Questions tagged [applied-mathematics]

the branch of mathematics that deals with the mathematical aspects of problems from science and engineering: applied analysis, numerical mathematics, applied statistics etc. (For applications of mathematics in general, cf. also the [applications] tag.)

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Non-Noetherian (classical) algebraic geometry

My starting point for this question is that, in a very classical sense, algebraic geometry is the study of solution spaces of systems of polynomial equations over an algebraically closed field. It is ...
Daniel W.'s user avatar
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What is this three dimensional curve that looks like an infinity sign called?

What is this three dimensional curve that looks like an infinity sign called? (Is there a known parametric equation for it?) It was generated with this Sagemath - script, where you can zoom in 3d in ...
mathoverflowUser's user avatar
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Numerical method for mixed system of equations and nonlinear inequalities

I am currently encountering challenges in determining the solution method for the following system of equations and inequalities: $$ \begin{aligned} &F(x) = 0\\ &G(x) < 0\\ \end{aligned} $$ ...
AnNam's user avatar
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1 answer
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Application of Yamabe and Liouville type equation

Let $\Omega$ be a domain in $\mathbb{R}^n$. I am interested in the following critical elliptic partial differential equations (PDEs): The Yamabe Type Equation (for $n>2$): \begin{equation} -\...
Paul's user avatar
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Do the exceptional root systems arise in the real world?

I am looking for a list of real world examples where the exceptional roots systems $E_6, E_7, E_8, F_4$, and $G_2$, and their associated Lie algebras and Lie groups, arise. To make this question a ...
Lorenzo Del Vecchiopontopolos's user avatar
2 votes
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112 views

Reference book for stochastic processes

I am looking for a good reference book for properties of stochastic processes for applied research. What I would like the reference to have is a collection of results on a large list of stochastic ...
HRSE's user avatar
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Is there a fractional derivative that preserves the composition of the one-parameter Mittag-Leffler function with $x\mapsto x^{\alpha}$?

Let $\alpha\in (0,1)$. The Riemann-Liouville fractional derivative of order $\alpha$ is defined by $$ \sideset{_0^R}{}{D^{\alpha}f(t)} =\frac{1}{\Gamma{(1-\alpha)}} \frac{d}{dt}\left(\int_{0}^{t} \...
Medo's user avatar
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Gaussian white noise model in application

I am interested in applications (to data) of non-parametric statistics, and my question concerned the Gaussian white noise model defined by, $$ X_{t_1, \ldots, t_d}=f\left(t_1, \ldots, t_d\right) d ...
BabaUtah's user avatar
2 votes
1 answer
293 views

Does there exist a Python package that samples random special unitary matrices such that the matrices are parameterized

For reference, the linked paper is Composite parameterization and Haar measure for all unitary and special unitary groups by Christoph Spengler, Marcus Huber and Beatrix C. Hiesmayr (J. Math. Phys. 53,...
Silly Goose's user avatar
3 votes
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Sheaf theory in TDA

I was wondering wether anyone had any examples as to why it more useful to consider a sheaf theory approach to TDA problems. I am familiar with some of the benefits of using cellular cosheaves to ...
amd1234's user avatar
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Mach's principle, Newton's law and Hilbert sphere?

(This question has originally been posted on reddit, but I thought, that the question raised in the post above, might fit as well here on MO.) I wanted to share with you something I stumbled upon ...
mathoverflowUser's user avatar
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Literature on Lyndon words and the Lie commutator

Since I lost my paper notes in a domestic conflagration in Japan some ten years ago, I've occasionally tried to recall one particular author who wrote in the 1900s about Lyndon words / strings, or ...
Tom Copeland's user avatar
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Which real functions benefit from the Fundamental Theorem of Interval Analysis?

I'm reading Introduction to Interval Analysis, by Moore, Baker & Cloud and complementing it with Global Optimization using Interval Analysis, by Hansen & Walster. Theorem 5.1 - Fundamental ...
Lost in Traslations's user avatar
9 votes
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442 views

Useful applications of applied category theory

Led by John Baez, applied category theory (e.g. [1]) seems to accumulate much popularity. As someone who has noticed the importance of category theory in pure mathematics (e.g. homotopy theory, tqfts, ...
Student's user avatar
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A metric geometry problem which calculates the limitation of human eyes

This is the update version of this question A functional inequality which calculates the limitation of human eyes Let an Euclidean space $M$ (or a path connected metric space) be partitioned into ...
Veronica Phan's user avatar
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1 answer
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What are the right mathematical tools / language to analyse complex networks over time?

