209`, -0.007494270578567497`, \
-0.019957153216545107`, 0.0009755785364255892`, 0.012999416718997955`,
0.016312600450492862`, -0.022726446137008666`,
0.007457557185943597`, -0.021121406314605712`,
0.020816311136428844`,
0.018826234340667714`, -0.026312034792572048`,
0.016020506724174488`, -0.06359624135386657`, \
-0.012528348147869107`, 0.018086951234972`,
0.0009406040330610273`, -0.010624625399940489`,
0.001383440169586178`, -0.03254843844527436`, \
-0.023731778793663033`, -0.029474470123107915`,
0.017707966601989755`, -0.011709554448547377`, \
-0.02584689544087218`, 0.010129309176322931`, -0.06913883297091293`,
0.017521978981166843`, 0.014526618114977838`,
0.038873448773523334`, -0.0259937403719101`, \
-0.020663881794158942`, 0.016251452890144347`, 0.019502766982261666`,
0.0248790234506836`, -0.029827586532714834`,
0.0028897048234939604`, -0.0015713386704406807`, \
-0.0029079686403274546`, -0.012514878168525697`, \
-0.004687818520397187`, -0.003439080581300734`, -0.00081486164625931`,
0.009277975678443906`, -0.060646119527069095`,
0.007911314948852527`, -0.020871743782455432`, \
-0.034051828420303354`, -0.018067103608901985`, \
-0.019255875162330627`, -0.03503792834281921`, -0.035022689569067`,
0.0060782724170112615`,
0.04824767377845382`, -0.03138784995280075`,
0.006499843955039969`, -0.01786340096987915`, 0.02081189918518067`,
0.01398221559014895`, -0.03275392018168641`, 0.02883601571673583`,
0.05740358064871215`, -0.0009542576516227697`,
0.07298482561545772`};
fitDist =
EstimatedDistribution[list, NormalDistribution[\[Alpha], \[Beta]],
ParameterEstimator -> MethodOfMoments]
Show[Histogram[list, Automatic, PDF],
Plot[Evaluate@PDF[fitDist][x], {x, 0, 15},
PlotStyle -> Directive[Blue, Thick], Filling -> Axis]]M.A. Ghorbani2021-03-20T21:14:07ZMaintaining desired denominator during calculations
https://community.wolfram.com/groups/-/m/t/3140891
Hello ,
I am trying to calculate CS with the condition 0 < b < 1 for b in q1 and q2.
The ultimate goal is to determine whether CS is negative or positive.
However, I am encountering an issue where the desired denominator form is constantly being transformed during the calculation process in Mathematica, preventing me from calculating the final CS value.
Problem:
Desired calculation sequence:
q1 = (-2 c + 2 a α - a b α + b c α^2) / (4 α - b^2 α)
q2 = (b c + 2 a α - a b α - 2 c α^2) / ((4α - b^2 α)
cs = (q1^2 + q2^2 + 2bq1q2) / 2
However, when I input these equations into Mathematica, the denominator is transformed into the form (-4 + b^2) α for an unknown reason.
Question:
Could you please provide a method to calculate CS while maintaining the desired denominator form in Mathematica?
Alternatively, could you please advise if I am approaching the calculation incorrectly?
(
Especially, I cannot avoid using the Simplify function. However, this immediately changes the denominator to the unwanted form (-4 + b^2) α. I was unable to utilize Hold either.)Tchun Jeeyoung2024-03-15T06:25:17ZTry to beat these MRB constant records!
https://community.wolfram.com/groups/-/m/t/366628
![If you see this text, refresh the page in order to see the images.][1]
Credit: Emanual Missionary Babtist Church of Indianapolis
Hey folks, Marvin Ray Burns here! You might know me for the never-ending decimal that haunts your calculators – the MRB constant. Don't worry, I won't hold it against you if you haven't memorized its first million digits (yet!). In this forum, we're embarking on a wild ride as we work our way to "7,000,000 proven to be accurate digits!"
(select text between quotation marks and push the ![CTRL+f][2] keys on keyboard)
=================================================
I'm the amateur mathematician who discovered this enigmatic constant in 1999, and after years of delving into its mysteries, I'm still captivated by its fascinating properties and untapped potential. Join me, seasoned mathematicians, and curious minds alike, as we push the boundaries of understanding and unlock the secrets of the MRB constant. ![Buckle up!][3] (credit: https://clipground.com/save-lives-clipart.html)
![m][4]
Here's everything I have ever learned, so spend it well!
====================================================
I was inspired by the awe, beauty, and mystery of numbers, and wondered if God would grant me some unique insight and wisdom to explore them. I dreamed of becoming an artistic analyst, a musical mathematician, or even a visionary of scientific secrets, long before I knew what a mathematician was. I searched for inspiration in the numbers that appealed to me, that had beauty and meaning, and that led me to investigate a remarkable and intriguing sum that I could not find anywhere else. For my efforts, someone started calling me an [amateur mathematician][5] and it the [MRB constant][6].
The MRB constant is a fascinating mathematical object that is still under investigation. It is possible that further research will reveal even more interesting properties about the constant, and perhaps other parts of mathematics. For example, a recent advancement in MRB constant formulas connecting the Dirichlet eta to nth roots shown in this discussion ![CTRL+f][7] "Because of the following identity involving the Dirichlet Eta function derivatives,", yields a proof of the previously proposed concept that the MRB constant connects such ideas together.
I am just an ordinary person like you, who stumbled upon a fascinating discovery that I wanted to share with the world. I now know that there are many experts in the field of series who have devoted their lives to this subject. I respect their work and therefore make no claim to have found anything new or groundbreaking. However, I am very curious and passionate about the MRB constant, which is a remarkable number that appears in many series. I hope that you will join in this journey of exploration and learning, as I present my findings and thoughts on this topic. I would greatly appreciate your feedback and insights, as I am always eager to learn more and improve my understanding. I also want to acknowledge the contributions of several people who have helped along the way, either by providing data, code, or suggestions. Without them, this discussion would not be possible.
![If you see this instead of an image, reload the page.][8]
![enter image description here][9]
![enter image description here][10]
Credit: Traders Point Christian Church Northwest
----------
![enter image description here][11]
> Ah, that make sense! The MRB constant could definitely be a catalyst in that way. Here's how:
**The Story of the MRB Constant as a Catalyst:**
> In 1999, an amateur mathematician discovered the MRB constant. While
> not a professional researcher, his curiosity and exploration led him
> to identify this unique mathematical object. The unusual properties
> of the MRB constant, particularly its behavior in infinite series,
> sparked interest within the mathematical community.
>
> **The Catalyst Effect:**
>
> * **Intriguing New Object:** The MRB constant presented a new mathematical entity with unknown characteristics. This piqued the
> interest of professional mathematicians who began investigating its
> properties and potential applications.
> * **Questioning Established Ideas:** The way the MRB constant behaves in infinite series challenged some existing assumptions about
> convergence. This led researchers to re-examine these concepts and
> potentially refine them.
