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- 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)
- modular arithmetic - Prove that that $U (n)$ is an abelian group . . .
1 Let a ∈ Un a ∈ U n then we have to show that there exists b ∈ Un b ∈ U n such that a b a b mod n = 1 n = 1 Let us suppose o(a) = p ap = e o (a) = p a p = e Now if b b is inverse of a a then a b a b mod n = 1 n = 1 holds i e a b = x(n) + 1 a b = x (n) + 1 for some x x (By division algorithm) Now multiply ap−1 a p 1
- Mathematics Stack Exchange
Q A for people studying math at any level and professionals in related fields
- How to find generators in - Mathematics Stack Exchange
For e g- in U(10) = {1, 3, 7, 9} U (10) = {1, 3, 7, 9} are elements and 3 3 7 7 are generators but for a big group like U(50) U (50) do we have to check each and every element to be generator or is there any other method to find the generators?
- (Un-)Countable union of open sets - Mathematics Stack Exchange
A remark: regardless of whether it is true that an infinite union or intersection of open sets is open, when you have a property that holds for every finite collection of sets (in this case, the union or intersection of any finite collection of open sets is open) the validity of the property for an infinite collection doesn't follow from that In other words, induction helps you prove a
- 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
- $U(n) \\simeq \\frac{SU(n) \\times U(1)}{\\mathbb{Z}_{n}}$ isomorphism
Groups definition U(n) U (n) = the group of n × n n × n unitary matrices ⇒ ⇒ U ∈ U(n): UU† =U†U = I ⇒∣ det(U) ∣2= 1 U ∈ U (n): U U † = U † U
- Prove that the sequence (1+1 n)^n is convergent [duplicate]
It is hard to avoid "the concept of calculus" since limits and convergent sequences are a part of that concept On the other hand, it would help to specify what tools you're happy with using, since this result is used in developing some of them (For example, if you define ex = limn→∞(1 + x n)n e x = lim n → ∞ (1 + x n) n, then clearly we should not be using ex e x in the process of
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