Wavelet packets with uniform time-frequency localizationPaquets d'ondelettes avec localisation temps-fréquentielle uniforme

We construct basic wavelet packets with uniformly bounded localization in both time and frequency. The corresponding orthonormal bases of wavelet packets are parametrized by dyadic segmentations obeying a local variation condition. To cite this article: L.F. Villemoes, C. R. Acad. Sci. Paris, Ser. I 335 (2002) 793–796.     

Travelling waves and dispersion relation in the spatial unfolding of a periodic orbitOndes progressives et relation de dispersion dans le déploiement spatial d'une orbite périodique

For a partial differential equation in spatial dimension one, admitting a spatially homogeneous time periodic solution, we show the generic existence, close to this solution, of a one-parameter family of travelling waves parametrized by their wave number k (k=0 corresponding to the spatially homogeneous initial solution). The argument is elementary and relies on a direct application of singular perturbation theory (Fenichel's global center manifold theorem). To cite this article: E. Risler, C. R. Acad. Sci. Paris, Ser. I 334 (2002) 833–838.     

Intersecting random half spaces with a cubeVolume de l'intersection d'un cube et de sous-espaces aleatoires

We compute the typical number of points of the discrete cube {?1,1}^N that belong to the intersection of M random half-spaces, when M is a small proportion of N. To cite this article: M. Talagrand, C. R. Acad. Sci. Paris, Ser. I 334 (2002) 807–809.     

Mixed formulations for a class of variational inequalitiesFormulations mixtes pour une classe d'inéquations variationnelles

This Note is an attempt to extend the mixed finite element method to a class of variational inequalities including the problems of Signorini and of unilateral contact in elasticity with or without friction. Existence and uniqueness for the continuous and the discrete problems as well as error estimates are established in a general abstract framework. As a result, the mixed approximation of the Signorini problem is proved to converge with an error bound in h^3/4. To cite this article: L. Slimane et al., C. R. Acad. Sci. Paris, Ser. I 334 (2002) 87–92     

Holonomic systems with solutions ramified along a cuspSystèmes holonomes avec solutions ramifiées le long d'un cusp

We classify the holonomic systems of (micro) differential equations of multiplicity one along a singular Lagrangian irreducible variety contained in an involutive submanifold of maximal codimension. We show that their solutions are related to _kF_k?1 hypergeometric functions on the Riemann sphere. To cite this article: O. Neto, P.C. Silva, C. R. Acad. Sci. Paris, Ser. I 335 (2002) 171–176.     

On a class of anisotropic asymptotically periodic HamiltoniansHamiltoniens anisotropes asymptotiquement périodiques

We construct a $\text{C}{}^1$-algebra $\text{C}$ proper to an anisotropic asymptotically periodic quantum system and we compute its quotient by the algebra of compact operators. We describe then the self-adjoint operators affiliated to $\text{C}$ and their essential spectrum. To cite this article: O. Rodot, C. R. Acad. Sci. Paris, Ser. I 334 (2002) 575–579.     

Local block bootstrapBloc re-échantillonnage local

For time series that are not stationary, the block bootstrap method is not directly applicable. However, if the underlying stochastic structure is slowly changing with time, one may employ a local block-resampling procedure. We define such a procedure, and give an example of its applicability. To cite this article: E. Paparoditis, D.N. Politis, C. R. Acad. Sci. Paris, Ser. I 335 (2002) 959–962.     

A reduced-basis element methodUne méthode d'éléments en base réduite

Reduced basis methods are particularly attractive to use in order to diminish the number of degrees-of-freedom associated with the approximation to a set of partial differential equations. The main idea is to construct ad hoc basis functions with a large information content. In this Note, we propose to develop and analyze reduced basis methods for simulating hierarchical flow systems, which is of relevance for studying flows in a network of pipes, an example being a set of arteries or veins. We propose to decompose the geometry into generic parts (e.g., pipes and bifurcations), and to construct a reduced basis for these generic parts by considering representative geometric snapshots. The global system is constructed by gluing the individual basis solutions together via Lagrange multipliers. To cite this article: Y. Maday, E.M. Rønquist, C. R. Acad. Sci. Paris, Ser. I 335 (2002) 195–200.     

S-arrangements avec répétitionsS-arrangements with repetitions

We study natural correspondances between the set of arrangements of subsets with repetitions and families of objects met in various areas of mathematics (walks in lattices, pre-order) and computer science (formal languages, Petri nets, Artificial Intelligence), using the framework of formal languages. For n=2, they are enumerated by Delannoy numbers. To cite this article: S.R. Schwer, C. R. Acad. Sci. Paris, Ser. I 334 (2002) 261–266.     

