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Michaelmas Term 2003 J. M. E. Hyland Linear Algebra: ...
https://www.dpmms.cam.ac.uk/~jmeh1/Teaching/2ndla03.pdf12 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. -
Michaelmas Term 2003 J. M. E. Hyland Linear Algebra: ...
https://www.dpmms.cam.ac.uk/~jmeh1/Teaching/4thla03.pdf12 Aug 2008: 20. Prove Hadamard’s Inequality: if A is a real n n matrix with |aij| k, then. | -
Michaelmas Term 2003 J. M. E. Hyland Linear Algebra: ...
https://www.dpmms.cam.ac.uk/~jmeh1/Teaching/3rdla03.pdf12 Aug 2008: . . . 20. Let P2 = P2(x,y) be the space of polynomials in x,y of degree 2 in each variable. -
A Term Calculus for Intuitionistic Linear LogicNick Benton1, Gavin ...
https://www.dpmms.cam.ac.uk/~jmeh1/Research/Pub91-00/bbdphtlca93.pdf27 Aug 2008: Samson Abramsky. Computational interpretations of linear logic. Technical Report90/20, Department of Computing, Imperial College, London, October 1990.2. -
Abstra t Games for Linear Logi Extended Abstra t ...
https://www.dpmms.cam.ac.uk/~jmeh1/Research/Pub91-00/hs99.pdf22 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. -
Topological GroupsPart III, Spring 2008 T. W. Körner March ...
https://www.dpmms.cam.ac.uk/~twk10/Topg.pdf8 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 -
THE CARTESIAN CLOSED BICATEGORY OFGENERALISED SPECIES OF STRUCTURES…
https://www.dpmms.cam.ac.uk/~jmeh1/Research/Publications/2008/fghw08.pdf19 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 -
Variations on Realizability: Realizing the Propositional Axiom of…
https://www.dpmms.cam.ac.uk/~jmeh1/Research/Publications/2002/vor02.pdf13 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. -
Abstract and ConcreteModels for Recursion Martin HYLANDDPMMS, CMS,…
https://www.dpmms.cam.ac.uk/~jmeh1/Research/Publications/2008/acmr08.pdf22 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. -
Categorical Proof Theory of Classical PropositionalCalculus Gianluigi …
https://www.dpmms.cam.ac.uk/~jmeh1/Research/Publications/2006/bhru06.pdf18 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. -
K0 AND THE DIMENSION FILTRATION FOR p-TORSIONIWASAWA MODULES…
https://www.dpmms.cam.ac.uk/~sjw47/rankskzero.pdf20 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 -
mlics.dvi
https://www.dpmms.cam.ac.uk/~jmeh1/Research/Publications/2002/hs02.pdf13 Aug 2008: Theoretical Computer Science,20:265–321, 1982. [3] P.-L. Curien. Categorical Combinators, Sequential Algo-rithms and Functional Programming. -
doi:10.1016/j.entcs.2006.04.024
https://www.dpmms.cam.ac.uk/~jmeh1/Research/Publications/2006/hnpr06.pdf18 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. -
TRANSACTIONS OF THEAMERICAN MATHEMATICAL SOCIETYVolume 00, Number 0,…
https://www.dpmms.cam.ac.uk/~taf1000/papers/pfaffians.pdf16 Jul 2008: n1)/2i=1 ai)x. (n1)/20. Since the ai are non-zero this Pfaffian is non-zero. -
Linear �-Calculus and Categorical ModelsRevisitedNick Benton1, Gavin…
https://www.dpmms.cam.ac.uk/~jmeh1/Research/Oldpapers/bbdphcsl93.pdf27 Aug 2008: Computational interpretations of linear logic. Technical Report90/20, Department of Computing, Imperial College, London, October 1990.2. -
Linear �-Calculus and Categorical ModelsRevisitedNick Benton1, Gavin…
https://www.dpmms.cam.ac.uk/~jmeh1/Research/Pub91-00/bbdphcsl93.pdf27 Aug 2008: Computational interpretations of linear logic. Technical Report90/20, Department of Computing, Imperial College, London, October 1990.2. -
Proof Theory in the Abstract J. M. E. Hyland ...
