Let $K$ be a local field with mix char, $k$ residue field. We have an exact sequence $0 \longrightarrow I \longrightarrow G_{K} \longrightarrow G_{k} \longrightarrow 0$ Then we o …

Assume that $f$ is (Euclidean) $L-$biLipchitz mapping of the unit circle onto a triangle $\Delta(A,B,C)$. Can we find a $10000 L$ bi-lipchitz extension of $f$ onto the whole plane. …

For $n=1$ the answer is "yes." -- A group is abelian iff its generators commute. Let $G_0=G$ be a group and let it be generated by $X_0=X$. For each $n>0$ let $G_n=[G_{n-1},G_{n- …

I have the following, probably very elementary question: Let $Cl^{p,q}$ be the Clifford algebra on generators $e_i$, $i=1, \ldots, p+q$ with $e_i e_j = -e_j e_i$ and $e_{i}^{2}=-1$ …

It is commonplace to consider applications of mathematics to other fields, especially the exact sciences. But what I would like to know about is the converse topic, namely: Wha …

Let $p$ be a prime integer, and let $(\mathbb Z/p\mathbb Z)^*$ be the set of non-zero elements of $\mathbb Z/p \mathbb Z$. Denote by $S((\mathbb Z/p \mathbb Z)^*)$ the group of per …

Hello, everyone, I want to resolve one optimal problem, with the following probability inequality constraint. $Pr(h^H(W_1 - W_2 -W_3 -U)h \geq \sigma^2) \leq \rho$ where $h \sim …

Why do knot cobordisms result in functoriality with respect to knot homologies so often?

Ground field $\Bbb{C}$. Algebraic category. Elliptic surfaces are those surfaces endowed with a morphism onto some smooth curve, with generic fiber an elliptic curve. Suppose $E$ …

I have a convex optimization problem of finding a function Q(x,y) as below: Minimize $\int{k(x,y)Q(x,y)dxdy}$ subject to a list of constraints which are not relevant to the questi …

The following problem arises in the analysis of Bloom filters. Consider $m$ bins and $N=nk$ balls placed uniformly at random into the bins. A query chooses $k$ bins uniformly at …

I have four solutions which are termed: A1, A2, A3, A4. These are actually the results of a searching algorithm. I know that A1 is the best solution, A2 is next to A1, A3 is next t …

Let $R$ be a ring, $\Sigma$ be a multiplicatively closed subset of $R$. $M$ is an $R$-module. Denote the injective hull of $M$ by $E(M)$. $M$ is $\Sigma$-torsion if for any $m$ …

A knot in S^3 is small if its complement does not contain a closed incompressible surface. Is it a generic property for knots, meaning that among all knots with less than $n$ cross …

In algebraic geometry weighted projective spaces (WPS) are very popular ! In algebraic topology , WLS have been (cohomologically at least) studied. Roughly speaking , a WPS is a …