Mathematics Questions, Problems & Solutions : TransWikia.com ~ Page 92

How do I write the Laurent series for $frac{1}{z^2(z-i)}$ for $1<|z-1|<sqrt2$?

How do I write the Laurent series for $frac{1}{z^2(z-i)}$ for $1<|z-1|<sqrt2$? I know that I need to rewrite it somehow to fit the geometric series form of ...

Asked on 11/09/2021 by complexanalysis

2 answer

Are we guaranteed a Lie group by taking the algebraic closure of finitely many one-parameter groups acting (each periodically) on a Euclidean space?

We are given a Euclidean space $E$ and a finite subset ${A_{1}, ldots, A_{k}}$ of $GL(E)$. Consider the one-parameter groups $g_{k}^{t} : t mapsto e^{t...

Asked on 11/09/2021

0 answer

Proximal operator of conjugate function

Asumme $f$ is closed convex function and $f^*$ is the conjugate function. Domain of $f^*$ is $(0,1)$, otherwise $f^*$ is $infty$. If we directly...

Asked on 11/09/2021 by user11999776

1 answer

Calculate the fourier transform of $(ax^2+bx+c)^{-1}$

Find the fourier transform of the function $(ax^2+bx+c)^{-1}$ with $a>0$ and $b^2-4ac<0$.So my idea for this was using the fact that the fourier transform of the function...

Asked on 11/09/2021 by Jojo98

2 answer

Definition and intuition of a tubular neighborhood of a submanifold

Let $dinmathbb N$, $kin{1,ldots,d}$ and $M$ be a $k$-dimensional embedded $C^1$-submanifold of $mathbb R^d$ with boundary$^1$. Now let $$T_xM:=left{vinmathbb R^dmidexistsvarepsilon>0,gammain C^1((-varepsilon,varepsilon),M):gamma(0)=x,gamma'(0)=vright}$$ denote...

Asked on 11/09/2021

1 answer

Showing that $q=(z_1,z_2^2)$ is primary in $mathcal O_2 $

Show that if $q$ is primary, then $sqrt{q}$ is prime.Show that in the ring $mathcal O_2 = mathbb C{z_1, z_2}$, $q=(z_1,z_2^2)$ is primary.original...

Asked on 11/09/2021

1 answer

Common root of a cubic and a biquadratic equation

The value of $a$ given that the cubic equation $$x^3+2ax+2=0$$ and the biquadratic equation$$x^4+2ax^2+1=0$$ have a common root. I know how to use common root condition...

Asked on 11/09/2021 by UM Desai

4 answer

On the double series $sum_{(m,n)inmathbb{Z}^2setminus{(0,0)}}frac{m^2+4mn+n^2}{(m^2+mn+n^2)^s}$

I'm having a difficult time calculating the series $$sum_{(m,n)inmathbb{Z}^2setminus{(0,0)}}frac{m^2+4mn+n^2}{(m^2+mn+n^2)^s} quad , quad s>2$$ I don't even know where to start. Truth be told I don't have that much experience...

Asked on 11/09/2021

1 answer

Set of possible reflections of a vector.

How many vectors can one construct by by reflecting a vector $binmathbb{R}^d$ for $bneq 0$? Reflections can be described by Householder matrices $H=I-2vv^T/||v||_2^2$. In other words, I'm...

Asked on 11/09/2021 by Alexander Mathiasen

1 answer

limit of arithmetic mean of $|sin n|$, $ninmathbb{N}$

In this posting, it is stated thatit is well known that $$ lim_{nrightarrowinfty}frac{|sin 1|+ldots +|sin n|}{n}=frac{2}{pi} $$ which can be obtained by theuniform distribution.I have tried to...

Asked on 11/09/2021 by Jean L.

2 answer

Ask a Question

Get help from others!

Mathematics : Recent Questions and Answers (Page 92)

Ask a Question