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

**4**

votes

**2**answers

142 views

### Frobenius Groups of Automorphisms

Recently, I am looking different papers on the topic
$$\mbox{Frobenius groups of automorphisms of a group.}$$
But I am familiar with Frobenius groups only; not with their (faithful) actions on groups. ...

**1**

vote

**0**answers

96 views

### Full version of Soucaliuc's research announcement “Réflexion entre deux diffusions conjuguées”

Florin Soucaliuc published the following research announcement in 2002 containing some results from his thesis on reflected diffusion processes:
[1] F. Soucaliuc, Réflexion entre deux diffusions ...

**6**

votes

**0**answers

155 views

### Shortest path to inspect a polyhedron

This is a variant of two as-yet unsolved MO questions cited below.
Let $P$ be a closed polyhedron in $\mathbb{R}^3$.
The task is to find a shortest path $\sigma$ on the surface of $P$ from which
all ...

**7**

votes

**0**answers

162 views

### A definition of the homotopy colimit of a coherent diagram

Suppose I am given a homotopy coherent diagram of spaces of shape $I$ (This is a simplicial functor $F:\mathfrak{C}[I] \to Top$, where $\mathfrak{C}$ is the standard cofibrant replacement functor in ...

**7**

votes

**1**answer

332 views

### On (a generalization of) the Gauss Circle Problem

Most (if not all) references I read about the Gauss Circle Problem that proves a bound below $O(R^{2/3})$ reduces the GCP to the Dirichlet Divisor Problem by the well known expression of $r_2(n)$, the ...

**9**

votes

**0**answers

292 views

### Is there an “Erlangen Program” for Graph Theory?

There are certain graph theoretic problems (especially optimization problems), whose solution-subgraph (i.e. the set of vertices and edges)), is invariant under certain modifications (especially ...

**3**

votes

**2**answers

89 views

### About Kurosch-Ore theorem

Where can I find the proof of Kurosch-Ore theorem in lattice theory?
The statement of this theorem is: Let $L$ be a modular lattice with $0$ and $1$ that satisfies both chain conditions. Then for any ...

**8**

votes

**2**answers

258 views

### Proofs of main probability results from other fields

Making connections between different areas is very exciting and probability has already made connections with other fields (BM used in proving complex analysis and PDE results).
To keep it short, I ...

**4**

votes

**1**answer

180 views

### Is Lax-Milgram true without the separability assumption?

I read the Lax-Milgram Theorem in the Navier-Stokes Equations by Temam:
Let $X$ be a separable Hilbert space (norm $\|\cdot\|_X$) and let
$$
a:X\times X\to\Bbb{R}
$$
be a bilinear continuous ...

**2**

votes

**1**answer

141 views

### Stiefel-Whitney classes of tensor product $\xi^m \otimes \eta^n$, computation

Let $\xi^m$ and $\eta^n$ be vector bundles over a paracompact base space. Where can I find a reference to the Stiefel-Whitney classes of the tensor product $\xi^m \otimes \eta^n$ being computed as ...

**4**

votes

**1**answer

210 views

### If $N = {q^k}{n^2}$ is an odd perfect number given in Eulerian form, is $n$ a square?

(I have asked a similar question in MSE four days ago, but did not receive any answers. I have therefore cross-posted it to this site, hoping to get some responses.)
An odd perfect number $N$ is ...

**1**

vote

**1**answer

162 views

### Generalizing Dedekind's Factorization Theorem

A classical theorem due to Dedekind states the following:
Let $O_{K}$ be the ring of integers of a number field $K$, and assume
$K$ is generated by adjoining the algebraic integer $\alpha$ to
...

**3**

votes

**0**answers

175 views

### Quartics containing twisted cubics

The set of quartic surfaces in $\mathbb{P}^3$ containing at least one twisted cubic forms the divisor on the space of all quartic spaces (parameterized by $\mathbb{P}^{34}$).
I'am wondering how one ...

**2**

votes

**2**answers

342 views

### A logarithmic cotangent inequality

I must be a terrible googling searcher but I cannot find a reference to the following inequality:
$$ \forall_{\phi\in(0;\frac \pi 4)}\ \ln(\cot(\phi)))\, <\, \cot(2\!\cdot\!\phi) $$
I have just ...

**2**

votes

**2**answers

228 views

### Behaviour of cohomology groups under extension of scalars

Let $\hat{R}\to R$ be a homomorphism of commutative unital rings and let
$\hat{M}$ be an $\hat{R}G$-module for a group $G$. Does the $R$-module isomorphism $$H^n(G,\hat{M}\otimes R)\cong ...

**8**

votes

**2**answers

453 views

### What is an ordered structure, in general?

This is basically a reference request, but the post is going to be relatively long (and a little bit verbose): I apologize in advance for that.
Premise. There are several examples of "ordered ...

**1**

vote

**1**answer

90 views

### Exponential sum estimates similar to the one for $\sum_p (\log p) e(p \alpha)$, but for different sequences

Obtaining a non-trivial estimate for $\sum_p (\log p) e(p \alpha)$ over the minor arcs is one of the estimates required for obtaining the ternary Goldbach for $n$ sufficiently large via the circle ...

