Wederive ahomeomorphism invariant for those tiling spaceswhich aremadeby rather general substitution rules on polygonal tiles, including those tilings, like the pinwheel, which contain tiles in in¢nitely manyorientations.The invariant is a quotient of C4 ech cohomology, is easily computed directly from the substitution rule, and distinguishes many examples, including most pinwheel-like tiling s...

We consider a vector kinetic BGK equation leading to isentropic gas dynamics in the relaxation limit. We prove the existence of a weak solution satisfying a kinetic entropy inequality for any initial data with nite energy. Key-words: isentropic gas dynamics { kinetic BGK model { kinetic entropy Mathematics Subject Classi cation: 35L65, 76N15, 35B35, 82C40 Work partially supported by European TM...

The criterion for con uence using decreasing diagrams is a generalization of several well-known con uence criteria in abstract rewriting, such as the strong con uence lemma. We give a new proof of the decreasing diagram theorem based on a geometric study of in nite reduction diagrams, arising from unsuccessful attempts to obtain a con uent diagram by tiling with elementary diagrams. 2000 Mathem...

We study some classes of generalized convex functions, using a generalized derivative approach. We establish some links between these classes and we devise some optimality conditions for constrained optimization problems. In particular, we get Lagrange-Kuhn-Tucker multipliers for mathematical programming problems. Key words: colinvex, colin…ne, generalized derivative, mathematical programming, ...

LetX be a smooth complex variety of dimension at most two, and let F be its function ¢eld. We prove that the K -groups of F are divisible above the dimension of X, and that the K-groups of X are divisible-by-¢nite.We also describe the torsion in the K -groups of F and X. Mathematics Subject Classi¢cations (2000). Primary: 19E08; secondary: 19E20, 14C35, 14F20.

We present two extensions of pCRL with time-stamped actions: pCRL for absolute time and pCRLr for relative time. We de ne timed bisimilarity for both versions and prove that the given axiomatisations are ground complete, provided that the data types have built-in equality and Skolem functions. We base the completeness proofs on the completeness results for untimed pCRL. 1991 Mathematics Subject...

We consider the process theory PA that includes an operation for parallel composition, based on the interleaving paradigm. We prove that the standard set of axioms of PA is not !-complete by providing a set of axioms that are valid in PA, but not derivable from the standard ones. We prove that extending PA with this set yields an !-complete speci cation, which is nite in a setting with nitely m...

This is an extension of work presented in [12]. It is proved that the seemingly weak architecture Basic Splice introduced there {in which the coordination of processes is done using only a global set with read/write primitives{ can support a distributed implementation of a large class of requirements speci cations, namely LPEs (a CRL intermediate representation of speci cations). 2000 Mathemati...

1991 Mathematics subject classi cation: 11R11, 11D09 We study the density of the set of real quadratic fields for which the norm of the fundamental unit equals 1 inside the set of real quadratic fields containing elements of norm 1. A conjectural density is derived from a single heuristic assumption, and experimental data supporting this assumption are given. We finally discuss how close one ca...

We exhibit a recursive procedure that enables us to construct a maximal union of k chains in a nite partially ordered set P for every positive integer k. As a consequence, we obtain an algorithmic proof of Greene's Duality Theorem on the relations between the cardinalities of maximal unions of chains and antichains in a nite poset. Mathematics Subject Classi cations (2000). 05A17, 06A07, 68Q25,...