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2 Apr 2023: The bootstrap estimate of the variance of Ĥ is. σ̂2 =. Bb=1. [Ĥ(b) Ĥ()]2/(B 1),. where Ĥ() =B. b=1 Ĥ(b)/B; similarly for H̃. ... Neural Comp., 15: 1191–1253,2003. [5] B. Pittel. Asymptotic growth of a class of random trees.

28 Nov 2023: Operator-valued measures. A resolution of the identity of H over K is amap P : B B(H) such that. ... By (2), the sequence. (Φ(sn). )is Cauchy in B(H), and hence.

7 Jan 2023: a b = [(a b′) (b a′), a′ b′]=. [(b′ a) (a′ b), b′ a′]. ... Thus(a c′) (b b′) = ((a c′) b) b′ = (a (c′ b)) b′. =

29 Nov 2023: 10if (ii) holds then (i)(a) is equivalent to (i)(b).11(ii) gives that (x,x) R. ... a2 3b2 2c2). Thus we see quickly that b = 0, a 2c = 0 and a2 2c2 = 6.

28 Nov 2023: Then for each A F we have ν+(A) = sup{ν(B) : B A, B F}.This motivates the proof of Theorem 2. ... µ(X) < and µ(A) = inf{µ(U) : A U G} A B.

10 Feb 2023: Ṽ = AtC, Ẽ = B.6. • The endpoints of an edge b B are φ(b) A and ψ(b) C.The graph Γ̃Y is bipartite, and therefore has a canonical structure ... Then f inducesmaps A′ A, B′ B, C′ C which we also denote by f.

23 Jan 2023: Suppose there exists a class [b] B(G,{µ}) such that ν[b] = µ(such a class is necessarily unique if it exists by the above remark). ... µ. ′. INDEPENDENCE OF FOR FROBENIUS CONJUGACY CLASSES 11. (2) Let [b] B(G,µ) and [b′] := [f(b)] B(G′,{µ′})

20 Dec 2023: LetB be a K-Banach algebra, let θ: A B is a K-Banach algebra homomorphismand b B. ... b) (i) b B,(ii) bθ(a) θ(a)b = θ(δ(a)) for all a A,.

6 Mar 2023: 2.2) Σ(C) = Γ(G,). // Σ(X). Σ(W) = ω = QR // Σ(B). ... stacks. We remind the reader that allproducts in this square are taken over B.

14 Sep 2023: If χ: A B is an algebra homomorphismthen there is b B such that χ(x) = bxb1 for all x A. ... OF kD. We have Nrdι = NL/F by [23, Proposition 16.2(b)].