The utilization of advanced computing technology in mathematical research: new mathematical results discovered partly or entirely with the aid of computer-based tools.

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Can these steps be converted to a mathematical expression using equations/graph theory/Calculus/Set theory/functions/? [migrated]

Want to convert below algorithm into a mathematical model:- General points 1. Let there be a Connected Directed Graph. G = (V, E) V vertices or nodes E edges. This graph can be seen as a network ...
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90 views

how to calculate the covariance of sample central moments

$\bar{x}= \sum_{i=1} ^{n} \frac{1}{n}x_{i}$ $m_1=\sum _{i=1} ^{n} \frac{1}{n} (x_{i}-\bar{x})$ $m_2=\sum _{i=1} ^{n} \frac{1}{n} (x_{i}-\bar{x})^2 $ $m_3=\sum _{i=1} ^{n} ...
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303 views

Problem on limit involving complex numbers

I have $${\frac{(6 k+1)^{k}}{(2 k+5)^{k}}}*(z-2 i)^k$$ and I need to find it's limit for $k$ approaching infinity. ...
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168 views

Can degenerating Nicomachus' triangle down to $0$ area by using `Graph` be done?

I noticed a pattern in Nicomachus' Triangle that might be used to reduce the triangle to the number line. If the Edge size could be set to the absolute difference ...
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250 views

How can we get this infinite prism lattice to look more like `PolyhedronData[{“Prism”, 3}]`?

This is D$_3$h prism with order 12 (8 currently, needs 4 more edges) and rotational symmetry D$_3$ with order 6. A d=11 version is shown here. Using this code: ...
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532 views

Partial fraction decomposition of $1/(e^x-1)$

This link has discussion on finding partial fraction decomposition of $1/(e^x-1)$, so I experimented with Mathematica to see if M can do it, but looks like not. Similar is the case with one more CAS I ...
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197 views

Getting the Cumulative Distribution Function of f(x) from a dataset of x

I've a data set $\mathcal{X}$ which consists of randomly generated numbers. Let's say for example data = RandomVariate[ExponentialDistribution[1], 10^4]; My aim ...
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132 views

Can you compute more terms in this sequence?

I am trying to identify a sequence related to the von Mangoldt function matrix. Since I believe/conjecture that the columns in the matrix have period lengths as in this sequence b: ...
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126 views

Making a conjecture concerning a certain upper-triangular matrix

I have searched for commands which will let me to create matrices and do matrix operations, but I don't know how to apply Mathematica to the following exercise. Make a conjecture for the result of ...
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104 views

factorization of integer into two parts with specific prime factors

I would like to write a Mathematica code to decompose an integer into two or more parts with primes in special intervals. For instance, I want to decompose $m=\binom{n}{k}$ into two parts U and V ...
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69 views

Does it help to do any preprocessing before `FindSequenceFunction`?

I am always amazed how smart FindSequenceFunction can be in discovering general term formula for a sequence of rational numbers. The documentation says it can work ...
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How to mathematically represent MMA 9 Spikey?

I am trying to figure out how to mathematically represent the MMA 9 Spikey in order to send to a 3D printer. According to this page, " In particular, spikeys for version 2 and up are based on a ...
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125 views

Integration of DiracDelta

I just came across the following curiosity and I'm not sure whether it's a bug or just me missing something. Here's a minimal example: I defined the following "function" ...
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Can Mathematica propose an exact value based on an approximate one?

Sometimes, I use Mathematica to do some hypothesis on homeworks to make the question easier. For instance, when I have to compute big sums when $n\to\infty$ and Mathematica can't give the exact ...