All Questions

I refer to the paper ["Normal Subgroups in the Cremona Group"][1]. In the last paragraph of the proof of proposition 5.13, the author wrote the following: "Assume now that $h\in \text{Bir}(X)$ ...

This is a complement of my previous question about the sequence spaces (I'm afraid, there will be a third part). Let $\rho:[0,+\infty)^{\mathbb{N}}\to[0,+\infty] $ satisfy the following properties: $...

A box contains n balls marked from 1 to n. two balls are drawn in succession with replacement. find the probability that number on the balls are consecutive integers (ignore the order of balls)?

Let $X$ be a (sub)gaussian r.v. on $\mathbb{R}^d$; say $X\sim\mathcal{N}(\mathbf{0},\mathbb{1}_d)$; and let $a\colon\mathbb{R}^d\to [0,1]$ be a function with $\mathbb{E}[a(X)] > 0$. It is not hard ...

Let $K\subset \mathbb{R}^n$ be a (nonempty) compact of covering dimension $\le n-2$. In particular, $K$ does not separate $\mathbb{R}^n$ (even locally). I will equip $M=\mathbb{R}^n-K$ with the ...

Is there always a strictly increasing approximation of the identity in a separable $C^*$-algebra?

I was wondering which $S^n/\Gamma$ can be smoothly embedded into $\mathbb R^{n+1}$, where $\Gamma \subset O(n+1)$ is a finite subgroup. To my knowledge, the case $n \le 3$ is known. It has been proved ...

Let $M$ be an $n$-dimensional open manifold. We assume that there are two compact sets $K_1$ and $K_2$ of $M$ such that $M\backslash K_1$ is diffeomorphic to $N_1 \times (0,1)$ and $M\backslash K_2$ ...

The $T\bar{T}$ deformation is based on the original work of Zamolochikov [1] explored deformations of two-dimensional conformal field theories (CFT) by an operator that is quadratic in the stress-...

Cross posted from MSE. I have a mathematical problem arising from a physics application, which I am sure has been solved before, but I don't know the terminology associated with it. I am looking for ...

Given a connected space, it is easy to tell if there is a connected expansion because maximal connected spaces (those admitting no finer connected topology) have the property that every dense subset ...

For usual graphs on $n$ vertices, a edge-minimal connected graph is nothing but a spanning tree of this graph. It is well-known that any spanning tree has $n-1$ edges. I would like to know whether ...

Consider the equation $$\Delta u+(1+|x|^2)^{l}e^u=0 \: \text{ in } \: \mathbb{R}^2,$$ where $\gamma,l>0$ are constants. Assume $$ \frac{\partial u}{\partial r}>-2(l+2)\frac{r}{1+r^2} \: \hbox{...

I am using the software "Singular" for computing the geometric genus of a space curve, but something is going wrong. Let me consider the following 3-dimensional curve: $$\begin{array}{c}x_3 D(x_1,x_2)...

Fix a category or $\infty$-category $C$ with all small limits. We call a natural transformation $\alpha\colon f\to g$ between two functors $f,g\colon K\to C$ Cartesian, if for every arrow $k\colon a\...