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I'm trying to find if the solution of the following initial value problem is unique.begin{align}y' &= 3 (y^{2/3})\y(0) &= 0end{align}I have tried with...
Asked on 12/27/2021
2 answerA prime number is a natural number N > 1, that is divisible only by 1 and N (N/1).The number 1 is given special treatment in this definition, and...
Asked on 12/27/2021
1 answerI have been looking but cannot find the following: an example of a topologically transitive map on $mathbb{S}^n$ or on $mathbb{R}^n$ (for arbitrary $n$). Here, by...
Asked on 12/27/2021
1 answerSuppose we have$$begin{align}cos x + cos y + cos z &= frac{3}{2}sqrt{3} \[4pt]sin x + sin y + sin z &= frac{3}{2}end{align}$$ How...
Asked on 12/25/2021 by mbalasundar
2 answerExample image Given 3 normally distributed points in 2D space, what would the distribution of the angle $alpha$ between the three points be & can it...
Asked on 12/25/2021 by simejanko
1 answerLet P be a polyhedron and let G be its associated graph. Suppose P has Vvertices, E edges, and F faces. For each k, let $V_k$ be the...
Asked on 12/25/2021 by Dang Dang
1 answerLet $r in mathbb{R}$ be an arbitrary real number. Show that $beta=left{1, x-r,(x-r)^{2},(x-r)^{3}, ldots,(x-r)^{n}right}$ is a basis of $P_{n}(mathbb{R})$. I know that if I can show this...
Asked on 12/25/2021
2 answerMy maths TB says: For the simultaneous equations, $a_1x + b_1y + c_1 = 0$ and $a_2x + b_2y + c_2 = 0$ if $dfrac{a_1}{a_2} = dfrac{b_1}{b_2}...
Asked on 12/25/2021
2 answerIf $x,y$ are i.i.d uniform random variables on $[0,1]$. I know that the PDF of $|x-y|$ is: $$f(z) = begin{cases}2(1-z) & text{for $0 < z...
Asked on 12/25/2021
2 answerIn Willard, it's given that, for Hausdorff non-singleton spaces -$prod_{alphain A}X_alpha$ is separable iff $X_alpha$ is separable $forallalphain A$ and $|A|lemathfrak{c}$From reading the proof, I found...
Asked on 12/25/2021
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