This tag is used if a reference is needed in a paper or textbook on a specific result.

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3
votes
1answer
98 views

Reference request: Invariant sets of dynamical systems

(I should preface this with the disclaimer that this is a slightly elaborated version of a question that I posted onto math se recently to which I received no responses, and have since deleted the ...
13
votes
0answers
331 views

Geodesics in finite groups

It seems that I can generalize a result from compact, connected Lie groups to finite groups, but in order to do so, I need to have some kind of geodesics on finite groups. Below is a proposition for ...
8
votes
1answer
698 views

How can I have a copy of this old paper?

How can I have a copy of this old paper and a translation of it? Frobenius, G. (1902). Uber primitive Gruppen des Grades n und der Klasse n - 1. S. B. Akad. Berlin 1902, 455-459.
1
vote
0answers
38 views

Looking for the manuscript “Uniform polytopes” by N. Johnson

The manuscript Uniform Polytopes (1991) by Norman Johnson is cited in the wikipedia page on uniform polytopes (http://en.wikipedia.org/wiki/Uniform_polytope). Is there an electronic copy of this ...
3
votes
2answers
253 views

Intuition behind $\zeta(2) = \frac{\pi^2}{6}$ [on hold]

In literature, there are many proofs of the well-known result $$\zeta(2) = \frac{\pi^2}{6}.$$ However, as far as I know, they do not offer an intuitive explanation of why this result should be true. ...
2
votes
1answer
132 views

A number array related to colored necklaces and the primes

I stumbled upon entry OEIS-A208535 on the enumeration of certain kinds of colored necklaces and noticed that the integers for the odd prime rows of the table there seem to be given by the Moreau ...
1
vote
1answer
176 views

Is the Cassels-Tate pairing defined for elliptic curves over function fields?

The Cassels-Tate pairing is typically defined for elliptic curves (or abelian varieties) over number fields, but it seems like it should be defined for elliptic curves over function fields as well. ...
33
votes
1answer
1k views

Pach's “Animals”: What if the genus is positive?

Janos Pach asked a deep question 23 years ago (1988) that remains unsolved today: Can every animal—a topological ball in $\mathbb{R^3}$ composed of unit cubes glued face-to-face—be ...
3
votes
0answers
34 views

Reference for existence results for 2D forced viscous Burgers equation

I am looking for results concering the following parabolic PDE $$u\cdot\nabla u + \Delta u = F(x),$$ where $$u\colon\Omega\to\mathbb{R}^2,$$ and $\Omega\subset\mathbb{R}^2$ is a 2D domain (bounded or ...
18
votes
21answers
3k views

History Question: AUTObiography of Mathematicians

According to Wikipedia, an autobiography is an account of the life of a person, written by that person sometimes with a collaborator. An autobiography offers the author the ability to recreate ...
1
vote
0answers
111 views

Runge-Kutta with all nodes at n+1 or zero weights otherwise [migrated]

So, lets say for the family of the explicit Runge-Kutta methods: $$y_{n+1} = y_n + \sum_{i=1}^s b_i k_i$$ where, $$k_1 = hf(t_n, y_n)$$ $$k_2 = hf(t_n+c_2h, y_n+a_{21}k_1)$$ $$\vdots$$ $$k_s = ...
1
vote
2answers
131 views

Calculating Exterior Distance from Measurements of Inner Geometry

Gauss has proven in his famous Theorema Egregium, that it is possible, to calculate the gaussian curvature from measuring angles and distances on the surface, irrespective of how the surface is ...
3
votes
0answers
45 views

The 4-th generator of $K_1$ group for 3-dimensional NC tori algebra

An $n$-dimensional NC torus algebra $A_\theta^{(n)}$ is defined for any antisymmetric $n\times n$ matrix $\theta$ of real numbers as the universal $C^*$-algebra, generated by unitaries ...
2
votes
0answers
51 views

Invariant Theory over finite adeles

Classical invariant theory, among the other things, classifies polynomial functions over a vector space $V$ endowed with a quadratic form $Q$ which are invariant under the action of $SO(V,Q)$. I am ...
2
votes
3answers
390 views

Simple functions on a product measure space

Let $ (X,\mathcal{F},\mu) $ and $ (G,\mathcal{G},\nu) $ be two measure spaces with $ \mu $ and $ \nu $ being $ \sigma $-finite. Per definition, the linear span of $$ \{ \mathbf{1}_{C} ~|~ C \in ...
0
votes
1answer
48 views

Reference request for stably free modules

I am looking for some references on the theory of stably free modules. I will call (F) the following property for a ring $R$: every f.g. stably free module over $R$ is free. 1) Is there a standard ...
5
votes
1answer
126 views

What version of the wreath product embedding theorem is actually stated in the famous paper of Kaloujnine and Krasner?

