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5
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1k views

Choosing the branch of a logarithm

The problem: I am integrating complex logarithms over an angle $\phi$ over $[0,2\pi]$. It is quite complex (pun not intended) and I called Mathematica in to aid me. I am calculating an energy of a ...
4
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0answers
57 views

Algorithm for FindSequenceFunction

What algorithm might Mathematica be using to compute FindSequenceFunction? Does anybody know if there is any online material on this topic?
4
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0answers
192 views

How to integrate $\left(1+\ln(x)\right)\sqrt{1+(x\ln(x))^2}$ with Risch algorithm?

How would you integrate $\left(1 + \ln\left(x\right)\right)\, \sqrt{1 + \left(x\ln\left(x\right)\right)^{2}\,}$ using the Risch algorithm? I want to know this because Mathematica is using the Risch ...
3
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0answers
128 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 ...
3
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0answers
125 views

Algorithm to find the “optimal” path in a given graph

Assume that $G=(V,E)$ is an undirected connected graph and that $H: V \to \mathbb R$ is a function that assign at each vertex $v \in V$ its height $H(v)$. Think of the pair $(G,H)$ as an energy ...
3
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0answers
359 views

SAGE vs. Mathematica for Lie algebras / groups?

What math software is better for working with Lie algebras and Lie groups, SAGE or Mathematica?
3
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0answers
50 views

How to visualize a function to aid in optimization?

I am working on minimization of a function with more than two parameters. I want to see variations, local extremes, saddle points, etc. of this function to get some idea of how is this function in ...
3
votes
0answers
145 views

Perturbation problem

This is a mathematica exercise that I have to do, where $y(x) = x - \epsilon \sin(2y)$ and it wants me to express the solution $y$ of the equation as a power series in $ \epsilon$.
2
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0answers
49 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 ...
2
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0answers
31 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 ...
2
votes
0answers
87 views

Solution of nonlinear waves( breathers)

The sine-Gordon equation is known as $$\frac{\partial^2 u}{\partial t^2} - \frac{\partial^2 u}{\partial x^2} + \sin u = 0,$$ Can you please derive the equation which is known as breather equation ...
2
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0answers
318 views

$\int^{\infty}_{0}x^{r +s- 1}(1 + x)^{-s}(1 + x^2)^{-\frac{rm}{2}}dx$

I'm trying to solve the integral $\int^{\infty}_{0}x^{r +s- 1}(1 + x)^{-s}(1 + x^2)^{-\frac{rm}{2}}dx$, where $s$, $r$ and $m$>1 are positive integers. My question is whether a closed form ...
2
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0answers
510 views

Calculate periodicity in 1-dimensional array with noise

I have a 1-dimensional array with some integers, which are periodically increasing. Something like this (1 period here): ...
1
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0answers
28 views

I am not able to label the vertex of the following graph in mathematica, can some one please help me.

Graph[{1, 2, 3, 4, 5, 6}, {1 -> 2, 1 -> 3, 2 -> 5, 2 -> 6, 5 -> 6}, VertexLabeling -> True] Graph::optx: Unknown option VertexLabeling in Graph[{1,2,3,4,5,6},{1->2,1->3,2->5,2->6,5->6},...
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0answers
21 views

Symbolic Constrained Optimization in Matlab or Mathematica

I hope you are having a nice day. I am learning MATLAB at the moment and the best way for me to learn is to use it to tackle some of my problems. I am currently trying to solve the following problem ...
1
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0answers
19 views

How do I extract the factor in Mathematica

If I get a equation $\left(\left(1-s_K\right) K^w+\left(1-s_L\right) L^w\right)\left(4 b a_m-4 a+2 b \tau +c \tau n^w-2 c n \tau \right)-\left(s_K K^w+s_L L^w\right)\left(4 b a_m-4 a+2 b \tau -c \...
1
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0answers
18 views

Integer solutions to a polynomial $f(x,y)$

How can I find the integer solutions of a polynomial $f(x,y)$ such that $a<|x|,|y|<A$ using Mathematica?
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0answers
29 views

Creating a grid of coloured points

I wish to create a grid of $31\times31$ points with coordinates of the form $(\frac k{30};\frac n{30})$ within the unit square, and give each point a colour based on the 2-adic value of both its ...
1
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0answers
71 views

Minimize the number of non-zero elements of a matrix

I have a matrix A, which is huge, and all its elements are non-zero. I want to perform the operation: $ U_1\otimes U_2 \otimes U_3...\cdot A \cdot U_1^{\dagger}\otimes U_2^{\dagger}\otimes U_3^{\...
1
vote
0answers
33 views

What is following limit?