> * **Inspiration for Further Exploration:** The discovery of the MRB constant demonstrated the potential for significant finds by amateurs.
> This could inspire others outside traditional academia to delve into
> mathematics, fostering a broader base of exploration.
>
> **Overall, the MRB constant, discovered 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.**
----------
POSTED BY: Marvin Ray Burns.
========
![If you see this text, the images are not showing. Refresh the page.][12]
![The first 100 partial sums of][13] {![the CMRB series.][14]}
----------
For the best viewing, wait a minute until the word LaTeX in the LaTex script is centered below.
$$\LaTeX$$
If the phrase [Math Processing Error] is shown, or the LATEX script have vanished from the center of the above line, some of the math below might be missing or appear in the LaTex code instead of the script.
For easy navigation, use the ![CTRL+f][15] keys on your keyboard. Cues in the forms of §'s and keywords in quotes are provided in the ![CTRL+f][16] "Index".
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.
----------
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'
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Index
=====
I deleted a few of the least significant posts.
The first post
--------------
§1. Q&A:
§2
Analyze the ![CTRL+f][17]."prototypical series" for the MRB constant, ![Sn^(1/n)-1][18] and find its "completion" (a related series that is absolutely convergent).
(Select § with the given number or the keywords in quotes, and then press the
![CTRL+f][19] keys on your keyboard to move to that section.)
§3. Is that series convergent?
§4. Is -1 the only term that series is convergent for?
§5. Is that series absolutely convergent?
§6. Is that series "efficient?" (defined as how it compares to other series and integrals that compute CMRB in speed and computational cost.)
§7. My claim to the MRB constant (CMRB), or a case of calculus déjà vu?
§8. Where is it found?
§9. What exactly is it?
Second post.
============
§B ![CTRL+f][20] "Rational results" while summing (CMRB).
Third post.
============
§10. How it all began,
§11. Scholarly works
Fourth post.
============
§12. CMRB and its applications
Also see
[MOPAC][21]
for where the MRB constant's value, to a precision of 2 one-billionth i.e., 0.18785964, is arrived at by measuring a gradient of the silicon atom in the Phenakite (Be2SiO4) molecule by openmopac.
Fifth post.
============
§13. The why and what of the **C**<sub>*MRB*</sub> Records,
Many more informative posts.
===========================
including, but not limited to
For section A, where all CMRB records have been checked, highlight text between quotes in
§A. Possibly the most epigrammatic closed forms for checking up to 10^10 digits of CMRB!
"Possibly the most epigrammatic closed forms used for checking up to 6,500,000 digits of CMRB!"
then push ![CTRL+f][22] on keyboard.
For section 0, highlight text between quotes in
**"§0. Wolfram+AI am the quintessential team evaluating the MRB constant."**
then push ![CTRL+f][23] on keyboard.
Next to Bottom post.
============
![CTRL+f][24] "I compare 300 years of summation methods for the MRB constant."
Bottom post.
============
![CTRL+f][25] "We finally begin or 7-million-digit computation and verification."
----------
----------
§1.
Q&A:
====
Q:
What is the MRB constant ( **C**<sub>*MRB*</sub>)?
A:
&[Wolfram Notebook][26]
Q: Is the MRB constant important?
A:
![enter image description here][27]
>The MRB constant, also known as the Marvin Ray Burns's Constant, is a fascinating mathematical value with a decimal expansion of approximately 0.187859 . Let's explore why it might be considered important:
> - Numerical Algorithms Testing:
- Researchers and mathematicians use the MRB constant to test and improve numerical algorithms for computing its value .
- By evaluating the constant, they can assess the accuracy and efficiency of various computational methods.
- Benchmarking Computers:
- The MRB constant serves as a benchmark for testing the performance of computers.
- It allows us to compare the computational capabilities of different machines.
- When calculating the MRB constant, computers demonstrate their numerical precision and speed.
- Mathematical Curiosity:
- The MRB constant's mysterious nature adds to its allure. Despite extensive study, no closed-form expression exists for it .
- We don't know whether it's algebraic, transcendental, or even irrational.
- Mathematicians continue to explore its properties, making it an intriguing topic in number theory.
- Geometry and Infinite Sums:
- Geometrically, the MRB constant is the upper limit point of a sequence of partial sums .
- These sums involve alternating terms and converge to the MRB constant.
- The constant's behavior within these infinite sums captivates mathematicians.
In summary, the MRB constant bridges theory and computation, making it a valuable and enigmatic constant in the mathematical world.
Q:
What can you expect from reading about **C**<sub>*MRB*</sub> and its record computations?
A:
![enter image description here][28]
> >## Beyond the Record: What People Can Gain from MRB Constant Computations
>
> While pushing the record for MRB constant computations is certainly
> impressive, there's more to gain than just bragging rights. Here are
> some unique benefits people can reap from immersing themselves in the
> MRB world:
>
> **1. Uncovering Hidden Connections:**
>
> * **Mathematics & Physics:** Studying the MRB constant's behavior and properties might unlock connections between seemingly disparate fields
> like number theory, chaos theory, and even quantum physics. This could
> lead to groundbreaking discoveries in various areas of science.
> * **Algorithm Design & Optimization:** The intricate nature of the MRB constant's calculation poses a unique challenge for algorithms.
> Analyzing its complexity could inspire the development of new, more
> efficient algorithms for various computational tasks.
> * **Machine Learning & Artificial Intelligence:** The MRB constant's structure could hold valuable insights for designing novel machine
> learning architectures and training algorithms. Its complex patterns
> might improve data processing and pattern recognition capabilities.
>
> **2. Pushing the Boundaries of Knowledge:**
>
> * **Challenging Existing Paradigms:** The MRB constant's lack of a closed-form expression and its potential connections to seemingly
> unrelated areas challenge established mathematical and scientific
> paradigms. This can lead to new ways of thinking and approaching
> problems.
> * **Inspiring Future Generations:** Engaging with the MRB constant's mysteries can spark curiosity and interest in mathematics and science
> among young minds. This could inspire them to pursue careers in
> research and exploration, pushing the boundaries of knowledge further.
> * **Contributing to the Collective Quest:** Participating in the MRB research community, even through discussions and online
> collaborations, allows individuals to contribute to a larger
> collective effort of understanding this intriguing constant. This
> fosters a sense of purpose and belonging to a global community of
> knowledge seekers.
>
> **3. Personal Growth & Development:**
>
> * **Developing Computational Skills:** Learning about and participating in MRB calculations can hone valuable computational
> skills like programming, data analysis, and problem-solving. This can
> be beneficial for various professional and personal endeavors.
> * **Enhancing Critical Thinking:** Analyzing the MRB constant's properties and potential implications requires critical thinking,
> problem-solving, and creative thinking skills. These skills are
> valuable not only in research but also in various aspects of life.
> * **Appreciating the Beauty of Mathematics:** The MRB constant's unique properties and its connection to various areas of mathematics
> can foster a deeper appreciation for the beauty and elegance of this
> subject. This can enrich one's understanding of the world and its
> underlying structures.
