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3answers
28 views

What is the difference between linear regression on y with x and x with y

I'm plotting the regression line of (GDP$\%$ Change, Poverty Rate$\%$)$\to (x,y)$ in Mathematica What would it mean if I were to switch the axis? (Poverty Rate $\%$, GDP change $%$) ...
0
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0answers
15 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
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0answers
29 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 ...
1
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1answer
40 views

Why is the right half of the output for the Plot[(-x)^(2/3), {x, -30, 30}] missing?

I want to get a figure for $(-x)^{\frac23}$. After using the following code, I found that only the left part of the function $(-x)^{\frac23}$ was plotted. ...
0
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1answer
36 views

Formal expansion of matrices using Maple or Mathematica

I'd like to evaluate some powers of sum of matrices, say I would like to evaluate $\left(A+B\right)^{n}$ with $A$ and $B$ some matrices. Since I'd like to go to high order, I'd like to use Maple or ...
-1
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0answers
44 views

Mathematica integration

I want to integrate $$ \int (-\frac{1}{2 p^{1/4}\sqrt{\left(-\sqrt{p}+\text{a}\right)}})$$. Using Mathematica $$\text{Integrate}\left[-\frac{1}{2 ...
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0answers
19 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
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1answer
11 views

MLE for Parameter Estimation using Mathematica

I am using Mathematica (MMA) 10.0.0.0 with MathStatica do determine parameters using MLE for several PDFs. I have tried the approach below for several PDFs but I keep getting messages that Mathematica ...
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1answer
28 views

How to find the Limit of two variable using mathematica ?

I was wondering if there is a method to solve the limit of two variable using Mathematica , I try to do this Limit[(x^4+y^2)/(x^2+y^2),(x,y)->(0,0)] Limit[(x^4+y^2)/(x^2+y^2),x->0,y->0] but non of ...
0
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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 ...
0
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2answers
51 views

What does the terminology “characteristic polynomial” mean?

In the documentation of the command "MininimalPolynomial" in Mathematica it says "Find the characteristic polynomial of Sqrt[2] over the extension E^(I Pi/4). The code: MinimalPolynomial[Sqrt[2], x, ...
0
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0answers
17 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 ...
1
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0answers
20 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 ...
0
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0answers
12 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
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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 ...
1
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1answer
41 views

What does the comma mean between two matrices represent?

For example [A,B] ? It has been many years since I needed to know.
1
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0answers
18 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 ...
0
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1answer
27 views

Double integral multivariable calculus

Consider the following integral $$\int_0^1 dx_1 \int_0^{1-x_1} dx_2 \, (1-x_1-x_2)^{-\epsilon-1} (-sx_2 - x_1p_1^2)^{-\epsilon-1}$$ where $s$ and $p_1^2$ are to be treated as constants throughout the ...
1
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2answers
57 views

Different eigenvectors obtained with Mathematica

Suppose that we have a matrix $$ \begin{pmatrix} a&c\\c&b \end{pmatrix}. $$ The eigenvalues of this matrix are given by $\lambda_1=(a+b-D)/2$ and $\lambda_1=(a+b+D)/2$, where ...
6
votes
1answer
132 views

Improper integral: $\int_1^\infty\frac{\sin(\sqrt{x})}{\sqrt{x}}dx $.

mathematica is reporting that the improper integral $\int_1^\infty\frac{\sin(\sqrt{x})}{\sqrt{x}}dx $ coverges to $2\cos(1)$. However, when I try to confirm this by actually integrating it using ...
3
votes
3answers
81 views

Solution of the equation $\cot \theta = 2\cot 2\theta$

I've tried to solve the equation $\cot \theta = 2\cot 2\theta$ with the command 'Reduce' of Mathematica and obtained $\theta = n\pi$ as the solution with n an integer. But $\theta=n\pi$ is clearly a ...
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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1answer
27 views

How to find a pair of basis vectors for the plane given by the equation?

Find a pair of basis vectors for the plane given by the equation x+2y+3z=0 I was given the Hint: you can find points on the plane by choosing values for two variables and solving for the third I am ...
1
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2answers
42 views

Does the inverse of $f(x)=x^3$ have a non-negative domain to have a real output?

