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- Mathematics Stack Exchange
Stack Exchange Network Stack Exchange network consists of 183 Q A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers
- What are some interesting un-intuitive problems in probability aside . . .
there's the rare illness test - despite no symptoms, a man takes a test for an illness that occurs in one in a billion people
- Intuitive proof that $U(n)$ isnt isomorphic to $SU(n) \\times S^1$
This is a sort of addendum to Qiaochu's answer, the purpose of which is to tie up the loose end it leaves in the sense that it only considers isomorphisms compatible with the short exact sequence associated to the surjective $\det\colon \mathrm{U}(n) \to S^1$
- general topology - (Un-)oriented manifold with (un-)oriented interfaces . . .
An un-oriented manifold is glued from pieces of oriented manifolds [with boundaries], separated by interfaces [where boundaries are glued]? I suppose a Mobius strip is one example, but do we have any concrete 4-dimensional example [glued from 3-dimensional interfaces] and 3-dimensional manifold examples [glued from 2-dimensional interfaces]?
- Limit sequence (Un) and (Vn) - Mathematics Stack Exchange
Stack Exchange Network Stack Exchange network consists of 183 Q A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers
- 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
- Order of the group $U(n)$ - Mathematics Stack Exchange
Stack Exchange Network Stack Exchange network consists of 183 Q A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers
- 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)
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