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9 Nov 2020: a) All words w {0, 1} consisting of either the string 01 repeated some number oftimes (possibly none), or the string 010 repeated some number of times (possiblynone). ... b) All words w {a, b, c} consisting of some number of a’s (possibly none),

5 Jun 2020: nlog Qn(B(X. n1 , D)) some finite R bits/symbol, w.p.1. – This suggests a natural lossy analog for the Shannon code-lengths:. ... with either: (a) n(θ) =. dim(Qθ)2 log n. (b) n(θ) =. (θ) for θ in some countable Γ Θ;. otherwiseConsistency? Does

31 Jul 2020: no f B(l,u) are negative definite if either fl(x) 0 for some x 0, or fs(x) 0 for somex 0. ... Evaluation of 1, 1, and 2. Some lemmas. Evaluation of 3 and 3.

22 Oct 2020: 2) If µ is noncentral, then. π0(X({µ},b)K) = π1(G)σΓ0. 0.3. Now we discuss some applications. ... Our first major step is to show that every point in X({µ},b) is connected to a point in Xw(b)for some σ-straight element w Adm({µ}).

10 Mar 2020: d(B,gB. ). Pick some h1 G(S {e}) and let R = d(B,h1B. )> ... And. 2d = infgG(S{e}). dX(B,gB. )= inf. hHd(B,gB. ),. so the infimum is achieved at some h0 H.

5 Oct 2020: 4. If the map f of Question 3 is a conformal equivalence, show that F(z) = λz µfor some λ C. ... 5. Show that complex tori C/⟨1,τ1⟩ and C/⟨1,τ2⟩ are analytically isomorphic ifand only if τ2 = (aτ1 b)/(cτ1 d), for some matrix ( a bc d ) SL2

5 Jun 2020: This makes a direct comparison possible and enables us topresent some theoretical results. ... There exists some number K such that k(n) < K for all n.

19 Oct 2020: ii) M R n N x S |fn(x)| 6 M. (b) In this case assume that S is a metric space. ... Prove that there is some subinterval [a,b] of [0, 1] with a < b on which f isbounded.

5 Jun 2020: for some appropriate rate function R(P,Q,D), except perhaps for a single value of Ddenoted Dmin. ... 1n. log Q̂nn(B(Xn1 ,D)). a.s. infQΘ1n. log Qn(B(Xn1 ,D)) n,. for some sequence (n)n1 with n 0 as n.

9 Nov 2020: Some of the results in our paper have been obtained by Hong in [10] for the two-slope case usinga different method. ... Therefore. b = m1υ(p)m2 = υ(p)h. for some h M(OL). By Lang’s theorem for M, there exists m′ M(OL) such that m′σ(m′)1 =