On the volume of the intersection of a sphere with random half spacesSur le volume de l'intersection d'une boule avec des demi espaces aléatoires

We find an asymptotic expression of the volume of the intersection of the N dimensional sphere with p=αN random half spaces when α is less than a critical value. This expression coincides with the one found by Gardner [3] using replica calculations. We get also the same value for α_c. Our proof is rigorous and based on the cavity method. The required decay of correlations is obtained by means of a geometrical argument which holds for general Hamiltonians. To cite this article: M. Shcherbina, B. Tirozzi, C. R. Acad. Sci. Paris, Ser. I 334 (2002) 803–806.     

Transfert lisse d'intégrales de KloostermanSmooth transfer of Kloosterman integrals

We establish the existence of smooth transfer between absolute Kloosterman integrals and Kloosterman integrals relative to a quadratic extension. To cite this article: H. Jacquet, C. R. Acad. Sci. Paris, Ser. I 335 (2002) 229–232.     

Analyse d'un problème de tsunamiAnalysis of a tsunami problem

This article presents a model and a mathematical analysis of a tsunami problem due to the displacement of the lithosphere. We give some results showing the existence, smoothness and uniqueness of the solution. To cite this article: B. Di Martino et al., C. R. Acad. Sci. Paris, Ser. I 334 (2002) 551–556.     

The 3-XORSAT thresholdLe seuil de 3-XORSAT

We prove the existence of a threshold phenomenon regarding the random 3-XORSAT problem (or more generally k-XORSAT). We provide the value of the threshold as the solution of two transcendental equations. These results confirm rigorously those obtained by physicists using the one-step replica symmetry breaking method and thus give for the first time the proof of the validity of this method for a problem of the class of satisfiability problems. To cite this article: O. Dubois, J. Mandler, C. R. Acad. Sci. Paris, Ser. I 335 (2002) 963–966.     

The symplectic reduced spaces of a Poisson actionLes espaces réduits symplectiques d'une action de Poisson

During the last thirty years, symplectic or Marsden–Weinstein reduction has been a major tool in the construction of new symplectic manifolds and in the study of mechanical systems with symmetry. This procedure has been traditionally associated to the canonical action of a Lie group on a symplectic manifold, in the presence of a momentum map. In this Note we show that the symplectic reduction phenomenon has much deeper roots. More specifically, we will find symplectically reduced spaces purely within the Poisson category under hypotheses that do not necessarily imply the existence of a momentum map. In other words, the right category to obtain symplectically reduced spaces is that of Poisson manifolds acted upon canonically by a Lie group. To cite this article: J.-P. Ortega, C. R. Acad. Sci. Paris, Ser. I 334 (2002) 999–1004.     

On self attracting/repelling diffusionsDiffusions auto attractives/repulsives

We present an almost sure ergodic theorem for a class of self-interacting diffusions on a compact Riemannian manifold. To cite this article: M. Benaim, O. Raimond, C. R. Acad. Sci. Paris, Ser. I 335 (2002) 541–544.     

Contractive liftings and the commutatorDilatations contractive et le commutateur

This paper presents the solution to a problem proposed by B.Sz.-Nagy about extending the commutant lifting theorem to the case when the underlying operators do not intertwine. The main theorem establishes minimal norm liftings of certain commutators. The proof is constructive. To cite this article: C. Foias et al., C. R. Acad. Sci. Paris, Ser. I 335 (2002) 431–436.     

Some extremely amenable groupsQuelques groupes extrêmement moyennables

A topological group G is extremely amenable if every continuous action of G on a compact space has a fixed point. Using the concentration of measure techniques developed by Gromov and Milman, we prove that the group of automorphisms of a Lebesgue space with a non-atomic measure is extremely amenable with the weak topology but not with the uniform one. Strengthening a de la Harpe's result, we show that a von Neumann algebra is approximately finite-dimensional if and only if its unitary group with the strong topology is the product of an extremely amenable group with a compact group. To cite this article: T. Giordano, V. Pestov, C. R. Acad. Sci. Paris, Ser. I 334 (2002) 273–278.     

A new approach on estimation of the tail indexUne nouvelle méthode pour l'estimation de l'index d'une queue

A new approach on tail index estimation is proposed based on studying the in-sample evolution of appropriately chosen diverging statistics. The resulting estimators are simple to construct, and they can be generalized to address other rate estimation problems as well. To cite this article: D.N. Politis, C. R. Acad. Sci. Paris, Ser. I 335 (2002) 279–282.     

Exact inversion of a compound conical Radon transform and a novel nuclear imaging principleInversion exacte d'une transformation conique de Radon composée et nouveau principe d'imagerie nucléaire

A new integral transform arising from a theory of imaging based on Compton scattering is introduced and the explicit expression for its inverse is established. Its properties serve as foundation to a new nuclear emission imaging principle. To cite this article: M.K. Nguyen, T.T. Truong, C. R. Acad. Sci. Paris, Ser. I 335 (2002) 213–217.