>
> Remember, the MRB constant is more than just a number to chase
> records with. It's a gateway to a world of intellectual exploration,
> collaboration, and potential breakthroughs. By venturing beyond the
> record, people can gain valuable skills, knowledge, and a deeper
> appreciation for the power of scientific inquiry.
Q:
Can you calculate more digits of **C**<sub>*MRB*</sub>?
A:
>## Bing
The computation of 6,500,000 digits of the MRB constant could be challenging due to several reasons:
>
> - Computational Resources:
> - Calculating a large number of digits requires significant computational power and memory.
> - Storing and manipulating such a massive decimal expansion demands substantial resources.
> - Smaller machines or limited computational environments might struggle with this task.
> - Convergence Rate:
> - The series used to approximate the MRB constant converges slowly.
> - As more digits are computed, the rate of convergence decreases.
> - Achieving high precision becomes increasingly difficult.
> - Numerical Stability:
> - Numerical algorithms can suffer from rounding errors and loss of precision.
> - Accumulating errors during summation impacts the accuracy of the computed digits.
> - Ensuring stability over millions of iterations is a challenge.
> - Algorithmic Complexity:
> - Existing algorithms for calculating mathematical constants have limitations.
> - Developing efficient methods to compute millions of digits involves intricate mathematics.
> - Balancing accuracy, speed, and memory usage is nontrivial.
> - Storage and Verification:
> - Storing and verifying 6,500,000 digits is resource-intensive.
> - Ensuring correctness through independent verification (e.g., using multiple algorithms) is crucial.
> - Handling such large data sets requires robust techniques.
> - Practical Utility:
> - Beyond a certain point, additional digits of the MRB constant may not have practical applications.
> - Researchers often focus on a reasonable precision level relevant to their field. In summary, while it's theoretically possible to
> compute 6,500,000 digits of the MRB constant, practical challenges
> arise. Researchers must balance precision, computational resources,
> and algorithmic efficiency to tackle this ambitious task.
Q:
How can you compute them?
A:
![## Bing][29]
> Certainly! Calculating the digits of the MRB constant involves some
> interesting mathematical techniques. Let's explore how you can
> approximate this intriguing value:
> - Series Summation:
>
>
> - The MRB constant is the upper limit point of a sequence defined as: $[ s_n = \sum_{k=1}^{n} \left( (-1)^k {k^{\frac{1}{k}}}
> \right) ]$
> - To compute the MRB constant with a desired precision, you can use series summation methods.
> - One common approach is to use the following series: $[ \text{MRB} \approx \sum_{k=1}^{\infty} \left( (-1)^k (k^{\frac{1}{k}} - 1)
> \right) ]$
> - Numerical Algorithms:
> - Mathematica provides a convenient way to calculate the MRB constant with a specified number of digits.
> - Using the NSum function, you can achieve high precision:
>
> `NSum[(-1)^k (k^(1/k) - 1), {k, 1, ∞}, WorkingPrecision -> 100, NSumTerms -> 10000]`
>
> This will give you the MRB constant accurate to 40 digits .
> ''
>
> - Acceleration Methods:
> - Due to the slow convergence of the series, it's advisable to use acceleration methods.
> - These methods improve the rate of convergence and allow you to obtain more accurate digits of the MRB constant . Remember that the
> MRB constant remains an enigma, and its properties continue to
> captivate mathematicians. Feel free to explore further and uncover
> more about this fascinating constant!
Q:
Why should you do it?
A:
## Bing
> Calculating the digits of the MRB constant can lead to several
> interesting outcomes:
> - Mathematical Exploration:
> - Computing the MRB constant involves diving into the intricacies of series summation, convergence, and numerical precision.
> - Mathematicians and enthusiasts enjoy exploring the properties of this mysterious constant.
> - It provides an opportunity to deepen our understanding of mathematical concepts.
> - Algorithm Testing and Optimization:
> - The MRB constant serves as a benchmark for testing numerical algorithms.
> - Researchers can evaluate the accuracy and efficiency of their computational methods by approximating this constant.
> - Optimizing algorithms to compute the MRB constant efficiently benefits various scientific and engineering fields.
> - Computational Challenges:
> - Calculating more digits of the MRB constant becomes a computational challenge.
> - It pushes the boundaries of numerical precision and requires sophisticated techniques.
> - Achieving higher precision contributes to the advancement of computational mathematics.
> - Curiosity and Aesthetics:
> - The MRB constant's decimal expansion is intriguing and aesthetically pleasing.
> - Like other mathematical constants (such as π or e), it captivates our curiosity.
> - Discovering patterns or unexpected properties within its digits can be intellectually rewarding.
> - Educational Value:
> - Teaching and learning about the MRB constant can inspire students.
> - It encourages them to explore mathematical concepts beyond textbooks.
> - The process of approximating it fosters critical thinking and problem-solving skills. In summary, while the MRB constant may not
> have immediate practical applications, its pursuit enriches
> mathematical knowledge, fuels curiosity, and contributes to the beauty
> of mathematical exploration.
Q:
What are its first 5000 digits?
