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I am trying to find the Fourier transform of $|x|$ in the sense of distributions in its simplest form. Here is what I have done so far: Let...
Asked on 11/29/2021
3 answer$y'=y^2-13y+77, y(0) = frac{13}{2}$ Exists $t^*in mathbb{R}$ such that $y(t^*)=-1$?. How to prove without solving the ode? Any hint? Using previous post: We have: $y^2-13y+77=0...
Asked on 11/29/2021 by user514695
2 answerI have tried doing this exercise, Let $m,ninmathbb{N}, mleq n$, prove that$$logleft(frac{4^n}{displaystylesqrt{2n+1}{2nchoose n+m}}right)geq frac{m^2}{n}$$ I achieved some results like for example,$$displaystylesum_{i=0}^n 2^ibinom{2n-i}{n} = 4^n$$ and...
Asked on 11/29/2021 by Zaragosa
2 answerAssume there is the dynamical system $$begin{align}frac{d}{dt} x_1 &= -x_1 + x_2 \frac{d}{dt} x_2 &= x_1 - x_2^3end{align}$$ The system is at rest...
Asked on 11/29/2021 by user3137490
1 answerLet $U$ be a non-trivial finite-dimensional vector space over $mathbb R.$ I am trying to use a bijective and continuous map $f: U to [0,1]$ and ...
Asked on 11/29/2021 by kaaaTata
3 answerIf $displaystyle lim_{ntoinfty}|a_{n+1}/a_n|=L$, then $displaystylelim_{ntoinfty}|a_n|^{1/n}=L$.There're plenty of proofs available on the internet or books, such as the following one. There exists an $N$, such that whenever ...
Asked on 11/29/2021 by diiiiiklllllll
2 answerLet $text{Ob}:textbf{Cat}rightarrowtextbf{Set}$ be the forgetful functor mapping a small category to its set of objects. Consider the functor $R:mathbf{Set}rightarrowtextbf{Cat}$ mapping a set $X$ to the category having...
Asked on 11/29/2021 by alf262
1 answerIt's always fun (however irresponsible) to make random conjectures, if you don't have to bear the burden of proving them. And thus, I conjecture - Every polynomial expression (of the...
Asked on 11/29/2021 by BeBlunt
1 answerWe know that given the dimension $N$, we can construct the corresponding spinors for the $Spin(N)$ group (which has $Spin(N)/mathbb{Z}_2=SO(N)$ so $Spin(N)$ is a double cocver...
Asked on 11/29/2021
0 answerWe know that the converging sequences of a discrete space are the stationary sequences. I am looking for two examples for spaces (not empty or reduced to a singleton)connected and...
Asked on 11/29/2021
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