Mathematics Questions, Problems & Solutions : TransWikia.com ~ Page 187

Permutation involving different outcomes

So say I have want to find, with the lowercase alphabet, how many strings of 9 different letters that can be formed that have the letter z in front, a...

Asked on 12/02/2020 by Adam Mansfield

1 answer

Approximating convolution with $L^1$ function by sum of translation operators

Let $G$ be a locally compact topological group. Let $mu$ be left Haar measure on G. Suppose $f in L^1(G)$. Then convolution with $f$ defines an...

Asked on 12/02/2020 by clhpeterson

0 answer

How to approach proof of "For an integer n, if $n > 7$, then $n^2-8n+12$ is composite"?

For the first part of this question, I was asked to find the either/or version and the contrapositive of this statement, which I found as follows: i) either $n...

Asked on 12/02/2020 by lswift

2 answer

Distance from vectors in $mathbb{Z}^d$ to the cube $[-1/2,1/2]^d$

Let $|;|_2$ be the Eucliden norm on $mathbb{R}^d$. Problem: Suppose $xin Q:=big[-tfrac12,tfrac12big]^d$. Is$$|x-k|_2geq frac{1}{2sqrt{d}}|k|_2$$for all $kinmathbb{Z}^d$? Notice that for all ...

Asked on 12/02/2020 by Oliver Diaz

1 answer

Let $T:X to Y$ be a linear operator and $dim X=dim Y<infty$. Show $Y=mathscr{R}(T)$ if and only if $T^{-1}$ exists, without dimension theorem.

The problem I am trying to solve is:Let $T:X to Y$ be a linear operator and $dim X = dim Y = n < infty$. Show that ...

Asked on 12/02/2020 by André Armatowski

2 answer

sum of terms of series

If $$F(t)=displaystylesum_{n=1}^tfrac{4n+sqrt{4n^2-1}}{sqrt{2n+1}+sqrt{2n-1}}$$ find $F(60)$.I tried manipulating the general term(of sequence) in the form $V(n)-V(n-1)$ to calculate the sum by cancellation but went nowhere. I also tried...

Asked on 12/02/2020 by Albus Dumbledore

2 answer

Find possible solution for minimization of a functional with free boundary condition

Find a possible solution for the minimization of the functional:$$J[x]=int_0^1 (tdot{x}+dot{x}^2) , dttag1$$ with $x(0)=1$ and $x(1)$ is a free variable. I am trying to solve...

Asked on 12/02/2020 by Nicole Douglas

2 answer

What are some examples of non-trivial series that are equal to $0$?

By non-trivial, I mean not only non-zero but also a neat looking one, so something you get by normalizing well known series wouldn't work, example : $sum_{n=0}^{infty}left( frac{1}{en!} -...

Asked on 12/02/2020 by the_firehawk

3 answer

Find the limit of $f(n)$ where $f(n)=(2-f(n+1))^2$

Let $f:mathbb{N}to[0,2]$ such that $f(1)=2$ and: $$f(n)=(2-f(n+1))^2qquadforall ninmathbb{N}$$ Prove that the limit of $f(n)$ as $ntoinfty$ exists and show it is equal to $1$;...

Asked on 12/02/2020 by Amit Zach

2 answer

On the spectral decomposition for compact operators in a Banach space

Let $T$ be a compact operator in a Banach space, then the spectrum of $T$ contains $0$ and a sequence (either finite or infinite) of eigenvalues ...

Asked on 12/02/2020 by NessunDorma

0 answer

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