$\mathsf{Mathematica}$ evaluates $$\lim_{N\rightarrow\infty}\lim_{\epsilon\rightarrow0^+}\frac{\binom{N^{\frac{3}{2}}-N^{\frac{1}{2}}}{N^{1-8\epsilon}}}{\binom{N^{\frac{3}{2}}}{N^{1-8\epsilon}}}$$ to $...
1
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0answers
46 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} \frac{z^n}{n!}\,\,\,\...
1
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0answers
45 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 ...
1
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0answers
73 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 ...
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0answers
45 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 ...
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0answers
49 views

ODE with Reflection

Some Background: I come from a computer science background and differential equations was not part of my course work. I'm still in contact with my professor that I ...
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0answers
22 views

Determining the sign of a function containing ratio

Problem We want to know for which values of $x,y,z,w$ the function $\sigma$ is positive or negative: \begin{equation} \sigma = \frac{A}{A^2-B^2}, \end{equation} where \begin{eqnarray} A & = &...
1
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0answers
25 views

Assigning a variable as constant and find out the minimum value

I have got a problem in assigning a variable as constant and solving a equations for minimum value. These are my equations: kd (2 h2 Cos[[Theta]2] - b2 Sin[[Theta]2]) (b1 - (b1 + b2) Cos[[Theta]...
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0answers
48 views

Is there any interactive spline fitting software?

I'd like to know if there's any software (freeware) for interactive data interpolation. What I want is to be able to visualize my data on an XY plot and drag the points to see how it affects the ...
1
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0answers
27 views

Computer Code Friendly Books On Differential Equations?

When I need a differential equation for this or that application I generally search (by hand) through old paper and ink books written by mechanical or electronical (electrical) engineers. Sometimes my ...
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0answers
53 views

Can nodes of Gaussian quadrature shift range?

I used my Python program to generate Gaussian's nodes and their weights. My python program could generate nodes as default in rage of (-1, 1). And my friend used Mathematica to generate them also but ...
1
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0answers
50 views

How to evaluate Bessel functions $K_{i x+\frac{9}{4}}(2\pi)+K_{i x-\frac{9}{4}}(2\pi)$ with $x>1.5*10^8$ in Mathematica 7?

I am trying to evaluate Bessel functions $K_{i x+\frac{9}{4}}(2\pi)+K_{i x-\frac{9}{4}}(2\pi)$ with $x>1.5*10^8$ in Mathematica 7. This function is the first Polya approximation to Riemann $\xi(s)$...
1
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0answers
53 views

Plotting in Mathematica

I'm new to mathematica. How would I plot the following functions in the polar complex plane? $$ \phi={-k\over 2\pi r}\cos(\theta_0-\theta) $$ and $$ \psi={-k\over 2\pi r}\sin(\theta_0-\theta) $$ ...
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0answers
147 views

What is the Fourier series of $e^{\mu\cos\theta}$?

Motivation: I want to solve this convolution problem on the circle: find $f$, given $g$ and $$ g(\theta) = \int_{S^1} e^{\mu\cos(\theta-\phi)}g(\phi)\ d\phi. $$ To do this, I want to find the Fourier ...
1
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0answers
86 views

Roots and Weights

I use a Mathematica package to compute roots and weights (and other things) but the package gives me only the expression of the roots in $\omega$-basis (basis of fundamental weights) and in the $\...
1
vote
0answers
179 views

Which symbolic programming language for manipulation of nonlinear equations?

