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What are some good resources for mathematical translation?

I am currently in the process of translating a lecture on the étale topology by John Hubbard from French into English (and from transparencies into Beamer). For the most...

Asked on 01/05/2022 by Matt Noonan

7 answer

Inequality for hook numbers in Young diagrams

Consider a Young diagram $lambda = (lambda_1,ldots,lambda_ell)$. For a square $(i,j) in lambda$, define hook numbers $h_{ij} = lambda_i + lambda_j' -i - j +1$ and...

Asked on 01/05/2022 by Igor Pak

2 answer

Most tensor subspaces of low dimension have rank-1 defining equations

Let $V_1,ldots , V_k$ be vector spaces of dimensions $n_1,ldots , n_k$ over a field of characteristic zero. Consider the rational map$newcommand{PP}{mathbb{P}}newcommand{bs}{boldsymbol}DeclareMathOperator{Gr}{Gr}DeclareMathOperator{im}{im}...

Asked on 01/05/2022

0 answer

Prime ideals of formal power series ring that are above the same prime ideal

Let $R$ denote a commutative ring with identity and let $R[[X]]$ denote thering of formal power series over $R$ in an indeterminate $X$. If ...

Asked on 01/05/2022 by A. C. Biller

1 answer

Pull back of a Bounded form

Let $(X, omega) $ be a complex manifold and let $alpha $ be a $p$-form $omega$-bounded on $X$.Let $f:Yto X$ be a holomorphic...

Asked on 01/05/2022 by Kamel

0 answer

Set-theoretic generation by circuit polynomials

Let $P$ be a prime ideal in $S=mathbb{C}[x_1,ldots , x_n],$ and write $[n] = { 1, ldots , n }.$ The algebraic matroid of $P$ can...

Asked on 01/05/2022

0 answer

How to prove that $ sum_{m=0}^{infty} { Gamma{(1+2m)/alpha}over Gamma(1/2+m)} { (-t^2/4)^{m}over m !} ge (alpha/2)^{3}exp(-t^{2}/4) $

I would love to prove the following inequality$$ {1over sqrt{pi} } sum_{m=0}^{infty}Gamma{(1+2m)/alpha}{ (-t^2)^{m}over (2m) !}=$$$$sum_{m=0}^{infty}{ Gamma{(1+2m)/alpha}over Gamma(1/2+m)}{ (-t^2/4)^{m}over m !}...

Asked on 01/03/2022

0 answer

Clarification regarding the definition of absolute height of an algebraic number

According to page 1-2 of this paper (https://arxiv.org/abs/0906.4286), Mahler has established the inequality$$|alpha_1 - alpha_2| geq H(alpha_1)^{-(d-1)} tag 1 $$to be valid for all...

Asked on 01/03/2022

0 answer

Appearance of proof relevance in "ordinary mathematics?"

I've been wondering recently what—if any—applications proof theory has to ordinary mathematics (by which I mean algebra, analysis, topology, and so on). In particular, I'd be fascinated to see a...

Asked on 01/03/2022 by mcncm

2 answer

Reference to a Classical Regularity Theorem

(Edited)I need a reference to the following result:If $u in H^2(B_1^+) cap {rm Lip}(B_1^+)$ satisfiesbegin{cases} {rm div}(F(x,u,nabla u)) = F_0(x,u,nabla u) quad &...

Asked on 01/03/2022 by artful_dodger

1 answer

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