$A$ is a non-negative, integer, irreducible, $m$ by $m$ matrix. It is well known (Perron-Frobenius) that $A$ has a positive eigen value (denote it by $\lambda$) with a positive eig …

Yitang Zhang recently published a new attack on the Twin Primes Conjecture. Quoting Andre Granville: “The big experts in the field had already tried to make this approach w …

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 have posted the following question also here a longer time ago, but due to no answers I thought it might fit better to MO. Let $(\Omega,\mathcal F)$ be a measurable space and $\ …

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 …

I recently started reading about hyperbolic dynamics in the notes of L. Wen, http://www6.cityu.edu.hk/rcms/publications/ln5.pdf and in this (page 8) there is the following s …

There was a previous post on the correspondence between Riemann surfaces and algebraic geometry. I want to ask a related but more detailed question. BACKGROUND: Engelbrekt gave a …

In A Generalization of Brouwer's Fixed Point Theorem by Shizuo Kakutani, he defined $S^{(n)}$ be the $n$-th barycentric simplicial subdivision of $S$. In which $S$ is an $r$-dimens …

Recall that Kobayashi metric is defined on any complex manifold $M$. This is a pseudo-metric according to which a tangent vector $v$ at $P$ has length at most $1$ if there is hol …

[edited!] Given a group $\pi$ and an integer $n>1$, what are examples of Eilenberg-Maclane spaces $K(\pi, n)$ that can be constructed as "known" manifolds? (or if not a manifold …

Let's define a net and subnet in this way: A net is a any function of the form $n:(P,\le)\to X$ where $(P,\le)$ is a (preordered) directed set. A net $m:(P',\le)\to X$ is a subne …

Let $G$ be a commutative algebraic group stack over $\mathbb{F}_q$ (I don't really care about the precise definition: I'm secretly thinking about the Picard stack of a projective c …

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 …

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 …

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 …