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Problem The sides of a triangle are $a$, $b$ and $c$ and the lengths of the corresponding medians are $m_a$, $m_b$ and $m_c$. I...
Asked on 12/22/2020 by Daniel Kawai
2 answerLet us define the differential operator$$Z=x_1 partial_{x_2} - x_2 partial_{x_1}, $$where $(x_1, x_2, x_3)$ are the standard Cartesian coordinates on $mathbb R^3$. I would...
Asked on 12/22/2020 by Giuseppe Negro
1 answerProve $vec{nabla} cdotleft ( vec{A}timesvec{B} right )=vec{B}cdotleft ( nabla timesvec{A} right )-vec{A}cdotleft ( nabla timesvec{B} right )$ I have expanded the LHS for this and obtain a horrible expression that...
Asked on 12/22/2020 by Mathematicing
2 answerSo suppose that we have already shown that the radical of an ideal $I$, $sqrt{I}$, is an ideal. Can we just conclude that the $sqrt{I}$ is a...
Asked on 12/22/2020
1 answerLet $L/k$ be a (Galois) quadratic field extension, and let $sigma in operatorname{Gal}(L/k)$ be the nontrivial automorphism. Let $h$ be a Hermitian form on $L^{4}$, and...
Asked on 12/22/2020 by Joshua Ruiter
1 answerLet $P_1,dots,P_n$ be simple polygons which don't intersect each other and $Ssubseteqmathbf{R}^2$ the set of points lying in the interior of an odd number of the $P_i$,...
Asked on 12/22/2020 by fweth
0 answerThe problem: Let $mu_n$ act on $mathbb{C}[u,v]$ with weights $(1,-1)$. I would like to show that the rings $mathbb{C}[u,v]^{mu_n}$ and $mathbb{C}[x,y,z]/(xy-z^n)$ are isomorphic. Explanation of terminology: $mu_n subset mathbb{C}$ is...
Asked on 12/22/2020
1 answerI am doing a meeting of 18 people. I want each person to have a few minutes to speak to each person with no wasted time. So in Session...
Asked on 12/22/2020 by JimK
0 answerLet $e$ be the base of the natural logarithm. Is there a sequence of rational numbers $a_n$ such that $$frac{a_1}{e} + frac{a_2}{e^2} + frac{a_3}{e^3} + cdots...
Asked on 12/22/2020 by NiloS
1 answerJech states the following lemma in his book:Lemma 21.9 Let $j:Vto M=operatorname{Ult}_U(V)$ be an elementary embedding with a critical point $kappa$. If $mathbb{P}in M$ is a forcing...
Asked on 12/22/2020 by Hanul Jeon
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