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16 Sep 2019: Proof. Results 1 to 3 are immediate from the definition of conditional probability.For result 4, note that A B B, so P (AB) P (B) and thus P (A | B) ... 1.P (B | B) = 1 (obviously), so it just remains to show the Axiom III.

30 Aug 2019: Now suppose given a frame homomorphism h : B A. We say two nuclei j andk on A are B-equivalent if j(h(b)) = k(h(b)) for all b B. ... By considering the nucleus{o(h(b)) c(j(h(b))) | b B} (where j is an arbitrary nucleus), show that each B-.

30 Aug 2019: H(,B) are natural in B B. Part III, Paper 22. 3. ... B(KB′,B)B(ρ. B′,B). B(B′,B). is a bijection. (iii) ρB : B KB is an isomorphism in B.

29 Aug 2019: δrbπb: (. t(b))r= δrbπb. (58). Note that, for any B B matrix A:. ... t(b))b. (by (69)) (77). = πb 2((P P2 P3 PN. )t(b))b.

30 Aug 2019: a) Let G act on B B by g(B1,B2) = (gB1, gB2). ... B B | (B,F(B)) O(w)}. Show that X(w) can be identified with the variety L1(BwB)/B, for a rational Borelsubgroup B, and show that there exists a

23 Nov 2019: field, the Hamiltonian becomes. H =P2. 2M µsBSz , (5.28). where B = |B|. ... The TDSE for this system is thus(ȧ. ḃ. )= i. (B b cos(ωt).

6 Dec 2019: find. LHS =2. 4|a (b b′)| whereas RHS =. 2. 4(1 b b′). ... In particular, suppose a and b are unit vectors, with a b = 0 and b′ = b cos α a sin α.Then we find.

6 Feb 2019: C(t) = Tr [ ρ B(t) B(0)] = Tr[ρ eitH B eitH B. ]. ... This would require conditionson the matrix elements of B and B′, i.e.

4 Dec 2019: M. Frasca-Spada. B. Vaux. K. Black-Hawkins. L. R. R. Gelsthorpe. G. ... J. Virgo. J. L. Caddick. B. B. Groisman. K. J. Wilkinson.

28 Aug 2019: The b†b term is. familiar and we can check that b† create positive energy states as expected,. ... We still have the expansion (5.4) of and † in terms of b, b†, c and c†.