For questions concerning the popular computational software program published by Wolfram Research. (Note: you are more likely to get quicker and more accurate response if you ask the question on their user forum or on the Mathematica StackExchange site.)
0
votes
2answers
30 views
Series expansion with remaining $log n$
I'm studying the asymptotic behavior $(n \rightarrow \infty)$ of the following formula, where $k$ is a given constant.
$$ \frac{1}{n^{k(k+1)/(2n)}(2kn−k(1+k) \ln n)^2}$$
I'm trying to do a series ...
0
votes
1answer
97 views
Mathematica vs Wolfram Alpha integration results
When I insert the following integration command in wolframalpha:
...
0
votes
2answers
42 views
WolframAlpha functionality: Computing nested integrals
Can wolframpalpha support the numerical calculation of the following type:
$$
\int_{x=0}^\infty f(x) e^{\int_{z=0}^\infty g(x,z)dz} dx
$$
Note that the inside integral is in such form where ...
1
vote
0answers
28 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 $x_i$ ...
0
votes
0answers
32 views
How to estimate true value and 95% bands when distribution is asymmetrical? [migrated]
I have a set of results of independent measurements of some physical quantity. As an example I give here real expermental data on methanol refractive index at 25 degrees Celsius published in ...
1
vote
1answer
38 views
Help calculating variance of a random variable
This is related to this question Average end point of 1-dimensional random walk?
Given several discrete random variables such that $p(Z_i=1-2k)=p$, where $k$ is a small real number, and ...
0
votes
1answer
20 views
Using Mathematica to solve equations - no answer returned?
I'm trying Mathematica and finding it can't seem to solve very basic equations. I started with something REALLY basic:
Solve[y == 2 x, x]
and it correctly returned that x = y/2.
Then I tried it ...
1
vote
0answers
27 views
Mathematica code for solving MHD viscoelastic fluid flow [migrated]
Where might I find Mathematica code for solving MHD viscoelastic fluid flow using Homotopy Analysis method?
0
votes
1answer
18 views
Is there a closed-form expression that allows me to triangulate a point in 2D?
Please consider the case where I have three points on a 2D plane - $(p_1, p_2, p_3)$ - and a third point, $p_0$, at some unknown position $(x_0,y_0)$. However, I know that $p_0$ is a distance $d_1$ ...
0
votes
1answer
51 views
Is it possible to guess n-th term of given number sequence?
Consider if we have number sequence e.g. $\left\{ 1, 6, 62, 344, ... \right\}$
I'd like to ask if is it possible to compute or estimate form of $n$-th element of this series.
Is it possible with ...
0
votes
0answers
90 views
Mathematica or Matlab: Which one should a Computer Science under-graduate choose? [closed]
I regret if you find this question green-horn.But I really need your expert advice to make my choice.I am a CS graduate student whose core subjects are stuff like programming,algorithm ...
0
votes
0answers
31 views
Mathematica will not integrate with a constant [closed]
I don't know what is wrong, Mathematica will only give me the original integral but won't evaluate it. any help?
eq1 = 0.048519*x
eq2 = -0.0134
eq3 = {sin[(n*[CapitalPi]*x)/0.586667]}
eq4 = ...
0
votes
0answers
12 views
Lead operator problem
Define the lead operator $L^{-1}$, by $L^{-1}E_t X_t=E_t X_{t+1}$ for any variable $X$.
Then $$(1-\frac{1}{1+r}L^{-1})Z_t-\frac{r}{1+r}E_t Z_t=-\frac{1}{1+r}(E_tZ_{t+1}-Z_t)$$
I'm confused. How can ...
5
votes
4answers
189 views
Sum up numbers from 1 to 100000 after removing zeroes
Ok so i have numbers from 1 to 100000.I need to remove the zeroes from all numbers and sum up numbers from 1 to 100000.So if the number is 405 consider it as 45 , if number if 20039 consider it 239.
...
0
votes
0answers
31 views
Symbolic computations in field extensions with Mathematica
In Mathematica I would like to make symbolic computations in field extensions. For example, if $a$ is a root of $x^3+3x-1$, I would like to get
$$ a^4 = a-3a^2 $$
if I asked the machine to compute ...
0
votes
0answers
35 views
Problem in soution similarities
Details on the article Article
From the article equation (9) I got the forth order expansion,
$$ \ddot \phi_4+ \phi_4= a\cos 2 \tau+b \cos \tau+ c \cos (2 \tau-3)+d(\cos2 \tau-3)^2+e \cos^2 \tau+f ...
0
votes
1answer
76 views
Finding roots of $e^x\sin^2(x)-\cos(x)=0$ using Mathematica
$$e^x\sin^2(x)-\cos(x)=0$$
I'm trying to find 5 roots of this equation but mathematica keeps giving me back an error saying $\sin^2$ is not a well-formed equation.