https://www.dpmms.cam.ac.uk/~jmeh1/Research/Publications/2002/pta02.pdf13 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. -
Term Assignment for Intuitionistic Linear Logic�(Preliminary…
https://www.dpmms.cam.ac.uk/~jmeh1/Research/Oldpapers/bbdph92.pdf27 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 -
Michaelmas Term 2003 J. M. E. Hyland Linear Algebra: ...
https://www.dpmms.cam.ac.uk/~jmeh1/Teaching/1stla03.pdf12 Aug 2008: 20. An n n magic square is a square matrix whose rows, columns and two diagonals all sum to the samequantity. -
Term Assignment for Intuitionistic Linear Logic�(Preliminary…
https://www.dpmms.cam.ac.uk/~jmeh1/Research/Pub91-00/bbdph92.pdf27 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 -
ALGEBRAIC TOPOLOGY (PART II)EXAMPLE SHEET 1 CAUCHER BIRKAR (1) ...
https://www.dpmms.cam.ac.uk/study/II/AlgebraicTopology/2007-2008/top-exa1.pdf4 Feb 2008: We can define the. Date: 20 Jan 2008. 1. 2 CAUCHER BIRKAR. -
Optimization Michael Tehranchi/DPKExample sheet 2 - Easter 2008 16.…
https://www.dpmms.cam.ac.uk/study/IB/Optimization/2007-2008/example2.pdf1 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. -
COMPLEX DIFFERENTIAL EQUATIONS – Example Sheet 3 (For…
https://www.dpmms.cam.ac.uk/~tkc10/ComplexDE/Exercise_3_answers.pdf15 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 -
Example sheet 4, Galois Theory, 2007. 1. (i) Let ...
https://www.dpmms.cam.ac.uk/study/II/Galois/2007-2008/ex4.pdf4 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. -
ANALYSIS II EXAMPLES 1 Michaelmas 2005 J. M. E. ...
https://www.dpmms.cam.ac.uk/~jmeh1/Teaching/an05-1.pdf19 Mar 2008: 4 ANALYSIS II EXAMPLES 1. 20. A space-filling curve (Exercise 14, Chapter 7 of Rudin’s book). -
BT08 Part II Representation Theory Sheet 3 Unless otherwise ...
https://www.dpmms.cam.ac.uk/study/II/RepresentationTheory/2007-2008/repex3.pdf12 Feb 2008: Hence findthe character table of S5. Repeat, replacing S4 by the subgroup 〈(12345),(2354)〉 of order 20 in S5. -
Combining algebraic effects with continuations Martin Hyland,1 Paul…
https://www.dpmms.cam.ac.uk/~jmeh1/Research/Publications/2007/hlpp07.pdf7 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 -
Complex analysis IB 2007 — lecture notes A J ...
https://www.dpmms.cam.ac.uk/~ajs1005/complex/notes_2006-7.pdf1 Feb 2008: Combining this with Theorem 2.5.6 we get:. 20. Corollary 2.6.2 (“Identity Theorem”). -
Complex Analysis IB, 2007 Example sheet 1 1 (i) ...
https://www.dpmms.cam.ac.uk/study/IB/ComplexAnalysis/2007-2008/ex-sheet1.pdf1 Feb 2008: 20 Show that the following functions do not have antiderivatives on the domains indicated:. -
Complex Analysis IB, 2008 Example sheet 2 1 (i) ...
https://www.dpmms.cam.ac.uk/study/IB/ComplexAnalysis/2007-2008/ex-sheet2.pdf10 Mar 2008: 20 Show that the power series. n=1 zn! defines an analytic function f on D(0, 1). -
PART II REPRESENTATION THEORYSHEET 3 Unless otherwise stated, all ...
