The applications tag has no usage guidance.

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### Applications of space filling curves

I am seeking articles where a space filling curve has been used as a theoretical application, such as in the study of general orthogonal polynomials.

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**0**answers

48 views

### Applications of systems with multiple time

A dynamical system with multiple time is an action of a group $\mathbb{Z}^d$ or $\mathbb{R}^d$ on a metric space.
I am interested in informative examples and applications of such systems. I know ...

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votes

**2**answers

304 views

### Non-Formal Applications: Higman and Kruskal

After looking through many papers, I noticed that most of the discussions and proofs for Higman's Lemma and Kruskal's Tree Theorem only have formal applications in set theory, logic, and type theory. ...

**6**

votes

**1**answer

71 views

### Least-squares solution of systems of Sylvester equations

The Sylvester equation $AX+XB=C$ has been studied quite a lot and there are known algorithms for solving it.
But has the situation where (an over-determined) system of equations $A_{i}X+XB_{i}=C_{i}$ ...

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**0**answers

408 views

### Examples of beautiful theories without applications [closed]

What are examples of beautiful theories, which have no known applications?

**6**

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**4**answers

278 views

### Application and usage of representation of integers as sum of powers?

We know that there are many articles and manuscripts from the ancient to date talking about representation of integers as sum of squares, cubes etc. I would like to know what is it the usage and ...

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votes

**4**answers

2k views

### How is differential geometry used in immediate industrial applications and what are some source to know about it?

Intuitively it might be clear that differential geometry is a very applicable subject in engineering and industry. I'd like to know how some industries/companies use differential geometry. I'd guess ...

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votes

**0**answers

577 views

### Which journals publish applied mathematics with mostly pure mathematics content?

In the spirit of Which journals publish expository work? please advise:
What consistently high quality journals$^1$ today publish results that would otherwise go to a pure mathematics journal if ...

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votes

**1**answer

266 views

### Information theory from negative probability

Szekely provides a convincing argument of negative probability here:
http://www.wilmott.com/pdfs/100609_gjs.pdf
What does a reformulation of classical information theory built from negative ...

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votes

**7**answers

4k views

### Deep Learning / Deep neural nets for mathematician

I am interested in finding out the math ideas behind the technologies that are under the umbrella of "Deep Learning" or "Deep neural nets".
Most of the papers/books that are often quoted in papers/...

**3**

votes

**2**answers

245 views

### Applications of Szemeredi's Theorem

Szemeredi's Theorem is a famous theorem in Additive Combinatorics, Ergodic Theory and maybe some other parts of Mathemtaitcs:
(Szemeredi's Theorem) Let $\Lambda \in \mathbb{Z}$ be a subset of ...

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votes

**1**answer

704 views

### Prime labelling of graphs

A prime labeling of a graph is an injective function $f: V(G) \to \{1, 2, ..., |V(G)|\}$
such that for every pair of adjacent vertices $u$ and $v$, $\text{gcd}(f(u), f(v)) = 1$ (labels of any two ...

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**4**answers

2k views

### Robotics, Cryptography, and Genetics applications of Grothendieck's work? [closed]

I was reading about the passing of Alexander Grothendieck, and something caught my interest:
Mr. Grothendieck was able to answer concrete questions about these relationships by finding universal ...

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votes

**2**answers

223 views

### Can a monotone exponentially decreasing function be uniformely approximated bt Gaussians?

This question originates an engineering application.
There is a certain process that is presumed to be a sequence of diffusions and is usually modelled as a sum of Gaussians:
$$\Sigma_n w_ne^{-\...

**15**

votes

**5**answers

1k views

### Examples of research on how people perceive mathematical objects

What examples are there on research related to human perception and mathematical objects?
For example, the shape of a beer glass influences drinking habits,
since people are bad at integrating.
...

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votes

**0**answers

41 views

### Where to read about this kind of “measure of irredundancy” of a set from a family of sets?

Studying a very practical problem from psychometrics, I encountered the following construction.
Let $(X,\mu)$ be a measure space; if preferred, you can presume $\mu$ is a probability measure. In any ...

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vote

**2**answers

272 views

### What is known about $\displaystyle \sum_k{a^{b^k}}$?

What is known about $\displaystyle \sum_k{a^{b^k}}$? I am very interested in the possible applications of this series.
I have asked about this on Mathematics Stack Exchange here.
I'm wondering if ...