I'm not familiar with complex analysis. While playing with Mathematica (a mathematics software), I found that it keeps spitting out unexpected results, and the reason was that it considers differently ...
0
votes
1answer
35 views

Lattice Reduction in Mathematica

I have some trouble understanding the concept of lattice reduction. As I understand, an integer lattice $$\{ A k : k \in \mathbb{Z}^n \} \subset \mathbb{Z}^n $$ is defined by a regular matrix $A \in ...
0
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0answers
24 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 ...
0
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0answers
28 views

Approximating a Riccati Differential Equation/Differential equation of two variables

I am currently really struggling to solve/approximate this Riccati equation $x'(t, v) = cv(1-x(t)) + \beta x(t)(1-x(t)) - \gamma x(t)$ st. $0 < c, \gamma, x_{0} < 1$ $ 0 \leq v \leq 1$ $ 0 ...
0
votes
1answer
34 views

How to find elements of a ring $\mathbb{Z}_n$ in Mathematica

How to find elements of a commutative ring with unity $\mathbb{Z}_n$, (under addition and multiplication modulo $n$) by using Mathimatica, which satisfying the following condition. Let $x, y \in R = ...
1
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1answer
60 views

Bug or feature? If statement inside double integrals [closed]

Generally speaking, $$ \int_c^a f(x) dx = \int_c^{a-b} f(x) dx + \int_{a-b}^a f(x) dx$$ However, consider the following Mathematica code: So apparently, the sum of the two sub-integrals $1/32 + 0 ...
1
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2answers
91 views

Revolution of fractal

How to find the volume and surface area of a shape which made from revolution of Koch Snowflake? (I think the surface area will be an infinity, because length of the Koch snowflake is infinity.) And ...
1
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1answer
27 views

Focal distance on a parabola

If focal distance of a point on the parabola $y = x^2 - 4$ is $25/4$ . And the points are of form $(\pm \sqrt{a}, b$ then how can we find $a , b$ or sum of these . I think the focus of parabola would ...
0
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1answer
31 views

Plotting a function around $0$ shows it is jumping around, although the limit as $x\to 0$ exists

My problem revolves around the function: $$ f(x) = \frac{\sin(\tan x) - \tan(\sin x)} {\arcsin(\arctan x) - \arctan(\arcsin x)} $$ The $\lim_{x\to 0}f(x)= 1$. However, whilst approaching 0, there is ...
11
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1answer
3k views

Fractional oblongs in unit square via the Paulhus packing technique

Oblongs of size $ \frac{1}{1} \times \frac{1}{2}$, $ \frac{1}{2} \times \frac{1}{3}$, $ \frac{1}{3} \times \frac{1}{4}$, $ \frac{1}{4} \times \frac{1}{5}$, ... have a total area of 1. ...
0
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0answers
31 views

How can I find $\int {\sqrt {{{\left[ 1 - {r k \cos \left( {(w - t )s + p} \right) } \right]}^2} + {{\left( {r w } \right)}^2}}} \mathrm{d}s$?

I have to integrate $$ \int {\sqrt {{{\left[ 1 - {r k \cos \left( {(w - t )s + p} \right) } \right]}^2} + {{\left( {r w } \right)}^2}}} \mathrm{d}s. $$ I have tried solving it with Mathematica, but ...
0
votes
1answer
21 views

How to alternate alternating negatives in a series (summation)?

Note: while this isn't a strictly Mathematica, I am using it to find my results. I have a problem where I integrate E^x x^n and I'm given results like ...
0
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1answer
27 views

Verifying general solution to differential equation

to the following differential equation: $y^{(6)}-2y'''+y=0$ I obtained the following general solution: $y=C_1e^x+C_2x ...
0
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1answer
29 views

efficient mathematica code to reduce computational time

I am trying to a code in Mathematica that is taking unacceptably long time (day) to run as it involves four summations. I am wondering is there any way to do some changes in the code so that it ...
1
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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
66 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 ...
5
votes
2answers
713 views

Should I trust Mathematica or numerous other sources on this Fourier transform

Assume $a>0$ So Mathematica claims $$F\{e^{-a|t|}\}(\omega) = \frac{a\sqrt{\frac{2}{\pi}}}{a^2+\omega^2}$$ However, I've read about another transform pair (page 3): $$F\{e^{-a|t|}\}(\omega) = ...
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1answer
61 views

mathematica / maple

I have an expression of products and divisions of q-binomials. I want to check if the expression is always greater than 1. Is there a way I can do that with matlab/ mathematica/ maple?
0
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1answer
96 views

Why is it incorrect to integrate by $d(2x)$?

I tried to prove the volume of a cone. If you let the radius be $r$ and let the height be equal to the radius, then all you need to do is integrate the area of a circle with radius $r$ by $dr$. ...
0
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1answer
70 views

Visualising a 1-(50,15,15) design.

The problem I have is the visualisation of a 1-(50,15,15) design. That is a set of 50 points and 50 blocks (lines), so that each point is on 15 lines, and each line contains 15 points. My attempts ...
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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
votes
1answer
59 views

Code Wolfram Mathematica [closed]

Sorry but I do not know English very well. The question is very simple, I hope someone knows the code that makes my case. In fact, writing: ...
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 ...
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0answers
44 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} ...
0
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1answer
29 views

Problem with Solve a Differential Equation

I Have a little problem . I wrote this function ( function describe dynamics of ball-hoop system): ...
1
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0answers
44 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
157 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 ...