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12 Aug 2008: . 1 0 3 01 3 1 20 0 1 01 2 1 1. ... 1. 11. Consider the matrix A =. . 1 0 20 1 10 1 0.

12 Aug 2008: 20. Prove Hadamard’s Inequality: if A is a real n n matrix with |aij| k, then. |

12 Aug 2008: . . . 20. Let P2 = P2(x,y) be the space of polynomials in x,y of degree 2 in each variable.

27 Aug 2008: Samson Abramsky. Computational interpretations of linear logic. Technical Report90/20, Department of Computing, Imperial College, London, October 1990.2.

22 Aug 2008: 20. If theexponential omonad on C is entral, then both the loose ategory G(?)(C)and the tight ategory G?(C) are models for lassi al linear logi. ... CUP, 1995.[20 P.-H. Chu. -Autonomous ategories, hapter Constru ting -autonomous ategories.

22 Aug 2008: 20. If theexponential omonad on C is entral, then both the loose ategory G(?)(C)and the tight ategory G?(C) are models for lassi al linear logi. ... CUP, 1995.[20 P.-H. Chu. -Autonomous ategories, hapter Constru ting -autonomous ategories.

8 Mar 2008: 20. 9 Characters. Recall that a character θ on a commutative Banach algebra B is non-zerolinear functional θ : B C such that θ(ab) = θ(a)θ(b) for all

19 Aug 2008: Applications are discussed in Section 6. The construction leading to the Kleisli bicategory of generalised speciesis analogous to the construction of the relational model of linear logic [20].This model can ... Winskel, Two-dimensional Kleisli struc-tures

13 Aug 2008: 21This analysis appears in Beeson [2]. 20. Logic in Computer Science, pages 188–198. ... Rosolini, editors, Category Theory, pages 131–156.Springer-Verlag, 1991. 21. [20] J. M.

22 Jan 2008: We refer the reader to [1], to [2] and to [20]for the basic mathematical theory. ... This situation is discussed in detail in [20], but for completeness we give asketch here.

13 Aug 2008: Theoretical Computer Science,20:265–321, 1982. [3] P.-L. Curien. Categorical Combinators, Sequential Algo-rithms and Functional Programming.

20 Feb 2008: 20 KONSTANTIN ARDAKOV AND SIMON WADSLEY. 10. Some special cases. 10.1. ... Proof. This follows from Corollary 8.2. 10.2. A localisation sequence. Consider the localisation sequence of K-theory[20, Theorem 5.5] for the Serre subcategory Fi of the abelian

18 Aug 2008: The cyclic choiceof order may be familiarfrom non-commutative linear logic (Ruet [20]). ... 20. identifications. This gives a groupoid enriched functorSAut : Poly! Aut and agroupoid enriched adjunctionSAut a SPoly.

18 Aug 2008: DD as a retract of D [20]. One obtains such a category by taking the Cauchy. ... LDPL 1996,Mathematical Structures in Computer Science 7 (1997) 453–468. [20] D.S.

16 Jul 2008: n1)/2i=1 ai)x. (n1)/20. Since the ai are non-zero this Pfaffian is non-zero.

27 Aug 2008: Computational interpretations of linear logic. Technical Report90/20, Department of Computing, Imperial College, London, October 1990.2.

27 Aug 2008: Computational interpretations of linear logic. Technical Report90/20, Department of Computing, Imperial College, London, October 1990.2.

13 Aug 2008: Thusformally we have. A = ((U X) α(u,φ(u))7U). 20. which we interpret by means of the formulae. ... before. Since the above describes the maps in the category RDill there is indeed anassociative composition.20.

12 Aug 2008: 20. An n n magic square is a square matrix whose rows, columns and two diagonals all sum to the samequantity.

27 Aug 2008: Term Assignment for Intuitionistic Linear Logic(Preliminary Report)Nick Benton Gavin Bierman Valeria de PaivaComputer LaboratoryUniversity of Cambridgefpnb,gmb,vcvpg@cl.cam.ac.ukMartin HylandDepartment of Pure Mathematics and Mathematical

27 Aug 2008: Term Assignment for Intuitionistic Linear Logic(Preliminary Report)Nick Benton Gavin Bierman Valeria de PaivaComputer LaboratoryUniversity of Cambridgefpnb,gmb,vcvpg@cl.cam.ac.ukMartin HylandDepartment of Pure Mathematics and Mathematical

4 Feb 2008: We can define the. Date: 20 Jan 2008. 1. 2 CAUCHER BIRKAR.

1 Nov 2008: 20. Give sufficient conditions for strategies p and q to be optimal for a two-person zero-sumgame with payoff matrix A and value v. ... 29. Sources 1, 2, 3 stock candy floss in amounts of 20, 42, 19 tons respectively.

