Mathematics Questions, Problems & Solutions : TransWikia.com ~ Page 151

Positivity of an operator

Consider a function $f:mathbb{R}to mathbb{R}$ of class $C^1$. If $f(0)=0$ and $f'(0)>0$ it's clear that there exist some $t_0>0$ such that $f(t_0)>0$. Now if...

Asked on 01/14/2021 by ECL

1 answer

How the square model of Fano 3-space, a.k.a. $PG(3, 2)$, embeds in the MOG?

I'm studying deeply the Curtis' MOG original article, i.e. a New combinatorial approach to $M_{24}$ and I'm still struggling a bit in reading the final 35 6x4 matrices representing...

Asked on 01/13/2021 by riccardoventrella

0 answer

Closed-form analytical solutions to Optimal Transport/Wasserstein distance

Kuang and Tabak (2017) mentions that:"closed-form solutions of the multidimensional optimal transport problems are relatively rare, a number of numerical algorithms have been proposed."I'm wondering if there...

Asked on 01/13/2021 by random_shape

2 answer

Questions about set cardinalities (infinite/finite).

I have a couple questions that I undertstood (maybe) intuitively and tried to prove them somehow, I would like if someone can give feedback and tell me if I'm doing...

Asked on 01/13/2021 by Pwaol

1 answer

Forming 2 teams of five from 11 people, but first person of each team has the captain role.

(a) A coach wants to form two (2) teams of five (5) from the eleven players on the team for a scrimmage game (i.e., just a small practice game where...

Asked on 01/13/2021 by diagoot

0 answer

An easier evaluation of $detlimits_{1leqslant i,jleqslant n}left{frac{x_i-x_j}{x_i+x_j}right}$

I'm looking for an easier proof of the identity (attributed to K.$,$F.$,$W.$,$Rohn)$$R_n(bar{x}):=det_{1leqslant i,jleqslant n}left{frac{x_i-x_j}{x_i+x_j}right}=prod_{i<j}left(frac{x_i-x_j}{x_i+x_j}right)^2,$$where $bar{x}:=(x_1,ldots,x_n)$ and $n$ is even...

Asked on 01/12/2021 by metamorphy

1 answer

Gaussian concentration of measure, equivalent definitions

I need some help going between two equivalent definitions. First some notation : $bullet$ For $Asubseteq mathcal{X}$ and $r>0$ define what is called the r-blowup of ...

Asked on 01/12/2021 by Monty

1 answer

Markov's Chain stationary matrix determination

I have the following transition matrix $P$ begin{equation}P=begin{pmatrix}1/2 & 1/3 & 1/6\1/4 & 3/4 & 0\1/5 & 2/5 & 2/5end{pmatrix}end{equation} I...

Asked on 01/12/2021 by Ignacio Toro

2 answer

Show that if $A+delta A$ is singular, $|delta A| = |A^{-1}|^{-1}$

I'm trying to show the following. Let $A$ be an invertible $ntimes n$-matrix and $delta A$ be the smallest possible matrix, measured in a subordinate (natural) matrix...

Asked on 01/12/2021 by Flerovium

0 answer

Shelah's uncountable categoricity theorem

Morley's theorem says if $T$ is a complete theory in a countable language and $T$ is $kappa$-categorical for some uncountable $kappa$, then $T$ is ...

Asked on 01/12/2021 by user826451

1 answer

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