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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56 views

Find if the function $\frac{(1-2xy)}{(x^2 +y^2)}$ has a max or min value for $(x,y)=/=(0,0)$

Does the function $\frac{1-2xy}{x^2 +y^2}$ have a max or min value for $(x,y)=/=0$? What I've tried so far is to take the the partial derivatives: $$\frac{\partial f}{\partial x} = \frac{2(-x+x^2*y ...
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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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173 views

Bernoulli differential equation applications? [closed]

Just like the title states, I’m interested in practical applications of Bernoulli differential equations.
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Intersection of isometries of a polygon

Suppose we have a two dimensional polygon $P$. And a sequence of polygons $(P_i)$, where each $P_{i+1}$ is a small translation/rotation of $P_i$. I am interested in situations where $\cap P_i$ is ...
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The importance of estimates of frame bounds.

A theorem contained in Christensen, Ole (1995), "A Paley-Wiener theorem for frames." Proceedings of the American Mathematical Society, 123, 2199-2201. states that Let $\{x_n\}_{n\in\mathbb Z}...
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Understanding a function space

I was reading a paper on Homogenization theory, where the author uses the spaces of vector valued functions. Let us consider such a space $D[\Omega; C^\infty_P(Y)]$, consisting of all the compactly ...
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2answers
4k views

How to calculate a monthly mortality rate?

If the instantaneous mortality rate for a species (or a group of humans) is 0.1/year, what is the mortality rate per month? Can you just divide $0.1/12$? This seems too simple and incorrect because ...
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2answers
46 views

Optimal time for three people to travel

Three men need to travel 60 km. They have a motorbike that can travel at 50 km/h but only two people can fit on it. They can walk at a speed of 5km/h. Can they get to their destination in 3 hours? I ...
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1answer
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Application of logs

The number of milligrams, $d$, of a drug remaining in a patient's bloodstream, $t$ hours after it has been administered, is given by the equation $d = 5(2.7^{.04t})$. To the nearest minute, how long ...
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Real-world applications of prime numbers?

I am going through the problems from Project Euler and I notice a strong insistence on Primes and efficient algorithms to compute large primes efficiently. The problems are interesting per se, but I ...
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46 views

Recommended knowledge for Applied Math

I would like to know which topics below are important for applied math and why? If you know about only one subject, share your answer with me please. Topology Set Theory Linear Algebra Abstract ...
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1answer
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Could families of “Airys” and “Bairys” of integer “frequencies” be useful?

A very famous family of functions are the complex exponentials and in the case of real valued functions, the sin and cos functions. They are related by the famous Euler formulas: $$\exp(i\phi) = \cos(...
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105 views

What are some applications of subdirect product?

I have studied direct products. I know a few applications of direct products, like group isomorphism, etc. What are some applications of sub-direct product of groups?
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1answer
57 views

Convolution via Fourier transform in a window

The question is related to an engineering application I am writing. We are computing convolutions of large amounts of data with a few kernels with bounded support. The standard way to do so is to ...
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Do there exist discrete and self-orthogonal wavelets on non-cartesian grids?

Most 2D DWT:s that I know about are rather straight-forward separable 1D wavelets, for example Meyer, Daubechies famous maxflat, CDF as used in JPEG-2000, spline wavelets like Unser's and so on. Has ...
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1answer
35 views

Closed-form solution for $f(x)/x=y$ using $f^{-1}$

I'm programming a piece of math that requires solving an equation of a form $f(x)/x=y$. Now I already have $f^{-1}(z)$ coded (efficiently, and not by me) so I'd prefer using this implementation ...
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64 views

Can we motivate mathematically why wind turbines almost always have 3 flappers and aeroplane propellers can have any number of flappers?

Firstly I know some might frown upon a question so very broad and applied as this one. It really may not be a well defined mathematical question as some people would prefer on the site. I am okay with ...
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1answer
59 views

How do I tell the rank of the electric susceptibility tensor (and others)?

I understand that a tensor is a multilinear map from $V^*\times\cdots\times V^*\times V\times\cdots\times V$ to $V$'s underlying field, where $V$ is a vector space and $V^*$ its dual. This is fine, ...
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1answer
45 views

A collection of lines drawn between points in a regular 13-gon - how to determine where the points sit relative to each other?

So I have 4 collections of lines drawn between points each making a path. The angles are measured. The problem I am attempting to solve is to determine whether or not each of the collections of points ...
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3answers
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What are some applications of mathematics whose objectives are not computations?

In mathematics education, sometimes a teacher may stress that mathematics is not all about computations (and this is probably the main reason why so many people think that plane geometry shall not be ...
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1answer
23 views

Can we solve the functions describing the bend of a cable at rest fixed at two positions?

Assume we have a cable which endpoints is attached to two points at $(x,h)$ and $(x+\Delta_x,h)$. Further assume it has some mass density distribution, $\rho(m),m \in [0,l]$ and is of some length $l ...
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applications of Multivariate Calculus in computer science

I am currently studying Multivariate Calculus (Larson and Edwards book). I want to do a project in computer science to see some nice applications of things I am learning. Any specific source of papers/...
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635 views

Optimisation Problem for Pipe Nesting

I work in a company where we are supposed to produce and send pipes using trucks to buyers. Pipes of smaller diameter can be nested inside pipes of larger diameter while sending to minimize number of ...
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4answers
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How to solve this problem without letting coordinates as $(a \cos\theta , a\sin\theta)$

Q. Tangent to the circle $x^2 + y^2 = a^2$ at any point on it in the first quadrant makes intercepts $OA$ and $OB$ on $x$ and $y$ axes respectively, $O$ being the centre of the circle. Find the ...
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1answer
137 views

Path of a simple turning car?

