This question may be a simply problem for experts. Let $G$ be a connected compact Lie group and $T$ be its maximal torus. Let $\mathfrak{g}$ and $\mathfrak{t}$ be the corresponding …

What is the definition of an analytic mapping between two Banach spaces? This is a problem I ran into when solving an integral equation. One of the related coefficients is represen …

Let $f(x,y)=0$ and $g(x,y)=0$ be bivariate polynomial equations where the polynomials have the same degree, say, $N\geq 3$. Furthermore, both of them have the same terms but differ …

I hesitate to ask a question like this, but I really have tried finding answers to this question on my own and seemed to come up short. I readily admit this is due to my ignorance …

Hi, I am a student teaching myself basic abstract algebra (group theory right now). I am working through Lang's "Undergraduate Algebra" together with Artin's "Algebra," and from La …

Physicists said that for a given Calabi-Yau 3-fold with the topological Euler number e, |e|/2 corresponds to the number of gdnerations of the elementary particles. My question i …

Let $p_1, p_2, \ldots$, be the power sum symmetric functions. Let $p_n^* = n \frac{\partial}{\partial p_n}$. Then $$ p_n^* p_m - p_m p_n^* = \delta_{m, n} 1. $$ Where could I find …

If $X,Y$ are vector fields and $\def\Fl{\operatorname{Fl}}\Fl^X_t$ and $\Fl^Y_t$ their local flows, let $[\Fl^X_t,\Fl^Y_t]:= \Fl^Y_{-t}\Fl^X_{-t}\Fl^Y_t\Fl^X_t$ denote the group co …

I have an array of 150 coordinates with which to provide the highest probability "center". How would you solve for the center of a cluster of data points? Here's a map an example …

If so, can you show me how? Here's Rossmo's Formula on Wikipedia. I tried embedding images of the formula but I'm new here and that's not allowed. If you're not familiar with th …

Let $H$ be a separable infinite dimensional Hilbert space. Denote by $\mathcal{B}(H)$ the space of bounded operators on $H$, and $\mathcal{K}(H)$ the ideal of compact operators. Wh …

I'm intererested in open surjective geometric morphisms induced by fibrations of sites $S\to T$ a la Moerdijk, but as a warm-up, let's consider the case $S \to \ast$. In the case t …

My friend and I are attempting to learn about spectral sequences at the moment, and we've noticed a common theme in books about spectral sequences: no one seems to like talking abo …

My earlier related question http://mathoverflow.net/questions/134156/lower-degree-elements-in-an-algebraic-number-field has been given a clean answer for the first part. My prese …

Let C_n={0,1}^n be the hypercube and denote by G(N,p) the Erdos-Renyi random graph (edges appear independently with probability p). Assume that N=2^n. Could one pin down p=p(n) suc …