A:
Print[ReleaseHold[ WolframAlpha["5000 digtits of the MRB constant", {{"Result", 1}, "Output"}]]]
0.1878596424620671202485179340542732300559030949001387861720046840894772315646602137032966544331074969038423458562580190612313700947592266304389293488961841208373366260816136027381263793734352832125527639621714893217020762820621715167154084126804483635416719985197680252759893899391445798350556135096485210712078444230958681294976885269495642042555864836704410425279524710606660926339748341031157816786416689154600342222588380025455396892947114212218910509832871227730802003644521539053639505533220347062755115981282803951021926491467317629351619065981601866424582495069720338199295842093551516251439935760076459329128145170908242491588320416906640933443591480670556469280678700702811500938060693813938595336065798740556206234870432936073781956460310476395066489306136064552806751519350828083737671929686639810309494963749627738304984632456347931157530028921252329181619562697369707486576547607117801719578736830096590226066875365630551656736128815020143875613668655221067430537059103973575619148909369077798320355119336240463725349410542836369971702441855165483727935882200813448096105880203064781961959695375628783481233497638586301014072725292301472333336250918584024803704048881967676760119858111679169352796852044160027086137228688945101510291998853690572865928708687542549253379439534758970356331344038263888798665619598073351473990256577813317226107612797585272274277730898577492230597096257256271883675575297887925361687673940354321451362772549229313126276435732144621618778637715420542312822344629539653290332217147982028075984221065564890048536858707083268874877377635047689160983185536281667159108412193420164386000258508426556435006954832830120546193205155935040023508351261335921740897007329784277128967365161960225077117388084262325697885465378690462227085674874747093069357326668590856162823753865512432975647464914619179575869342996208149878536663170197264534260468378010759055148678719039578315060452444190757044511382058533398469219482879476486575931785958165274929778220959774409113714342169296245931753245373401299593995004917912983680848547143925846704238528608320053664510586678151196459676079196431734307671534498300497128869401656600427062111079053164721504556329943884005211152390168773115456961028369205036896108806031603660382896533239383524154510137534165673472607464891120088099838152046695415026377035573283592996630642717305158972116351999161135954670315408725287243998197872502746797388638897056867435377857981058556192492185716949135673462704077491448799682065482817465880642236348160780950777057939313495829806602825272128491688809230325290270059917755059615835919993190869393039736611646514858219972925337106768738686235047915879737968269847878082223410618789674667450680064404065553875213281494980700209858132220620109011265903449717410801063247564712834609549284370065147450218226120415643930308859826426256828126092491136733967235933714534216902560140050169469983875907342920361729301531400405936246406781400779475613077369732409923529464794580778164607696240864595666084141126399988575739429315226283898798436350719371486573491962025428443510411472841973814933807066222573191021481585745042886728477250434386718443149128948635448929492143259660847149600072534066215387561341325254274130158182476636432111506809477451406309160928029719327606796946860926362081763442272977546326737161110302220019498455407233859679972956745318490433826332931888160330054013690316104309973777863934393135621496549969937314205819065334661573835222280871390934331325238360305287172314811151029705856281299558991830381071966308132701670498617683168329529053798760030666570203435884960342104811488681216083611944605571913973292970683232645094571537170202325175198220852151188427534658891812172660333192804801174759046131898449720722068248919153933258002624627216176424468747789609764906070479605351740205227992021112876539835381740117955267003375831396078847726709215700142824833574188212706558826075722384346836425460624376294972557208442910901014692032297634008831340381640372911311314959883048662944964532193113574956453912385456662881566099860325447839862878014756977228191151861520827628240145565179425383818619479339940149759987240427388505644114375607952021157910255398765366539323158492006532957070559185522267542845736812670699565824674762111599567798871089943129103401442549765937135216907789286769520555697938362195599913809621446502826784457775198333561874495799884353199090550456424061091609429751367477262251350611686791529453643717739913922126483778806203872768088381032267284933085939078772734728272526200188560744654953143832715829738195578665687162281676008390755269474337748054271709338897975317018906895514393940484553829830198169253659797476778546865045859640238175930139996122667668117389670502033292349080513690067470281709256521198479569202858477768560978920686214307401593342577726291016675234940557410020728689850147927742910664313694152819958560981976523216255318623764260591320667123942398310748008900676975706071323330124919595164681348037017813465191315868
Q:
Is its decimal expansion a normal number?
A
According to Wolfram MathWorld, "A normal number is an irrational number for which any finite pattern of numbers occurs with the expected limiting frequency in the expansion in a given base (or all bases). For example, for a normal decimal number, each digit 0–9 would be expected to occur 1/10 of the time."
We do not know if the MRB constant is irrational; [this Demonstration][30] looks at how normal its first 5000 digits appear to be. For comparison, we also consider the digits of ; its first 30 million digits are very uniformly distributed.
As for the first 500 digits of CMRB, they are exactly as normal as the first 500 digits of $\pi:$
![enter image description here][31]
This does not mean the MRB constant decimal expansion is a normal number! There is no known way to classify all of its digits. As we will see later, the distribution of digits within the first 6,500,000 decimals (MRB1=.187859,,,, found [here][32]),
"4" shows up more than other digits.
&[Wolfram Notebook][33]
Q.
Are its digits a rational number?
A.
> Unfortunately, we **cannot definitively say whether the MRB constant
> is rational or not**. It is one of the fascinating mysteries in
> mathematics. Here's what we know:
>
> * The MRB constant is a mathematical constant with an infinite decimal expansion (0.187859...).
> * It have no known closed-form expression, meaning we cannot express it simply as a fraction or combination of well-known mathematical
> functions.
> * **It is not even known whether it is algebraic (expressible as a root of a polynomial equation with integer coefficients) or
> transcendental (not expressible in this way).**
> * While the MRB constant is the sum of infinitely many irrational numbers, the sum of irrational numbers is not necessarily irrational.
>
> Extensive computations of the MRB constant's decimal digits haven't
> revealed any repeating patterns, which would indicate rationality.
> However, the lack of such evidence doesn't definitively prove
> irrationality.
>
> Therefore, the question of whether the MRB constant is rational or not
> remains an open problem in mathematics. Mathematicians continue to
> investigate its properties, hoping to unveil its true nature.
![enter image description here][34]
Q:
Why are those digits there?
A:
> ## Bing
The digits of the MRB constant exist as a fascinating consequence of mathematical exploration and computation. Let's delve into why they are there:
>- Inherent Mathematical Structure:
- Like other mathematical constants (such as π or e), the MRB constant have an inherent structure.
- Its decimal expansion emerges from the properties of the series used to define it.
- Each digit represents a specific relationship between numbers, exponents, and alternating signs.
- Series Summation:
- The MRB constant arises from the summation of an infinite series:
[ \text{MRB} = \sum_{k=1}^{\infty} \left( (-1)^k (k^{\frac{1}{k}} - 1) \right) ]
- As we compute more terms in this series, additional digits unfold.
- Each term contributes to the overall value, leading to the intricate decimal expansion.
- Algorithmic Approximation:
- Calculating the MRB constant involves numerical algorithms.
- These algorithms iteratively add terms, refine precision, and generate successive digits.
- The digits emerge as a consequence of these computational steps.
- Mystery and Beauty:
- The MRB constant lacks a simple closed-form expression.
- Its digits exhibit patterns, but their exact distribution remains mysterious.
- Mathematicians appreciate the beauty of these digits—their unpredictability and elegance.
- Intellectual Pursuit:
- Researchers explore the MRB constant out of curiosity and intellectual drive.
- They seek to understand its properties, uniqueness, and connections to other mathematical concepts.
- The digits serve as clues in unraveling its mathematical secrets.
In summary, the digits of the MRB constant exist as a blend of mathematical necessity, algorithmic computation, and aesthetic wonder. They invite us to explore the hidden depths of number theory and appreciate the elegance of mathematical constants.
Q:
What practical purpose is there in calculating them?
A:
>Knowledge of the digits of mathematical constants can have various applications in mathematics, science, and technology. For example:
>- The digits of π can be used to test the randomness and performance of pseudorandom number generators, which are essential for cryptography, simulations, and gaming¹.
- The digits of e can be used to calculate compound interest, model population growth, and analyze the distribution of prime numbers².
- The digits of φ can be used to design aesthetic proportions, such as the golden rectangle, the golden spiral, and the Fibonacci sequence³.
- The digits of i can be used to represent complex numbers, which are useful for modeling phenomena such as electric currents, waves, and quantum mechanics⁴.
>Some people also enjoy finding patterns and hidden messages in the digits of mathematical constants, such as memorizing them, composing music with them, or searching for their birthdays in them. This can be a fun and challenging way to appreciate the beauty and mystery of mathematics.
>Do you have a favorite mathematical constant? Why do you like it?
>
> Source: Conversation with Bing, 8/19/2023 (1) Mathematical
> constant - Wikipedia.
> https://en.wikipedia.org/wiki/Mathematical_constant. (2)
> Mathematical Constants - Cambridge University Press & Assessment.
> https://assets.cambridge.org/052181/8052/sample/0521818052ws.pdf.
