# Questions tagged [applications]

The [application] tag is meant for questions about applications of mathematical concepts and theorems to a more practical use (e.g. real world usage, less-abstract mathematics, etc.)

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### Applications of resolution of singularities

I would like to know applications of Resolution of Singularities. What are the benefit of resolving singularities of a variety by blow-up maps in a context outside of mathematics? I'm fine with both ...
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### How does a Maclaurin spheroid become a Jacobi ellipsoid? What happens?

A Maclaurin spheroid can become a Jacobi ellipsoid but I don't understand how this happens. From the plot I see that it must be spinning fast enough and from the text there seems to be some viscous ...
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### Easy Applications of Model Theory

The question is inspired by this MathOverflow post and this post on MathSE. The applications mentioned are usually pretty complicated (except for Ax-Grothendieck, but it seems to be a rare occurrence)...
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### Has knot theory led to the development of better knots?

Knot theory was likely originally motivated by the study of real-world knots such as these: Indeed, mathematical knot tables to this day look not too dissimilar from the familiar "age of sail"-style ...
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### How is graph theory used to solve problems in number theory?

What are some applications of graph theory in number theory? How can a graph theory approach be useful to solving number theory problems? In general, is graph theory ever useful in making number ...
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### Swinging factorial and swinging constant

The Swinging factorial $n≀$ defined as $$n≀=\frac{n!}{\left\lfloor{n/2}\right\rfloor!^2}$$ is relatively common and I found some results on Google. But when $$\sum_{n=0}^{\infty}\frac{1}{n≀}$$is ...
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### Are ordinals greater than $\varepsilon_0$ used outside Ordinal Analysis?

I know of Conway's use of ordinals to exhibit the algebraic closure of $\mathcal{F}_2$. I also read a document about the Cantor Bendixson rank of some family of groups. But I found no applications of ...
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### The Mathematics of Skateboarding Tricks.

This question is just for fun and I apologise if it's too broad or off topic. The Details: As anyone who has played the Tony Hawk games can tell you, skateboarding - at least in part - can be scored ...
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### Who knows Krotov's Method in Optimal Control Theory

I'm finishing my PhD thesis about applications of optimal control theory in the field of energy harvesting. In the course of my PhD I dealt with different ways to compute optimal controls, and I found ...
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### How is it possible to change the pitch and the tempo of an audio track independently of each other?

If you slow down a turntable or cassette-player, both pitch and tempo are decreased. How is it possible to change one without affecting the other?
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### Derivation of index decomposition analysis

I’m currently reading a paper on index decomposition. The paper is here for reference : https://www.sciencedirect.com/science/article/pii/S0140988315001772 The paper is setting out how it has gone ...
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### Do repeated roots (and Real Jordan form) for ODE's come up in real world applications of ODE's

An equation like $y^{\prime \prime} + 2 y^{\prime} + y = 0$ has repeated roots: The characteristic polynomial is $r^2 + 2r + 1$ which has repeated roots $(-1,-1)$. Two basic solutions of the ODE are ...
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### Helical "packing" of deltahedra?

I'm looking for help with terminology: I'm a glass artist / PhD researcher aiming to use a modular, geometric approach to making. I've been looking to use repeated polyhedra (with regular polygonal ...
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### Reference request: Applications of representation theory of finite groups

I'd like to know if there's a book with a lot of examples (from physics, chemistry, etc..) of applications of representation theory of finite groups. I think it must exist, but I couldn't find ...
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### Are there practical applications of Mersenne primes?

Mersenne primes are prime numbers which are one less than a power of two, i.e. primes expressible as $M_n=2^n-1$. They are notoriously far apart and unpredictable, which is indicated by the fact that ...
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### Applications of Prüfer sequence

Reading a book about a graph theory I found out about Prüfer's sequences which converts a labeled tree of $n$ vertices into an array of $n-2$ numbers. I was actually pretty surprised by this and was ...
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### Looking to assign percentage contribution among 4 variables in a simple equation

I have a seemingly simple problem, that is giving me some trouble in solving. I have a 4 variable equation and want to determine the contribution of each variable in moving the dependent variable from ...
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