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0
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1answer
112 views

Trouble in proving that $\|x\|_p = \max|x_j|$

We define p-norm in this way: $\|x\|_p = \{\sum ^N_j=_1|x_j|^p\}^ {1\over p}$ We know that It change to $\|x\|_p = \max|x_j| $ when $ p \to \infty $ How can I prove this ?
2
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0answers
39 views

Is this system of inequalities (and equality) tractable?

I have some real parameters here. The $\mu_i$ - for $i=1,2,3,4,5$ - are 'convex coefficents' in that $\mu_i\geq 0$ and $\sum_{i}\mu_i=1$. The $x$ and $z$ are such that $x^2+z^2\leq 1$. The ...
1
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0answers
27 views

Convergence of a hypergeometric function

The hypergeometric function, ${}_{2}F_1(a,b,c;z)$ can be written in terms of a power series in $z$ as follows, $${}_{2}F_1(a,b,c;z) = \sum_{n=0}^{\infty} \frac{(a)_n (b)_n}{(c)_n} ...
1
vote
1answer
381 views

Newton backward interpolation in Mathematica

I have the following task: Create a function (in Wolfram Mathematica), called $\mathrm{NewtonBackward}$[n_,x0_,h_,f_] which interpolates backwards the function $f(x)$ with nodes {x_i = x_0 + ...
0
votes
0answers
31 views

Using Mathematica to calculate expected time to absorption

I am trying to solve a standard ETA on a birth-death process with $n$ states $\in \{0,\cdots,n-1\}$ where state $n-1$ is absorbing. Also $\mu_i$ is the expected time to absorption starting at state ...
0
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0answers
30 views

Requesting programming implementations for $\mathbb{F}_{p^n}$ and $SL_2(\mathbb{F}_{p^n})$.

I would like a programming language capable of doing computations over finite fields and matrix groups over those finites fields. I do not want to have to construct bases and what not on my own. What ...
0
votes
1answer
394 views

Solve 4 A (L^(3/4)) - wL (((24 - L) w)^(-3/4)) = -(((24 - L) w)^(1/4)) for L? Using Mathematica

I'm trying to solve $$4 A (L^{3/4}) - wL (((24 - L) w)^{-3/4}) = -(((24 - L) w)^{1/4})$$ for $L$ using Mathematica, and it spits the following out: ...
0
votes
2answers
312 views

Graeffe's root finding method

What are the practical applications of Graeffe's root finding method?I searched a lot but couldn't find.I found that it is used in aerodynamics and electric circuit analysis.But don't know much about ...
2
votes
1answer
63 views

Mathematica Solutions and Student's Exam [closed]

I do not know if this is an acceptable question. But I wanted to ask some of you if you can generate for me what MathematicaAlpha answers (as I do not have a subscription) to a few questions. One ...
0
votes
1answer
25 views

Problem with Solve a Differential Equation

I Have a little problem . I wrote this function ( function describe dynamics of ball-hoop system): ...
3
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1answer
98 views

Fun/Frustration With Coding Coding Theory

it's time for practical coding theory. I am trying to write a simple program that will detected if a given binary code word is "correct" or not. If it is not correct, I want to detect/correct (since ...
0
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0answers
18 views

Using Orthogonal Collocation to solve Coupled Ordinary Differential Equations

I am trying to solve six first order coupled ODE's, two of these are associated with a heat balance of a catalyst pellet, and four are mass balances. I have been trying to solve these equations using ...
3
votes
2answers
146 views

Solving $\frac{dx}{dt} = A \frac{ (1-x)}{(t-t^2)} - \frac{(B*x -C*x^2)}{(t-t^2 )*(t-x)}$ (using wolfram/mathematica)

I would like to solve the following non-linear ordinary differential equation: $$\frac{dx}{dt} = A \frac{ (1-x)}{(t-t^2)} - \frac{(B*x -C*x^2)}{(t-t^2 )*(t-x)}$$ -I need an analytic solution. -I ...
0
votes
1answer
54 views

Mathematica - Searching a clever way to do a computation

I am solving this differential equation using Mathematica $$x ~y''(x)+\alpha ~ y'(x)+\frac{1-3\mu (x)}{(1-x) x}=0$$ where $\mu(x)$ is a polynomial: $$\mu ...
1
vote
1answer
53 views

Mathematical symbol for Symbolic Replacement

(Posted at mathematica.SE, as it might be better there) I'm searching for a mathematical symbol, that describes the symbolic replacement done for instance in Mathematica: ...
0
votes
1answer
59 views

How to plot a phase portrait for system of differential equations in mathematica or R?