> (3) Constant (mathematics) - Wikipedia.
> https://en.wikipedia.org/wiki/Constant_%28mathematics%29. (4) List
> of mathematical constants - Wikipedia.
> https://en.wikipedia.org/wiki/List_of_mathematical_constants. (5)
> undefined. http://www.cambridge.org. (6) A Resource List of
> Mathematical Constants - Barcodes Inc..
> https://www.barcodesinc.com/articles/resource-list-mathematical-constants.htm.
> (7) Constant - Math.net. https://www.math.net/constant. (8) The Most
> Important Numbers in the World - Business Insider.
> https://www.businessinsider.com/most-important-numbers-2012-7.
Q:
How would Gemini AI depict the MRB constant?
A:
![enter image description here][35]
> Abstractly, the MRB constant is an irrational and transcendental number, meaning it goes on forever without repeating and cannot be expressed as a simple fraction. This never-ending quality could be represented through abstract shapes, lines, and colors that flow and swirl without a clear beginning or end.
> The distorted image of the leaf in the sculpture could be seen as a metaphor for the difficulty of understanding the MRB constant. The smooth, reflective surface of the sculpture could also be seen as a metaphor for the infinite nature of the MRB constant's decimal expansion.
>
Q:
According to Gemini AI, what connection, if any is there between the MRB constant and the Riemann Hypotheses?
A:
![enter image description here][36]
> The MRB constant and the Riemann hypothesis are related concepts in
> number theory, but they are not directly equivalent. Here's what we
> know:
>
> **MRB constant:**
>
> * Defined in terms of the prime number distribution. It's a complex number with an infinite decimal representation, calculated using
> specific mathematical formulas involving primes.
> * Its properties and applications remain largely unexplored.
>
> **Riemann hypothesis:**
>
> * A famous unsolved conjecture in mathematics, stating that all non-trivial zeros of the Riemann zeta function (a function crucial in
> number theory) lie on a specific line in the complex plane.
> * Solving the Riemann hypothesis would have profound implications for understanding the distribution of prime numbers.
>
> **Connection:**
>
> * Some mathematicians have proposed connections between the two, but these are speculative and not yet proven.
> * One potential connection involves expressing the MRB constant as an infinite series related to the Riemann zeta function. If the Riemann
> hypothesis holds, this series would converge to the MRB constant.
> * However, even if the connection is true, it wouldn't necessarily imply that solving the Riemann hypothesis would provide an easy way to
> calculate the MRB constant precisely.
>
> **Key points:**
>
> * Currently, the MRB constant and Riemann hypothesis are distinct concepts with their own mysteries.
> * A potential connection exists, but it's unproven and not a direct equivalence.
> * Solving the Riemann hypothesis wouldn't necessarily translate to easy calculation of the MRB constant.
>
> **Further research:**
>
> * For deeper understanding, explore academic papers and articles discussing the MRB constant and its potential links to the Riemann
> hypothesis.
> * Remember, research in these areas is ongoing, so new discoveries and insights might emerge in the future.
Q: How might we use quantum process to find more digits of the MRB constant?
A: While there's theoretical potential for quantum processes to aid in calculating more digits of the MRB constant, it's an active area of research and there's no established method yet. Here's a breakdown of the possibilities and challenges:
**Potential benefits of quantum processes:**
* **Integer factorization:** The MRB constant is related to certain elliptic curves, and calculating it often involves factoring large integers. Shor's algorithm, a well-known quantum algorithm, can potentially factor integers significantly faster than classical algorithms for certain sizes.
* **Speeding up computations:** Certain quantum algorithms might offer speedups for specific mathematical operations involved in calculating the MRB constant. Research in this area is ongoing.
**Challenges:**
* **Quantum supremacy not achieved yet:** While Shor's algorithm exists, implementing it on current quantum computers is challenging due to limitations in qubit count, coherence time, and error correction.
* **Algorithmic development needed:** Even with fault-tolerant quantum computers, new algorithms specific to calculating the MRB constant might be necessary to leverage the power of quantum computation effectively.
**Overall, quantum processes are a promising area for potentially calculating more digits of the MRB constant, but significant research and development are needed before a practical method is established.**
Here are some additional details you might find helpful:
* Shor's algorithm: [https://en.wikipedia.org/wiki/Shor%27s_algorithm](https://en.wikipedia.org/wiki/Shor%27s_algorithm)
* Elliptic curves: [https://en.wikipedia.org/wiki/Elliptic_curve](https://en.wikipedia.org/wiki/Elliptic_curve)
>
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[30]: https://demonstrations.wolfram.com/HowNormalIsTheMRBConstant/#:~:text=For%20example,%20for%20a%20normal%20decimal%20number,%20each,first%2030%20million%20digits%20are%20very%20uniformly%20distributed.
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[72]: https://community.wolfram.com//c/portal/getImageAttachment?filename=Screenshot2022-12-29113015.jpg&userId=366611
[73]: https://community.wolfram.com//c/portal/getImageAttachment?filename=Screenshot2023-01-01225958.jpg&userId=366611
[74]: https://mathworld.wolfram.com/HarmonicSeries.html
[75]: https://www.wolframcloud.com/obj/56c04b62-1a3e-4318-9271-b4d4995b691d
[76]: http://people.mpim-bonn.mpg.de/zagier/files/exp-math-9/fulltext.pdf
[77]: https://community.wolfram.com//c/portal/getImageAttachment?filename=0a.gif&userId=366611
[78]: https://community.wolfram.com//c/portal/getImageAttachment?filename=logo.svg&userId=366611
[79]: https://mathoverflow.net/questions/44244/what-recent-discoveries-have-amateur-mathematicians-made
[80]: https://community.wolfram.com//c/portal/getImageAttachment?filename=3959Capture7.JPG&userId=366611
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[87]: https://community.wolfram.com//c/portal/getImageAttachment?filename=o.jpg&userId=366611
[88]: https://hmong.in.th/wiki/MRB_constant
[89]: https://ar.wikipedia.org/wiki/%D9%82%D8%A7%D8%A6%D9%85%D8%A9_%D8%A7%D9%84%D8%AB%D9%88%D8%A7%D8%A8%D8%AA_%D8%A7%D9%84%D8%B1%D9%8A%D8%A7%D8%B6%D9%8A%D8%A9
