Mathematics Questions, Problems & Solutions : TransWikia.com ~ Page 138

Algebraic Operations with Summation within summation

Given $x_i = (X_i - bar{X})$, where $bar{X}$ is the sample mean of $X$; and given the variable $k_i = frac{x_i}{sum x_i^2}$. How do I show...

Asked on 01/26/2021 by Rom

1 answer

Prove monotone convergence theorem when $int |f_1| dmu < infty$ holds

This question is from 3.A exercise 20 from Axler's MIRA book. Suppose $(X,S,mu)$ is a measure space and $f_1, f_2, dots$ is a monotone sequence of $S$-measurable...

Asked on 01/26/2021 by Evan Kim

1 answer

Prove that $frac{1}{x+1}$ is positive.

Let $x>1$. I'm trying to prove that the function $y=frac{1}{x+1}$ is positive. I've managed to prove that: $$frac{1}{x+1}=frac{1}{x} + 1$$$$frac{1}{x} > 0$$$$frac{1}{x} +...

Asked on 01/26/2021 by M. Choy

3 answer

For a projection $Pi$, is $text{tr}(Pi X)leq text{tr}(X)$?

All matrices are finite dimensional symmetric positive semidefinite matrices in this question. Let $Pi$ be projection i.e. in its eigenbasis, it is the the identity matrix with some diagonal...

Asked on 01/26/2021 by user1936752

2 answer

Does the homotopy pullback of a diagram of spaces who are homotopy equivalent to CW-complexes have the homotopy type of a CW complex?

Consider the diagram of compactly generated weakly hausdorff topological spaces: If each space has the homotopy type of a CW-complex,...

Asked on 01/26/2021

0 answer

Prove that $f(x)=frac{1}{x}$ is uniformly continuous on $(frac{1}{2},infty)$

Prove that $f(x)=frac{1}{x}$ is uniformly continuous on $(frac{1}{2},infty)$Attempt: We must show that for any $epsilon>0$ we can find a $delta > 0$, such that if ...

Asked on 01/25/2021 by siobhan.ren

1 answer

Action of a Lie subgroup

Let $G$ be a Lie group and $H$ be a Lie subgroup acting on G by right multiplication and acting on $mathfrak{g}^*$ by the adjoint action. What...

Asked on 01/25/2021

0 answer

Is the next map a quotient map?

Let $X=[0,1] cup (2,3]$, let $Y=[0,2]$ and suppose $X$ and $Y$ have the usual topologies. Define $f: X to Y$ by $f(x)=x$ if ...

Asked on 01/25/2021 by erika21148

1 answer

Number of iterations to find the root of $x^3+2x-54$ using Newton's Method

I am asked to calculate the (theoretical) minimum number of iterations needed to find the root $alpha$ of $x^3+2x-54$ using Newton's Method, guaranteeing an absolute error less than...

Asked on 01/25/2021 by Gibbs

1 answer

Convergence of $int_mathbb{R^n} frac1{x^p}dx$

1)$int_mathbb{R^n}$ $frac{1}{x^p}dx$ For what values of $p$ would this converge? I mean should p be less than the dimension of $mathbb{R^n}$ or what?My second question...

Asked on 01/25/2021 by user854662

1 answer

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