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

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1answer
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Graphs of tensoring modules

Let $A$ be a ring, and $L,M,N$ an $A^\mathrm{op} \otimes A$-modules. $L \otimes_A M$ is then an $A \otimes A^\mathrm{op}$ module so we can tensor it again with $N$ to get an abelian group $(L ...
5
votes
2answers
174 views

How many isolated roots can a polynomial in $z$ and $\overline{z}$ have?

This is probably well-known by I can't find it now online. My guess is that if the degree is $n$ then it's $2n$ but it's just a hunch. EDIT: This is an edited version. Before I asked about roots ...
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0answers
178 views

Does Nelson try to prove PA inconsistent directly?

Edward Nelson is known for his serious attempts to show that Peano axioms, and sometimes even weaker theories, are inconsistent. I wasn't able to find Nelson's papers anywhere, so I wanted to ask a ...
3
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0answers
58 views

Number of orbits of $\mathrm{SL}_2(\mathcal O_A)$ on $\mathbf P^1(A)$ when $A$ is a quaternion algebra

This is a reference request. Let $A$ be an anisotropic quaternion algebra over $\mathbf Q$. Let $\mathcal O_A$ be a maximal order in $A$. Then $\mathrm{SL}_2(A)$ acts transitively on the right on ...
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0answers
37 views

What is the state of art MIQP solver

I used Gurobi with a MIQP with 26 binary variables and 26*4 interaction term without any other constraint. The speed is very slow already.... I want to ask what is the state of art of MIQP solvers. ...
4
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0answers
167 views

Any counterexamples known for the Generalized Tate conjecture?

One can state the generalized Tate conjecture over arbitrary finitely generated fields; to this end one should just define Galois representation to be effective if the eignevalues of the actions of ...
5
votes
2answers
206 views

Which groups are LERF?

A finitely generated group $G$ is called LERF if every finitely generated $H \leq G$ is closed in the profinite topology on $G$ (equivalently, there is a family of finite index subgroups of $G$ ...
3
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1answer
118 views

Reference for a fact (?) on homeomorphic knot complements

Does somebody have a reference (or an argument why it should be true) for the following statement? “Let $K$ and $K'$ be knots in $S^3$. If there is an orientation-preserving homeomorphism $h : S^3 ...
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0answers
18 views

Central automorphisms of groups act transitively on Krull-Schmidt decompositions

(Cross posted from math.SE) I'm looking for a modern reference to the subject line, preferably one that doesn't use Ore's generalizations to modular lattices. To clarify terminology... Suppose we ...
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0answers
85 views

Reference request: functional analysis results used in Taubes paper (1980)

I'm studying Taubes paper 'Arbitrary N-vortex solutions to the first order Ginzburg-Landau equations'. I'm looking for a reference of three following theorems: Let $f(x)$ be a convex funtional ...
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244 views

Second Hardy-Littlewood Conjecture theme

If Second Hardy-Littlewood Conjecture is true then we can claim that $\pi(x)-\pi(y)\leq \pi(x-y)$. Thus the conjecture gives an upper bound for the number of primes between $x$ and $y$. I have found ...
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0answers
44 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 ...
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1answer
1k views

How can I have a copy of this old paper by Frobenius?

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.
3
votes
2answers
315 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. ...
3
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0answers
43 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 ...
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2answers
149 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
1answer
153 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 ...
4
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1answer
130 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 ...
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0answers
93 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 ...
3
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0answers
50 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 ...
4
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2answers
423 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 = ...
5
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1answer
134 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 ...
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1answer
91 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 ...
5
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1answer
135 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 ...
1
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1answer
88 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 ...
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186 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
70 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 ...
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1answer
49 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 ...
3
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0answers
97 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, ...
4
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1answer
89 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 ...
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35 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 ...
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0answers
71 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" ...
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1answer
180 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. ...
2
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2answers
197 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 ...
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371 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 ...
5
votes
3answers
262 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
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1answer
74 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
1
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1answer
150 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 $0 < k \le n+1,$ ...
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0answers
103 views

Gauss's Cirlce Problem #lattice points in circle

Can someone link me the proof that $E(r)/r^{1/2}$ -> infinity when $r$->infinity? Where #lattice points in circle = $Pi*r^2+E(r)$
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171 views

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 ...
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121 views

Moduli interpretation of Hecke operators on Shimura curves

In his book on Automorphic Forms, Shimura gives (chapter 9) definitions of the the Hecke operators for Shimura curves. One can give definitions of the Hecke and Atkin-Lehner operators in terms of the ...
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0answers
104 views

Face poset of a subcomplex complement

Let $P$ denote the face poset of a simplicial complex, $\Delta$ the order complex of a poset, and $\simeq$ homotopy equivalence. It's known that for any finite simplicial complex $\mathcal{K}$ that ...
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votes
2answers
886 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 ...
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2answers
355 views

What is the minimal $C_k$, such that every $f\colon \{-1,1\}^n\to \mathbb{R}$ of degree at most $k$ satisfies $\|f\|_2\le C_k\|f\|_1$

Every $f\colon\{-1,1\}^n\to \mathbb{R}$ can be repsenented as a multilinean polynomial of the form $$f(x_1,x_2,\ldots ,x_n)=\sum _{S\subseteq [n]} \hat{f}(S)\prod_{i\in S} x_i $$ The degree of the ...
3
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1answer
47 views

Selecting Rays for Simulated Radon Transform

I have the task of determining approximations of a 2D function $f: (x,y)\in \mathbb{R}^2\mapsto\mathbb{R}$ from integrals along lines, i.e. from its Radon transform $R(\phi,\tau)[f(x,y)]$ and, because ...
3
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0answers
87 views

An example of mean curvature flow that does not preserve embeddedness

Let $F: M^n \to \mathbb R^{n+k}$ be an embedding and $F_t$ be a families of immersions so that $F_0=F$ and $$\frac{\partial F_t}{\partial t} = \vec H$$ It is known that in hypersurface case ...
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0answers
70 views

books on very large scale linear optimization

Recently in my material science research, I have encountered problems of very large scale linear optimization. I read the introductory book "Introduction to Linear Optimization (Athena Scientific ...
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0answers
101 views

current status of combinatorial optimization solvers [closed]

What is the current status of the solvers in combinatorial optimization? For example, what is the "usual feasible size" for a traveller sale's man problem, say, how many nodes and edges are "usually ...
3
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1answer
194 views

How to change the successor of a singular with a Woodin?

I'm looking for references on how to change the successor of a singular cardinal from "more or less" minimal assumptions. If possible, then without adding bounded subsets to the singular either. In ...
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61 views

Pullback of the tautological vector bundle and the nubmer of trivializations

I've heard about the followign result: for each two natural numbers $d,n \in \mathbb{N}$ one can find a number $k \in \mathbb{N}$ with the following property: for each CW-complex $X$ with $\dim X \leq ...