**1**

vote

**0**answers

42 views

### “Harmonic oscillator” with $p$-Laplacian

I wonder if there is any literature on the eigenvalue problem for the "$p$-harmonic oscillator" $$-(|u'|^{p-2}u')'(x)+(x^2-\lambda) |u(x)|^{p-2} u(x)=0$$ in $L^p(\mathbb R)$, $p\in(1,\infty)$. Are ...

**2**

votes

**1**answer

50 views

### Complexity of recognizing equivalent translation surfaces

"A translation surface is a union of polygons with pairs of parallel edges identified by translation, up to cut and paste equivalence."
I take that succinct (and not fully precise) definition ...

**1**

vote

**1**answer

86 views

### Characterisation of the square root of the Laplacian as a Dirichlet to Neumann mapping

I am looking for a (classical and/or oldest) reference giving the characterisation of the operator $(-\Delta)^{\frac 12}$ as the Dirichlet to Neumann map $w_y$ where $w$ is the harmonic extension on ...

**2**

votes

**0**answers

204 views

### Why is the normalization of a general fiber the general fiber of the normalization?

Suppose $X \rightarrow Y$ is a map of reduced connected projective schemes of finite type over an algebraically closed field of characteristic 0, where $Y$ is a smooth connected curve. Let $Z ...

**3**

votes

**1**answer

98 views

### Homological characterisation of standardly stratified algebras using Ext

Let A be a finite dimensional algebra and $S_1,S_2,...,S_n$ the simple $A$-modules and $P_1,..,P_n$ the indecomposable projective $A$-modules. For $i=1,...,n$, define the standard module $\Delta_i$ as ...

**2**

votes

**0**answers

104 views

### Integral cohomology of elementary abelian groups

Let $p$ be a prime. I am looking for a reference or a short proof for the fact that cohomology groups $H^i((\mathbb{Z}/p\mathbb{Z})^n,\, \mathbb{Z}),\, i>0,$ have exponent $p$ (i.e., that they are ...

**4**

votes

**0**answers

145 views

### Does the cohomology comparison part of GAGA hold over the reals?

If $k=\mathbb{C}$, $X$ is a projective (or even proper) scheme over $k$ and $F$ a coherent sheaf on $X$, then there is an isomorphism
$$
H^p(X,F)\rightarrow H^p(X^{an}, F^{an})
$$
(and there is also ...

**2**

votes

**2**answers

216 views

### Maximal size of minimal generating set

Let $G$ be a finite group. Denote by $D(G)$ the maximal size of a minimal generating set, (minimal in the sense of inclusion). I vaguely remember seeing recently something on $D(G)$. Can anyone refer ...

**5**

votes

**0**answers

100 views

### When is a Hermitian matrix of the form $g^*g$ for some matrix $g$

I tried asking this question on Math StackExchange and didn't get any replies. I was hoping that maybe someone here could help, sorry for duplicating.
I'm trying to figure out some properties of ...

**5**

votes

**1**answer

264 views

### Good references for K-theory of modular curves?

The title says it. I am looking for a good exposition on the K-theory of the curves $X_{i}(N)$, $Y_{i}(N)$, where $i\in\{0,1\}$.
I have some background in $K$-theory and also some background in ...

**4**

votes

**0**answers

210 views

### The original proof of Szemerédi's Theorem

Nowadays there are plenty of different proofs of the celebrated Szemerédi's Theorem but for historical reasons I would like to read and understand the original proof. The proof is very tricky and, for ...

**2**

votes

**1**answer

53 views

### Bounding exceedance probabilities for correlated normal variables

Suppose $y\sim N(0,\Sigma)$ is an $n-$dimensional vector. I'm interested in an upper bound for $\Pr(\max_{1\leq i\leq n} y_i > k)$ for $k$ large. I know a little about $\Sigma$: ...

**0**

votes

**1**answer

90 views

### Finding many disjoint sub-trees with many leaves

Let $T$ be a rooted binary tree with $L$ leaves, and let $\ell$ be a natural number smaller than $L$. The question is what is the maximal number of disjoint rooted sub-trees with at least $\ell$ ...

**1**

vote

**0**answers

140 views

### Looking for Uehara, Massey article

Not sure if this is the right place to ask this kind of a question. But I cannot find the following article:
Uehara, Hiroshi; Massey, W.S. The Jacobi identity for Whitehead products.
Algebraic ...

**2**

votes

**1**answer

192 views

### Path integral methods

Are there detailed expositions of the path integral methods in (mathematical) physics other than Feynman-Hibbs and Glimm-Jaffe?

**27**

votes

**0**answers

659 views

### Grothendieck's “List of classes of structures”

In Lawvere's article Comments on the Development of Topos Theory, the author writes:
Similarly, Grothendieck and others unerringly recognized which kinds of mathematical structures are 'preserved ...

