Mathematics Questions, Problems & Solutions : TransWikia.com ~ Page 59

Prove a metric space is totally bounded

Let $X = 2^{mathbb{Z+}}$ be the space of binary sequences $(x_k)_{kge1}$ with each $x_k in {0,1}.$ Define a metric on $X$ by $d(x,y) = sum^infty_{k=1}...

Asked on 12/01/2021

2 answer

Discussion of continuous functions in topology

Here is the definition of continuous function that I like to go with even in topology:Let $X$ and $Y$ be any topological spaces, let $f colon X...

Asked on 12/01/2021

2 answer

Is there a specific name for this geometrical shape?

I’m looking for the name of this shape which is basically created by shaping symmetrical round edges of a 2D circle after forming it roundly from the center (I hope...

Asked on 12/01/2021

1 answer

Are regular/Riemann integrals a special case of a line integral?

It would seem that this is the case since Riemann integration is integrating $f(x,y)$ along a trajectory in $mathbb{R}^2$-- a segment of, or the entirety of, the x-axis....

Asked on 12/01/2021 by Pendronator

2 answer

Injection from $(Kotimes_{mathbb{Z}}hat{mathbb{Z}})^to prod_p(Kotimes_{mathbb{Z}}mathbb{Z}_p)^$?

Suppose $K$ is a number field. The projections $hat{Bbb{Z}} = prod_pBbb{Z}_ptoBbb{Z}_p$ give a map$$(Kotimes_{Bbb{Z}}hat{Bbb{Z}})^*to prod_p(Kotimes_{Bbb{Z}}Bbb{Z}_p)^*.$$I want to show that this map is injective. It is...

Asked on 12/01/2021

1 answer

How to calculate matrix divergence in polar coordinates

How to calculate the divergence of the following matrices in polar coordinates: $$left(begin{array}{cc} sigma rho (r,varphi ) & tau (r,varphi ) \ tau (r,varphi ) &...

Asked on 12/01/2021 by Please correct GrammarMistakes

1 answer

Classification of triply transitive finite groups

A permutation group $G$ on a set $X$ is said to be $k$-transitive if it is both transitive on $X$ and either $k=1$ or the point stabilizer $G_x$ is $(k-1)$-transitive...

Asked on 12/01/2021 by Jack Schmidt

1 answer

Lebesgue Measure Space and a converging, increasing sequence. Show that the sequence in increasing.

Let $(R,L,lambda)$ be the Lebesgue measure space and let $f: R → R$ be a non-negative, measurable function. Define a sequence $f_n =f.chi _{(frac1n,1]} : R→R, n...

Asked on 12/01/2021 by martinhynesone

1 answer

What is the derivative of $log det X$ when $X$ is symmetric?

According to Appendix A.4.1 of Boyd & Vandenberghe's Convex Optimization, the gradient of $f(X):=log det X$ is $$nabla f(X) = X^{-1}$$ The domain of the...

Asked on 12/01/2021 by evangelos

3 answer

Uncertainty of a Weighted Mean with Uncertain Weights

I have a program which creates a model of a non-isothermal system where masses are distributed throughout a number of pre-defined, discrete temperature bins. You can look at each bin...

Asked on 12/01/2021 by Alex Howard

1 answer

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