- functional analysis - Where can I find the paper Un théorème de . . .
J P Aubin, Un théorème de compacité, C R Acad Sc Paris, 256 (1963), pp 5042–5044 It seems this paper is the origin of the "famous" Aubin–Lions lemma This lemma is proved, for example, here and here, but I'd like to read the original work of Aubin However, all I got is only a brief review (from MathSciNet)
- Mnemonic for Integration by Parts formula? - Mathematics Stack Exchange
The Integration by Parts formula may be stated as: $$\\int uv' = uv - \\int u'v $$ I wonder if anyone has a clever mnemonic for the above formula What I often do is to derive it from the Product R
- Intuitive proof that $U(n)$ isnt isomorphic to $SU(n) \\times S^1$
and what you'd really like is for an isomorphism U(n) ≅ SU(n) × U(1) U (n) ≅ S U (n) × U (1) to respect the structure of this short exact sequence (If there were some random isomorphism that didn't have this property that would be less interesting ) For starters, this requires that det: U(n) → U(1) d e t: U (n) → U (1) have a section, or equivalently that the short exact sequence
- modular arithmetic - Prove that that $U (n)$ is an abelian group . . .
But we know that ap−1 ∈ Un Gcd(ap−1, n) = 1 a p 1 ∈ U n G c d (a p 1, n) = 1 i e there does not exist any s s such that s s divides n n as well as ap−1 a p 1
- Order of the group $U(n)$ - Mathematics Stack Exchange
Is it true that the order of the group U(n) U (n) for n> 2 n> 2 is always an even number? If yes, how to go about proving it? U (n) is the set of positive integers less than n and co-prime to n ,which is a group under multiplication modulo
- Limit sequence (Un) and (Vn) - Mathematics Stack Exchange
Limit sequence (Un) and (Vn) Ask Question Asked 8 years, 6 months ago Modified 8 years, 6 months ago
- Expectation of Minimum of $n$ i. i. d. uniform random variables.
You'll need to complete a few actions and gain 15 reputation points before being able to upvote Upvoting indicates when questions and answers are useful What's reputation and how do I get it? Instead, you can save this post to reference later
- Calculate the cohomology group of $U(n)$ by spectral sequence.
We have Ep,q2 ≅ Λ[c1,c3] E 2 p, q ≅ Λ [c 1, c 3] By lacunary reasons, this spectral sequence collapses on the second page, and so we deduce H∗(U(2)) ≅ Λ[c1,c3] H ∗ (U (2)) ≅ Λ [c 1, c 3] In general, the spectral sequence for the fiber bundle U(n − 1) → U(n) → S2n−1 U (n 1) → U (n) → S 2 n 1 always collapses on the second page, and you can use induction to prove
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