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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 ...
AmirHosein Sadeghimanesh's user avatar
8 votes
0 answers
562 views

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 ...
uhoh's user avatar
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8 votes
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505 views

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)...
user avatar
8 votes
0 answers
393 views

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 ...
user avatar
8 votes
0 answers
721 views

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 ...
okarin's user avatar
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7 votes
0 answers
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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 ...
pjmathematician's user avatar
7 votes
1 answer
203 views

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 ...
Guillermo Mosse's user avatar
7 votes
0 answers
966 views

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 ...
Shaun's user avatar
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7 votes
0 answers
132 views

Is there a polynomial $p$ such that it is bijective and $ p: \mathbb{Q}^n \rightarrow \mathbb{Q}$ for $ n>1$ ??

Let us define a polynomial $p$ defined as follow $$p: \mathbb{Q}^n \rightarrow \mathbb{Q}.$$ I acrossed this question in mind. Is there a polynomial $p$ such that it is bijective and $p: \mathbb{Q}...
zeraoulia rafik's user avatar
7 votes
0 answers
348 views

What is the motivation behind the study of pattern-avoiding permutations?

There is a ton of research on pattern-avoiding permutations (permutations that do not contain some designated permutation pattern). We're figuring out how to enumerate them, what random ones are like,...
Alexander Gruber's user avatar
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6 votes
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Extending a common-neighbor statistic to more than two nodes

first time poster here (happy to edit if I am violating any guidelines, please just let me know) :) I am curious whether the following formula from this paper by Li and Liang for the probability of an ...
Gabe Simmons's user avatar
6 votes
0 answers
748 views

Cryptocurrency Math

I'm looking for any relevant books/articles on the maths of cryptocurrency transactions. Also open to any resources that may have some cryptocurrency transactions but not it may not be the main bite. ...
Sam King's user avatar
6 votes
0 answers
405 views

Applications of the Kuratowski closure-complement theorem

I crossed with the Kuratowski closure-complement theorem while learning Munkres's Topology (Problem 21 in Section 17; Page 102, 2nd edition). The following description is from B.J. Gardner and M. ...
hengxin's user avatar
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5 votes
0 answers
753 views

Galois theory occurence in (very) Applied Mathematics

Can Galois theory be used in (very) Applied Mathematics; e.g. Population Dynamics, Biostatistics or $\langle$some Mathematics course that is (almost) opposite of Abstract Algebra$\rangle$. I know that ...
Algebear's user avatar
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5 votes
0 answers
572 views

Calculating half life from proteins

I have no idea if this would be the right place to post. I am a biologist by trade so mathematics is not my forte. I am having problems calculating the degradation/synthesis constants and protein ...
Gandalf the Grey's user avatar
5 votes
0 answers
65 views

What are some examples of algorithms besides crypto and integer factorization that use elliptic curves?

I've heard that elliptic curves have applications in strange places, due to their connection to elliptic functions and then elliptic integrals, which have nice algebraic addition formulas. I see ...
ctesta01's user avatar
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Significance and application of Riesz Decomposition Theorem

The Riesz Decomposition Theorem in Operator Theory is given as: Let $a \in \mathcal{A}$ (for unital Banach algebra $\mathcal{A}$) Suppose $\sigma(a) = \sigma_1 \cup \sigma_2$ where $\sigma_1 \cap \...
Alex's user avatar
  • 505
5 votes
1 answer
718 views

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 ...
Rafael Rojas's user avatar
5 votes
1 answer
279 views

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?
isomorphismes's user avatar
4 votes
0 answers
125 views

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 ...
hmmmm's user avatar
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4 votes
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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 ...
Smithey's user avatar
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4 votes
0 answers
71 views

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 ...
Georgia's user avatar
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4 votes
0 answers
181 views

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 ...
Dac0's user avatar
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4 votes
0 answers
2k views

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 ...
Jules's user avatar
  • 447
4 votes
0 answers
707 views

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 ...
Salvador Dali's user avatar
4 votes
0 answers
352 views

Applications of a theorem of Cartier and Gabriel

In a representation theory course I took we stated and proved the following Theorem due to Cartier and Gabriel: Theorem: Suppose $H$ is a cocommutative Hopf algebra over a field $k$ such that $ \...
Anette's user avatar
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4 votes
1 answer
490 views

dynamic mean: measurement of randomly distributed events

Aim is to estimate an error on a stochastic event rate. I read out the event counter second-wise, every black $1$ is a counted event (new events over time, see the plot below). During the measurement ...
IljaBek's user avatar
  • 376
3 votes
0 answers
114 views

Why all the inequalities?

I have recently seen questions involving bizarre inequalities, usually consisting of cycling over variables; here's one example (see also related links): $$\sum\limits_{cyc}\frac{1}{\sqrt{2a^2+5ab+2b^...
David Raveh's user avatar
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3 votes
0 answers
173 views

Classifying divergent sequences in a metric space

To my understanding, in $\mathbb{R}$, we have the following ways in which a sequence can diverge: The sequence could diverge off into $\infty$ or $-\infty$ (relevant generalization) Divergence by ...
Babu's user avatar
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3 votes
0 answers
88 views

Applications of Pluripotential Theory in real world

I am reading for a math PhD with research in Pluripotential Theory (a subfield in Several Complex Variables). I particularly do study and develop theory related to extremal functions associated with a ...
Extremal's user avatar
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3 votes
1 answer
118 views

Recommendations on Intermediate Level Probability/Applied Statistics Book

So I'm an Internal Medicine Resident with an interest in mathematics and I have a BS in physics and MS in math. Lately I've been getting more into the statistical interpretation of diagnostic test, ...
huck's user avatar
  • 31
3 votes
0 answers
202 views

Does this function come up anywhere in mathematics? $f(s)=\sum_{n=0}^\infty\frac{(-1)^n}{n!}\zeta(-ns)$

I'm wondering if anyone knows if this function comes up anywhere in mathematics: $$f(s)=\sum_{n=0}^\infty\frac{(-1)^n}{n!}\zeta(-ns)$$ where $\zeta(s)$ is the Riemann Zeta function. I'm asking because ...
zeta space's user avatar
3 votes
0 answers
62 views

What are the applications of dynamical odometers?

