The applied-mathematics tag has no wiki summary.

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### MPE and MAPE averages [migrated]

I am a computer science graduate with a minor in mathematics, however it has been a long while since taking any statistical courses.
I am looking at calculating the Mean Percent Error and Mean ...

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**16**answers

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### How does one justify funding for mathematics research?

G. H. Hardy's A Mathematician's Apology provides an answer as to why one would do mathematics, but I'm unable to find an answer as to why mathematics deserves public funding. Mathematics can be ...

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**0**answers

31 views

### 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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**2**answers

194 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 ...

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692 views

### Malaysia Airlines Flight 370? [closed]

News reports about Flight 370's disappearance have given a sketchy idea of how hourly pings to a satellite have helped build up a picture of where it went.
From a naive intuitive point of view, if ...

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**2**answers

205 views

### Average number of distinguished leaves in a binary tree

By a binary tree, I mean in this question a full rooted binary tree in which left and right child are labeled. A leaf of such a tree is a vertex of degree at most 1 (most references would probably ...

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**1**answer

140 views

### Solving a difficult equation for a variable?

I'm trying to obtain the maximum likelihood estimate of the parameters for a model I'm building. I have constants $\sigma$, $\mu$, and $q_0$; a boolean matrix $\alpha$; and vectors $A, \beta, r, d,$ ...

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134 views

### To what extent can Gielis' so-called “Superformula” be used to improve the efficiency of WIFI antennas? [closed]

In 2003, the Belgian plant biotechnologist Johan Gielis proposed a formula that allows for the description of a wide variety of shapes in 2$d$, 3$d$ and higher dimensions. This is the formula
$$r( ...

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**2**answers

274 views

### Is there a source linking Robinson's work in wing theory with his theory of infinitesimals?

Abraham Robinson worked in applied mathematics for several decades. MathSciNet lists 12 articles by Robinson in wing theory. His production included the book
Robinson, A.; Laurmann, J. A. Wing ...

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**0**answers

200 views

### Contour integral (inverse Laplace transform) with arctan

I have what I think is a relatively simple contour integral involving arctan, but it is giving me difficulty. I would really appreciate any help.
The integral itself is, with $\tau$, $\lambda$, and ...

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**5**answers

1k views

### Differentiable functions with discontinuous derivatives

For years I've taught my honors calculus students about functions like (the continuous extension of) $x^2 \sin 1/x$, and for just as many years I've told them that they won't encounter functions like ...

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**2**answers

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### How difficult will it be for me to switch fields (details below) after my Ph.D. in pure mathematics?

I'm a first year postdoctoral researcher, working in pure areas of Riemann surfaces and differential geometry, after just finishing my Ph.D. in 2013. Recently I've also started taking interest in ...

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**0**answers

116 views

### Job sites for applied/interdisciplinary Mathematics?

I was wondering whether there're job sites that post jobs in applied/interdisciplinary mathematics, more specially, say postdocs or higher positions in mathematics and medical imaging, mathematics and ...

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**3**answers

337 views

### New trends in Applied Graph Theory [closed]

What are current trends in Applied Graph Theory? I am interested mainly in non-algorithmical problems. Maybe even in applications of graphs to other mathematical disciplines. For example, abstract ...

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**1**answer

278 views

### A particular contour integral

Mathoverflow,
I'd like to carry out the following integral,
$$f(t) = \int_{- \infty}^{\infty}\frac{-i\Omega e^{i \Omega t}}{1-\sqrt{-i\Omega}\coth(\sqrt{-i\Omega})} d\Omega.$$
Here's what I've ...

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**1**answer

184 views

### Request for some references exploring the connections of Riemann surfaces with medical imaging

I'd like to know some references for a beginner who has basic background in Riemann surfaces and differential geometry, and would like to start learning/working on more applied areas, medical ...

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**2**answers

258 views

### Visualizing a graph

I have a finite but huge metric graph with say 1000 vertices.
It comes say as 10000x10000 symmetric matrix filled by $0,1,\dots$ and $\infty$;
0's on the diagonal and $\infty$ is for pairs of vertices ...

