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Mathematics : Recent Questions and Answers (Page 30)

Find answers to your questions about Mathematics or help others by answering their Mathematics questions.

Division of Positive Definite Matrix - Inner Product Space

I am trying to derive a simplified expression of something requiring some linear algebra. I have gotten the stage below: $$G = frac{mathbf{1}^H mathbf{A}^{-1} mathbf{B} mathbf{A}^{-1} mathbf{1}}{mathbf{1}^H mathbf{A}^{-1}mathbf{1}}$$...

Asked on 12/20/2021 by David Carey

1 answer

The connection between Kolmogorov complexity and mathematical logic

We know that Kolmogorov complexity has connections to mathematical logic since it can be used to prove the Gödel incompleteness results (Chaitin's Theorem and Kritchman-Raz). Are there...

Asked on 12/20/2021

1 answer

Is MVUE (Minimum Variance Unbiased Estimator) unique in every case?

I am studying statistics, and I read that when the estimator is complete and sufficient, then that estimator is MVUE and unique. I think if the estimator is incomplete...

Asked on 12/20/2021 by Block Jeong

2 answer

What are some applications of these specific pure math areas?

I'm a pure math PhD specialized in hyperbolic topology, doing a research postdoc right now which ends in August of 2018. So I'll be starting to apply for my next...

Asked on 12/20/2021 by j0equ1nn

3 answer

Let $f: mathbb{R}^2to mathbb{R}^2$ given by $f(x, y) = (e^x cos y, e^x sin y)$.

Let $f: mathbb{R}^2to mathbb{R}^2$ given by $f(x, y) = (e^x cos y, e^x sin y)$. Take $S$ to be the set $S = [0, 1]times [0, pi]$. (a) Calculate $Df$...

Asked on 12/20/2021 by user482152

3 answer

Spectral Characterization of Strong-Mixing

Let $(X, mathcal X, mu)$ be a probability space and $T:Xto X$ be an invertible measure preserving transformation. We get a unitary operator $U_T:L^2_muto L^2_mu$ which takes...

Asked on 12/20/2021 by caffeinemachine

1 answer

Integer exponent equation

Show that $$(2^a-1)(2^b-1)=2^{2^c}+1$$ doesn't have solution in positive integers $a$, $b$, and $c$.After expansion I got $$2^{a+b}-2^a-2^b=2^{2^c},.$$ Any hint will be appreciated....

Asked on 12/20/2021 by rashed a564

2 answer

Can this be accepted as a proof of the question.

Let $a,bin+mathbb Z$ such that $dfrac{a^2+b^2}{ab+1}=k.$ Prove that $k$ is the square of an integer when $$a^2+b^2$$ is divisible by $ab+1$. Soln. For $k$...

Asked on 12/20/2021

0 answer

How to derive ${ A vdash C }$ from ${A lor B vdash C}$ in the sequent calculus LK?

How to derive ${ A vdash C }$ from ${A lor B vdash C}$ in the sequent calculus LK? It seems obvious that if ${A lor...

Asked on 12/20/2021 by Julja Muvv

1 answer

Drawing non-intersecting curves (or segments) connecting non-adjacent vertices in a regular polygon

In a regular $n$-gon, we are allowed to connect any pair of non-adjacent points by a continuous curve. The curve cannot intersect any other curve or side except at...

Asked on 12/20/2021

2 answer

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