## Tagged Questions

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### How to combine correlated signals !?

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) …
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### Finitely generated monoids are finitely presented?

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 $P_1\rightrightarrows P_0\rightarrow M$ …
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### What are the main structure theorems on finitely generated commutative monoids?

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 …
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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 …
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### Closed geodesic loops around points in compact manifolds

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 …
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### An integral with Gamma functions (Part 2)

I was wondering if there is a generalization of the integral discussed here to a case like, \int \frac{d^dq}{q^{\nu_1}\vert \vec{q} \pm \vec{k}_1\vert ^{\nu_2}\ver …
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### How do I find abelian subcategories of periodic triangulated categories?

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, …
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### Question about the nullstellensatz for projective schemes

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. …
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### Connected groupoids and action groupoids

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 …
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### A duality on partial permutations

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 …
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### How many orders of infinity are there?

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 …
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### Why is Set, and not Rel, so ubiquitous in mathematics?

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 …
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### Octonions and the Fano plane.

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 …
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### DAG graph and topologic order question

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 …
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### Is a Cauchy principal value invariant under a “change of variables”?

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 …
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### Importance of separability vs. second-countability

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 …
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### decomposition of the injective hull of a torsion free module

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?
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### exceptional divisor on a smooth surface

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 …
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### Under exactly what (extra) conditions (if any) is a connected Hausdorff manifold with a Riemannian metric a metric space?

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 …
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### Strong convergence in the Bochner space L^p([0,T],X)

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 …
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### Vector field pull back from embedding

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 …
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### Good uses of Siegel zeros?

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" …
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### Geodesics on a Grassmannian

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 …
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### Fundamental cycle separators and crossing numbers

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 …
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### How can I randomly draw an ensemble of unit vectors that sum to zero?

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 …
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### Gradient estimates for subsolutions of elliptic equations

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 $|\nabla u|$ …
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### Volume growth of covers and growth of deck-transformation groups

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 …