Mathematics Questions, Problems & Solutions : TransWikia.com ~ Page 100

Find a specific countable atlas for a smooth submanifold with boundary

Let $M$ be a $k$-dimensional embedded $C^1$-submanifold of $mathbb R^d$ with boundary.$^1$ We know that there is a countable family $((Omega_i,phi_i))_{iin I}$ of ...

Asked on 11/02/2021

1 answer

First prolongation formula

My question is about the derivation of the prolongation formula from Olver's book:"Applications of Lie groups to differential equations" Page 109. Considering a differential equation with independent variable(x) and one...

Asked on 11/02/2021 by geo sd

0 answer

Reference request for conjecture about bridge and crossing number of knots

Murasugi in his book (Knot theory and its applications, page 60) writes:Conjecture. If $K$ is a knot, then $c(K) ge 3(br(K) - 1)$, where equality only holds when...

Asked on 11/02/2021 by R. Suwalski

1 answer

Weak convergence of Radon-Nikodým derivatives

I am working at the moment with a sequence of finite measures $nu_n << mu_n$ converging weakly to $nu << mu$. I have seen that if the Radon-Nikodým...

Asked on 11/02/2021 by Mushu Nrek

0 answer

How can I prove that these definitions of curl are equivalent?

I am reading the book "Div, Grad, Curl, and All that" and I got to the section about curl. In this section, the author defines the curl to be$$...

Asked on 11/02/2021

2 answer

Find if a random variable is a proxy variable using neural networks

I have a probabilistic graphical model (a toy example): where $B$ is a proxy variable to $A$. I...

Asked on 11/02/2021

0 answer

Bounds of $1^n + 2^{n-1} + 3^{n-2} + cdots + n^1$

I want to estimate the value of this sequence for large $n$ (with a reasonable lower bound and upper bound). That is, can we find a function...

Asked on 11/02/2021

3 answer

Optimizing a quadratic in one variable with parameterized coefficients

Recently I was doing a physics problem and I ended up with this quadratic in the middle of the steps: $$ 0= X tan theta - frac{g}{2} frac{ ...

Asked on 11/02/2021

6 answer

Can the step-functions be chosen monotonically?

Assume we are on the interval $[a,b]$. Assume we have a partition of the interval ${a=x_0<x_1<x_2,<ldots x_{n+1}}$. A step-function is a function $f$ where there exists ...

Asked on 11/02/2021

4 answer

Measurability of a function on sub sigma algebra

Let $Omega$ be a compact Hausdorff space in $mathbb{C}^2$. Let $sigma_Omega$ be the Borel sigma algebra on $Omega$. Let $f: Omegalongrightarrowpartial mathbb{D}$ be a non...

Asked on 11/02/2021 by user531706

1 answer

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