# All Questions

140,634
questions

0
votes

0
answers

5
views

### confusing limits

calculate this limit when x tend to infinity :
f(x) = (x+5)^(1+1/x) - x^(1+1/x+5)
I used Laurent series at infinity but in the middle I confuesd and can not solve it but I am sure the correct answer ...

0
votes

0
answers

12
views

### What is the regularized value of the numerocity of primes?

Let numerocity of a subset $S$ of integers to be a sum $\sum_{k=-\infty}^\infty p(k)$ where $p(k)$ is the indicator function of the set $S$. We also can write it as $p(0)+\sum_{k=1}^\infty (p(k)+p(-k))...

1
vote

0
answers

13
views

### A Lipschitzian's condition for the measure of nonconvexity

I'm actually working on the measure of nonconvexity and its application. Especially, the Eisenfeld–Lakshmikantham MNC defined - in a Banach space - by:
$$\alpha(A)=\sup_{b\in\overline{\operatorname{...

0
votes

0
answers

67
views

### Why is $\mathrm{SO}(4)$ not a simple Lie group?

$\DeclareMathOperator\SO{SO}$I'm not asking for a proof but for some hint that might be helpful to understand this "anomaly" in 4 dimensions. I'm aware of the parallelism with the $A_4$ ...

0
votes

0
answers

44
views

### Elements of $ K(x,y) $ in $ K[[x^{\pm {1}},y^{\pm {1}}]] $

Let $ K(x,y) $ be fraction field of $ K[x,y] $. Now take an arbitrary element $ f/g \in K(x,y) $ where $ f, g \in K[x,y] $. Suppose $ f = \sum_{m \in {\mathbb{Z}}^{2}} y^{m_{1}} z^{m_{2}} $ and $ g = ...

1
vote

1
answer

25
views

### About Palm distribution

Can someone explain the Palm distribution? Or provide some information about Palm distribution. The
article called 《A tutorial on Palm distributions for spatial point processes》 is hard to understand.

0
votes

0
answers

9
views

### First order condition HJB only one solution in R for my domain

I am working on a macroeconomic model and I need to derive a first order condition from a HJB equation. Simplified, I can write the FOC as $ac+bc^{1/2}-1 = 0$ and want to solve for $c$. I have $a>0$...

-1
votes

0
answers

26
views

### On size of product of integer and inverse in a residue class?

$p$ is a large prime. Let $|a|=\min(a,p-a)$.
Given a small $\epsilon>0$ and a real $t>1$ how many integers $a$ are there in $\{1,2,\dots,p-1\}$ such that $|a|>p^{1/t}$ and $|a||b|<p^{1+\...

4
votes

0
answers

40
views

### Is there a connected Hausdorff anticompact space that is countably infinite?

Cross-posted from MSE.
Following Bankston - The total negation of a topological property, a topological space is called anticompact if all its compact subsets are finite. The linked MSE post above ...

4
votes

0
answers

79
views

### Intuition for Luna's Étale Slice Theorem

I am trying to understand the intuition for Luna's Étale Slice Theorem in the affine setting over $\mathbb{C}$.
Here is the setup. Let $X$ be an affine algebraic variety and $G$ a reductive group ...

1
vote

0
answers

41
views

### Resolving complexes of coherent analytic sheaves

Background
Throughout, let $X$ be a smooth complex manifold.
It is a classical fact that a coherent analytic sheaf admits a local resolution by locally free sheaves (also known as a local syzygy). ...

2
votes

0
answers

34
views

### Approximation by gaussian mollification in Sobolev spaces

I have been trying to find a good estimate on the constant in the inequality (in dimension $d=3$ to simplify)
$$\label{0}\tag{0}
\|(1-e^{t\Delta})f\|_{L^{5/3}(\Bbb R^3)} \leq C_0\,t^{2/5}\, \|\nabla \...

-1
votes

0
answers

20
views

### Is there an equation for the space bounded by multiple curves made of lines

https://www.desmos.com/calculator/jax0qssltb
Basically, you can make an approximation for a curve by drawing many lines segments, in my problem, my curve approximation is given by the equation
$y = (-\...

2
votes

0
answers

50
views

### Manifestation of Hecke operator on the category of abelian varieties (or motives)

If we are given some postivie integer $N$ and a prime $p$, then we have the Hecke operator $T_p$ on modular forms, which is a cohomological manifestation of the Hecke correspondence
$$X_0(N)\leftarrow ...

0
votes

0
answers

49
views

### Approximate range of Radon-Nikodym derivative in a dynamical system

Suppose $(X, G, \Omega, \mu)$ is a dynamical system where $(X, \Omega, \mu)$ is a Borel measure space and $G$ is acting on $X$ such that each group action $x\mapsto g\cdot x$ defines a measurable ...