Please, help me. I'd like the phase portrait for this system: If anyone can make this portrait and post a print screen here, I would thank you very much.
0
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0answers
27 views

free tool for algebraic manipulations of commutator expressions

Is there an (ideally) free tool for algebraic manipulations of commutator expressions of the form: given $$c(A,B):=\tfrac{1}{2}[A,B]+\tfrac{1}{12}[A,[A,B]]+\tfrac{1}{12}[B,[B,A]]$$ simplify (express ...
11
votes
2answers
316 views

Twilight Zelda Guardian Puzzle : Shortest Path (UPDATE: ADDED RULES)

I'm playing a video game right now and in it is a puzzle (see here). There are solutions to solving it (see here) on the Internet, but I'd like to know if this path is the shortest path (least amount ...
0
votes
1answer
30 views

How can i view solutions of Solve as multiples of pi in mathematica 10

i am new to Mathematica and can't find the option to show solutions of Equations like Solve[6.5 == 2 \[Pi]*r] as multiple of pi. I only get the numerical output ...
1
vote
1answer
63 views

How can I solve numerically this partial differential equation?

I am reading this paper and came across a system of differential equations with 4 ODEs and 1 PDE. The PDE is given below. My question is how to solve this numerically in MATLAB , Python or ...
0
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0answers
19 views

Closed form for a Bartlett's formula for AR(2)

Consider a stationary AR(2) process $$ Y_t=\phi_1Y_{t-1}+\phi_2Y_{t-2}+e_t $$ with $e_t$'s are i.i.d. with mean $0$ and variance $1$. Let $r_s$ be the $s$-th autocorrelation ...
0
votes
1answer
18 views

Graphing Fourier transforms on a frequency versus intensity plot (how to deal with complex numbers)

I am trying to understand how Fourier transforms are used to make HNMR plots. HNMR basically consists of hitting some molecules with some radiation and listening to the radio signal that results. ...
2
votes
1answer
52 views

Is the adjacency matrix of a given graph (OR any graphs isomorphic to a given graph) a Kronecker product, and if so what are the factors?

I have a few triangular grid graphs that I am trying to express as the direct products of smaller graphs, if possible. ...
0
votes
2answers
68 views

Techniques to solve nonlinear first-order ODEs

I am trying to solve the following nonlinear ODE: $$\frac{dy}{dx} = \frac{1}{x(ayx-b)},$$ where $a, b$ are constants and $a>0$. Moreover, you may assume that $b \neq 0$ if necessary. This ...
2
votes
1answer
180 views

Help me understand Gröbner basis result please

I'm practicing a bit with Gröbner bases but I'm not understanding the following result I obtain from Mathematica: ...
0
votes
1answer
55 views

Summation giving incorrect value (I think) in Mathematica

I have the problem $\displaystyle\sum\limits_{x=2}^4 \dfrac{1}{x^2}$. I know the answer to this problem should be $\dfrac{61}{144}$. When I type the problem into Wolfram Mathematica, I get the answer ...
1
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0answers
37 views

Precision of starting values in FindMinimum

I am currently working on an optimization of chemical kinetic model. Starting points for FindMinimum is defined as: k10 = 2.45*10^-1 and k20 = 8.65*10^-11. The step monitor is used to show calculated ...
0
votes
0answers
382 views

Complex exponential integral: Mathematica and MATLAB give unexpected results

I currently compare analytical vs. numerical evaluation of the complex exponential integral and find mismatches: The imaginary part differs by $\pm \pi$ and the real part has a large error when ...
1
vote
1answer
51 views

Dual curve of the lemniscate of Bernoulli?

Does anybody happen to know the homogeneous equation $F(u,v,w) = 0$ for the algebraic curve dual to the lemniscate of Bernoullli: $$ F(x,y,x) = (x^2 + y^2)^2 - A (x^2 -y^2)z^2 = 0?$$ I looked at the ...
1
vote
0answers
61 views

What is $\int (1-e^{-x})^n dx$?

For my purposes, $n$ is a non-negative integer, and $x > 0$. I didn't know how to evaluate this integral, so I plugged it into Mathematica. It told me the solution is $(-1)^n B(e^x; -n, n+1)$ I ...
1
vote
2answers
46 views

Solving differential equations with Wolfram Mathematica

So i saw this differential equations in my textbook $\frac{{{d^4}\omega }}{{d{x^4}}} + 4{\lambda ^4}\omega = 0$ and i figured why not solve it with majestic Wolfram Mathematica, so i write this ...
0
votes
0answers
29 views

Sum of a Normal and a Truncated Normal distribution on Mathematica

I asked a question about the "Sum of a Normal and a Truncated Normal distribution" about 11 days ago, and someone helped me (I appreciate his\her help a lot). I tried to do same procedure as he\she ...
3
votes
2answers
2k views

How to draw a family of curves and its envelope?