https://www.dpmms.cam.ac.uk/study/II/RepresentationTheory/2008-2009/repex3.pdf17 Nov 2008: Hence find the complete character table of S5. Repeat, replacing S4 by the subgroup 〈(12345), (2354)〉 of order 20 in S5. -
ANALYSIS II EXAMPLES 2 Michaelmas 2005 J. M. E. ...
https://www.dpmms.cam.ac.uk/~jmeh1/Teaching/an05-2.pdf19 Mar 2008: Show that E is finite dimensional. 20. Let E be a normed space. -
Combining effects: sum and tensor Martin Hyland,1 Gordon Plotkin2 ...
https://www.dpmms.cam.ac.uk/~jmeh1/Research/Publications/2006/hpp06.pdf7 Aug 2008: References for mathematical theory that supportsthe tensor product are [19,20,21], for which this is a leading example. -
Pseudo-commutative monads and pseudo-closed 2-categories⋆ ⋆⋆ Martin…
https://www.dpmms.cam.ac.uk/~jmeh1/Research/Publications/2002/hp02.pdf29 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 -
Michaelmas Term 2008 T.A. Fisher Linear Algebra: Example Sheet ...
https://www.dpmms.cam.ac.uk/study/IB/LinearAlgebra/2008-2009/lin_alg-08-2.pdf31 Oct 2008: . 1 1 00 3 20 1 0. . ,. . . 1 1 10 3 20 1 0. . ,. . . 1 1 11 3 11 1 1. . -
ANALYSIS II EXAMPLES 4 Michaelmas 2005 J. M. E. ...
https://www.dpmms.cam.ac.uk/~jmeh1/Teaching/an05-4.pdf19 Mar 2008: 20. Suppose that (X, d) is a complete metric space. Let U X be a proper open subset withcomplement A = X U. -
Some improvements to 4-descent on an elliptic curve Tom ...
https://www.dpmms.cam.ac.uk/~taf1000/papers/fourdesc.pdf2 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. -
Groups, Rings and Modules(example sheet 4) NIS-B, Lent 2008 ...
https://www.dpmms.cam.ac.uk/study/IB/GroupsRings%2BModules/2007-2008/grm_ex5_latex.pdf6 Mar 2008: . . then. hn =. . . 1 na n(n 1)ac/20 1 nc0 0 1. -
On full abstra tion for PCF:I. Models, observables and ...
https://www.dpmms.cam.ac.uk/~jmeh1/Research/Oldpapers/ho00.pdf22 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. -
On full abstra tion for PCF:I. Models, observables and ...
https://www.dpmms.cam.ac.uk/~jmeh1/Research/Pub91-00/ho00.pdf22 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. -
Electronic Notes in Theoretical Computer Science 83 (2004)URL:…
https://www.dpmms.cam.ac.uk/~jmeh1/Research/Publications/2003/chp03.pdf19 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. -
Linear Analysis T. W. Körner January 8, 2008 Small ...
https://www.dpmms.cam.ac.uk/~twk10/LA.pdf8 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.). -
A Term Calculus for Intuitionistic Linear LogicNick Benton1, Gavin ...
https://www.dpmms.cam.ac.uk/~jmeh1/Research/Oldpapers/bbdphtlca93.pdf27 Aug 2008: Samson Abramsky. Computational interpretations of linear logic. Technical Report90/20, Department of Computing, Imperial College, London, October 1990.2. -
Combining computational effects: commutativityand sum Martin Hyland,1 …
https://www.dpmms.cam.ac.uk/~jmeh1/Research/Publications/2002/hpp02.pdf19 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. -
Abstra t Games for Linear Logi Extended Abstra t ...
https://www.dpmms.cam.ac.uk/~jmeh1/Research/Oldpapers/hs99.pdf22 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.
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