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Hilbert's tenth problem is the problem to determine whether a given multivariate polyomial with integer coefficients has an integer solution. It is well known that this problem is undecidable and...
Asked on 11/17/2020
2 answerI have a simple proposition about groups, but it is not obvious for me. (This question is motivated by the last answer in Show identity of subgroup is same...
Asked on 11/17/2020 by Kapur
1 answerI am struggling with one problem in particular. $y'' + y'''sin(y) = 0$ is the equation. I am told to let $y' = z$ and do reduction of...
Asked on 11/16/2020 by Trevor Frederick
1 answerLet $V,W$ be banach spaces and $T:Vto W$ be linear map. The closed graph theorem says $T$ is continuous iff the graph of $T$ is closed...
Asked on 11/15/2020 by Lord Shadow
1 answerLemma : If a number which can be written as a sum of two squares is divisible by a number which is not a sum of two squares, then the...
Asked on 11/15/2020 by Soham Chatterjee
0 answerI am not sure if there exists a closed form for $$I=int_0^{pi/2}frac{x^2 text{Li}_2(sin^2x)}{sin x}dx$$ which seems non-trivial. I used the reflection and landen's identity, didn't help much. In case...
Asked on 11/15/2020 by Ali Shadhar
0 answerI know that by Kolmogorov’s $0-1$ Law, that for independent r.v, the tail $sigma$-algebra is trivial (e.g all events have probability either $0$ or $1$). This...
Asked on 11/14/2020 by Davi Barreira
1 answerI need to prove the following inequality. Let $a_1, ..., a_n$ be positive real numbers with $a_n ge 1$. Then $$frac{a_1}{(a_1+cdots+a_n)log^2(a_1+cdots+a_{n}+1)}+frac{a_2}{(a_2+cdots+a_n)log^2(a_2+cdots+a_n+1)}+cdots+frac{a_n}{a_nlog^2(a_n+1)} le C$$for some constant...
Asked on 11/14/2020 by JCAA
1 answerI managed to work this proof using a diagram. Then when I googled I found similar proofs. But aren't they incomplete? Because they prove the formula works only in first...
Asked on 11/13/2020 by across
1 answerI am doing the weak formulation of the equation: $nabla ( k nabla u) = f text{in } Omega$ I want to find the correct space for k...
Asked on 11/12/2020 by Vitagor
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