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3
votes
1answer
75 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 ...
13
votes
3answers
1k 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
0answers
360 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 ...
6
votes
1answer
243 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
0answers
128 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: ...
1
vote
1answer
55 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 ...
14
votes
0answers
331 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 ...
2
votes
1answer
216 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 ...
4
votes
7answers
1k 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
11
votes
3answers
772 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 ...
0
votes
0answers
91 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
1answer
324 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 ...
9
votes
1answer
396 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 ...
3
votes
2answers
2k 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 ...
9
votes
4answers
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 ...
2
votes
6answers
312 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 ...
2
votes
4answers
723 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 ...
6
votes
3answers
350 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 ...
7
votes
2answers
2k 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 ...
6
votes
1answer
229 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 ...
1
vote
0answers
73 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 $\phi_0$ ...
4
votes
0answers
249 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 ...
3
votes
1answer
235 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 ...
0
votes
0answers
95 views

What are Effective Regression Techniques for Linguistic Analysis of Linked Data?

I am in the early stages of a problem that involves parsing a large number ($\approx 5 \times 10^9$) of documents (web pages) and estimating values from them. In particular I need to identify pages ...
0
votes
1answer
593 views

Frequency calculation using fourier transform [closed]

How to calculate the frequency of an audio file using Fourier Transform
2
votes
2answers
578 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
1answer
444 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 $PA\vdash$ ...
3
votes
2answers
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 ...
5
votes
2answers
490 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 ...
1
vote
3answers
267 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 ? ...
13
votes
5answers
2k 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 ...
4
votes
1answer
451 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, ...
1
vote
1answer
369 views

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

Have the stochastic following 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 zeroth-order ...
11
votes
1answer
360 views

Application for Morse-Smale systems

All my life I do topological classification of Morse-Smale systems (flows and cascades). Today, fundamental science is not in fashion, to receive grants require an application. Can you please tell ...
11
votes
8answers
2k views

Mathematics and cancer research ?

What are applications of mathematics in cancer research ? My answer. Unfortunately I heard quite small about math, but I heard something about applications of physics. And let me put this story ...
0
votes
0answers
202 views

L1-regularized Least Squares on a matrix with Toeplitz Blocks (not block-Toeplitz)

I am trying to speed up a sparse signal recovery algorithms. My sensing matrix is a set of Toeplitz Blocks, M = [T1,T2,T3,...,Tk] The objective is min ||Mx - b||_2^2 + ||x||1 What I'm actually ...
3
votes
1answer
318 views

Applications of Chevalley groups theory for dummies

As an algebraist i frequently receive questions from my friends-mathematicians and non-mathematicians about applications of my topic "in real life". I study algebraic groups in the stream of ...
8
votes
4answers
739 views

Applications of Hilbert's metric

Among the fascinating constructions in mathematics is the Hilbert metric on a bounded convex subset of ${\mathbb R}^n$. Where, within mathematics, is it used ? I know at least a proof of the ...
7
votes
1answer
522 views

Any nice examples of small cancellation theory appearing in applied mathematics?

Are there any nice discussions of applications of small cancellation theory, or other cases of the word problem, in applied mathematics or algorithms for seemingly non-group theoretic problems? I ...
2
votes
2answers
270 views

Diffusion processes in probabilistic modelling

I'm working on a PhD project that involves parameter estimation for diffusion processes. I'm based in a machine learning research group, and the emphasis here is strongly on "practical" research. ...
12
votes
3answers
796 views

Applications of and motivation for von Neumann's mean ergodic theorem

I stated von Neumann's mean ergodic theorem (VNMET) in a talk recently and someone in the audience asked what it was good for. The only application I knew of VNMET was to prove Birkhoff's ergodic ...
3
votes
0answers
362 views

Concrete questions that turn into math problems [closed]

I'm writing an article about the way we teach math, trying to find out why so many people are discouraged from learning, and have no interest for math and logic. At some point, I want to show that ...
31
votes
12answers
3k views

Recent Applications of Mathematics

What are the recent and new applications of Mathematics in other Sciences ? Let me try to be more precise about the question: By "recent" I mean the last 15 years. By "new" I want to exclude the ...
6
votes
4answers
1k views

Applications of commutative algebra

Hi. I'm preparing a thesis in commutative algebra, and when I say this to my friends they always ask me what are the applications to "real-world", and I don't know what to answer. This let me think ...
66
votes
18answers
5k views

Occurrences of (co)homology in other disciplines and/or nature

I am curious if the setup for (co)homology theory appears outside the realm of pure mathematics. The idea of a family of groups linked by a series of arrows such that the composition of consecutive ...
50
votes
10answers
5k views

Applications of mathematics

All of us have probably been exposed to questions such as: "What are the applications of group theory...". This is not the subject of this MO question. Here is a little newspaper article that I found ...
11
votes
6answers
2k views

Nice applications of the spectral theorem?

Most books and courses on linear algebra or functional analysis present at least one version of the spectral theorem (either in finite or infinite dimension) and emphasize its importance to many ...
0
votes
1answer
270 views

Helpful services based on mathoverflow API [closed]

My area of research is math information retrieval. In particular, I come up with several basic ideas how to make use of a promising discussion platform offered by mathoverflow.net (MO). That's why I'd ...
2
votes
2answers
1k views

Rotationally-Invariant 2D Discrete Transforms

Hello all, I'm interested in 2D discrete transforms (such as discrete wavelet transforms, Curvelets, Ridgelets, Beamlets etc.) that operate on a discrete unit disk and: Are invariant to rotations ...
3
votes
0answers
2k views

What is the geometric meaning of third derivative of a function at a point? [closed]

What is the geometrical meaning of third derivative of a function at a point? The question is now open in the sister site ...