I am planning to build a small car that needs to travel through three specific points. Obviously, the car will need to travel in a partial circle to do this. In order to do this, I need to calculate ...
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1answer
55 views

Applications of coupled systems of $\;2\times 2\;$ linear differential equations

I am providing maths help to some students studying just before University level in mathematics. I am writing some practice questions for them on solving coupled first order linear equations and I ...
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“Real”-life applications of algebraic geometry

Before you tell me that this question has been asked, give me a bit of your time please to read this question because it is not as simple as it sounds. I did my undergraduate degree in mathematics, ...
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1answer
62 views

set up triple integral for volume

I was working on practice problems in the textbook and got stuck on this question. Any help would be greatly appreciated. Set up two triple integrals with two different orders of integration that ...
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82 views

Applications of Riemann surfaces in engineering or physics

I know that the maximal analytic continuation of a holomorphic function is an example of Riemann surfaces but don't know what it is used for. What can we do with this surface?
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1answer
43 views

Lagrangian of an equation, a particle with a time dependent constraint

I'm currently studying for an exam and I came across the following question. Consider a bead of mass m constrained to move along a wire which is on the vertical $(x, y)$ plane. The wire has equation $...
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1answer
36 views

Is there a right identity for Application in Lambda calculus?

Such a function E that: ∀F (F E = F) It's obviously, that the left identity E' (E' F = F) ...
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136 views

Is there any “good” definition for what constitutes “applied mathematics”?

Is there any "good" definition for what constitutes "applied mathematics"? Wikipedia lists stuff such as statistics, optimization. However, e.g these have certainly "pure mathematical" aspects to ...
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107 views

Paasche price index: cost of living adjustment (economics)

I am trying to figure out the following question involving the Paasche price index: two goods are perfect substitutes (let's assume for simplicity that indifference curve has slope of -1) relative ...
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379 views

Real world applications of Riemann surfaces of holomorphic functions [closed]

The maximal analytic continuation of a holomorphic function is an example of Riemann surfaces. What is it used for? Please edit the question to limit it to a specific problem with enough detail ...
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8answers
15k views

Real world uses of Quaternions?

I've recently started reading about Quaternions, and I keep reading that for example they're used in computer graphics and mechanics calculations to calculate movement and rotation, but without real ...
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0answers
57 views

Applications of $L_p$ spaces

I'm studying Lebesgue integration theory and understand the definition of $L_p$ spaces. What can we do with $L_p$ spaces?
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1answer
460 views

Validating a mathematical model (Lagrange formulation and geometry)

I am working on computing phase diagrams for alloys. These are blueprints for a material that show what phase, or combination of phases, a material will exist in for a range of concentrations and ...
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2answers
49 views

One train travels north at $140$ mph towards Traveler's Town, while a second train travels west at $150$ mph away from Traveler's Town.

One train travels north at $140$ mph towards Traveler's Town, while a second train travels west at $150$ mph away from Traveler's Town. At time $t=0$, the first train is $70$ miles south and the ...
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10 views

Applications for quasi-groups and loops outside of cryptography

I've been studying the group-like structures lately. Loops (and more generally quasigroups) seem strange in that they are defined, and we've studied their properties, but they don't seem to actually ...
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69 views

Any textbooks on applications of topology to natural and social sciences?

Here is a Mathematics Stack Exchange post on applications of topology. Now my question is, are there any easy-to-read textbooks that discuss (rather thoroughly) applications of elementary topology to ...
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Applications of polynomials of a high degree

What is the highest polynomial degree that has an application in real life, and what is that application? My google search yielded 3rd degree at most.
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1answer
115 views

Three Point Vortices Fluid Dynamics

I have been assigned a problem with two point vortices: Find two point vortices whose locations in the 2D plane and strengths $\gamma_1,\gamma_2$ are such that their positions remain fixed in time. ...
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1answer
43 views

Optimizing Video Game Crafting with Two Variables

In a certain video game, it is desirable to maximize the occurrence of crafting an item $B$, which depends on possessing the proper quantities of material. To construct 1 $B$ one needs 1 of ingredient ...
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1answer
69 views

About Codd's theorem

I was learning about databases and I have developed a rough idea that the design of databases has got quite a lot to do with mathematics. The most common and probably advanced form of databases are ...
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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 model theory to analysis

Some of the more organic theories considered in model theory (other than set theory, which, from what I've seen, seems to be quite distinct from "mainstream" model theory) are those which arise from ...
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Optimized surface covering using rolls of membrane

I want to cover a surface that has quite a complex geometry limited with straight lines. Covering will be done using a membrane that is sold in 2 meters wide and 25 meters long rolls, with an overlap ...
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1answer
43 views

Working out my holiday/vacation entitlement

I am trying to figure out my holiday (vacation) entitlement. Can somebody please tell me if I am right? I get $27$ days holiday plus the bank holidays (public holidays). My work year is $1$st of ...
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Design of “balancing” networks with loopbacks

Say that you have a network of conveyor belts with nodes, where each node is a 2-lane crossover switch (2 in, 2 out, either straight-through or crossed-over). Beneš networks work to solve the problem ...
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1answer
322 views

Proving that cuboid of maximum volume in a sphere is a cube.

I was preparing for my maths test . And preparing application of derivative (theory based question ) there I saw a problem of proving rectangle of maximum area in a circle is square . So there were ...