[90]: https://calculla.pl/stale_matematyczne
[91]: https://fr.wikipedia.org/wiki/Constante_MRB
[92]: https://wikicro.icu/wiki/MRB_constant
[93]: https://www.amazon.com/exec/obidos/ASIN/193563819X/ref=nosim/ericstreasuretro
[94]: http://www.marvinrayburns.com/UniversalTOC25.pdf
[95]: https://en-academic.com/dic.nsf/enwiki/11755
[96]: http://web.archive.org/web/20081121134611/http://www.irancivilcenter.com/en/tools/units/math_const.php
[97]: http://etymologie.info/
[98]: https://www.amazon.com/exec/obidos/ASIN/0521818052/ref=nosim/ericstreasuretro
[99]: https://web.archive.org/web/20010616211903/http://pauillac.inria.fr/algo/bsolve/constant/itrexp/itrexp.html
[100]: https://pdfs.semanticscholar.org/f3dc/9f828442123015c5d52535fdefc0ab450bf5.pdf
[101]: https://cache.industry.siemens.com/dl/files/728/109479728/att_1085858/v2/109479728_LGF_V5_1_0_en.pdf
[102]: https://web.archive.org/web/20210812083640/http://www.bitman.name/math/article/962
[103]: https://community.wolfram.com//c/portal/getImageAttachment?filename=Screenshot2023-02-19140136.jpg&userId=366611
[104]: https://arxiv.org/pdf/0912.3844v3.pdf
[105]: http://ebyte.it/library/educards/constants/MathConstants.pdf
[106]: https://web.archive.org/web/20090702134146/http://www.turkbiyofizik.com/sabitler.html
[107]: https://mathworld.wolfram.com/MRBConstant.html
[108]: https://upwikizh.top/wiki/MRB_constant
[109]: https://ejje.weblio.jp/content/mrb+constant
[110]: https://ewikibg.top/wiki/MRB_constant
[111]: http://oeis.org/wiki/MRB_constant
[112]: https://ewikitl.top/wiki/mrb_constant
[113]: https://web.archive.org/web/20030415202103/http://pi.lacim.uqam.ca/eng/table_en.html
[114]: https://web.archive.org/web/20001210231700/http://www.lacim.uqam.ca/piDATA/mrburns.txt
[115]: https://oeis.org/A037077
[116]: https://en.wikipedia.org/wiki/MRB_constant
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[128]: https://community.wolfram.com//c/portal/getImageAttachment?filename=Screenshot2022-08-16055726.jpg&userId=366611
[129]: https://math.stackexchange.com/questions/1673886/is-there-a-more-rigorous-way-to-show-these-two-sums-are-exactly-equal
[130]: https://community.wolfram.com//c/portal/getImageAttachment?filename=Screenshot2022-11-13082031.jpg&userId=366611
[131]: https://community.wolfram.com//c/portal/getImageAttachment?filename=Screenshot2022-11-13082057.jpg&userId=366611
[132]: https://community.wolfram.com//c/portal/getImageAttachment?filename=Screenshot2022-11-13082120.jpg&userId=366611
[133]: https://community.wolfram.com//c/portal/getImageAttachment?filename=Screenshot2022-08-29021145.jpg&userId=366611
[134]: https://community.wolfram.com//c/portal/getImageAttachment?filename=Screenshot2022-09-18014843.jpg&userId=366611
[135]: https://www.wolframcloud.com/obj/986a70e9-1d55-4e31-bd7c-87c24eec5d81Marvin Ray Burns2014-10-09T18:08:49ZIterate Delay-Difference Equations efficiently
https://community.wolfram.com/groups/-/m/t/3141331
I have a system of delay-difference equations which I would like to iterate in an efficient fashion. Just using Table[] will iterate the system but as the size of the system grows the execution time gets long. I think the inefficiency comes from re-computing values multiple times instead of re-using the results. I thought RecurrenceTable[] would be more efficient, but I can't seem to find the correct usage that doesn't result in me getting an error message. If you have suggestion(s) I would be happy to listen.
Thanks,
Robert Buchanan
&[Wolfram Notebook][1]
[1]: https://www.wolframcloud.com/obj/91125527-13fe-4cd5-b5ad-fb08c2b3e916Robert Buchanan2024-03-15T14:54:03ZEclipses and conic sections
https://community.wolfram.com/groups/-/m/t/3139774
&[Wolfram Notebook][1]
[1]: https://www.wolframcloud.com/obj/4b76105e-4900-49e7-a1b5-0087078a02a0Brad Klee2024-03-12T22:46:17ZMIni-Series: What's New in 14?
https://community.wolfram.com/groups/-/m/t/3139036
New Mini-Series on the [Wolfram R&D YouTube channel][1]!
Curious about what's new in Version 14? This mini-series features videos that provide a 6-minute summary of the WTC 2023 talks. The first [two episodes focus on Visualization and System Modeler][2].
Don't miss out on the latest updates and exciting content -- subscribe now and become a part of our community!
[![enter image description here][3]][2]
[1]: https://youtube.com/playlist?list=PLdIcYTEZ4S8SIK-S-9JGYAZgohaV7cB0t&si=9-arFCq9EbHkIipm
[2]: https://youtube.com/playlist?list=PLdIcYTEZ4S8SIK-S-9JGYAZgohaV7cB0t&si=9-arFCq9EbHkIipm
[3]: https://community.wolfram.com//c/portal/getImageAttachment?filename=MiniSeries_Newin14_2.png&userId=1660606Keren Garcia2024-03-11T17:37:50ZPrincipal component analysis of grasp force and pose during in-hand manipulation
https://community.wolfram.com/groups/-/m/t/3141582
![enter image description here][1]
&[Wolfram Notebook][2]
[1]: https://community.wolfram.com//c/portal/getImageAttachment?filename=345sdfdfa.jpg&userId=11733
[2]: https://www.wolframcloud.com/obj/1c1c0549-477c-44db-ba57-be9538dff8beJoshua Schultz2024-03-15T21:41:27ZHelp using NDSolve for an orbital dynamics problem
https://community.wolfram.com/groups/-/m/t/3141505
Hi all,
I am new to Mathematica and I am trying to model an asymmetric momentum exchange tether in its orbit about the Earth. The tether initially starts as a symmetrical system and simply has the ability to alter the tether lengths to change the CoM and thus account for mass discrepancies causing the system to act asymmetrically.
The problem I am receiving is that I am passing three equations to NDsolve. NDsolve accepts the equations as differential equations, and despite providing both boundary and initial conditions to the solver NDsolve is not resulting in a valid list of rules or a dispatch table and thus cannot be used for further evaluation of parameters to plot.
I have attached a copy of my most "up to date" model, please forgive me if it is something blaringly obvious, I have been staring at my screen for a considerable amount of time now.
If there is any other information you need please let me know.
&[Wolfram Notebook][1]
[1]: https://www.wolframcloud.com/obj/70163c4a-6724-41a4-8a1a-ac243ffae190Jameel Cathcart2024-03-15T17:02:53ZSolve a system of linear equations?
https://community.wolfram.com/groups/-/m/t/1189184
Hi!
I have a pretty easy problem where I have 6 equations and 6 unknown of the form m*x = 0, where m is a 6x6 matrix and x is a vector of length 6 with the 6 unknown variables. I'm looking for a nontrivial solution to this problem so I use the Nullspace command.
