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MathOverflow : Recent Questions and Answers (Page 24)

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Is a direct sum of flabby sheaves flabby?

Consider a family of flabby (= flasque) sheaves $(mathcal F_i)_{iin I}$ of abelian groups on the topological space $X$.My question : is their direct sum sheaf ...

Asked on 11/03/2021

1 answer

Algebraicity of a ratio of values of the Gamma function

The following ratio: $$frac{Gamma(2/5)^3}{piGamma(1/5)}$$ has kept appearing in my research, and the only thing I know about its value is that it is $cong 0.7567213$, whence the following...

Asked on 11/03/2021 by JeCl

1 answer

Classification of subgroups of finitely generated abelian groups

A finitely generated abelian group $A$ is isomorphic to a direct sum of cyclic groups. I am interested in an extension of this result on couples of abelian groups...

Asked on 11/03/2021

2 answer

An enumeration problem for Dyck paths from homological algebra

In their article "On n-Gorenstein rings and Auslander rings of low injective dimension" Fuller and Iwanaga gave a homological characterisation of 2-Gorenstein Nakayama algebras with global dimension at most three,...

Asked on 11/03/2021

1 answer

Circular track riddle

I'm puzzled by the following riddle, which seems easy at first, but turns out to be more complex than it looks. I would like to go to the bottom of...

Asked on 11/03/2021

1 answer

Fundamental group of a compact branched cover

My problem originates from the following classical result, proved, as far as I know, by Grauert and Remmert:Theorem. Let $Y$ be a compact complex manifold, $B subset Y$...

Asked on 11/03/2021

2 answer

When is a bi-Lipschitz homeomorphism smoothable?

Suppose I have a smooth Riemannian manifold $X$ with induced distance function $d$, and a bi-Lipschitz (with respect to $d$) homeomorphism$$phi: X to X.$$ Under...

Asked on 11/03/2021 by Rohil Prasad

2 answer

How do you know that you have succeeded-Constructive Quantum Field Theory and Lagrangian

Quantum Field Theory is a branch of mathematical physics which is begging for a better understanding.In fact there are no rigorous constructions of interacting QFT in four dimensions. By...

Asked on 11/03/2021

2 answer

Does Morita theory hint higher modules for noncommutative ring?

Two possibly noncommutative rings are called Morita equivalent if their left-module categories are equivalent. In the commutative case, Morita equivalence is nothing more than ring isomorphism. Otherwise, there are many...

Asked on 11/03/2021

3 answer

Bounding the smallest eigenvalue of a matrix generated by a positive definite function

Let $g:mathbb{T}tomathbb{R}$ and is given as $$g(x) = sumlimits_{etainmathbb{Z}}frac{1}{1+gamma eta^2}cos{2pieta x}$$ Consider the matrix $$G_{gamma} = [g(x_i-x_j)]_{1le i,jle n}$$ where $x_1,x_2,...x_n in (0,1)$ and pairwise distinct....

Asked on 11/03/2021 by Rajesh D

1 answer

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