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26 Jun 2024: Typically AB is not the same as BA. The commutator [A, B] captures. ... the dierence between these. Clearly [A, B] = [B, A] and the same also holds foroperators: [Ô, M̂] = [M̂, Ô].

3 Jul 2024: Josephine Crawley Quinn, B.A., Oxford, M.A., Ph.D., UC Berkeley. Sidney Sussex College. ... Professor Joanne Martin, M.A., SID, M.B.B.S., Ph.D., London, MRCPath, CBE. Prakash Melwani, M.A., SID, M.B.A., Harvard.

13 Jun 2024: 2 marks]. (b) For each of the following OCaml declarations, if they pass the type checker givetheir inferred types, or if not then give a program fragment using them thatwould violate ... iv) fun a b -> b (a b) [3 marks]. (v) fun a b -> a b b [3 marks].

18 Jun 2024: type map =Nil : map. | Cons : (module TYPEABLE with type t = ’b) (’b ’b) map map. ... type map =Nil : map. | Cons : (module TYPEABLE with type t = ’b) (’b ’b) code map map.

27 Jun 2024: ii) Given finite sets A, B G, show that there exists a set X B of size |X| 2|A B|/|A| 1 such that for every b B, there are ... more than |A|/2 triples(x, a, a′) X A A such that b = a a′ x.Deduce that B B A A X X.

1 Jul 2024: A |= [ {'} A. B |= [ {'} B. Anuj Dawar June 2024. ... Anuj Dawar June 2024. Substructures. For structures A = (A, RA1 ,. , RAr ) and B = (B, RB1,. , RBr ) in avocabulary , we say.

2 Jul 2024: p pDeadline for abstract submission:Friday 6 March./p p(Also please note that a “late registration” surcharge will apply afterMonday 16Marchb.)/b/p Date for the Diary: European Conference on ... a

3 Jul 2024: where q = Q(ξ1 = 1 b). (b) Consider the case where g(s) = log s. ... by. E′|| = E|| , E′ = γ(E v B) ,. B′|| = B|| , B′ = γ. (B. v. c E.

26 Jun 2024: insists that they can’t exist. This is the Maxwell equation. B = 0. ... Bi2Te3. – 11 –. θ=π. θ=0. B. B E. θ=π. θ=0.

13 Jun 2024: For a subset X A,define the subset CR(X) B as. CR(X) = {b B | a X. ... 4 marks]. (d ) We shall refer to a given function f : A B as locally singleton when forevery b B, the inverse image f1{b} A has exactly one element.