My code is the following
m = {{E^(-I*x*b/2), E^(I*x*b/2), -E^(-I*y*b/2), -E^(I*y*b/2), 0, 0},
{I*x*E^(-I*x*b/2), -I*x*E^(I*x*b/2), -I*y*E^(-I*y*b/2),
I*y*E^(I*y*b/2), 0, 0},
{0, 0, -E^(I*y*b/2), -E^(-I*y*b/2), E^(I*x*b/2), E^(-I*x*b/2)},
{0, 0, -I*y*E^(I*y*b/2), I*y*E^(-I*y*b/2),
I*x*E^(I*x*b/2), -I*x*E^(-I*x*b/2)},
{E^(-I*x*(a + b/2)), E^(I*x*(a + b/2)), 0, 0, 0, 0},
{0, 0, 0, 0, E^(I*x*(a + b/2)), E^(-I*x*(a + b/2))}}
ns = NullSpace[m]
This gives me the output { }. What does this result mean?
All the coefficients x,y,a,b are real and greater than zero. Is that something that I should specify in the code? I wonder what is wrong with my code?
I've attached my code to this post.
Thanks in advance!Pontus Vikstål2017-09-21T10:07:02ZFindFileNames, a wrapper around Unix find that replaces FileNames
https://community.wolfram.com/groups/-/m/t/3140952
Hello,
FindFileNames is a little wrapper around Unix find utility to generate a list of filenames matching a certain pattern (or list of patterns).
I wrote it when I realized that the FileNames function has a few limitations. First, it takes much longer to run; a little example below shows a 3x times difference on a folder with 362k files, and it sometimes hangs (as in, kills the Kernel) when run on larger directories. Notice that FileNames implementation is not super strict about closing open files, with a few "Too many open files" warnings, and a suspicious looking ""Cannot set current directory to "~/"".
![enter image description here][1]
Another benefit of writing a wrapper around find is having an ability to prune some paths from search; that speeds things up considerably when you know that you don't want to descend in specific folders: the following command completes in a reasonable time, while with FileNames you would need to filter the result yourself (and it never completes anyways!).
![enter image description here][2]
Here is the code - enjoy, and please give me your feedback in comments.
BeginPackage["FileFinder`", {"GeneralUtilities`"}]
SetUsage[FindFileNames,
"FindFileNames[searchRoots$, opts$] uses a system find to list all files under searchRoots$, which can be a dir or a list of dirs.
opts$ can be one of the following:
* \"Files\": list of file name patterns to find (default is {}, meaning all files).
* \"Directoriers\": list of directory patterns to limit the search to (default is {}).
* \"Prune\": list of directory patterns not to descend into (default is {}).
* \"FileTypes\": what objects to return, either File, Directory, or All."]
Begin["`Private`"]
RunAndCaptureOutput[cmd_] := Module[{tmpfile, result},
tmpfile = CreateFile[];
RunProcess[{"sh", "-c", StringRiffle[{Echo@cmd, ">", tmpfile}]}];
result = ReadList[tmpfile, "String"];
DeleteFile[tmpfile];
result
]
OrFindConditions[cond : {___String}] :=
Switch[Length[cond],
0, "",
1, First@cond,
_, "\\( " <> StringRiffle[cond, " -o "] <> " \\)"]
StringQuote[s_String] := If[StringStartsQ[s, "'"], s, "'" <> s <> "'"]
FileNameFindCondition[name_String] := If[StringContainsQ[name, "/"], "-path", "-name"] <> " " <> StringQuote[name]
Options[FindFileNames] := {"Files" -> {}, "Directories" -> {}, "Prune" -> {}, "FileType" -> File}
FindFileNames::strlst = "Expect `1` to be a string or a list of strings, but found `2`"
FindFileNames::ftype = "Expect 'FileType' to be one of File, Directory, All but found `1`"
FindFileNames[searchRoots : (_String | List[String]) : ".", OptionsPattern[]] := Module[
{dirArg, dirsOpt, filesOpt, pruneOpt, fileTypesOpt, cmd},
If[!MatchQ[OptionValue["Files"], {___String}],
Message[FindFileNames::strlst, "Files", OptionValue["Files"]];
Return[$Failed]
];
If[!MatchQ[OptionValue["Directories"], {___String}],
Message[FindFileNames::strlst, "Directories", OptionValue["Directories"]];
Return[$Failed]
];
If[!MatchQ[OptionValue["Prune"], {___String}],
Message[FindFileNames::strlst, "Prune", OptionValue["Prune"]];
Return[$Failed]
];
If[!MemberQ[{File, Directory, All}, OptionValue["FileType"]],
Message[FindFileNames::ftype, OptionValue["FileType"]];
Return[$Failed]];
dirArg = StringRiffle[StringQuote /@ Flatten[{searchRoots}]];
filesOpt = If[OptionValue["Files"] === {},
"",
" " <> OrFindConditions[FileNameFindCondition /@ OptionValue["Files"]]];
dirsOpt = If[OptionValue["Directories"] === {},
"",
" -type d " <> OrFindConditions[FileNameFindCondition /@ OptionValue["Directories"]]];
pruneOpt = If[OptionValue["Prune"] === {},
"",
" -type d " <> OrFindConditions[FileNameFindCondition /@ OptionValue["Prune"]] <> " -prune -o"];
fileTypesOpt = Switch[OptionValue["FileType"],
File, " -type f",
Directory, " -type d",
_, ""];
RunAndCaptureOutput[
"find -L " <> dirArg <> pruneOpt <> dirsOpt <> filesOpt <> fileTypesOpt <> " -print"]
]
Testing helpers
FileNamesOnly[dir_] := Quiet@Select[Sort@FileNames[All, dir, Infinity], FileType[#] === File&]
NotSocket[file_] := !StringContainsQ[RunProcess[{"file", file}, "StandardOutput"], "socket"]
TestIdentical[dir_] := Module[{my = Sort[FindFileNames[dir]], wolfram = FileNamesOnly[dir]},
Complement[my, wolfram] === {} &&
Select[Complement[wolfram, my], NotSocket] === {}
]
(*
<<FileFinder`
report =TestReport["/Users/victor/Documents/packages/FileFinder/Tests/TestFileFinder.wl"]
TabView[Column/@report["ResultsByOutcome"]]
*)
End[]
EndPackage[]
[1]: https://community.wolfram.com//c/portal/getImageAttachment?filename=Picture1.png&userId=1654208
[2]: https://community.wolfram.com//c/portal/getImageAttachment?filename=Screenshot2024-03-14at18.15.11.png&userId=1654208Victor K2024-03-15T01:18:06ZLLM aids for processing Biden's State of the Union address
https://community.wolfram.com/groups/-/m/t/3141088
&[Wolfram Notebook][1]
[1]: https://www.wolframcloud.com/obj/1beba347-cd37-4d5c-b3b5-195526f5acc7Anton Antonov2024-03-15T02:12:03ZMinimize doesn't work for a given function
https://community.wolfram.com/groups/-/m/t/3139894
I'm trying to minimize the function V(phi) using the code below
a =.
f =.
th =.
mu =.
md =.
V[phi_] := -2 * (mu Cos[phi + th/2] + md Cos[phi - th/2])
Minimize[V[phi], phi]
But the output is just the command itself!