Thanks,
Joe
4
votes
2answers
129 views
Finding good approximation for $x^{1/2.4}$
I would like to a good (8 bits accuracy) approximation for $x^{1/2.4}$ in the range $[0, 1]$. This transform is used for converting linear intensities to SRGB compressed values, so it's important that ...
0
votes
1answer
44 views
Simplifying equation from an aggregate one
I have got the 4th order coefficient of $\epsilon$ from the equation (9) from the paper.
I got :
$$\phi_4+ \ddot \phi_4+\omega_2 \ddot \phi_2 - \Delta \phi_2+g_2 \phi_2^2+2 \phi_1 \phi_3+ 3g_3 ...
0
votes
0answers
28 views
mathematica, error when trying to solve nested optimization [closed]
I want to use the solution of Maximization, defined as a function, in another function. Here's an example:
f1[y_] := x /. Last[Maximize[{Sin[x y], Abs[x] <= y}, x]] (* or any other function *)
...
1
vote
1answer
40 views
Mathematica and Vector Representation of Planes
If the vectors $\vec{u}$ and $\vec{v}$ emanate from a point $A$, then its equation is
$\hspace{2in}$$x = A + su + tv$,
where $s, t \in \mathbb{R}$. I'm wondering how I can display these planes in ...
0
votes
2answers
92 views
Mathematica returns wrong limit
I just started limits as part of my calculus class, and I have a simple limit to evaluate, $\mathop{\lim}\limits_{x \to 1}~f(x)$ . I found the limit to be 2 using the $f(x)=\mathop{\lim}\limits_{h \to ...
0
votes
1answer
72 views
Computation of the minimal polynomial of a matrix in Mathematica
On the wolfram website, the following program is given for computing the minimal polynomial of a square matrix $a$ in the variable $x$:
MatrixMinimalPolynomial[a_List?MatrixQ,x_]:=Module[
{
...
0
votes
0answers
59 views
Unit tangent, normal, and binormal vectors for a given $r(t)$
I need to find $T(t), N(t)$, and $B(t)$ for $t=1, 2, and -1$ for my Calc III class, given $r(t)=\{t,t^2,t^3\}$.
I've got Mathematica, but I've never used it before and I'm not sure how to coerce it ...
1
vote
2answers
35 views
Solving for x. Do I require iterations?
I have the following expression (used in a computer program):
$$f(x)=b^{{k}^{ax}}$$
where $k$ is a constant and $a$ and $b$ are given. I need to calculate the distance from this curve to a point $P: ...
1
vote
2answers
81 views
Plot of x^(1/3) has range of 0-inf in Mathematica and R
Just doing a quick plot of the cuberoot of x, but both Mathematica 9 and R 2.15.32 are not plotting it in the negative space. However they both plot x cubed just fine:
...
0
votes
1answer
284 views
WolframAlfa/Mathematica how to find function local maximum on interval
I have a polynomial function and i want to find it's minimum and maximum on a the interval [0, 5] with Wolfram Alphaa but i forgot the proper input.
I recall it went something like so: $x^4 + x^3 + ...
0
votes
0answers
52 views
Simulating the balls and bins problem in Mathematica (or similar)?
The 'balls and bins' problem
Distribute $n$ balls into $d$ bins in a way which minimises the difference between the highest and lowest loaded bins.
Reasoning for performing simulation
I have some ...
-1
votes
1answer
375 views
Matrix equation solver (Mathematica) [closed]
I have matrix
$$A = \left( \begin{array}{ccc}
-1 & 1 & 1 \\
2 & 3 & -1 \\
-2 & 3 & 3
\end{array} \right)$$
and matrix
$$B = \left( \begin{array}{ccc}
-1 & 2 & -1 \\
...
1
vote
1answer
93 views
Matrix solving problem
Hi there math experts.
I have the following matrix:
$$
\begin{equation}
\begin{pmatrix}
-1x & 0y & 0 & 0 & 0.004 & 0\\
-1x & -1y & 0 & 0 & 0.001 & 0
...
0
votes
1answer
71 views
Relative error plot in mathematica
I was plotting the relative error of the $e^{11/12 -n}n^{n+1/2}$ approximation to the factorial as $n$ gets larger and larger and at after some very large value of $n$ mathematica gives this plot:
...
2
votes
1answer
114 views
Automatic calculation of the intersection of discrete curves
first of all, let me apologize for a poor math-english translation, I'll try my very best.
I have the following situation:
I have over 16.000 data files which I generated from a biometric ...
