Hi everybody There are 11 signals: S_main : The original signal S1 ~ S10 : 10 signals that are correlated to S_main with different correlation coefficients (coeff1 ~ coeff10) …

I saw in the answer of this post that any finitely generated monoids are finitely presented in the sense that there is a coequalizer diagram $P_1\rightrightarrows P_0\rightarrow M$ …

I should read J. C. Rosales and P. A. García-Sánchez's book Finitely Generated Commutative Monoids and L. Redei's book The Theory of Finitely Generated Commutative Semigroups. I h …

Are there tetrahedra which can be subdivided into three parts similar to the original? I believe this would require splitting one face into three parts. I know some types of tetrah …

Since in a compact Riemannian manifold $M$ the only totally convex subset is the whole manifold itself, see http://mathoverflow.net/questions/106169/closed-manifold-has-no-nontrivi …

If we let $K$ be a number field, thank to the fact that we can extend it integer ring to an UFD where the group of units is finitely generated, we can show that $K^\ast\cong K^\as …

Building off of Qiaochu's comment on my answer to a previous mathoverflow question, I would like to know: can the Recursion Theorem, $$\forall e\exists k[\Phi_e\text{ is total }\im …

Let $G$ asimply connected group over $k=\bar{k}$, $B$ a Borel subgroup and $I$ the corresponding Iwahori in G(k[[t]]), $T$ a maximal torus and $K=G(k[[t]])$. Let $\lambda\in X_{*} …

I was wondering if there is a generalization of the integral discussed here to a case like, \begin{equation}\int \frac{d^dq}{q^{\nu_1}\vert \vec{q} \pm \vec{k}_1\vert ^{\nu_2}\ver …

If $T$ is a triangulated category, then the formalism of $t$-structures gives a way to find abelian subcategories inside. You're supposed to find two strictly full subcategories, …

Yeasterday I asked a question on math stackexchange which simplifies to the following: Assume that $G$ is a graded ring and $A \subseteq G$ is a homogeneous radical ideal. …

It is written in Wikipedia http://en.wikipedia.org/wiki/Groupoid, that any connected groupoid $A\rightrightarrows X$ is isomorphic to an action groupoid $G\ltimes X$ coming from a …

A partial permutation matrix $\pi$ is one with at most one 1 in any row and column (the rest 0s). Given one, we can cross out to the East and South (but not Southeast) of each 1. S …

Define a growth function to be a monotone increasing function $F: {\bf N} \to {\bf N}$, thus for instance $n \mapsto n^2$, $n \mapsto 2^n$, $n \mapsto 2^{2^n}$ are examples of grow …

The concept of relation in the history of mathematics, either consciously or not, has always been important: think of order relations or equivalence relations. Why was there the n …

Does the Fano plane mnemonic for octonion multiplication have any deeper meaning? http://upload.wikimedia.org/wikipedia/commons/2/2d/FanoPlane.svg The symmetry group of the Fano …

The action of a group $G$ on a topological space $X$ can be viewed as a functor $F: G \to \mathcal{Top}$ with $F(*)=X$. (Here I'm viewing a group as a category with one object, $ * …

I find myself unable to solve question 24.1 of T. Jech's Set Theory: If $\beta<\omega_1$ and if $2^{\aleph_{\alpha}}\leq\aleph_{\alpha+\beta}$ for a stationary set of $\ …

I need to find the maximum number of topological sorts on Direct Acyclic Graph of N-order. I've checked by running Depth first search algorithm on various Direct Acyclic graphs, an …

Let $f \in C^{\gamma}_c(\mathbb{R}) $. Let $K:\mathbb{R}^n \backslash {\vec{0}} \rightarrow \mathbb{R}^n$ be a singular integral kernel with the following properties: 1) K smooth …

For me second-countability always felt like to be the more important and fundamental concept from general topology than separability. I wonder whether there are any points which ca …

Let R be any ring and let A be a torsion free R-module. when would we be able to decompose the injective hull E(A) of A, i.e. when can we write E(A) as a sum E_i, i in I?