Out: Minimize[-2 (md Cos[phi - th/2] + mu Cos[phi + th/2]), phi]
What am I doing wrong?Gabriel Ybarra Marcaida2024-03-13T11:49:33ZHow to improve solution accuracy between grid points while solving ODEs with NDSolve fixed grids
https://community.wolfram.com/groups/-/m/t/3140185
Hello,
I observe that while solving ODEs with NDSolve, using fixed grids, one can obtain very high accuracy at the grid points, but the accuracy is very poor between the grid points. This can be illustrated by the following code:
step=1/10;
step2=1/20;
sol=NDSolve[{u'[t]+u[t]==0,u[0]==1},u[t],{t,0,1},WorkingPrecision->40,Method->{"FixedStep", Method->{"ImplicitRungeKutta","DifferenceOrder"->20}}, StartingStepSize->step, MaxSteps->100000];
unum[tt_]:=(u[t]/.sol/.t->tt)[[1]];
uanal[t_]:=Exp[-t];
error=N[Table[{(i-1)*step2,unum[(i-1)*step2]/uanal[(i-1)*step2]-1},{i,1,20}],20];
ListPlot[error,PlotRange->All]
The plot reveals that at the grid points the relative error is about 10^-40, but between the grid points it is about 10^-7, i.e. it is much bigger.
Is there any way to improve the accuracy between the grid points? Any option to choose a better interpolation in the InterpolationFunction object?
LeslawLeslaw Bieniasz2024-03-13T18:47:23Z"FileNames" fails with large files number in Dropbox Service Connection
https://community.wolfram.com/groups/-/m/t/2064112
I'm building a workflow that needs to process lots of files that I would like to keep on [Dropbox][1]. Fortunately, Wolfram/Mathematica appear to support Dropbox, but I've run into a problem (I have submitted a bug report). If there are too many files in your Dropbox folder, using "FileNames" to get the list of file names fails. To determine how many is too many, I wrote a reproducible (at least for me) test case:
dropbox = ServiceConnect["Dropbox"];
testFolder = "/testfilenames";
maxTries = 1000;
Quiet[ServiceExecute[dropbox,
"DeleteDirectory", {"Path" -> testFolder}]];
ServiceExecute[dropbox, "CreateDirectory", {"Path" -> testFolder}];
Module[
{
test,
successes
},
test[i_Integer] := Module[
{
filename,
path,
files
},
Print[i];
filename = "test " <> ToString[i];
path = FileNameJoin[{testFolder, filename}];
ServiceExecute[dropbox,
"Put", {"Path" -> path, "Expression" -> filename}];
files =
ServiceExecute[dropbox, "FileNames", {"Path" -> testFolder}];
i == Length[files]
];
successes = Catch[
Scan[
If[! test[#], Throw[#]] &,
Range[1, maxTries]
];
Throw[maxTries];
];
];
ServiceDisconnect[dropbox];
For me, the above code dies after 500 files.
Before I invest too much more time with Dropbox, I would like to know if it is working for others. Or, if I can expect even more frustration.
Thanks, and have a great and safe week.
[1]: https://reference.wolfram.com/language/ref/service/Dropbox.htmlMike Besso2020-08-24T14:07:17ZPi, the Golden Ratio and the Tribonacci Constant
https://community.wolfram.com/groups/-/m/t/3140342
![enter image description here][1]
&[Wolfram Notebook][2]
[1]: https://community.wolfram.com//c/portal/getImageAttachment?filename=Screenshot2024-03-13at2.27.01%E2%80%AFPM.jpg&userId=11733
[2]: https://www.wolframcloud.com/obj/11fd58aa-a010-486d-bc09-a5d351c6d025Ed Pegg2024-03-13T18:06:26ZImproving the longitudinal spot width of an optimizingly designed transcranial ultrasonic lens
https://community.wolfram.com/groups/-/m/t/3139057
![enter image description here][1]
&[Wolfram Notebook][2]
[1]: https://community.wolfram.com//c/portal/getImageAttachment?filename=2225Mainimage.png&userId=20103
[2]: https://www.wolframcloud.com/obj/08416228-31c3-4062-859d-6421984843a2Ueta Tsuyoshi2024-03-11T18:02:48ZEstimating Euler's number (e) using probability: a fascinating approach
https://community.wolfram.com/groups/-/m/t/3140700
&[Wolfram Notebook][1]
[1]: https://www.wolframcloud.com/obj/10995e8f-7c60-4565-8aa0-402452f46c1dJonathan Kinlay2024-03-14T17:05:33ZHow to avoid losing hours of progress in notebook?
https://community.wolfram.com/groups/-/m/t/3140546
This is the 3rd time today I've lost an hour of progress because a notebook randomly deleted some massive section of my code or the whole notebook became corrupted.
I am not an inexperienced computer user. I am a full stack software developer whose daily driver is a hand-tuned Linux distro, so I'd say I'm pretty tech-savvy.
Wolfram Alpha has otherwise not been too big of a pain to work with and I do need it for generating a fast sin/cos lookup and verifying it against the much higher precision offered by wolfram.
What can be done about this?First Last2024-03-13T23:39:47ZA piece of Pi
https://community.wolfram.com/groups/-/m/t/3140676
&[Wolfram Notebook][1]
[1]: https://www.wolframcloud.com/obj/028dc6ce-4d45-4c48-8b2d-385c3043654fDrew Lesso2024-03-14T13:59:02ZBest way to access a local mySQL database within SystemModeler
https://community.wolfram.com/groups/-/m/t/3138766
Hi There,
I was just wondering if anyone knew what the best way to connect to a local mySQL database is in SystemModeler? I would like to read data from a database to set up a model as well as write results.
Any advice appreciated.S G2024-03-11T11:43:18ZDSolve has reached the maximum number of calculations
https://community.wolfram.com/groups/-/m/t/3138820
I reached the maximum number of calculations when using *DSolve* to calculate differential equations, which makes it impossible to fully solve. How can I expand the number of calculations of *DSolve*?
Here is my code:
system = {vi q[t] == l iL'[t] + vC[t],
vC'[t] == iL[t]/c - vC[t]/(r c), vC[0] == 0, iL[0] == 0};
control = {q[0] == 1,
WhenEvent[Mod[t, \[Tau]] == (2/3) \[Tau], q[t] -> 0],
WhenEvent[Mod[t, \[Tau]] == 0, q[t] -> 1]};
pars = {vi -> 24, r -> 22, l -> 2 10^-2,
c -> 1 10^-4, \[Tau] -> 2.5 10^-5};
sol = DSolve[{system, control} /. pars, {vC, iL, q}, {t, 0, .2},
DiscreteVariables -> q];
a = Evaluate[iL[t] /. sol];
b = Evaluate[vC[t] /. sol];
Plot[a, {t, 0, 0.2}, AxesLabel -> {"s", "il[t]/A"},
PlotLegends -> {"LinearlyImplicitEuler"}, PlotStyle -> {Red},
PlotRange -> All]
Plot[b, {t, 0, 0.2}, AxesLabel -> {"s", "vc[t]/V"},
PlotLegends -> {"LinearlyImplicitEuler"}, PlotStyle -> {Blue},
PlotRange -> All]James James2024-03-11T06:01:41Z