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30 May 2020: Theorem 1.3 (Classification of surfaces of finite type). Every connected, oriented surface of finitetype is diffeomorphic to some Sg,n,b for some g,n,b > 0, where ... If b′ leaves and returns on the right, then b′ is included in some copy of α,

9 Mar 2020: some a,b 0. Hence prove that the class group of K is cyclic and find itsorder.

5 Jun 2020: Corollary 2.2: Fix some b > 0 consider the rates RN :=. 1The result of [24] is actually for source coding with side information,which subsumes the fixed-length lossless source setting. ... fix some b R+ and define τN :=. σ2(p)N b and RN :=. H(p) τN.

14 Oct 2020: δ is abelian.(c) Assume that δ(g) = 1 for some g G. ... irreducible. 3 Find an example of a representation of some finite group over some field of charac-teristic p, which is not completely reducible.

11 Nov 2020: We will need the following stronger result. To state it, we introduce some nota-tions. ... In the following, we hence assume without loss of generality that b iss0-decent, for some fixed s0 N.

10 Oct 2020: algebra. 1.2. Show that the following sets of subsets of R all generate the same σ-algebra:(a) {(a,b) : a < b}, (b) {(a,b] : a < b}, (c) {(,b] : b ... 1.9. Let (E,E,µ) be a measure space. Call a subset N E null if N B for some B E withµ(B) = 0.

6 Jun 2020: Two examples. Adaptive SRWM. Adaptive SRWM. I All MCMC algorithms depend on some design parameters. ... PV (x) λV (x) b1C(x) V (x) =(π(x). supX π. )τ(1β)for some λ (0, 1), b < , a set C, τ (0, 1].

4 Mar 2020: subse-quence (using a diagonal argument) such that (µn (UA,B))n>1 converges to some real number µ (UA,B)for all A B Γ with B finite. ... Therefore,ρ = ϕα for some ϕ AX, so Ker α 6 Ker ρ.

5 Oct 2020: az b, for some a C and b C. ... conformally equivalent). 9. Define an equivalence relation on C by z w iff z = 2sw for some s Z.Show that the quotient space R = C/ has the natural structure of

5 Jun 2020: Such asymptotic results may be of limited use if we wantto have some sort of guarantee that, after a certain number of. ... the sense that|F (x)| CV (x) for all x A, for some constantC).