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votes

**2**answers

360 views

### Physical and real life interpretation of the concept of regularity used in differential equations?

I guess the title kind of speaks for my questions: I'm curious to know what could be the physical interpretation or real life application of the concept of regularity that arises in PDE: take for ...

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**3**answers

2k views

### Algebra and Cancer Research

Let me start by acknowledging the existence of this thread: Mathematics and cancer research ?
It is well-known that mathematical modeling and computational biology are effective tools in cancer ...

**3**

votes

**0**answers

541 views

### Does Pure Mathematics glue Science together? [closed]

A little while ago, I was reading Cathy O'Neil's post Why is math research important (subtext: why does Pure Math deserve funding), where she discusses 3 possible answers. One of these is the usual "...

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votes

**1**answer

336 views

### Costa's minimal surface and the structure of lungs

Seeing this image of Costa's minimal surface
(MathWorld image)
made me wonder if the fine-grained structure
of the human lung is somehow composed of pieces of ...

**2**

votes

**0**answers

138 views

### When is it possible to split a non-linear operator into a composition of a linear and local one?

Let $A: L^2(R^n)\to L^2(R^n)$ be a non-linear operator. Is it known when it's possible to split $A$ into a composition of a linear operator $B: L^2(R^n)\to (L^2(R^n))^k$ and a local operator $C: (L^2(...

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votes

**1**answer

61 views

### Optimal radiating $(d{-}1)$-flats within a sphere

Permit me to revisit an earlier unresolved MO question,
"Chord arrangement that avoids confining small or large disks"
with a (very!) specific version, inspired by radiation therapy.
The main idea is ...

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votes

**2**answers

1k views

### Applications of Lawvere's fixed point theorem

Lawvere's fixed point theorem states that in a cartesian closed category, if there is a morphism $A \to X^A$ which is point-surjective (meaning that $\hom(1,A) \to \hom(1,X^A)$ is surjective), then ...

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**15**answers

8k views

### How does the work of a pure mathematician impact society? [closed]

First, I will explain my situation.
In my University most of the careers are doing videos to explain what we do and try to attract more people to our careers.
I am in a really bad position, because ...

**2**

votes

**1**answer

352 views

### A mathematical version of the Magic Eye optical illusion

The magic eye optical illusions create stereographic pictures by taking two rectangles and slightly shifting the patterns, so that when you cross your eyes to overlap them, the subtle differences ...

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votes

**7**answers

3k views

### Is Riemannian integration sufficient in physics?

Are there any applications in physics or engineering which require the Lebesgue integral and cannot be treated by Riemannian integration

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votes

**3**answers

1k views

### Applications of visual calculus

Mamikon's visual calculus (see Mamikon, Tom Apostol, Wikipedia) is a very beautiful and surprisingly efficient tool.
The basis is
Mamikon's theorem. The area of a tangent sweep is equal to the ...

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votes

**0**answers

103 views

### Application of Morse theory to second order systems

Hello
I'm looking for some applications of Morse theory to second order differential system,( or boundary value problems )
Someone can help me with a pdf or a book which has these applications ?
...

**0**

votes

**1**answer

364 views

### Mathematical properties of financial prices

Prices of financial assets (stock-market prices or currency exchange rates) obviously resemble trajectories of stochastic processes.
What is known about their mathematical properties ?
I know ...

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votes

**1**answer

478 views

### Examples of applications of the Freyd-Mitchell embedding theorem.

The Freyd-Mitchell embedding theorem states the following:
Let $\mathcal{A}$ be a small abelian category. There exists a unital ring $R$ and a full, faithful and exact functor $F\colon\mathcal{A}\...

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votes

**2**answers

4k views

### On mentioning recommenders' names in cover letter for postdoctoral applications

If I want to apply for a postdoctoral job, can I mention the name of my recommenders in my cover letter just to bolster my application, particularly when I am sure that the people who will read my ...

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votes

**4**answers

1k views

### Role of applications in modern mathematics [closed]

Older days scientists were universalists and philosophy, physics and mathematics were a part the same question - understanding the world.
Nowadays one may get feeling that the role of applications ...

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votes

**6**answers

366 views

### Applications of discrete-time dynamics

Hello,
I am a graduate student in the field of discrete-time dynamics. I am wondering about applications of this field outside of mathematics. More precisely, I would like to know if there are "real ...