1
vote
0answers
262 views
$\int^{\infty}_{0}x^{r +s- 1}(1 + x)^{-s}(1 + x^2)^{-\frac{rm}{2}}dx$
I'm trying to solve the integral
$\int^{\infty}_{0}x^{r +s- 1}(1 + x)^{-s}(1 + x^2)^{-\frac{rm}{2}}dx$,
where $s$, $r$ and $m$>1 are positive integers.
My question is whether a closed form ...
1
vote
0answers
49 views
Plotting a dot product [closed]
From a conic equation obtained from a dot product, I want to plot its 2D graph, while being able to manipulate the variable.
...
1
vote
2answers
75 views
Unexpected results when integrating definite integral with variable bounds
When I plug something like this into Mathematica:
$$\int_0^{x^2-1} k y \, dy$$
I get exactly what I would expect:
$$\frac{k}2 (x^2-1)^2 $$
However, when I change my bounds ever so slightly, from ...
1
vote
1answer
78 views
Solve autonomous ODE with Mathematica
I'm given a problem with the ODE
y'[x]=y[x]*Sqrt[4-2y[x]]
I've tried
DSolve[{w'[x] == w[x]*Sqrt[4 - 2*w[x]]}, w[x], x]
which gives me
{{w[x] -> -2 (-1 + Tanh[1/2 (-2 x - Sqrt[2] C[1])]^2)}} but ...
0
votes
0answers
110 views
A (contour?) integration (even if by using Mathematica!)
I need to be able to calculate integrals of this type where the sum over $R$ is the sum over representations of a Lie group $G$ on whom $dU$ is the Haar measure and $\chi _ R ()$ is the character of ...
1
vote
4answers
351 views
Get numbers that have only 2,3 and 5 as prime factors
I am given an integer N. I have to find first N elements that are divisible by 2,3 or 5, but not by any other prime number.
...
-1
votes
5answers
281 views
Cryptography in Maple and Mathematica
Is Maple or Mathematica preffered over the other for Cryptography/Number Theory? What are the advantages for each in terms of this area of mathematics?
Also could someone compare and contrast ...
2
votes
3answers
47 views
A way to identify a unique number '$a_1$' has performed operations on '$x$'
The problem I have is bit vague, so I will try to explain as best as I can.
Suppose we have a base number '$x$' and a set of unique number $'a_1', 'a_2', 'a_3', 'a_4'$ and so on
Now $a_1$ perform ...
1
vote
1answer
535 views
Existence of non-trivial solution of Sylvester equation.
I'm trying to solve a special case of Sylvester equation
in my case it looks like
$$A*X=X*B$$
so it can be written in form
$$A*X+X*(-B)=C$$ where C consist of all 0 items.
I tried to solve it in ...
5
votes
3answers
121 views
Computer Algebra Systems which implement Cylindrical Algebraic Decomposition
My understanding is that Mathematica's Reduce function is based on Cylindrical Algebraic Decomposition (CAD).
The only other system I've seen which implements CAD ...
2
votes
1answer
437 views
Solution to a second order semilinear elliptic PDE
I am trying to find a solution (if one exists) to this PDE where (r,z) are cylindrical coordinates. $$u_{rr}+u_{zz}+u_{r}/r-u/r^2 = u^2u_{r}/r+u(u_{r})^2+u(u_z)^2$$ u is a dimensionless function ...
0
votes
1answer
100 views
Using a Bivariate Gaussian Distribution to Predict Range of Movement
I am currently attempting to use a bivariate normal distribution to identify the most likely range of movement for a blob in computer vision. This itself is not the problem, however; I do not ...
3
votes
2answers
182 views
Visualization of Cantor set by Mathematica or Maple!
We all know what it is the Cantor set. The Cantor set is created by repeatedly deleting the open middle thirds of a set of line segments. One starts by deleting the open middle third $(\frac{1}{3}, ...
2
votes
1answer
133 views
Closed form with of a series Mathematica
I've these two series, and I would like a closed form:
$$ \sum_{k=-\infty}^{\infty} \frac{x+kx_0-h}{|x+kx_0|^3}$$
$$ 3\sum_{k=-\infty}^{\infty} \frac{(x+kx_0-h)(x+kx_0)^2}{|x+kx_0|^5} $$
...
3
votes
0answers
101 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$.
0
votes
1answer
80 views
Plot3D Mathematica: how to use parameters while using Plot3D [closed]
I am trying to plot a function f on the domain {x,0,100},{y,0,100}.
this function f has two parameters A and B in it such that $ 0< A < 100 $ and $a < B ...
0
votes
0answers
26 views
generating random density operators
A quantum (mixed or pure) state is a Hermitian, positive semi-definite operator with unit trace. I need to construct states by using available pseudo-random number generators (I personally use ...
0
votes
0answers
106 views
