$\newcommand{\RR}{\mathbb{R}}$The present question arises from some confusion on my part regarding the precise statement of the strong Whitney embedding theorem for non-compact man …

Lets define new differintegral formula as $$\mathbb{D}^s_xf(x)= \sum_{m=0}^{\infty} \binom {s}m \sum_{k=0}^m\binom mk(-1)^{m-k}f^{(k)}(x)$$ or, equivalently, $$\mathbb{D}^s_xf(x …

Consider the following function repeatedly applied to a rational $r = a/b$ in lowest terms: $f(a/b) = (a b) / (a + b - 1)$. So, $f(2/3) = 6/4 = 3/2$. $f(3/2) = 6/4 = 3/2$. I am wo …

Let $X$ be a smooth and projective variety over a field of characteristic zero. Let $Y$ be a normal variety, with finite quotient singularities (an orbifold!) and let $\pi: Y \to X …

I have seen a discussion about Bourbaki’s usage of categories before. So let me ask a different question: why did he not use universal algebra? Well, universal algebra is not much …

The theorem of Artin and Brauer of the title are the famous theorem in the theory of representation of finite groups. For example, Artin's theorem is the statement that for every …

QUESTION They had plenty of time to adopt the theory of categories. They had Eilenberg, then Cartan, then Grothendieck. Did they feel that they have established their approach alr …

Hello everyone, I already asked this question on the TCS Stack Exchange, but it has not been resolved yet. Maybe readers of this forum will have other ideas or information, althou …

Suppose we have polynomials $f$ and $g$ over a field $F$ and for some $a\in F$ we know $(x-a)^m$ divides $f\circ g$, i.e. $f\circ g$ has a zero of order $m$ at $a$. Then we have th …

Can one define Laplacian for a diffeomorphism from a Riemannian manifold to another Riemannian manifold? If yes, what kind of object is that?

Consider the class of rooted trees and suppose I have at my disposal a lowest common ancestor (LCA) operator given by $$ \textrm{lca}(u,v) = \text{the lowest common ancestor of $u$ …

A standard Carleman-type estimate is of the form $$ \sum_{|\alpha|<m}{\tau^{2(m-|\alpha|-1)}\int{|D^{\alpha}u|^{2}e^{2\tau\phi}}dx}\leq K\int{|Pu|^{2}e^{2\tau\phi}dx},\quad u\in …

Let $(X,||\cdot||_1)$ be a normed space and $Y$ a linear subspace of $X$. Let $||\cdot||_2$ be a norm on $X$ which is equivalent to $||\cdot||_1$ on $Y$. Does there exist a norm on …

There is a homological Chern character $ch_\ast \colon K_\ast(X) \to H_\ast(X)$ for $X$ a smooth, compact manifold. I found only one definition of it (in the paper "K-Homology and …

Hello to all of you : I would like to know if it is true that the Grothendieck period conjecture implies the Hodge conjecture in the case of non-singular complex algebraic varietie …