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248 views

### Distribution of random vectors

Two positive numbers $\alpha$ and $\beta$ are given. We are going to describe a process of choosing a random vector on the unit sphere $S$ in $\mathbb R^3$ (given by $x^2+y^2+z^2=1$).
A vector $u\in ...

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**1**answer

153 views

### Approximating $\prod_{i=1}^{n-1} (1-ai)$ for large $n$

I have a function of the form:
$f(n) = \prod_{i=1}^{n-1} (1-ai)$
Here, $a \geq 0$ and $(a*i) < 1$. For $n > 10^5$ or $10^6$, what is the best possible analytic approximation for $f(n)$ that ...

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**1**answer

156 views

### Regular Perturbation Series soln to eqn

I want to find the a 3 term perturbation soln of
(i) $(1+x)^3 = ex$ where $e\ll1$
Direct substitution of the regular perturbation series $x = x_0 + ex_1 + e^2x_2$
into (i) does not work
I ...

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**1**answer

602 views

### 2/3 power law in the plane

I've recently come across a particular problem whose solution turns out to be a probability distribution given by $f(x) = \alpha \|x\|^{-2/3}$ in the unit disk in $\mathbb{R}^2$ and zero elsewhere (I ...

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**0**answers

149 views

### Number of breakpoints in parametric maximum flow problems

The parametric maximum flow problem can be formulated as
$$f(\lambda) = \min_{x\in\{0,1\}^n} \left( \sum_{i}(a_i + b_i\lambda)x_i + \sum_{i,j}c_{ij}x_ix_j \right),
$$
where all $c_{ij}<0$ (so that ...

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### Interesting mathematical topics arising from Biology

I've heard that there's a relatively new field of science called Mathematical Biology.
It will certainly apply well known and less known mathematical techniques to the understanding of some ...

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**1**answer

505 views

### name for $\underset{x}{\operatorname{argmin}} \displaystyle\sum\limits_{i=1}^n |x_i - x|$

Given a real-valued data set $ x_1, \dots, x_n $, what do you call the quantity
$$\underset{x}{\operatorname{argmin}} \displaystyle\sum\limits_{i=1}^n |x_i - x|$$
This seems like a pretty basic ...

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**4**answers

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 ...

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**28**answers

7k views

### Examples of theorems misapplied to non-mathematical contexts

For something I'm writing -- I'm interested in examples of bad arguments which involve the application of mathematical theorems in non-mathematical contexts. E.G. folks who make theological arguments ...

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**1**answer

958 views

### On the non-rigorous calculations of the trajectories in the moon landings

In a paragraph written by a person emphasizing that rigour is not everything in mathematics (I wish I had written down the details), it was stated that the moon landings would have been impossible ...

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**1**answer

2k views

### Is fuzzy mathematics useful in pure mathematics ?

Fuzzy sets and logic seem to be mostly used for applying to real-world situations, control-theory, game-theory, economics, statistics, data management, artificial intelligence, automated reasoning etc
...

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### 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 ...

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**4**answers

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### Applied linear algebra textbook? [closed]

I have a copy of Linear Algebra Done Right, which I worked through years ago in college. I have been using that book to refresh my knowledge, but it does not have an applied or computational aspect ...

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**4**answers

798 views

### Reasonable “Random” matrices to test numerical algorithms

Hello,
in numerical analysis, it is common to compare the behavior of different algorithms, and of different implementation of algorithms. This occurs not only on the theoretical level, but also on ...

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**5**answers

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### Matlab book recommendation

Which book or books do you recommend that cover advanced engineering topics and problem solving using matlab?
I already finished a very good introductory book and i want something more advanced.
Do ...

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263 views

### Orthogonal Projections in Lie Theory

I have been studying a finite element method where rigid & elastic spatial motions are separated using an orthogonal projection (actually two: one for translations/stretches, the other for ...

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**2**answers

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### Physical Meaning of Constant Velocity Gradient

I'm interested in representing homogeneous elastic deformations using Lie groups/algebras. Homogeneous deformations are those with a deformation gradient F which depends only on time (not position). ...

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210 views

### Use Lie Sub-Groups of GL(3, R) for elastic deformation ?

I'm interested in representing elastic deformations (e.g. stretching) using Lie groups. There are a few references to using $GL(3,\mathbf{R})$ but I'm wondering if possible to use subgroups of ...