This question is inspired by Terry Tao's blog post and the comments there. I have always cited M. Krasner and L. Kaloujnine, "Produit complet des groupes de permutations et le problème d'extension de ...
4
votes
2answers
420 views

Who first defined quantum integers?

Who first gave the defintion of quantum integers $$ [m]_q = \frac{1 - q^m}{1 - q} $$ and addition as $$ [m]_q \oplus_q [n]_q = [m]_q + q^m [n]_q $$ and multiplication as $$ [m]_q \otimes_q [n]_q = ...
1
vote
1answer
86 views

Connections between loops (algebraic structure) and graphs

I would like to know whether there are known constructions which provide a bijection between loops (isomorphism classes) and (possibly directed) graphs. Any reference to a useful paper in this ...
1
vote
1answer
87 views

hypergeometric at nearest singularity

Reference request. A prototype case: In $$ {}_2F_1\left(\frac{1}{12},\frac{5}{12};\frac{1}{2};x\right) = A\log\left(\frac{1}{1-x}\right) + B + o(1), \qquad x \to 1^- $$ what can we say about the ...
1
vote
1answer
148 views

A generalisation of Narayana-like numbers (walks on the 2D lattice)

I apologize in advance if this question has a trivial answer. I am pretty sure this kind of problem was already studied and I am mostly asking for good references. Given integers $0 < k \le n+1,$ ...
5
votes
1answer
123 views

O-minimal Theories with Non-Dense Order Type

I asked this question on MSE, but I haven't received any comments or responses (also, it has a very low view count), so I thought I would also ask it here. In this paper, Knight, Pillay, and ...
5
votes
1answer
476 views

Groups whose normal subgroups form a chain with respect to inclusion

Let G be a finite group. In general, given two normal subgroups N and K of G, we need not have N < K or K < N. The easiest example is the Klein 4-group V4 and its subgroups of order 2. So assume ...
5
votes
0answers
172 views

Canonical functions in set theory and their applications

Given regular cardinal $\kappa>\omega,$ we can define the canonical functions $f_\alpha: \kappa\to \kappa,$ for $\alpha<\kappa^+.$ Some of their properties are presented in Chapter 22 of the ...
0
votes
1answer
341 views

For what nonnegative measures $\mu$ does $\mu*e^{-|\cdot|}\in L^{\infty}$?

I am trying to characterize all measures on $\mathbb{R}$ such that $$ \sup_{x\in\mathbb{R}} \: (\mu*f)(x)<+\infty, $$ where $f(x)$ is some specific integrable functions, such as $f(x)=e^{-|x|}$, ...
0
votes
1answer
67 views

About the regularity of the boundary of a set

Consider $\Omega_1, \Omega_2$ two convex, bounded domains in $R^n$ with $\Omega_1 \supset \overline{\Omega_2}$ and suppose that $\operatorname{dist}(x, \partial \Omega_2) =\min_{y \in \partial ...
3
votes
1answer
360 views

The Weyl algebra modules which are also rings

Consider the space $C^\infty(\mathbb{R})$. We have on it a natural action of the Weyl algebra generated by $x$ and $d/dx$, where $x$ is the coordinate on $\mathbb{R}$, and there is plenty of Weyl ...
0
votes
1answer
243 views

Trace map for sepeared morphism of non-singular varieties

I read about for any separable morphism of non-singular varieties $f:X'\to X$, one can define a homomorphism $\text{Tr}:f_*(\Omega_{X'}^q) \to \Omega_{X}^q$,so that the map $\Omega_{X}^q \to ...
4
votes
3answers
249 views

Poincare duality for (co)homology of Lie algebras?

Let $R$ be a commutative ring and $\mathfrak{g}$ a Lie $R$-algebra that has an $R$-module basis with $n$ elements. In Algebra, Geometry, and Software Systems by Joswig & Takayama on p.200 it ...
2
votes
0answers
69 views

(Reference) Asymptotics of hitting probability by Brownian motion

The problem is: Given compact set A with positive finite volume (eg. ball,cube), what happens to $P_{x}(T_{A}>t)$ as $t\to \infty$, where $T_{A}=inf_{t>0}(B_{t}\in A)$ and x is in the "exterior" ...
4
votes
1answer
88 views

Euler characteristic of open varieties as degree of Chern class of logarithmic differentials

Let $U$ be a smooth variety over a subfield $k$ of $\mathbb{C}$. Let $X$ be a smooth projective variety containing $U$ as the complement of a normal crossings divisor $D$. Denote by $\chi(U)$ the ...
3
votes
0answers
95 views

On a problem of Berkovich

What is the real history of the following problem proposed by Berkovich [Y. Berkovich, Z.Janko, Groups of prime power order. Volume 2, Expositions in Mathematics, 56, Walter de Gruyter, New York, ...
8
votes
0answers
167 views

