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

Is a column-wise and row-wise Gaussian matrix, jointly Gaussian?

Let $Ainmathbb{R}^{ntimes m}$ be a random matrix that each of its rows or columns is a Gaussian vector with iid components. More formally we have $A_{i,cdot}simmathcal{N}(0,I_m),A_{cdot,j}simmathcal{N}(0,I_n)$ for all...

Asked on 12/29/2021 by kvphxga

1 answer

Lipschitz function, Berkeley problem 1.2.2

Problem 1.2.2Suppose that $f$ maps compact interval $I$ into itself and that$$mid f(x)-f(y) mid < mid x-y mid$$for all $x, y in ...

Asked on 12/29/2021 by Vinay Deshpande

0 answer

Is this proof right?

Let $f_n(x) = n^2 x e^{- n^2 x}$, $n=1,2,3,...$.Show that $sum_{n=1}^{infty} f_n(x) $ convergeces uniformly on $[a,infty]$, where $a>0$.Show that $sum_{n=1}^{infty} f_n(x) $ does...

Asked on 12/29/2021 by The Mathematician

2 answer

arrow category and functor category

Let A be an abelian category and D the category having two objects and only one nonidentity morphism between them. The functor category A$^D$ is also abelian and it...

Asked on 12/29/2021

2 answer

The locus of vertex of a parabola, given that an orthogonal intersection is made with another having specified latus rectum and orientation.

Full Question:A variable parabola of fixed latus rectum 4b and having axis parallel to x–axis, lies completely in Ist and IVth quadrant and cuts the fixed parabola $y^2=4ax$...

Asked on 12/29/2021

1 answer

Derivative of a symplectic form

Let $(M,omega)$ be a symplectic manifold and $gamma in C^infty(I,M)$ a path in $M$. For $X,Y in Gamma_gamma(TM)$ I would like to compute the derivative...

Asked on 12/29/2021 by TheGeekGreek

1 answer

Ellipse on complex plane

I have found that the curve $z(x)$ on the complex plane with$$z=frac{ax+b}{x^2+1}$$at real $x$ spanning from $-infty$ to $+infty$ looks very...

Asked on 12/29/2021 by Alexey Sokolik

2 answer

Can you find a function $beta(x)$ where if $a+b=n^m$ then $beta(frac{a}{b})$ is irrational?

Can you find a function $beta(x)$ where if $a+b=n^m$ then $beta(frac{a}{b})$ is irrational but if $a+b$ isn't equal to $n^m$ then it is rational (...

Asked on 12/29/2021

1 answer

Prove that $xge n(n-1)(n-3)/8$, where $x$ is the number of $4$-cycles in a graph on $n$ vertices with at least $frac12binom{n}{2}$ edges.

Prove that $xge dfrac{n(n-1)(n-3)}8$, where $x$ is the number of $4$-cycles in a graph on $n$ vertices with at least $displaystylefrac12,binom{n}{2}$ edges.If there are no...

Asked on 12/29/2021 by shakir

2 answer

In tetrahedron ABCD, prove that $r<frac{ABcdot CD}{2AB+2CD}$

Given tetrahedron $ABCD$, let $r$ be the radius of the sphere inscribed tetrahedron. Prove that $$r<dfrac{ABcdot CD}{2,AB+2,CD}$$This is difficult question, my friends and I could not find...

Asked on 12/29/2021 by mja

2 answer

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