# 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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### Equivalence of Wind Forces: Intensity vs. Duration [closed]

The strongest tornado in the world happened recently in Greenfield Iowa with winds over 318 mph: https://www.facebook.com/watch/?v=2176728102678237&vanity=reedtimmer2.0 I am curious, are less ...
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### On the relationship between graph isomorphism and equivalence in ETL workflow dependency graphs

$\newcommand{\inn}{\mathrm{in}}\newcommand{\out}{\mathrm{out}}$Let $G = (V, E)$ and $G' = (V', E')$ be two DAGs representing dependency graphs of ETL workflows. Each node $v \in V$ (or $v' \in V'$) ...
487 views

### Domino equation derivation

Can the functional form of $G$ in the expression $\frac{V}{\sqrt{gH}} = G\left(\frac{d}{H}\right)$ be rigorously derived from first principles, where $V$ is the limiting wave speed of a line of ...
82 views

### Practical applications of dandelin spheres

I know that dandelin spheres can be used to prove the focal properties of conic sections, but I heard that they can be used to help track the orbits of planets. All the sources I looked up only said ...
32 views

### Conjugate gradient-like algorithm with multiple search directions

I am solving an $n*n$ system $Ax=b$ in CUDA where $A$ is a sparse matrix. Currently I am solving it using the conjugate gradient algorithm. I have noticed that $Ax$ where $x$ is $n*1$ has roughly the ...
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### Spectral theory: a key to unlocking efficient insights in network datasets

In the context of directed or undirected graphs, matrices such as adjacency and Laplacian matrices are commonly used. The eigenbasis of these matrices addresses some practical implications, such as ...
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1 vote
84 views

### Maximizing the integral of a transformation that depends on a neighborhood of values of the original function

I'm not an expert in analysis whatsoever, so I might be posing a well-established question, or even an unanswerable one. Also, any suggestion on changes that might make the problem better are welcome. ...
84 views

### Interpolation polynomials with constraints

Lets consider a collection of $n$ points $\{Z_i\}_{i=1}^n\subseteq \mathbb{D}^k(1)=\{(z_1,\ldots,z_k)\in\mathbb{C}^k:\forall j\leq k, |z_j|\leq 1\}$. Let $h: \{Z_i\}_{i=1}^n \to \mathbb{D}^1(1)$ be a ...
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355 views

### 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 ...
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598 views

### 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 ...
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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} ...
1 vote
270 views

### 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 $n>2$): -\...
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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 ...
128 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 ...
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### 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,...
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162 views

### 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 ...
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1 vote
344 views

### 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 ...
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198 views

### 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 ...
• 10.2k
1 vote
117 views

### 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 ...
449 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, ...
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1 vote
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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 ...
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253 views

### 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 ...
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