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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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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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199 views

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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268 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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568 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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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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430 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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57 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 ...
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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 \...
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92 views

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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339 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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64 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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1k 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 ...
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263 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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880 views

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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247 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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81 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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71 views

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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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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505 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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381 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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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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109 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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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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50 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. ...
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1k views

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 ...
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25 views

Has the rigour of real analysis shown some unexpected truths about real life that would have otherwise not be discovered?

It is a common question, "what is the use of real analysis", and the answer is usually "it adds rigour to our mathematical tools and machinery to make sure that they work without just saying they do". ...
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33 views

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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72 views

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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63 views

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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31 views

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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38 views

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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27 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"...
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126 views

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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62 views

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 ...
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65 views

whats is the applications of the minimization of eigenvalue in the real life ( physics,the natural sciences…)

let $\lambda_{1}(\Omega),\lambda{2}(\Omega),\lambda_{3}(\Omega)...$ the eigenvlues of the laplacian Operator with Dirichlet condition on the boundary on $\Omega $ the classical spectrale optimisation ...
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127 views

Applications of the Hermite's criterion?

I found this statement on permutation polynomials and I was wondering in which domain we can find find applications and what is its aim. Here is the criterion : «If $q=p^n$ with $p$ a prime number ...
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70 views

Applications of Baire Class $1$ in other fields (Applied Maths, Statistics, Economics,etc)

Let $X$ be a Polish space (separable completely metrizable). A function $f:X\rightarrow\mathbb{R}$ is said to be of Baire Class $1$ if one of the followings is true: $(1)$ For any closed subset $P\...
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73 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 ...
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61 views

Question on modeling turbulence with Markov process vs high dimensional chaos

I basically asked this question over on Physics Stack Exchange, but that went nowhere and I've tried to refine my question to bring it here. When numerically modeling a natural system with ...
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117 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?(...
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137 views

What are some recent applications for Latin squares?

I know that the construct was originally used for scheduling, and in recent years has been found to be useful in areas such a Cryptography, Error-correcting code and Affine and Projective Planes. [...
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181 views

Applications of Topological Complexity of configuration space

I'm starting to work on Topological Complexity of configuration spaces . Articles say that it has applications in robotic and control theory . One important article belongs to Michael Farber My ...
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103 views

How might an applied mathematician view $ 1/x$, $\ln x$, and $e^x$?

I understand that the natural logarithm was developed by Gregoire de Saint-Vincent and Alphonse Antonio de Sarasa as to represent the area under the curve of the hyperbola $\frac1x$ before the ...
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In search of a College Leve Pre Algebra Applications Textbook

I am looking for a textbook at the college level that mainly focuses on applying algebra to situations. I want students to know how to set up the equations, not just solve them.
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63 views

Matrix identification

Is there any name for a square, symmetric matrix, created in the following format: $$M_{i,j} = \left\{\begin{matrix} i + j & i \neq j\\ 0 & i = j \end{matrix}\right.$$ where $i, j$ start ...