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votes

**4**answers

3k views

### Math behind databases management and SQL ?

Are there some mathematical theories/theorems/... behind modern development of database management systems and in particular of SQL ?
I am refreshing my knowledge of these things which are quite down-...

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**4**answers

588 views

### Signal Processing reference for pure mathematician

Before giving a more detailed question below, the basic one is: can anyone recommend a good signal-processing reference which would be maximally readable by a pure mathematician (who nevertheless ...

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votes

**2**answers

3k views

### Question on “publication List” for applying to post-doctoral jobs

1) Many Mathematics departments ask to send a "list of publications" while applying for research postdoctoral jobs. My question is: how important is it to post my papers in arXiv. I know, posting on ...

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votes

**1**answer

239 views

### Minimizing |FT(X)|_{\infty} by permutation of X_i - question on Fourier transform related to engineering problem (peak factor of OFDM system)

Consider vector X =( X_1 ... X_N), consider the discrete Fourier transform $Y=F(X)$.
I am interested to minimize $|Y|_{\infty}$, by permutation of numbers X_i, how to do it ?
Here $|Y|_{\infty}$ is ...

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vote

**0**answers

95 views

### Decay rate of Discrete Prolate Spheroidal Sequences in frequency

What is the decay rate of DPSS sequences in frequency?
Consider an interval $T\subset\mathbb{Z}$ of length N in time. Consider another interval $[-W,W]$ in frequency with $W<1/2$. Let $\phi_0$ ...

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votes

**0**answers

274 views

### Applications of moduli of curves theory

Are there some applications of moduli of curves theory? I was wondering if moduli of curves theory is used (or could be used) for doing research in applied mathematics.
I am doing my PhD in algebraic ...

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votes

**1**answer

325 views

### Distances on generalizations of the symmetric group

I'm a computer vision student, and I'm looking for some symmetric group literature guidance. I'm going to provide some context, and finally ask two questions.
The Cayley distance and other distances ...

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votes

**1**answer

1k views

### Frequency calculation using fourier transform [closed]

How to calculate the frequency of an audio file using Fourier Transform

**2**

votes

**2**answers

953 views

### Application of Catalan number [closed]

Hi guys just a quick questions
What are the real life application of catalan numbers?
Thanks a lot!

**4**

votes

**1**answer

817 views

### Non-trivial consequences of Lob's theorem

Informally, Löb's theorem (Wikipedia, PlanetMath) shows that:
a mathematical system cannot assert its own soundness without becoming inconsistent [Yudkowsky]
In symbols:
if $PA\vdash$ $Bew$(#...

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votes

**2**answers

2k views

### Applications of algebraic geometry/commutative algebra to biology/pharmacology ?

Are there applications of algebraic geometry/commutative algebra to biology/pharmacology ?
It might be that some Groebner basis technique is used somewhere ?
I know there are some applications to ...

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votes

**2**answers

860 views

### Applications of the knot theory to biology/pharmacology ?

What are the applications of the knot theory to biology/pharmacology ?
I guess there should be some, since proteins are quite long and probably some of their properties are related whether they are ...

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vote

**3**answers

344 views

### “Graphical models” and “gene finding and diagnosis of diseases” ?

Quote Wikipedia: Applications of graphical models include ... gene finding and diagnosis of diseases...
Unfortunately there is no comment what are these applications...
Can one comment on this ?
...

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votes

**6**answers

3k views

### Applications of group theory to math. biology (pharmacology) ?

Are there applications of group theory (take it broadly: representation theory, Lie algs., q-groups, whatever ... ) to math. biology ?
I am in particular interested about applications to pharmacology ...

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votes

**1**answer

623 views

### Any applications integrable systems (pde,ode, q-,…) to math. biology (pharmakinetics, pharmadynamics) ?

Question Are there any relations/applications of integrable system theory (take it as broadly as one can: ODE, PDE, quantum, box-ball,...) to mathematical biology (in particular pharmacokinetics, ...

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775 views

### Stochastic process with Bessel function autocorrelation. (Rayleigh (Jakes) fading for radiowave propagation)

Have the following stochastic process $f(t)$ been studied in mathematics ?
It is stationary, Gaussian, $f(t)-$complex independent Gaussians $N(0,1)$.
The autocorrelation is given by the
zero-order ...