MathOverflow Questions, Problems & Solutions : TransWikia.com ~ Page 14

Pairing up vertices in a graph

Given a connected (undirected) graph with an even number of vertices, consider how many ways are there to pair up vertices so that each pair is connected by an edge....

Asked on 11/24/2021

1 answer

Minimizing an f-divergence and Jeffrey's Rule

My question is about f-divergences and Richard Jeffrey's (1965) rule for updating probabilities in the light of partial information. The set-up:Let $p: mathcal{F} rightarrow [0,1]$ be a probability function...

Asked on 11/24/2021 by jw7642

0 answer

Rational functions with trivial Weil symbols at every point

Let $f, g$ be a pair of nonzero rational functions in $mathbb{C}(t).$ For $lambdain mathbb{C}$ let $a$ be multiplicity of $g(t)$ at $lambda$ and...

Asked on 11/24/2021 by Daniil Rudenko

0 answer

Regular singular point of non-linear ODE: $dot{x}(t) + t^{-1}Ax(t) = Q(x(t))$

Consider a system of ordinary differential equations of the form$$dot{x}(t) + frac{1}{t}Ax(t) = Q(x(t))$$where $x(t) in mathbb{C}^n$, $A in mathrm{Mat}_{ntimes n}(mathbb{C})$ is a...

Asked on 11/24/2021

1 answer

Inverse problem of Chern Classes

For my graduate (master) thesis I am studying the theory of Chern Classes. As a possible personal development the only sensible idea I have so far, and which I frankly...

Asked on 11/22/2021 by Temitope.A

4 answer

Reference for graduate-level text or monograph with focus on "the continuum"

I always had the dream to design a course for my graduate students like "mathematical models of the continuum". This course should cover history of real numbers, the Measure Problem,...

Asked on 11/22/2021 by Ruth-NO

5 answer

Do Poincaré residue and integrable log connection commute?

Here are some basic notations and definitions: (ignore this part if familiar) 1.Let $(X,omega)$ be a compact Kähler manifold of dimension $n$, and let $D=sum_{i=1}^r D_i$ be...

Asked on 11/22/2021

0 answer

Numbers of the form $x^2(x-1) + y^2(y-1) + z^2(z-1)$ with $x,y,zinmathbb Z$

Roger Heath-Brown conjectured that any integer $knotequivpm4pmod9$ can be expressed as $x^3+y^3+z^3$ with $x,y,zinmathbb Z$ in infinitely many different ways. Also it is well-known that some solutions...

Asked on 11/22/2021

0 answer

How to solve a differential equation in the form $frac{partial}{partial t}g(x,t)=g(x-Delta,t)+frac{partial^2}{partial x^2} g(x,t)$?

How to find the general solution of a differential equation with a shift, in the following form? $$frac{partial}{partial t}g(x,t)=g(x-Delta,t)+frac{partial^2}{partial x^2} g(x,t)$$ where $Delta > 0$. And what...

Asked on 11/22/2021

1 answer

Multidimensional series: an application of quantum field theory

While computing the quantum vacuum energy of a real scalar field defined on $mathbb{R}times mathbb{T}^3$, I encountered the following sum: $$ sum_{n_1^2+n_2^2+n_3^2geq 1}^{infty} frac{1}{(n_1^2+n_2^2+n_3^2)^2} $$ Does it have...

Asked on 11/22/2021 by Andrea T

0 answer

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