**0**

votes

**1**answer

155 views

### If $N = {q^k}{n^2}$ is an odd perfect number given in Eulerian form, is $n$ squarefree?

(I have asked a similar question in MSE around a week ago, but did not receive any responses. I have therefore cross-posted it to this site, hoping to get some answers.)
An odd perfect number $N$ is ...

**2**

votes

**1**answer

92 views

### Blaschke Condition for hyperbolic lattices

For $r$, $s$, small positive integers, do the complex numbers on the unit disc (without the hyperbolic metric) corresponding to the vertices of the hyperbolic tiling with Schläfli symbol $\{r,s\}$ ...

**3**

votes

**1**answer

96 views

### Duistermaat-Heckman integral formula on compact manifold with boundary

Let a compact Lie group $G$ acts on a closed symplectic manifold $(M,\omega)$. If the action is Hamiltonian with $\mu$ the moment map, then the integral $$\int_M e^{i\mu (X)+\omega}$$ is equal to the ...

**0**

votes

**0**answers

33 views

### Stochastic dominance for subsets

The subsets of a set $N=\{1,2,\ldots,n\}$ form a lattice, with larger sets being higher up, and a subset $B$ connected to another subset $A=B\cup\{x\}$ (for any $x\not\in B$) higher up by a "pipe". ...

**0**

votes

**0**answers

19 views

### A Statement about a General Property of Negative Cycle Detection Algorithms

in this paper from 1999, the authors Boris Cherkassky and Andrew Goldberg state in the abstract that
"The negative cycle problem is to find a negative length cycle in a network or to prove that ...

**7**

votes

**2**answers

205 views

### The Picard number of the Kummer surface of an abelian surface

Let $A$ be an abelian surface and $\text{Km}(A)$ be the Kummer surface of $A$. If I remember correctly, the Picard number $\rho(\text{Km}(A))$ is equal to $16+\rho(A)$.
Does anyone know any ...

**0**

votes

**0**answers

93 views

### A priori estimate for diffraction problem for linear elliptic PDEs

I am looking for a reference to show how to obtain a priori estimate of the solution $u\in H^1$ and $u\in C^{2,\alpha}$ to the diffraction problem of linear elliptic equation.
I looked at ...

**2**

votes

**2**answers

140 views

### Commutator 2-forms on Lie groups

Let $G$ be a compact Lie group and $\mathfrak g$ its Lie algebra.
For any $f$ in the dual space $\mathfrak g^*$, we can define a skew-symmetric bi-linear form on $\mathfrak g$ by $(A,B)\mapsto ...

**4**

votes

**2**answers

175 views

### How many minimal surfaces do we have if the metric in the target space is not flat

It is trivial that there are a lot of minimal surfaces in the flat $R^3$: for example, for any point, any 2-plane containing this point,
and any two othogonal vectors in this plane, and any ...

**5**

votes

**0**answers

93 views

### Gleason’s Theorem for non-separable Hilbert spaces: On a theorem of Solovay

Gleason’s theorem plays an important role in the foundations of
quantum mechanics. On the positive side it demonstrates how the probabilistic
structure of quantum theory follows from its logical ...

**5**

votes

**1**answer

353 views

### Anything about $\prod_{n \ge 1} (1 + n^{-n})$?

Sophomore's dream is especially the statement that the sum, let me call it $s$, of the (convergent) real series $\sum_{n \ge 1} n^{-n}$ is equal to the (improper) integral $\int_0^1 x^{-x} dx$. A few ...

**4**

votes

**1**answer

160 views

### Reference for a Heat Process in a Wedge

I would like to ask about an explicit suggestion/reference for the following type of heat processes:
Roughly, assume we have a "wedge" $W$ of the following form - a domain in $\mathbb{R}^n$ with a ...

**3**

votes

**2**answers

149 views

### Bellman-Ford for Matching Problems?

I am looking for a simple way of calculating minimum-weight perfect matchings in complete graphs with an even number of vertices.
I know that there are implementations that are based on Edmond's ...

**6**

votes

**1**answer

283 views

### Embedding of real trees into $\ell_1(\Gamma)$

It seems plausible that any real tree or ${\mathbb{R}}$-tree in the sense of the definition in https://en.wikipedia.org/wiki/Real_tree admits an isometric embedding into the Banach space ...

**3**

votes

**0**answers

70 views

### Classification of representation-finite algebras up to stable equivalence of Morita type

assume K is an algebraically closed field.
I wanted to ask if there is a classification of the representation-finite K-algebras up to stable equivalence of Morita type at least for some small numbers ...

**8**

votes

**0**answers

162 views

### A question about strongly compact cardinals

Is the following equiconsistent with the existence of a strongly compact cardinals:
For every $\lambda > \kappa$ there exists a $\lambda$-strongly compact embedding $j: V \to M$ with the ...

**2**

votes

**1**answer

131 views

### Additive functors to abelian groups: “additional structure” and functors induced by “additive pseudo-functors”; references?

Let $\mathcal{A}$ be a small additive category. Consider the category $PreSh(\mathcal{A})$ of all additive functors from $\mathcal{A}^{op}$ into abelian groups; note that this category is abelian and ...