# 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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### 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?
1answer
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### 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 ...
0answers
6 views

### 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 ...
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 ...
2answers
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 ...
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, ...
1answer
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### 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 ...
3answers
78 views

### 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 ...
1answer
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1answer
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### 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) ...
2answers
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 ...
1answer
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 ...
0answers
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 ...
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 ...
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?
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 ...
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 ...
0answers
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### 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 ...
0answers
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### 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 ...
2answers
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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.
1answer
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### 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. ...
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 ...
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 ...
0answers
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)...
3answers
2k views

### 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 ...
0answers
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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 ...
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 ...
0answers
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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 ...
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 ...