In this article about human physiology as a complex network the authors say that: "Lacking adequate analytic tools and a theoretical framework to probe interactions within and among diverse ...
mathoverflowUser's user avatar
4 votes
2 answers
246 views

A functional inequality which calculates the limitation of human eyes

Find all pair of function $f^-,f^+:[0,1]\rightarrow[0,1]$ such that: (1)$f^-(x)\leq x\leq f^+(x)$. (2)$f^-(x)+f^+(1-x)=1$. (3)$f^-(x)f^-(y)\leq f^-(xy)\leq f^-(x)f^+(y)$. (4)$f^+(x)f^-(y)\leq f^+(xy)\...
Veronica Phan's user avatar
8 votes
1 answer
691 views

Question on pure mathematics helping climate change research

While I am a pure mathematics tenured professor, still at a relatively young age, and fairly passionate about my area of research, I cannot help but feel that it may be more useful to humanity if I ...
Dr. Pi's user avatar
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How to construct lattice points in bounded symmetric domain?

Consider the Hermitian bounded symmetric domain for $k \leq m$: $$ C_{k, m} = \{ Z \in \mathbb{C}^{m\times k} \,|\, Z^*Z < I_k \} $$ where $I_k$ is the $k\times k$ unit matrix. If I am not mistaken,...
Vít Tuček's user avatar
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15 votes
4 answers
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Mathematicians learning from applications to other fields

Once upon a time a speaker at the weekly Applied Mathematics Colloquium at MIT (one of two weekly colloquia in the math department (but the other one is not called "pure")) said researchers ...
2 votes
1 answer
99 views

What are partial differential equations with fast reaction terms?

I know $u_t(t,x)=\Delta u^m(t,x),\;\; (t,x)\in (0,\infty)\times \mathbb{R}$ is the fast-diffusion equation when $m\in (0,1).$ But how are PDEs with fast reaction terms defined in general? I also wish ...
Devashish Sonowal's user avatar
2 votes
1 answer
357 views

Is it possible to obtain orthogonal (but not normalized) vectors after QR factorization?

After QR decomposition of a matrix, $M$, the columns of Q are orthonormal. Is it possible after obtaining Q, we recover unnormalized column vectors from $Q$? For example, the matrix M has the ...
AChem's user avatar
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What tools should I use for this problem?

Suppose we have $d$ cylindrical metal bars, with radius $l$, attached orthogonal to a support in random places: Now we have to attach bars with radius $k$ EVENLY SPACED, with distance $p$ between ...
Diego Santos's user avatar
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1 answer
280 views

General strategy of error bound of matrix exponential

I want to ask General strategy of the error bound of the matrix exponential. For example, suppose, $A, B$ are finite dimension $n \times n$ matrices with complex coefficients. Using Baker–Campbell–...
En-Jui Kuo's user avatar
37 votes
17 answers
10k views

Listing applications of the SVD

The SVD (singular value decomposition) is taught in many linear algebra courses. It's taken for granted that it's important. I have helped teach a linear algebra course before, and I feel like I need ...
28 votes
2 answers
3k views

Importance of integral equations

Differential equations are at the heart of applied mathematics - they are used to great success in fields from physics to economics. Certainly, they are very useful in modelling a wide range of ...
FusRoDah's user avatar
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2 votes
1 answer
135 views

Reference request: probabilistic models on climate (change)

I am looking for probabilistic models to address climate change. Are they known in the existing literature? I have found the post Math behind climate modeling. concerning PDE models. Many thanks for ...
user avatar
8 votes
3 answers
613 views

Explain seemingly non-random figures which arise from random Poisson points with normalization

Context Working with some biological datasets it was puzzling to see the patterns like Figure 2 (right) below. The first feeling was, that it corresponds to some biological effects like correlations ...
Alexander Chervov's user avatar
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232 views

How to measure perceived note similarity in music / simplicity of ratios?

I have discovered a method to measure the similarity of two successive musical notes which I wanted to share with a question: It is known in music theory that two successive pitches $a,b$ which sound “...
mathoverflowUser's user avatar
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A new method for processing music scores?

I have developed a method and python script: https://github.com/githubuser1983/algorithmic_python_music which allows the user to input a midi file and then chose a few numbers as parameters, and the ...
mathoverflowUser's user avatar
2 votes
1 answer
249 views

Applied Topology/Topological Data Analysis conferences and journals

Can someone point out links to Applied Topology/Topological Data Analysis conferences and journals? Thank you!
ilir's user avatar
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What is known about discrete versions of the spatially homogenous Boltzmann equation with finitely many (but arbitrarily many) velocities?

Consider a discrete version of spatially homogenous Boltzmann equation with finitely many (but arbitrarily many) velocities $v_i \in \mathbb R^n$ with $i \in I$. Equivalently, consider a system of ...
DC47's user avatar
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2 votes
1 answer
183 views

Ramp and Cliff Solutions to the Viscous Burgers Equation: Explicit Formula?

I read an article in which the authors describe an observed phenomenon as being related to the "classical ramp and cliff Burgers solutions''. Those are described as Burgers solutions that behave ...
Gateau au fromage's user avatar
1 vote
1 answer
533 views

I want to enter graduate school in pure math. Is doing REU in “mathematical modeling” a good idea? Is it an essential skill to learn?