An inequality for the ratio of standard Young tableau with {1,2,…,k} in the first row

For a partition $\lambda \vdash n$, define $\dim \lambda$ to be the number of standard Young tableaux of shape $\lambda$, and $\dim \lambda/(k)$ as the number of standard Young tableaux with ...
2
votes
0answers
67 views

Generators for lattice polytopes

Let $V$ be a finite set of integral vectors in $\mathbb{R}^n$. Consider the real (positive) convex cone $\mathbb{R}_+V$ spanned by $V$. We can assume that all vectors in $V$ are extremal in ...
-2
votes
0answers
34 views

Numerical method of lines for solving PDEs [closed]

Could you please advise some literature about the numerical method of lines (MOL) for parabolic PDEs? It is a method of solving PDEs with discretizing only by space but not by time. A system of ODEs ...
2
votes
2answers
193 views

Gauss Codes that produce classical knots as opposed to virtual knots

I have been doing some research in Gauss codes and have been reading Kauffman's paper Virtual Knot Theory. In section 3.3, Theorem 2, he states that If $K$ is a virtual knot whose underlying Gauss ...
5
votes
3answers
259 views

A. Markov's papers?

A. Markov published several papers on his chains, starting in 1906, so it is written, in the journal: (1) Извѣстія Физико-математического общества при Казанском университете I am surprised by the ...
7
votes
2answers
879 views

Is there an English translation of Minding's 1839 paper?

Is there an English translation of "Wie sich entscheiden lässt, ob zwei gegebene krumme Flächen auf einander abwickelbar sind oder nicht..." by Ferdinand Minding, Journal für die reine und angewandte ...
4
votes
0answers
158 views
+50

Decompositions of a compact Lie group into “fixed point set types”

Consider a compact Lie group $G$ which acts on a closed Riemannian manifold $M$ by isometries. Then it is well-known that there are only finitely many isotropy types of the $G$-action, i.e. finitely ...
-4
votes
0answers
88 views

Löwenheim–Skolem as an argument for discrete mathematics? [closed]

At least as far as first-order theories go, one could construe the (downward) Löwenheim–Skolem theorem as an incentive to invest more in discrete models rather than in continuous ones. This would ...
4
votes
4answers
879 views

History of the Sampling Theorem

In January, 1949, Shannon publishes the paper Communication in the Presence of Noise, Proc. IRE, Vol. 37, no. 1, pp. 10-21, available here, which establishes the Information Theory. In this paper, the ...
3
votes
6answers
1k views

Source needed (at final-year undergrad level) for the double cover of SO(3) by SU(2)

This is a bit of an ill-defined question, and I feel I should have been able to resolve it by combining Google with a few library trips, but I'm having difficulty narrowing down the search results to ...
5
votes
4answers
651 views

Quanitative de Moivre–Laplace theorem (reference request)

The classical de Moivre-Laplace theorem states that we can approximate the normal distribution by discrete binomial distribution: $${n \choose k} p^k q^{n-k} \simeq \frac{1}{\sqrt{2 \pi ...
3
votes
2answers
259 views

Textbook for Partial Differential Equations with a viewpoint towards Geometry

I don't know whether I should ask this question here or not but I asked this question on MSE but didn't get any answer so I am posting it here. Though similar questions have been asked at ...
18
votes
3answers
2k views

A book on locally ringed spaces?

Are there enough interesting results that hold for general locally ringed spaces for a book to have been written? If there are, do you know of a book? If you do, pelase post it, one per answer and a ...
0
votes
1answer
193 views

Sufficient conditions for equality of measures related to harmonic functions

In Axler's book "Harmonic function theory" on this link http://www.latp.univ-mrs.fr/~chaabi/ARTICLES%20IMPORTANTS/Autres%20articles%20interessant/Livres/Harmonic%20Function%20theory.pdf on page 112 ...
7
votes
6answers
2k views

Discrete Mathematics textbooks for undergraduates

For the first time, I will be teaching a course on Discrete Mathematics for electrical and computer undergraduates students. I intend to focus on practical applications. I would be grateful if ...
2
votes
1answer
72 views

Weight polytopes of the fundamental representations of simple Lie groups

Where can I find a description of the weight polytopes of the fundamental representations of the classical complex simple Lie groups? Thanks in advance
8
votes
1answer
726 views

Central extension of the algebraic loop group

I'm doing some constructions with the universal central extension $\widehat{\Omega G}$ of the loop group $\Omega G$ (here $G$ is a matrix group), where a priori the loops involved are just smooth, but ...
54
votes
9answers
4k views

How does one find out what's happening in contemporary mathematics research?

How does one find out what's happening in contemporary mathematics research? EDIT: I should have mentioned that I am looking for open access online sources. It so happens that I have been outside ...