Let $D=\sum d_iD_i$ be an exceptional divisor on a smooth projective surface $X$. i.e., the intersection matrix $(D_i.D_j)$ is negative definite. I have 2 stupid questions. Fix …

The setting is that manifolds are Banach manifolds, not necessarily finite dimensional. No other assumption is made about the topology of the manifold. In particular, it is not ass …

Dear mathoverflowers, I have a question concerning the strong convergence in $L^p([0,T],X)$. Let $X_1,X$ be two Banach spaces such that $X_1\subset X$ with compact embedding. Let …

Let $M$ and $N$ be finite dimensional smooth manifolds. A smooth map $f: M \to N$ is an embedding if and only if there is an open neighborhood $U$ of $f(M)$ in $N$ and a smooth ma …

The short version of my question goes: What is known to follow from the existence of Siegel zeros? A longer version to give an idea of what I have in mind: The "expectional zeros" …

Where can I find the most direct and simplest presentation of what geodesics on a (complex) Grassmannian look like? I know how to do it from scratch, but, if I want to provide a re …

Hi there, Consider a planar graph $G$ of radius $r$ and order $n$. Lipton and Tarjan proved that $G$ contains a cycle $C$ of length at most $2r+1$ whose removal leaves two connect …

Inspired by this question, I would like to determine the probability that a random knot of 6 unit sticks is a trefoil. This naturally leads to the following question: Is there a …

Let $M$ be a Riemannian manifold. Assume $u \in C^\infty(M)$ such that $u>0$ and $\Delta u + \lambda u = 0,$ where $\lambda \geq 0$. There is a poinwise estimate for $|\nabla u|$ …

This may be a stupid question, but I understand the proof of the theorem that states that for any differentiable $(n-1)$ form $\omega$ on a compact $n$ dimensional manifold in $R^{ …

I have a unit cube, and operating in the continuum limit (i.e. not on a lattice), I sequentially place spheres of some radius $r$ inside the cube until a filled volume "jamming lim …

This is a follow-up to a recent question by Allen Knutson here, involving a special type of tensor product multiplicity for a simple Lie algebra $\mathfrak{g}$ over $\mathbb{C}$ (o …

The motivation to this question can be found in http://mathoverflow.net/questions/103846/why-are-galois-representations-so-important-in-number-theory My question is concerned wi …

Where in literature can one find a construction of Steenrod reduced powers (for an odd $p$) that (1) works for the singular cohomology of arbitrary topological spaces (or, more …

Hi. I was wondering if someone could explain why we call affine Lie algebras affine. Thanks! Oliver

Let $A \to B$ be a finitely generated homomorphism between two commutative noetherian rings. As far as I understand, in various generalizations of this situation, such a map is ca …

Dear all, I stumbled on this question due to an application in physics, but I find it hard to find useful references for it. I looked into literature on projective geometry and po …

Given an undirected graph G (can be cyclic) with the promise that all its faces have 3 sides is it possible to find the minimum distace between a source and any other vertices in L …

I am writing a summary on a work on Fluid Dynamics that develops irrotational flow states that appear to interact amongst each other according to the equations of Electromagnetism …

I am trying to write a computer program which computes the action of the exponential of a differential operator on a function, for any given differential operator. Examples: $\ex …

It is well-known that if $\widetilde M\to M$ is a Galois cover of a compact Riemannian manifold $M$ with deck-transformation group $G$, then the growth of $G$ equals the volume gro …

This question deals with the gamma factor of a primitive function of the Selberg class. Writing the functional equation of such a function $F$ as $\Phi(s)=\overline{\Phi(\overline{ …

I would like to understand the accounts of P. Gabriel (link text), pag 365, when he shows that the composition of this category is well defined. Definition: Given a Serre subcateg …

Some math institutes offer programs in which a small number of researchers are enabled to meet at the institute for a week or more. A list seemed as if it could be useful.

Let $F(\alpha) := \mathbb{P}(\tilde{\alpha} \leq \alpha)$ be an arbitrary, strictly increasing and twice differentiable CDF that is defined on the interval $[0, \overline{\alpha}]$ …

This problem cropped up in the context of scale-insensitive methods for generating random variables. Let $X=R^n \cup \{\infty\}$. Suppose we consider a set of transforms $\cal{T} …

I encountered this quantity in my calculations and tried to simplify it. Approximate numeric calculations suggested it could be zero (more precisely, it is certainly less than $10^ …

How can we prove that if $\int_U{f}=0$,then the homogeneous Neumann problem $\Delta u=f$on U,and $\frac{\partial u}{\partial n}=0$ on $\partial U$ has a weak solution in $H^1(U)$? …