(please let me know if this question is not suitable here) Hello! I'm an undergraduate rising senior majoring in mathematics and it seems that I got rejected by an REU that is held in my university ...
jk001's user avatar
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3 votes
0 answers
114 views

Linearized NLS/GP around a soliton and the spectrum of the evolution operator

I apologize if this has been asked before but so far I haven't found it anywhere. Consider the Nonlinear Schrödinger equation with a potential (i.e. Gross- Pitaevskii) in $\mathbb{R}^{d}$ $$i\Psi_{t} =...
Taotology's user avatar
3 votes
0 answers
486 views

Another question from Villani's monograph "Hypocoercivity"

I think there is an (possible) error in Villani's monograph titled "Hypocoercivity". To be specific, in page 62 (the first snapshot), he defined a new inner product $((\cdot,\cdot))$ as in (...
Fei Cao's user avatar
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1 vote
0 answers
117 views

Recursive formula for integral of Chebyshev-type integral

Define $$ I_{m,n}(x,y,r) = \int_a^b T_m(x + r \sin(\gamma)) T_n(y-r \cos(\gamma)) d\gamma $$ where $T_m(x)$ are the Chebyshev polynomials of the first kind, and $a$ and $b$ are constants. Assume that ...
Oren B.'s user avatar
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0 answers
887 views

Is Steven J. Miller's "research" on election fraud sound? And was he paid for it? [closed]

I recently encountered the following piece regarding alleged massive voter fraud in Pennsylvania: https://justthenews.com/sites/default/files/2020-11/...
Citizen Mathematician's user avatar
11 votes
5 answers
492 views

What are efficient pooling designs for RT-PCR tests?

I realize this is long, but hopefully I think it may be worth the reading for people interested in combinatorics and it might prove important to Covid-19 testing. Slightly reduced in edit. The ...
Benoît Kloeckner's user avatar
3 votes
0 answers
130 views

Notions of "completeness" and "sufficiency" of a mathematical model

I'm modelling a real-world problem as having instances $i$ in a set $P$. As a very simple artificial example, consider the problem of choosing a meeting room given a certain number of people. Then $i =...
Peeyush Kushwaha's user avatar
5 votes
2 answers
417 views

Examples of applications of hyperbolic conservation laws

I am giving a talk in front of my applied PDE research group on hyperbolic conservation laws, the most basic form of which is the PDE $$ u_t + f(u)_x = 0 $$ where $u$ is the conserved quantity and $f$ ...
groupoid's user avatar
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28 votes
1 answer
2k views

Recent uses of applied mathematics in pure mathematics

In this answer Yves de Cornulier mentioned a talk about the possible uses of persistent homology in geometric topology and group theory. Persistent homology is a tool from the area of topological data ...
2 votes
0 answers
70 views

SIR model constraint [closed]

During these past months, I've heard a lot about some pandemic modelling techniques, specially the so-called SIR model. Before I begin, I'd like to stress that my interest and question are just a ...
IamWill's user avatar
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5 votes
1 answer
354 views

Renormalization group strategies

Before introducing block spin transformations in chapter four of Random Walks, Critical Phenomena and Triviality in Quantum Field Theory, the authors state the following: "In this chapter we sketch ...
IamWill's user avatar
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1 vote
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Gradient descent in $U(n)^r$

I have a function $f:U(n)^r\rightarrow \mathbb{R}$ which I would like to minimize. Here, $U(n)$ is the set of unitary matrices, and $r$ should be considered to be much bigger than $n$. For instance, $...
Springberg's user avatar
1 vote
0 answers
111 views

Spins in classical statistical mechanics

I'm reading Kupiainen's notes on the renormalization group and also caught my attention. Actually, this is something that often causes my some confusion. On page 43, in the section about Ginzburg-...
IamWill's user avatar
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2 votes
0 answers
65 views

Multiexponential analysis of infection counts with errors

In the past, I have seen some decompositions of sums of exponential decays into components by the Padé-Laplace method: Apply the Laplace transform $${\frak L}(\sum_{i=1}^n a_i e^{k_i t}) = \sum_{i=1}^...
Douglas Zare's user avatar
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1 vote
1 answer
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How many persons pass your 1.5 meter neighbourhood during 1 week ? If the distribution is power law what is the exponent?

Consider a graph with vertices being people (in some region), and make an edge if one person pass another closer than say 1.5 meter during say one week. (Such a graph might be thought a kind of ...
Alexander Chervov's user avatar
14 votes
8 answers
3k views

Relevant mathematics to the recent coronavirus outbreak

I would like to ask about (old* and new) reliable mathematical literature relevant to various mathematical aspects of the recent coronavirus outbreak: In particular, standard statistical/mathematical ...
2 votes
1 answer
128 views

Persistent homology stability results (query about Lipschitz functions)

One of the beneficial properties of persistent homology is its stability results (so called robustness to noise). Usually the referenced paper is this paper titled "Lipschitz functions have $L_p$-...
yoyostein's user avatar
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