Consider the “product” $\gamma = \alpha \times \beta$ of two binary strings $\alpha$, $\beta$ $\in \lbrace 0,1\rbrace^+$ which one gets by replacing every 1 in $\beta$ …

Let $V:=\oplus_{j\in\mathbb{Z}}V_j$ be a graded $\mathbb{F}$-vector space over the field $\mathbb{F}$. The graded tensor product of graded vector spaces is given by $V \otimes W: …

Hi, I was wondering about the following question: if you have a faithful action of a group G on the real line R by orientation-preserving homeomorphisms, it is easy to construct …

Suppose $Y$ is a pair of pants with a hyperbolic structure and $\gamma_i; i = 1, 2, 3$ are the geodesic boundaries of length $l_i; i=1, 2, 3$ respectively. Now consider a essential …

Given an invertible matrix $A \in \mathbb{R}^{n \times n}$, and index set $\langle n\rangle = \{ 1, \dots, n \}$, and the submatrix $A(\alpha)$ with the columns and rows of $A$ wit …

Let $X$ ad $Y$ be (noetherian) schemes and let $\mathcal I \subseteq \mathcal O_Y$ be a sheaf of ideals on $Y$. Let $f \colon X \to Y$ be a morphism of schemes. In general the shea …

Let $(X,\mathcal{O}_X)$ be a contractible complex analytic space. Suppose that $\mathcal{F}$ is a coherent sheaf of $\mathcal{O}_X$-modules. Can we invoke the fact that $X$ is cont …

Let $p=2^a-1>7$ be a Mersenne prime and so $a$ is an odd prime. Can we say that $(p^2+1)/2$ is not equal to the square of a prime number? Many thanks for your help BHZ

Is it true that for a given nonnegative number, there exists a measure-theoretical entropy value (supremum of entropies of all partitions under a measure-preserving transformation) …

Suppose I have the symmetric tridiagonal matrix: $ \begin{pmatrix} a & b_{1} & 0 & ... & 0 \\ b_{1} & a & b_{2} & & ... \\ 0 & b_{2} & a …

I wanna prove following equation $ \sum_{i=1}^n \prod_{k=1,k\neq i}^n \prod_{j=1,j\neq k}^{n+1}(x_j - x_k) = -\prod_{i=1}^n \prod_{j=1,j\neq i}^n (x_j - x_i) $ I have verified sev …

In section 5 in "The entropy formula for the Ricci flow and its geometric applications" Grisha Perelman has written: Fix a closed manifold $M$ with a probability measure $m$, and …

Iwaniec and Kowalski, in their famous book Analytic Number Theory states a strong form of the effective Chebotarev density theorem page 143, and prove it assuming both GRH for Arti …

I am interested in finding a canonical general expression for the area of a spherical polygon in $\mathbb{S}^2$ knowing the side lengths of the polygon and a bound on the internal …

Although I know that "ZFC & there exists a measurable cardinal" and "ZFC & there exists a real-valued measurable cardinal" are equiconsistent with one another, I am not sur …