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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Factorial of a matrix: what could be the use of it?

Recently on this site, the question was raised how we might define the factorial operation $\mathsf{A}!$ on a square matrix $\mathsf{A}$. The answer, perhaps unsurprisingly, involves the Gamma ...
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387 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)...
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Applications of resolution of singularities

I would to know applications of Resolution of Singularities, this means what is profits of having a resolution of singularities of a variety both in and out of mathematics and both in positive and ...
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275 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 ...
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571 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 ...
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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}...
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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 ...
6
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1answer
140 views

Show that the profile of the hill is a cycloid

I'm struggling with this problem: From George Simmons_ Differential Equations At sunset a man is standing at the base of a dome-shaped hill where if faces the setting sun. He throws a rock ...
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299 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. ...
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441 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 ...
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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 ...
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151 views

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 \...
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156 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?
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Derivation of 2D Korteweg-de-Vries equation

Coming from engineering rather than mathematics, I am recently dealing with non-linear partial differential equations e.g. like the well known Korteweg-de-Vries equation: $$u_{t} + uu_x + u_{xxx} = 0$$...
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361 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. ...
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71 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 ...
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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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266 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,...
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Differential vs difference equations in mathematical modeling

I'm reading a little about mathematical modeling and I've seen some population models based on differential equations. I've also seen some (not many) that can support both difference and differential ...
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251 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 $ \...
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1answer
408 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 ...
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98 views

What are practical examples of Toeplitz matrices?

A Toeplitz matrix is one in which each descending diagonal from left to right is constant. Given that structure, matrix operations are sometimes much faster. Where are Toeplitz matrices likely to ...
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1answer
71 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 ...
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System of equations and the Brouwer's Fixed-Point Theorem.

Let's consider the following system of equations: \begin{eqnarray}{ e^{xyz} = \frac{x}{\sqrt{e^{2xyz}+1}}\\ \cos(x+y+z) = \frac{y}{\sqrt{e^{2xyz}+1}}\\ \sin(x+y+z) = \frac{z}{\sqrt{e^{2xyz}+1}} }...
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28 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 ...
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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 \...
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78 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 ...
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526 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 ...
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420 views

Apps for practicing math (all levels)

I am looking for an app that I can use to PROVIDE me with math problems for practice and to stay fresh on various subjects in mathematics. This includes all levels of math (from low grade school to ...
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1answer
401 views

What are the applications of convex sets?

I am studying now convex sets and very interested in applications of them in Computer Science (maybe ACM problems) and other real life problems. Coud you please give some examples? P.S. I am ...
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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 ...
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3answers
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Applications of chemical reaction networks

I have recently read a bit on chemical reaction network theory. I was wondering whether the mathematical concepts have cross-field applications like neural networks. For example, can I apply chemical ...
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160 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 ...
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1answer
482 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 ...
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1answer
101 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-...
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64 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 ...
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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. ...
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Turning radius of a vehicle

What's the minimum turning radius of a vehicle, rectangular in shape, with length l units and width w units? One key point to consider, would be that, the inclination of the front wheels can be ...
2
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1answer
55 views

Is gaussian elimination “used”?

According to the book Linear algebra and its applications by Strang, "(The) good method is Gaussian Elimination. This is the algorithm that is constantly used to solve large systems of equations". Is ...
2
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1answer
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Were the wagers in the June 3, 2019 Final Jeopardy! round rationale?

The long-running U.S. television program Jeopardy! is a trivia question-and-answer (or answer-and-question) game show, involving three players competing to be the fastest to correctly answer questions,...
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Real world application of finding all simple paths on a graph

I am currently designing a general purpose graph database. Recently I have started to consider supporting the "find all simple paths between two nodes" operation on the graph. However while there are ...
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Practical applications of semidefinite programming

I am looking for practical applications of semidefinite- programming. So far, I found that the low-rank matrix completion problem (recomendendattion matrices) can be expressed as a semidefinite ...
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real world applications of direct sums

I understand how direct sums work and how they can be useful in proving certain conditional statements in linear algebra but it seems to me that direct sums are only useful in abstract settings. I was ...
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Using binary system for Henry Classfication System.

In my forensic science class, we learned about the Henry classification system of fingerprints to categorize fingerprints based on the type of print each finger had. The system itself uses the decimal ...
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How to randomly sample a social graph to find paths between at least 20% of profiles?

Given a Graph, where we know Total number of nodes (~100,000) Average no of connections per node (~200) Maximum distance between two nodes (~5) How many nodes (and its connections) do we have to ...
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Auctions - Placing Points to get into Classes

At my university there are not enough places in every class to accommodate every student. The scheme the university set up to solve this problem is as follows: Each student gets $1000$ points per ...
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Probability to be overtaken on circuit

I'm running on a treadmill in the gym and use the software (provided) which basically enables me to see other people running around me in the virtual race arena (standard 400 m circuit). I'm running ...
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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"...
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Applications of Algebraic Topology to urban planning

(Soft question) I was wondering if anybody knows of any applications of Algebraic Topology or Topological Graph Theory to Urban Planning/Public Transportation Planning. ¡Thanks!
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Linear algebra book revolved around modern day applications.

As the title says, I'm looking for a book which describes the modern day applications of linear algebra. I already had an introductory course on linear algebra, so I'm specifically looking for the ...