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1
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0answers
6 views

IVP accuracy - scheme accuracy Vs. derivative accuracy?

General Question: If I have an IVP with periodic and continuous initial condition, which rules the accuracy of the scheme - the manner in which we approximate spatial derivative or the acuuracy of the ...
4
votes
1answer
85 views

Continuity of the stationary distribution of $M/G/1$ queue w.r.t. the input rate

Let $(\lambda_n)_{n\geq0}$ be a sequence of positive numbers such that $\lambda_n\rightarrow \lambda$ as $n\rightarrow +\infty$. These $\lambda_n$ are the parameters of a sequence of Poisson Processes ...
0
votes
1answer
85 views

Comparing ideals in posets

Consider a partially ordered set $P$, and two upper sets $U_1$, $U_2$ in this poset. What are some natural ways to measure how equal these two upper sets are? This question arise naturally in the ...
12
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4answers
712 views

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. ...
2
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1answer
379 views

Computer Science applications of Roth's Theorem [closed]

I have been reading about Additive Combinatorics and in particular Roth's theorem which states any positive upper density set has infinitely many 3-step arithmetic progressions. Let $A \subset ...
1
vote
1answer
61 views

Explicitly relating two functions containing exponential terms [closed]

This is an extremely basic question for a forum like this, but I am unable to think of any workable approaches myself. I have two functions related to the distribution of administered drugs in the ...
75
votes
16answers
6k views

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 ...
2
votes
0answers
33 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 ...
3
votes
2answers
208 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 ...
12
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0answers
702 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 ...
5
votes
2answers
216 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 ...
-2
votes
1answer
145 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 $A, \beta, r, d,$ ...
1
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0answers
137 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( ...
3
votes
2answers
278 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 ...
0
votes
0answers
202 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 ...
25
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5answers
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 ...
10
votes
2answers
1k views

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 ...
0
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0answers
124 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 ...
5
votes
3answers
360 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 ...
3
votes
1answer
288 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 ...
1
vote
1answer
188 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 ...
4
votes
2answers
263 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 ...
1
vote
0answers
256 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 ...
1
vote
1answer
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 ...
0
votes
1answer
157 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 ...
12
votes
1answer
605 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 ...
2
votes
0answers
152 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 ...
23
votes
14answers
2k views

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 ...
1
vote
1answer
520 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 ...
6
votes
4answers
2k 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 ...
73
votes
28answers
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 ...
12
votes
1answer
973 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 ...
8
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1answer
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 ...
2
votes
2answers
1k views

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 ...
1
vote
4answers
1k views

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 ...
7
votes
4answers
814 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 ...
2
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5answers
2k views

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 ...
0
votes
0answers
266 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 ...
3
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2answers
1k views

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). ...
0
votes
0answers
211 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 ...