Let $\mathbf{s} = (s_0, s_1, s_2, \ldots), s_i > 2$, be a sequence and let $\Delta_{\mathbf{s}}$ be the set of all sequences of nonnegative integers $\mathbf{a} = (a_0, a_1, a_2, \ldots)$ such that ...
Pan Miroslav's user avatar
3 votes
1 answer
180 views

Applications of Model Theory and Category Theory

Do Model Theory and Category Theory have applications in solving Complexity and Game Theory problems in computer science? I am looking for an example of these...(If there is any...)
user850424's user avatar
3 votes
0 answers
111 views

Primer for mathematical models of epidemics

In a comment to my recent MO question Robert Israel wrote: "Mathematical models of epidemics are well-established. Of course we'd like to know the parameters (and to what extent something can be done ...
Gil Kalai's user avatar
  • 1,133
3 votes
1 answer
87 views

Applications of equation $x^y=y^x$

So there are several ways of finding general positive solutions for the equation $x^y=y^x$. But does this equation appear anywhere in physics or other science ? Or maybe there is some practical ...
Юрій Ярош's user avatar
3 votes
0 answers
37 views

Folding Problem

Here's one for you topologists out there to show your field has practical application. I have covers for my air conditioner units that are shaped like 5 sides of a rectangular sold with dimensions 31"...
A.L. Simons's user avatar
3 votes
0 answers
33 views

Applications of compact braided monodial categories

In this paper by Baez http://math.ucr.edu/home/baez/rosetta.pdf I read (page 3) that ‘compact braided monoidal categories’ became very relevant for Physics in the 90s....Could anyone provide me with ...
Javier Arias's user avatar
  • 2,033
3 votes
0 answers
30 views

Projection of sparse weighted graph into $\mathbb{Z}$

Problem statement in the title is simplified and this question is actually quite open-ended: I have a sparse undirected simple weighted graph $G$ and need to find an injective function $G \rightarrow \...
Joshua Gensler's user avatar
3 votes
0 answers
80 views

Game Theory-terrorism

A terrorist attack one of the two targets with some probability p to target1 and (1-p) probability to target2, and defender should allocate optimum amount of resources on these targets. The ...
glslmn's user avatar
  • 33
3 votes
0 answers
87 views

Cyclic/non-cyclic groups and their applications in credit card/ smart card security

Can someone point me to resources on "Cyclic/non-cyclic groups and their applications in credit card/ smart card security" What I have right now is some things on Diffie-Hellman Key exchange ...
Shreyas Kulkarni's user avatar
3 votes
0 answers
168 views

Applications of Several Complex Variables.

I am kinda curious about SCV because I saw (somewhere on Math Stackexchange) about all the math involved and I was thinking...what kinds of applications do SCV find in the natural sciences and maths?(...
André's user avatar
  • 159
3 votes
0 answers
777 views

Importance of graph planarity for applications

What is the real-life motivation for studying (or inventing) effective algorithms to check whether or not a graph is planar (which seems to have garnered interest in recent years)? Why is planarity an ...
Stan's user avatar
  • 361
3 votes
0 answers
37 views

Where can I find detailed information on industrial applications of the boolean satisfiability problem (SAT) in the car industry?

Where can I find detailed information on industrial applications of the boolean satisfiability problem (SAT) in the car industry? This article http://www.carstensinz.de/talks/RISC-2005.pdf presents ...
Derrick Hines's user avatar
3 votes
0 answers
287 views

Solution for 4th grade polinomial equation

I'm development a physics model that require a expression for elongation of a elastic material, $\lambda=\frac{L}{L_o}$ [where $L$ is the thickness of the material and $L_o \equiv L(\sigma = 0)$] as ...
Josè Luis Mietta's user avatar
3 votes
1 answer
137 views

Does measurability really matter?

I am studying applied math and I currently got stuck on proving that a function, which emerges in a model is measurable (Borel functon), so we can integrate it. I know, that there are examples of non-...
DIgg's user avatar
  • 41
3 votes
0 answers
172 views

Kahler-Einstein Metrics in Physics - Topic Suggestions

I am hoping to get some topic suggestions for a presentation I have to give in a couple of weeks. The course the presentation is for is called Kahler-Einstein metrics. I would really like the ...
JonHerman's user avatar
  • 2,911
3 votes
0 answers
91 views

What problems are related with the following type of FDE?

Consider the following type of functional differential equations: $$\begin{align} \frac{du}{dt} &= F(x,t,u(x,t),u_{x,t}), & (x,t) &\in [a,b] \times [0,T] \end{align}$$ where $u(x,t)$ is ...
Max's user avatar
  • 225
3 votes
1 answer
400 views

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 ...
imrek's user avatar
  • 31
3 votes
0 answers
55 views

Mathematical analysis of e-shop

I'm ukrainian student, studying applied mathematics in Kiev. I have an online store and some statistics data on it's work. Also I've learned a bit about optimization problems and operation reasearch. ...
Rachnog's user avatar
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