A proof of property (RD) for discrete cocompact subgroups of SL_3(R)

In this article we prove that discrete cocompact subgroups of SL_3(R) satisfy property (RD) of Jolissaint (this property was introduced in [Jol85, Jol87, Jol90]). The argument is a very close imitation of the argument of [RRS97]: in this article Ramagge, Robertson and Steger prove a general result (stated below) implying that discrete cocompact subgroups of SL_3(Q_p) satisfy property (RD). Our result is a special case of a conjecture of Valette which claims that any discrete group acting isometrically, properly and cocompactly either on a Riemannian symmetric space or on an affine building has property (RD) ([FRR93] page 74). Up to now property (RD) has been proved for free groups by Haagerup in [Haa79], and then for hyperbolic groups by de la Harpe in [dlH88], using [Jol87]. Recently, in [RRS97], Ramagge Robertson and Steger have proved property (RD) for any discrete group acting freely on the vertices of an..

Uniqueness and Error Estimates in First Order Quasilinear Conservation Laws Via the Kinetic Entropy Defect Measure

We give a new uniqueness proof for solutions to quasilinear scalar conservation laws. It is based on the kinetic formulation and does not make use of Kruzkov entropies and doubling of variables. It uses in a fundamental way the entropy defect measure appearing in the kinetic formulation. This measure also plays a central role for error estimates that we recast in our simplified approach. 1. Introduction We consider solutions u(t; x) to first order quasilinear scalar conservations laws @ t u + divA(u) = 0 in D 0 i (0; +1) \Theta IR d j ; (1:1) endowed with the family of entropy inequalities @ t S(u) + divj(u) 0 in D 0 i (0; +1) \Theta IR d j ; (1:2) for all lipschitz continuous (and thus sublinear) convex functions S and j i (¸) = Z ¸ 0 a i (v)S 0 (v)dv; (1:3) a(:) = A 0 (:) 2 L 1 loc (IR; IR d ): (1:4) We give a direct proof of the L 1 loc contraction property; any pair of entropy solutions u and v (i.e. those satisfying (1.1), (1.2)) also satisfies @ t ju ..

The True Self-repelling Motion

. We construct and study a continuous real-valued random process, which is of a new type: It is self-interacting (self-repelling) but only in a local sense: it only feels the self-repellance due to its occupation-time measure density at `immediate neighbourhood' of the point it is just visiting. We focus on the most natural process with these properties that we call `true self-repelling motion'. This is the continuous counterpart to the integer-valued `true' self-avoiding walk, which had been studied among others by the first author. One of the striking properties of true self-repelling motion is that, although the couple (X t ; occupation-time measure of X at time t) is a continuous Markov process, X is not driven by a stochastic differential equation and is not a semi-martingale. It turns out, for instance, that it has a finite variation of order 3/2, which contrasts with the finite quadratic variation of semi-martingales. One of the key-tools in the construction of X is a continuou..

On Removable Singularities for CR Functions in Higher Codimension

this paper, we study the higher codimensional case. Our results for the hypersurface case are weaker than those in [3] and [4], for the smoothness assumption. Note with T z 0 M the usual tangent space of a real manifold M ae

Improvements of the Attacks on Cryptosystems Based on Error-correcting Codes

. Many public-key cryptosystems and identification schemes based on error-correcting codes have been proposed as an alternative to the common cryptographic algorithms based on number theory. They rely on the NP-hardness of finding a fixed-weight word in a coset of a linear binary code. We here improve the previous attacks on these systems; this notably enables us to reduce the work factor involved in breaking McEliece's cryptosystem since our algorithm requires 2 64:2 operations that is 2 7 times less than Lee-Brickell's attack. Keywords: Error-correcting codes, Minimum weight codewords, Markov chains, McEliece's cryptosystem, Cryptanalysis. 1 Introduction Since the concept of public-key cryptography appeared in 1977, searching for secure public-key cryptosystems and identification schemes has been one of the most active areas in the field of cryptology. Seventeen years after the fundamental paper of Diffie and Hellman, public-key cryptography has however become dangerously depend..

A Decompositional Approach for Computing Least Fixed-Points of Datalog Programs with Z-Counters

We present a method for characterizing the least fixed-points of a certain class of Datalog programs in Presburger arithmetic. The method consists in applying a set of rules that transform general computation paths into "canonical" ones. We use the method for treating the problem of reachability in the field of Petri nets, thus relating together some unconnected results and extending them in several directions. R'esum'e Nous pr'esentons une m'ethode pour caract'eriser les plus petits points-fixes d'une certaine classe de programmes Datalog dans l'arithm'etique de Presburger. La m'ethode consiste `a appliquer un ensemble de r`egles qui transforment les chemins g'en'eraux de calcul en chemins "canoniques". Nous utilisons cette m'ethode pour traiter le probl`eme d'accessibilit'e dans le domaine des r'eseaux de Petri. Nous rapprochons ainsi des r'esultats consid'er'es jusqu'ici comme ind'ependendants, et nous les 'etendons dans plusieurs directions. A Decompositional Approach for Compu..