I have a set of (multivariate, nonlinear) equations which I want wo modify according to my own rules, i.e. not in a standard ways such as matlab's simplify function. I am looking for a mathematical ...
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0answers
76 views

Learning Resources: Mathematica Notebooks

A while ago, I stumbled upon someone's list of Mathematica notebooks for learning various topics. I've since lost the link, but I'm wondering now if I could find notebooks again. So my question is: ...
1
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0answers
71 views

Functions generating prime numbers in math packages

Does anyone have an idea on how prime number generating functions such as Prime[n] in Mathematica generate the $n^{th}$ prime number?
1
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0answers
70 views

Vector calculus: Finding a model fit from a 2D grid

First of all, I am a biologist. My knowledge of math is very limited. Therefore, I come here for help, but please take into consideration that I may not be very good at asking the question in a good ...
1
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0answers
46 views

What are the available libraries or programs for finding extremes of a function with no symbolic definition?

In my current mathematical inquiry, I would like to gain insight on behaviour of a $d$-dimensional continuous function by locating its maximum over the hyperplane $\sum_{i=1}^d x_i = 1$ for $x_i$ non-...
1
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0answers
580 views

How to make iteration for Newmark method in Mathematica 8

How to make iteration method for solving differential equations by Newmark method? There are just three equations which describe the Newmark method. I need q for time step for example 0.01. Also, for ...
1
vote
0answers
197 views

Euler method on differential equation problem

I have this problem to solve. I want to compute the inclination of a plane $\theta(t)$ at every frame of a simulation given the following rule for its angular speed of rotation $\omega(t)$ $$ \omega(...
1
vote
0answers
602 views

Mathematica: How to convert scales to frequencies?

According to the transform $$w(u,s)=\frac{1}{\sqrt{s}}\int _{-\infty }^{\infty }x(t) \psi ^*\left(\frac{t-u}{s}\right)dt,$$ the frequency should be $f=\omega/(2\pi)=1/(2\pi s)$ (is it right?), where ...
0
votes
0answers
16 views

How can I mark a specific point and vector in Mathematica?

How can I mark a specific point and vector in 3D in a Mathematica plot? I've draw a surface but I need to mark a point and vector on it. Thanks!
0
votes
0answers
31 views

Solving Quadratic Equation By Using Mathematica

I was bothered with the following very simple problem: Solving a quadratic equation $x^2+x+1=0$ in mathematica if I use "solve" function in mathematica as below: Solve[x^2 + x + 1 == 0, x] I ...
0
votes
0answers
25 views

Twin Prime Max Gaps

Ok, let's build a foundation here: A common way of testing primality, is dividing by all primes smaller than the number's square root. For instance, $97$ is prime because dividing by none of the ...
0
votes
0answers
9 views

Dynamic array for defining function.

I wanted to define a function in mathematica.For example Shifted Schur function, so I wander if there is a way to define a dynamic array that is to take a vector $\lambda=(\lambda_1,\lambda_2,...,\...
0
votes
0answers
21 views

How to obtain an analytic approximation of this wavelet-looking function?

I would like the approximating function to be infinitely differentiable. I have tried fitting (1) a polynomial and (2) a combination of sin, cos, and exp functions to approximate the function shown ...
0
votes
0answers
13 views

Plotting data with error bars with gaussian distributed error

I want to fit a straight line model of the form $y_i = a+ b\ x_i$ to the list of $(x, y)$ pairs given below. How can I plot the data with error bars in both coordinates? ...
0
votes
0answers
40 views

One dimensional integration that Mathematica cannot do

I want to evaluate $$\int_{a+b-c}^s\,\text{d}x\, \frac{(-x+ab/c)^{\epsilon}}{(x+c-a-b)^{\epsilon+1} (a-x)},$$ where $a,b,c,\epsilon$ are real numbers, and to be treated as constants in the integration....
0
votes
0answers
27 views

Convex Analysis - How To Find Non Convex Set

I have a problem regarding the following exercise (I considered to put this question on mathematica.stackexchange, but I changed my mind and though this was the right place for this particular ...