Let $\alpha$ be any positive irrational and $\beta$ be any positive real. We have the following results. H. Weyl (1909): The fractional part of the sequence $\alpha n$ is equidist …

$\underline{\textbf{Embedded associated prime}}$ I am reading the book "Joins and Intersections". In the proof of Rees theorem I have some doubt. Let $\mathbf M$ be a finitely ge …

Let $d_r$ be a divergent series of positive terms and let $s_r = \sum_{i=1}^{r}d_r$. We are interested in the sequence of numbers $S_{d_r} = s_1, s_2, \ldots$. For example if $d_r …

Let $\mathcal{C}$ is a grothendiect category and consider all of what follows in $\mathcal{C}$. Let $${\varepsilon_i: 0\to A_i \to B_i \to C_i\to 0\ ,\ \phi_i^j}$$ be a direct sy …

I'm wondering if a compact set $A\subset\mathbb{C}$ satisfying the properties that • $A$ and its complement have finitely many connected components • every connected component of …

Suppose we have two topological groups $G$, $H$ and a $G$-principal bundle $(p:P \to M;G)$ over a manifold $M$ and $H$ is acting on $P$ (from the left or right. Whatever fits bett …

Many years ago, when I was still a high school student, I came up with a certain first-order axiomatization of PA over the signature (+, x, ≤). Out of nostalgia, I've decided t …

What is the proper terminology for a complex of sheaves $\mathcal F^\bullet$ whose homology sheaves $\mathcal H^i\mathcal F^\bullet$ vanish for $i\ne 0$?

On this paper http://www.math.cornell.edu/~kbrown/6310/computation.pdf I read : This makes it easier for you to draw Schreier graphs as you read, which I encourage you to do. …

I would like to understand the accounts of P. Gabriel (http://archive.numdam.org/ARCHIVE/BSMF/BSMF_1962_90/BSMF_1962_90_323_0/BSMF_1962_90_323_0.pdf), pag 365, when he shows that t …

Hi, I have a random variable V with probability density g(V) and a sigmoid, or logistic, function Y=S(V). I'd like to calculate a closed-form expression for the expected value of t …

I develop an application in which i constantly get samples of heart pulse. I defined an interval of t seconds. In each t seconds I have n samples. In every interval, I want to c …

Hello, I am en engineer working in radar research. I came accross a problem I cannot seem to find math literature on it. I can ask it in two different ways. Perhaps depending on …

Can anyone cite an example of a mathematics paper that has been retracted? It is said that on the order of 100,000 new theorems enter the mathematics literature every year. For a …

maximal ideal generated by idempotent element why is noetherian ring ?