- 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
- $\\operatorname{Aut}(\\mathbb Z_n)$ is isomorphic to $U_n$.
This endomorphism ring is simply Zn, since the endomorphism is completely determined by its action on a generator, and a generator can go to any element of Zn Therefore, the automorphism group Aut(Zn) is the group of units in Zn, which is Un = U(Zn)
- 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
- Equation of a rectangle - Mathematics Stack Exchange
I need to graph a rectangle on the Cartesian coordinate system Is there an equation for a rectangle? I can't find it anywhere
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- When is the group of units in $\\mathbb{Z}_n$ cyclic?
Let Un U n denote the group of units in Zn Z n with multiplication modulo n n It is easy to show that this is a group My question is how to characterize the n n for which it is cyclic Since the multiplicative group of a finite field is cyclic so for all n n prime, it is cyclic However I believe that for certain composite n n it is also cyclic Searching through past posts turned up this
- Homotopy groups U(N) and SU(N): $\\pi_m(U(N))=\\pi_m(SU(N))$
As for your request regarding a table of the homotopy groups of SU(N), the groups πm(SU(N)) for 1 ≤ m ≤ 15 and 1 ≤ N ≤ 8 are given in appendix A, section 6, part VII of the Encyclopedic Dictionary of Mathematics This doesn't quite cover all the cases you asked for in the comment below, but the missing ones follow from complex Bott periodicity For completeness, here is the table you
- How many possible combinations in 8 character password?
I need to calculate the possible combinations for 8 characters password The password must contain at least one of the following: (lower case letters, upper case letters, digits, punctuations, spec
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