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  2. Γ-INVARIANT IDEALS IN IWASAWA ALGEBRAS K. ARDAKOV, S. J. ...

    https://www.dpmms.cam.ac.uk/~sjw47/InvIdeals.pdf
    21 Jan 2009: B[p] := {bp : b B}. in B provided that B is reduced.Let t be a positive integer. ... r. for all v V.Let B = Sym(V k) and let P be a graded prime ideal of B.
  3. The Thought-experiment

    https://www.dpmms.cam.ac.uk/~tef10/cam_only/langs-and-automata/1-2.html
    13 Aug 2009: Let us try some examples. Let L be the set of strings over the alphabet {a, b} which have the same number of as as bs. ... Let L be the set of strings over the alphabet {a, b} which have an even number of as and an even number of bs.
  4. MPhil ACS, module L16 Semantics of HOT Languages

    https://www.cl.cam.ac.uk/teaching/0910/L16/semhl-02-ann.pdf
    21 Nov 2009: Are these OCaml expressions contextually equivalent? let a = ref n infun x a :=! a x ;! a. let b = ref(n) infun y b :=! b y ;. (!b). ACS L16, lecture 2 ... let a = ref n infun x a :=! a x ;! a. let b = ref(n) infun y b :=! b y ;. (!b). Etymology of
  5. ECONOMICS TRIPOS PART IIA Thursday 4 June 2009 9-12 ...

    https://www.robinson.cam.ac.uk/iar1/teaching/p2apaper6_2009.pdf
    21 Apr 2009: b) Let π be the true probability that a one-litre water sample fromthis type of site contains pathogenic material. ... Show thatv is also an eigenvector of A1. (b) Let.  =. [2 11 2. ]. i. Find the eigenvalues of  and derive an eigenvector
  6. GEOMETRY — Example Sheet 1TKC Lent 2009 -1. Let ...

    https://www.dpmms.cam.ac.uk/~tkc10/Geometry_2009/Exercise_1.pdf
    28 Jan 2009: to. 4. Let A, B be two distinct points in the Euclidean plane. ... Let be a spherical triangle with sides of length a,b,c and angles α,β,γ.
  7. THE PHASE TRANSITION OF THEQUANTUM ISING MODEL IS SHARP ...

    www.statslab.cam.ac.uk/~grg/papers/qimfinalUS.pdf
    24 Jun 2009: Let A K be a finite setof sources, and let B B, G F. ... Let B B, G F, let A Kbe a finite set of sources, and write ψA = ψA(B,G) for the colouringgiven in the last section.
  8. Nominal domain theory for concurrency

    https://www.cl.cam.ac.uk/techreports/UCAM-CL-TR-751.pdf
    18 Jul 2009: Φω-ideal. Let x0 x1. be an ω-chain of Φω-ideals of P. ... Let A be a fixed infinite set whose elements are to be called names.
  9. GEOMETRY — Example Sheet 1TKC Lent 2009 -1. Let ...

    https://www.dpmms.cam.ac.uk/study/IB/Geometry/2008-2009/Exercise_1.pdf
    30 Jan 2009: to. 4. Let A, B be two distinct points in the Euclidean plane. ... Let be a spherical triangle with sides of length a,b,c and angles α,β,γ.
  10. Welcome to my list of puzzles. Any comments, suggested ...

    www.tcm.phy.cam.ac.uk/~sea31/puzzle.html
    18 Nov 2009: 4) And here a really hard one: Two logicians meet, let us call them A and B. ... B: I do not know the numbers. A: I do not know the numbers.
  11. Numbers and Sets (2009–10) Example Sheet 2 of 4 ...

    https://www.dpmms.cam.ac.uk/study/IA/Numbers%2BSets/2009-2010/examples-NS-09-2.pdf
    23 Oct 2009: What if we replace ‘injective’ by ‘surjective’ passim? 5. Let A = {1, 2, 3} and B = {1, 2, 3, 4, 5}? ... Let R be the relation on Z‘ aRb if b = a 3 ’. How many equivalence relations on Z contain R? 8. Let A be a set of n positive integers.
  12. Mich. 2009 GRAPH THEORY—EXAMPLES 1 PAR 1. Show that ...

