All Questions

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 ...

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))...

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{...

$\DeclareMathOperator\SO{SO}$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 $A_4$ ...

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 = ...

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.

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 $a>0$...

$p$ 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+\...

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 ...

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 ...

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). ...

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 \...

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 = (-\...

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 ...

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 ...