**19**

votes

**2**answers

620 views

+100

### Small quotients of smooth numbers

Assume that $N=2^k$, and let $\{n_1, \dots, n_N\}$ denote the set of square-free positive integers which are generated by the first $k$ primes, sorted in increasing order. Question: what is a good ...

**12**

votes

**1**answer

211 views

+50

### bi-Lipschitz gluing

Let $H$ be the Heisenberg group with
left invariant sub-Riemannian metric and $\varepsilon>0$ is small.
Let us denote by $|x-y|_H$ the distance from $x$ to $y$ in $H$.
I have a bi-Lipschitz ...

**4**

votes

**0**answers

117 views

+100

### Comparison of Constrained Optimization Methods

I am trying to solve a constrained optimization problem using filter methods and came across two papers on the topic that I am having some problems with. The original filter method paper is the ...

**6**

votes

**0**answers

209 views

+150

### A characterization of quadratics similar to an inverse sieve problem

Suppose $\mathscr{A} \subset \mathbb{N}$ enjoys for all large enough cutoffs $X$ the following properties:
$|\mathscr{A} \cap [1,X]| > \sqrt{X}/10$; and
the discriminant $\prod_{\alpha \neq ...

**4**

votes

**0**answers

127 views

+50

### Cartesian square root of a measure preserving action

Let $G \curvearrowright (X,\nu)$ be probability measure preserving action of a countable discrete group. When does there exist a probability measure preserving action $G \curvearrowright (Y,\mu)$ such ...

**1**

vote

**0**answers

108 views

+50

### A path optimisation problem

Consider a graph of $n$ nodes randomly located in $[0,1]^2$. Each node moves following a path randomly chosen from the set of all possible paths. Regard nodes as attackers. A policeman seeks an ...

**21**

votes

**0**answers

277 views

+50

### Isometric embeddings of finite subsets of $\ell_2$ into infinite-dimensional Banach spaces

Question: Does there exist a finite subset $F$ of $\ell_2$ and an infinite-dimensional Banach space $X$ such that $F$ does not admit an isometric embedding into $X$?
There are some results of the ...

**6**

votes

**0**answers

261 views

+100

### “The” natural double complex associated to a principal $G$-bundle?

Let $\pi: P \to M$ be a principal $G$-bundle. We have the associated adjoint bundle $ad(P)= P \times_{ad} \mathfrak g$ whose sections correspond to infinitesimal guage trasformations.
Consider the ...

**1**

vote

**0**answers

84 views

+50

### Shape-related vector fields

Assume that $M$ is a surface in $\mathbb{R}^{3}$. We denote its shape operator by $S$. A vector field $X$ is shape related to $Y$ if $S(X)=Y$.
(of course it is not an equivalent relation).
...