    https://www.dpmms.cam.ac.uk/study/II/Graphs/2009-2010/sheet1.pdf
    13 Oct 2009: a) How do we know that R(G) exists? (b) Let Ik be a set of k independent edges (so |Ik| = 2k). ... b) Let A be a collection of subsets of [s 1].
  13. 09-10sheet4.dvi

    https://www.dpmms.cam.ac.uk/study/II/TopicsinAnalysis/2009-2010/09-10sheet4.pdf
    2 Dec 2009: 3) Let a, b be positive integers. Let. x =1. a 1b+ 1. ... b) Let f : [0, 1] R be a bounded Riemann integrable function.
  14. Annalsof PureandAppliedLogic161 (2009)1–42 Contents lists available…

    https://www.cl.cam.ac.uk/~ad260/papers/apal09.pdf
    21 Sep 2009: Lemma 2.15. Let q N, A,aand B,bbe rooted trees.If A,a B,b, then (A q)a N. ... as) and b = (b,b1,. ,bs), where s 6 q. Let π : (A q)a A andπ : (Bq)b B bethenaturalprojections.Wenotethat foranynodea.
  15. EXAMPLE SHEET 2 (LECTURES 7–12) GALOIS THEORY MICHAELMAS 2009 ...

    https://www.dpmms.cam.ac.uk/study/II/Galois/2009-2010/ex2.pdf
    11 Nov 2009: Show that P(X b) = P(X) for every b Fp K.Now suppose that P does not have a root in K, and let L/K be a splitting field ... 5. (i) Let f K(X). Show that K(X) = K(f) if and only if f = (aX b)/(cX d)for some a, b, c, d K with ad bc
  16. Percolation of arbitrary words in one dimension Geoffrey R. ...

    www.statslab.cam.ac.uk/~grg/papers/grimmett6.pdf
    8 Jul 2009: Denote the first digit of Wm by a {0, 1}, and let b = 1 a be the complementarydigit. ... Proof of Theorem 1(b). Let. δp,q = vpq up,q, p,q 0.
  17. JRN Michaelmas 2009 Probability and Measure 2 3.1 Suppose ...

    www.statslab.cam.ac.uk/~james/Lectures/pmex2.pdf
    2 Oct 2009: 2 )dx 0. 3.8 Let u and v be differentiable functions on [a, b] with continuous derivatives u′. ... b. a. u′(x)v(x)dx. 3.10 Let (E, E) and (G, G) be measurable spaces and let f : E G be a measurablefunction.
  18. 15 Oct 2009: Let x [a, b]. Applying Theorem 1 ′to u′k and f on [x0, x] (or on [x, x0] if x < x0) we obtain. ... F (x) F (x0) = x. x0. f (x)dx. Differentiation in x gives F ′(x) = f (x) for x [a, b] as f is continuous.(2) Let ε > 0.
  19. More about bombs

    https://www.dpmms.cam.ac.uk/~tef10/cam_only/langs-and-automata/2-1-1.html
    13 Aug 2009: Let L be the language of palindromes over {a, b}. It isn't regular, but there is no obvious bomb. ... n. b. n. : n }. 2.1.1.2 The language {ww : w Σ} is not regular.
  20. A Coursework

    https://www.dpmms.cam.ac.uk/~tef10/cam_only/langs-and-automata/5-0.html
    13 Aug 2009: Let w. 1. and w. 2. be two words having no characters in common. ... c. Question 2. Now let L. 1. and L. 2. be regular languages.
  21. Michaelmas Term 2009 T.A. Fisher Linear Algebra: Example Sheet ...

    https://www.dpmms.cam.ac.uk/study/IB/LinearAlgebra/2009-2010/lin_alg-09-2.pdf
    30 Oct 2009: 5. Let A and B be n n matrices over a field F. ... 14. Let A be an n m matrix. Prove that if B is an m n matrix then.

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