Questions tagged [applications]
Applications of mathematics to any field inside or outside mathematics
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Applications of logic in theoretical and practical Computer Science [closed]
Can anyone suggest theoretical and/or practical applications of logic (modal, dynamic, Lukasiewici etc.) in Computer Science (like Markov Chains for linear algebra), as well as some open-source books ...
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References on computational PDE (in fluid dynamics, solid mechanics, etc) that emphasize both rigorous analysis and coding
I'm interested in learning about computational aspects of PDE and integro partial differential equations.
In particular, I'd like to know some reference monographs that cover PDE and IPDE from in ...
user102027
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Applications of Perfect Matching
I'm exploring some applications of perfect matching and I would like some input. I have found many applications in chemistry (storing information, estimating bond lengths, estimating resonance energy, ...
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Is algebraic geometry constructive?
Notes: 1) I know next to nothing about algebraic geometry, although I am greatly interested in the field. 2) I realize that "constructive" might be a technical term, here I am using it only in an ...
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Envelope of a parametrized family of convolutions
For a certain application I need to compute a pointwise supremum of this family of gaussian convolutions:
$$\sup_s f(x)\otimes e^{-\frac{x^2}{s^2}}$$
where $f(x),x\in \mathbb{R}^2$ is known and $\...
- 2,175
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Using High Level Probability Theory (eg Markov Chain Mixing) in Cryptography/Cryptanalysis
I'm currently doing a PhD in probability theory, specifically (discrete space) Markov chains and their mixing properties. As well as my current main project, I'm looking to have a side project, eg to ...
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3
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What are some applications of Sperner style theorems?
I'm currently working through "Combinatorics of Finite Sets" by Ian Anderson, mostly to improve at a style of mathematics that I've historically been quite bad at, and I find myself wondering why this ...
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Applications of linear programming duality in combinatorics
So, I know that one can apply the strong LP duality theorem to specific instances of maximum flow problems to recover some nontrivial theorems in combinatorics, such as Hall's theorem, Koenig's ...
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Application for Differential Equation of higher order [closed]
We found some interesting insights in differential equations of the form
$y^{(n)}(x)+F_\lambda(y(x),y'(x),...,y^{(n-1)}(x))=0$,
i.e. for ordinary differential equations of $n$-th order with $n\geq2$....
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Easy Applications of Model Theory
I've also posted this question on MathSE. I'm posting it here in hopes of a more comprehensive answer. The question is inspired by the following:
Model theoretic applications to algebra and number ...
user75685
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Applications of Topological Complexity of configuration space
I'm starting to work on topological complexity of configuration spaces.
Articles say that this field has applications in robotic and control theory. One of the important articles belongs to Michael ...
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Formalization of adaptive sampling [closed]
The notion on adaptive sampling or adaptive plotting is fairly popular, but I have not found a formal definition.
I have developed an algorithm for plotting implicit algebraic curves in the plane. ...
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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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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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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. ...
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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 $A_{i}X+XB_{i}=C_{i}$ ...
- 6,882
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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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How is differential geometry used in immediate industrial applications and what are some sources to learn 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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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 were ...
4
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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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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/...
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4
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Applications of Szemeredi's Theorem
Szemeredi's Theorem is a famous theorem in Additive Combinatorics, Ergodic Theory and maybe some other parts of Mathemtatics:
(Szemeredi's Theorem) Let $\Lambda \in \mathbb{Z}$ be a subset of ...
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What "real life" problems can be solved using billiards?
Recently I gave an interview to local media where I explained some basic open problems in billiard dynamics.
After a 45 min interview the reported asked me what "real life" problems can be ...
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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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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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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^{-\...
- 2,175
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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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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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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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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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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 research....
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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 "...
7
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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 ...
- 149k
2
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answers
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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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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 ...
- 149k
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2
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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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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 ...
3
votes
1
answer
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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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8
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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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3
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2k
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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 area ...
0
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0
answers
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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 ?
...
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1
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496
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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 ...
10
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1
answer
893
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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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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 ...
4
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6
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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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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-...
20
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6
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2k
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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 ...
13
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3
answers
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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
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1
answer
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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
0
answers
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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 $\phi_0$ ...
