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2 Nov 2019: B(t) = log A(t) = [B1,B2]t2 o(t2) and exp(B(t) = A(t). ... But thenalso limt0 B(t)/t. 2 = limt0([B1,B2] o(1)) = [B1,B2] g (as g is a closed subset ofmatrices).

19 May 2007: i) δ1(x, x′) > α for all but at most γ|B|2 pairs (x, x′) B2.(ii) δ1(x, x′) 6 α(1 η) for all but at most ... B. Otherwise, let 1 = 0(1 η)1/2. We. 22. then know that δ1(x, x′) > 1(1 η)1/2 for at least |B1|2 pairs (x, x′) B21 ,

26 Oct 2007: g : A1 A2 (B1 B2) ; g : (a1,a2) 7 c1(a1)c2(a2). ... Hint: Recall that H(A,B) = H(A|B) H(B).]. (b) Show that. H(I|Y,X) = 0.

21 Nov 2011: A 7 1000001 B 7 1000010 C 7 1000011a 7 1100001 b 7 1100010 c 7 1100011+ 7 0101011! ... 4 The product of two codes cj : Aj Bj is the codeg : A1 A2 (B1 B2).

17 Feb 2010: Thus, for b BQ, one has |b| = b2/b1.3.0.1. The cusps of MK(C) can be written as. ... φ̂(bg) = χ1,f (b1)χ2,f (b2)|b|fφ̂(g),. for all b =(b1 0 b2. )

15 Oct 2021: x B B B1 B2. b) Conversely, suppose that one is given a set S and a collection β of subsets ofS satisfying i), ii) above. ... Fix x B1 B2. Clearly x Band B β. I claim that B B1 B2 for.

15 Oct 2021: µ(O C) <. Then A = B1 N, where N B2 where B1,B2 B(Rn) with µ(B2) = 0. ... µ(O C) <. iii) A = B1 N, where N B2 where B1,B2 B(Rn) with µ(B2) = 0.

8 Mar 2024: Indeed, the minimalpolynomial of a/b with gcd(a,b) = 1 is xa/b. ... OK =. {a b 1 m. 1/2. 2: a,b Z. }if m 1 mod 4.

16 Nov 2004: If we define additionand multiplication on A B by. (a1,b1) (a2,b2) =(a1 A a2,b1 B b2). ... a1,b1) (a2,b2)a =(a1 A a2,b1 B b2)then (A B, ,) is a ring.We often write AB for the ring just defined and call it the external

16 Feb 2006: Suppose that the rectangle R = {x iy : a1 6 x 6 a2 , b1 6y 6 b2} lies within D and that R is the boundary curve of R, positively oriented.(a) ... for b1 6 y 6 b2.(b) Deduce that. R. f. x+ i.