It happens a lot of times that when one defines a new object (ring, module, space, group, algebra, morphism, whatever) out of given data one first chooses some additional structure …

$\min_{\beta}\beta^{T} A \beta$ $s.t. \ \beta^{T} C \beta=1\ and\ \beta\geqslant 0$ Here $A,C\in \mathbb{R}^{M\times M}$, $\beta \in \mathbb{R}^{M}$ I saw in one paper saying t …

I have never studied any measure theory, so apologise in advance, if my question is easy: Let $X$ be a measure space. How can I decide whether $L^2(X)$ is separable? In reality, …

EDIT: André Henriques has commented below that the correct separability condition is not weak-* separability as I have written below, but separability of the predual. This post c …

Composite numbers $n$ such that $A179382((n+1)/2)=(n-1)/(2^c)$ for some $c > 0$. I named this numbers "antiprimes". $a(1-5):92673, 143713, 3579553, 4110529, 28688897$ $a(6) > 68 …

I stumbled on the following simple matrix norm, which I haven't seen elsewhere. I wonder if it is well known, has a name, and has been studied elsewhere. The definition of this nor …

Hans Hahn is often credited with creating the modern theory of ordered algebraic systems with the publication of his paper Über die nichtarchimedischen Grössensysteme (Sitzungsber …

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- …

Dear mathoverflowers. Just wondering if the following inequality is true. For all $ p >1$ there is some $C$ such that $ | |x+1|^p-|y+1|^p -p(x-y)| \le C ( |x|+|y| + |x|^{p-1} …

I came across this problem when trying to solve the following integral equations arising in direct scattering: $$ \begin{align} n_{11}(x,z)=1+\int_{-\infty}^xe^{-izy}u(y)n_{21}(y,z …

Hi Guys, We have a d-regular bipartite Graph $G = (X,Y,E)$ with $|X| = |Y| = n$ and $|E| = nd$. i want to know a Upper Bound of the number of Matching Thankx

Let $K$ be a degree $n$ extension of ${\mathbb Q}$ with ring of integers $R$. An order in $K$ is a subring with identity of $R$ which is a ${\mathbb Z}$-module of rank $n$. Quest …

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 $E$ …

This question comes from the same place as my other one. In reading SGA 4 1/2, but not SGA4 itself (at least, not the obvious sections xv + xvi), one can learn about the "cospecia …

Given an action of a group $G$ on a topological space $X$, the associated homotopy quotient is $$X_G := (EG \times X)/G,$$ where $EG$ is the total space of a universal principal $G …