# 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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### 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,...
6k views

### 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 ...
84 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 ...
108 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 ...
735 views

### 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 ...
1 vote
110 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–...
4k 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 ...
2k 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 ...
110 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 ... 594 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 ...
174 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 “...
203 views

### 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 ...
151 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!
60 views

### 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 ...
110 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 ...
90 views

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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 ...
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 ...
112 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 $L_p$-...
1k views

### Physical interpretation of the Manifold Hypothesis

Motivation: Most dimensionality reduction algorithms assume that the input data are sampled from a manifold $\mathcal{M}$ whose intrinsic dimension $d$ is much smaller than the ambient dimension $D$. ...
155 views

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### Which high-degree derivatives play an essential role?

Q. Which high-degree derivatives play an essential role in applications, or in theorems? Of course the 1st derivative of distance w.r.t. time (velocity), the 2nd derivative (acceleration), and the ...
5k views

### Is the field of q-series 'dead'? [closed]

I had a discussion with my advisor about what am I interested as my future research direction and I said it is special functions and q-series. He laughed and said that the topic is essentially dead ...
724 views

### The collected works of John von Neumann

Might there be an online collection of John von Neumann's collected works in pdf format? I'm particularly interested in his approach to applied mathematics(ex. shockwaves, hydrodynamics). Note: I ...
1 vote
144 views

### Doubts related Shifting from Pure to Applied math [closed]

I am a second year (Pure) Math and (Theoretical) Physics undergraduate in India. I want to do a masters in Applied/Computational Science or Math, for which I have apply after next 7 months. I have ...
125 views

### Numerical instability of the axis-angle representation of rotations in 3D

Suppose that I have $1000$ pair of points where each pair consists of a point in $\mathbb{R}^3$ and its image after a rotation in $\mathrm{SO}(3)$ with some noise. I have used RANSAC to find the ...
I was wondering if versions of the Laplace/steepest descent methods exists for integrals of the type $$\int_C f(z) M(\lambda g(z)) dz$$ for $\lambda >>0$ functions \$f(z), g(z): \mathbb C \...