15 May 2008: z0 12 (ωh(ω)). 2. So ωh(ω) = 2(z zo)1/2 and hence ω is a power series in (z z1/20 , say ω = b1(z zo) b2(z

4 Feb 2008: 20. Write cos(2π/17) explicitly in terms of radicals. 21. Show that for any n > 1 the polynomial xn x 3 is irreducible over Q.

19 Mar 2008: 4 ANALYSIS II EXAMPLES 1. 20. A space-filling curve (Exercise 14, Chapter 7 of Rudin’s book).

12 Feb 2008: Hence findthe character table of S5. Repeat, replacing S4 by the subgroup 〈(12345),(2354)〉 of order 20 in S5.

1 Feb 2008: Combining this with Theorem 2.5.6 we get:. 20. Corollary 2.6.2 (“Identity Theorem”).

7 Aug 2008: The universal property of the tensor product can be naturally expressed in termsof countable Lawvere theories: given countable Lawvere theories L and L′, thetensor, which always exists [18–20] is the

1 Feb 2008: 20 Show that the following functions do not have antiderivatives on the domains indicated:.

10 Mar 2008: 20 Show that the power series. n=1 zn! defines an analytic function f on D(0, 1).

17 Nov 2008: Hence find the complete character table of S5. Repeat, replacing S4 by the subgroup 〈(12345), (2354)〉 of order 20 in S5.

19 Mar 2008: Show that E is finite dimensional. 20. Let E be a normed space.

7 Aug 2008: References for mathematical theory that supportsthe tensor product are [19,20,21], for which this is a leading example.

29 Sep 2008: Pseudo-commutative monads and pseudo-closed. 2-categories. Martin Hyland1 and John Power2. 1 DPMMS, Centre for Mathematical Sciences, University of Cambridge, WilberforceRoad, Cambridge CB3 0WB, England. email: M.Hyland@dpmms.cam.ac.uk Tel: 44 1223

31 Oct 2008: . 1 1 00 3 20 1 0. .  ,. . . 1 1 10 3 20 1 0. .  ,. . . 1 1 11 3 11 1 1. .

19 Mar 2008: 20. Suppose that (X, d) is a complete metric space. Let U X be a proper open subset withcomplement A = X U.

2 Feb 2008: The followingtheorem is a variant of a standard result (see for example [17], [20]). ... Com-put. Math. 5 (2002), 717 (electronic). 20. S. Stamminger, Explicit 8-descent on elliptic curves, PhD thesis, International Uni-versity Bremen, 2005.

6 Mar 2008: . . then. hn =. . . 1 na n(n 1)ac/20 1 nc0 0 1.

22 Aug 2008: Types of the languageare just Chur h's simple types [20. In the following we shall also refer to them asp f-types. ... 20 HYLAND AND ONGnatural way; that is, the global se tions fun tor will not be faithful.

22 Aug 2008: Types of the languageare just Chur h's simple types [20. In the following we shall also refer to them asp f-types. ... 20 HYLAND AND ONGnatural way; that is, the global se tions fun tor will not be faithful.

19 Aug 2008: 20] Power, A.J., Premonoidal categories as categories with algebraic structure,Theoretical Computer Science 278 (2002) 303–321. ... HB. Hf? βB- KB. Kf? 20. Introduction. Pseudo-monads. The 2-category of pseudo-algebras.

8 Jan 2008: 18 First example sheet 40. 19 Second example sheet 45. 20 Third example sheet 50. ... a f0‖2 ‖a f‖2. for all f F. (See also Exercises 20.4 and 20.5.).

27 Aug 2008: Samson Abramsky. Computational interpretations of linear logic. Technical Report90/20, Department of Computing, Imperial College, London, October 1990.2.

19 Aug 2008: 93, No. 1,pp. 55–92, 1991. 20. G. D. Plotkin, A Powerdomain Construction, SIAM J. ... 20, Amsterdam:Elsevier, 1999. 28. A. J. Power and G. Rosolini, A Modular Approach to Denotational Semantics, inProc.