# All Questions

**0**

votes

**0**answers

267 views

+50

### What is the Fourier transform of this function?

Consider the function
$$
f(x_1,x_2)=|x_1x_2|^{-\alpha/2}\int_{\mathbb{R}} \frac{e^{it(x_1+u)}-1}{i(x_1+u)} \frac{e^{it(x_2-u)}-1}{i(x_2-u)} |u|^{-\beta}du.
$$
It is known that $f(x_1,x_2)\in ...

**14**

votes

**0**answers

267 views

+50

### Monotone embedding of complete binary tree in hypercube

Embedding different graphs, especially binary trees, in the hypercube has a huge literature. However, I could not find anything if we restrict the embedding to be monotone. So I would like to ...

**2**

votes

**0**answers

101 views

+50

### Probabilities involving Beurling density

I am interested in calculating probabilities involving Beurling densities. Since it's likely probabilists are not familiar with the definitions, I give them below.
Definitions.
A metric space is ...

**3**

votes

**1**answer

293 views

+50

### Tannakian fundamental group of two explicit tensor categories

Let $K/k$ is a field extension and $G$ an affine group scheme over $K$. What are the Tannakian fundamental groups of these two $k$-tensor categories (with trivial fiber functors over $k$):
1. The ...

**0**

votes

**0**answers

106 views

+50

### The geometry of the holomorph of a Lie group

Every Lie group $G$ is naturally contained in its holomorph Hol($G$) = $G \rtimes $ Aut($G$)
Is Hol$(G)$ always a Lie group?
If the answer is yes our main questions:
1.For a left ...

**0**

votes

**0**answers

164 views

+50

### A (possible) equivalent relation on the space of vector bundles

Edit: According to the essential comment of Alex Degtyarev, we revise the question as follows;
Assume that $\alpha$ and $\beta$ are two oriention preserving automorphism of Lie groups $O(n)$ and ...

**1**

vote

**0**answers

140 views

+50

### Killing vector fields on sphere and nodal sets

Let $u$ be a smooth function on $S^2$ such that $\int_{S^2} ux_j =0$, for $j=1,2,3$. Does there exist a killing vector field $V$ on $S^2$ such that the nodal line of $\varphi=V(u)$ ($\{x\in S^2: ...

**4**

votes

**1**answer

142 views

+100

### Induced subgraphs of small strongly regular graphs

Consider a strongly regular graph $G$ with parameters $(76,30,8,14).$ Hoffman's bound tells us that $\overline{G}$ has an independent set of size at most $4$ and its not hard to see there are indeed ...

**9**

votes

**1**answer

263 views

+50

### On the boundary of the twindragon

Let $\mathcal T$ be the famous twindragon, i.e.,
$$
\mathcal T=\left\{\sum_{n=0}^\infty a_n\left(\frac{1+i}2\right)^n : a_n\in\{0,1\}\right\}.
$$
Then, as is well known, $\mathcal T$ has a ...

**1**

vote

**0**answers

95 views

+50

### Reference : Special case of Banach-valued function integration by parts

Let $u \in L^p (0,T; L^1(\Omega))$ with $\partial_t u \in L^p(0,T; L^1(\Omega))$ and $v \in L^q (0,T; L^\infty(\Omega))$ with $\partial_t u \in L^q(0,T; L^\infty(\Omega))$ (with $1/p+1/q=1$ and $p \in ...

**6**

votes

**0**answers

139 views

+500

### Does a semistable curve descend to a regular base?

Let $f\colon X \rightarrow S$ be a semistable curve of genus $g \ge 0$. Being a semistable curve means that $f$ is a morphism of schemes such that
$f$ is proper, flat, and of finite presentation;
...

**2**

votes

**1**answer

293 views

+50

### Bounds for constructing $n!$ with additions, subtractions, and multiplications starting from $1$

Found this on Complexity Zoo warning expired certificate
check NP Over The Complex Numbers.
[BCS+97] show the following striking result. For a positive integer $n$, let $t(n)$ denote the minimum ...

**2**

votes

**0**answers

140 views

+50

### Reference request for the relation of Ext groups and bar construction

I need a reference for the description of Ext groups in mixed categories (i.e. abelian categories with a weight filtration and semisimple graded quotients) by using the bar complex, as mentioned in ...

**10**

votes

**1**answer

263 views

+150

### Open problems in Berkovich geometry

I would like to know if there is a state of the art recent reference on non-archimedean analytic spaces mentioning/listing open problems, conjectures, unresolved questions in the theory (*). I have ...