Given a family of curves $$F=(x-t)^2+y^2-\frac{1}{2}t^2,$$ I am trying to compute the envelope of this family. The envelope is described by the equations $$F=0, \\ \dfrac{\partial F}{\partial t} ...
2
votes
0answers
24 views

Finding feasible solution of inequalities in math software

I have a Math problem where I have some true statements, and I want to know if there is a feasible solution to an equation. I would like to know how to do that in either Matlab or Mathematica. The ...
-1
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0answers
19 views

Creating a graph with linear regression together with error bar using mathematica

Can anyone help me with incorporating error bars (standard deviation) into a graph showing linear regression?
0
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0answers
30 views

Importing microsoft excel data to Mathematica

I used the import function in Mathematica to import an excel file and while Mathematica did perform that, the data in the cells in excel appear in curly brackets in Mathematica. What can I do to ...
0
votes
0answers
14 views

FindRoot[rhs==lhs, {X,x1,x2}] Vs. FindRoot[rhs==lhs, {X,x1}]

What is the difference between these two commands: FindRoot[rhs==lhs, {x,x1,x2}] and FindRoot[rhs==lhs,{x,x1}] They give me completely different solutions. Thanks
22
votes
1answer
462 views

The positive root of the transcendental equation $\ln x-\sqrt{x-1}+1=0$

I numerically solved the transcendental equation $$\ln x-\sqrt{x-1}+1=0$$ and obtained an approximate value of its positive real root $$x \approx 14.498719188878466465738532142574796767250306535...$$ ...
0
votes
0answers
25 views

Irregular Implicit Plot in Mathematica

While studying the implicit relation $ y=x\tan(a\sqrt{x^2+y^2}+b)+c$ I came across some spurious looking parts in the graph WolframAlpha produces. These are jagged circles with radii that appears to ...
10
votes
4answers
282 views

A numerical evaluation of $\sum_{n=1}^{\infty}(-1)^{\frac{n(n+1)}{2}}\frac1{n!}\int_0^1x^{(n)} dx$

I would like to obtain a numerical evaluation of the series $$S=\sum_{n=1}^{\infty}(-1)^{\frac{n(n+1)}{2}}\frac1{n!}\int_0^1x(x+1)\cdots(x+n-1)\: dx$$ to five significant digits. I've used ...
0
votes
0answers
23 views

How do I compute uncertainties in the positions transformed using Helmert transformation?

I am familiar with Python, MATLAB and Mathematica. My data is given by Cartesian coordinates (positions in X,Y,Z (meters), standard deviations XX, YY, ZZ (meters) and a correlation matrix (XY, YZ, ...
0
votes
0answers
18 views

Solve multivariate exponential inequality via program

I am trying to solve a complicated exponential inequality with six parameters and one variable t. This can't be done with mathematica command "Solve, Reduce or FindInstance". Is there any other ...
0
votes
1answer
66 views

Mathematica Homework Question

I had a mathematica assignment the other day that was fairly simple. I thought I did it correctly, but I guess not. Question: Write a single Mathematica Command which will display (plot) both $y = ...
0
votes
0answers
21 views

Getting a part of a matrix in mathematica

I was trying to get an element of a matrix, and use in further computation of my program. Problem was that its not reading the value unless and until I specify it again. My code is: ...
1
vote
1answer
79 views

Inverse gradient as line integral in Mathematica

I found a nice paper about inverse vector operators here. I have successfully defined a Mathematica function for inverse curl and inverse divergence, however I can't figure out how to do inverse ...
1
vote
1answer
100 views

How does Matlab, Maple, etc…solve algebraic and differential equations internally?

I would be very interested finding out how does Matlab, Maple, etc…solve algebraic and differential equations internally? Anyone know how they do it?
4
votes
2answers
184 views

How to actually use the Weierstrass-Enneper parameterization to draw a minimal surface?

I'm interested in drawing (with Mathematica for example) the generalized Scherk saddle tower with threefold symmetry, a shape that I find very attractive. In an article (see here) I found the ...
3
votes
0answers
71 views

The mathematics of anaglyph images

Note: I'm not quite sure whether this question properly belongs to the Mathematica or to the mathematics Stack Exchange. But because my question mainly concerns general mathematical principles rather ...
21
votes
8answers
3k views

LaTeX/TeX Vs. Mathematica for Typesetting [closed]

I know Mathematica like the back of my hand, but I do not know a speck of $\LaTeX$ or $\TeX$. With regards to mathematical typesetting, is there something significant I can do in $\LaTeX$/$\TeX$ that ...
1
vote
1answer
49 views

Minimizing a function in Mathematica

Edit: I simplified the function using $\textbf{Simplify[...]}$ How can I minimize this function of $x$, where $l$ is a positive constant? $$\frac{1}{2} \sqrt{\frac{x}{l}+\frac{l}{x}+4 x^2-2}$$ ...