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  2. 3 The Formalism of Quantum Mechanics In the previous ...

    www.damtp.cam.ac.uk/user/tong/qm/qm3.pdf
    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. Staging Generic Programming

    https://www.cl.cam.ac.uk/~jdy22/papers/staging-generic-programming.pdf
    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.

  4. Model Theory of Tame Classes of Finite Structures Part 1: Locality

    https://www.cl.cam.ac.uk/~ad260/talks/LogColloq24-lecture1.pdf
    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.

  5. MAMA/129, NST3AS/129, MAAS/129 MAT3 MATHEMATICAL TRIPOS Part III…

    https://www.maths.cam.ac.uk/postgrad/part-iii/files/pastpapers/2024/Paper_129.pdf
    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.

  6. Preprint typeset in JHEP style - HYPER VERSION 2018 ...

    www.damtp.cam.ac.uk/user/tong/gaugetheory/gt.pdf
    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.

  7. Fixed-Memory Capacity Bounds for theGilbert-Elliott Channel Yutong…

    sigproc.eng.cam.ac.uk/foswiki/pub/Main/AG495/isit2024_gec.pdf
    20 Jun 2024: G B1 b. b. g. 1 g. 0 0. 1 1. ... which solving for q(0) gives. q(0) =g b (1 g)δb (1 b)δg.

  8. Submitted to:ML 2017 c© J. Yallop & S. DolanThis ...

    https://www.cl.cam.ac.uk/~jdy22/papers/first-class-subtypes-draft.pdf
    18 Jun 2024: Finally, this proof can beused to coerce a proof of the reflexivity of B-subtyping (at type a) a B a to a proof that a B b. ... Thatis, from a proof a A b, the operations of A.sub and B.sub produce a proof a B b.

  9. MAMA/329, NST3AS/329, MAAS/329 MAT3 MATHEMATICAL TRIPOS Part III…

    https://www.maths.cam.ac.uk/postgrad/part-iii/files/pastpapers/2024/Paper_329.pdf
    27 Jun 2024: You may assume that. b. b. tdt. (1 t)2 =2b. (1 b)2 ln(1 b1 b. ... You may assume that. b. b. (c2 t2)dt1 t = 2b (1 c.

  10. First-class modules: hidden power and tantalizing promises Jeremy…

    https://www.cl.cam.ac.uk/~jdy22/papers/first-class-modules.pdf
    18 Jun 2024: type (’a, ’b) eq = (’a -> ’b) (’b -> ’a). ... Here is a definition of trans:. let trans (type a) (type b) (type c) a_eq_b b_eq_c =let module TC = Subst(struct type ’x tc = (a, ’x) eq

  11. MAMA/133, NST3AS/133, MAAS/133 MAT3 MATHEMATICAL TRIPOS Part III…

    https://www.maths.cam.ac.uk/postgrad/part-iii/files/pastpapers/2024/Paper_133.pdf
    27 Jun 2024: You may assume that SL2(Z) can be written as an amalgamated free product⟨A⟩ ⟨A⟩⟨B⟩ ⟨B⟩, where. ... b) Prove that any isometry of T either fixes a point or translates a line.

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