Explicit Plancherel formula for the p-adic group GL(n)

We provide an explicit Plancherel formula for the p-adic group GL(n). We determine explicitly the Bernstein decomposition of Plancherel measure, including all numerical constants. We also prove a transfer-of-measure formula for GL(n). To cite this article: A.-M. Aubert, R. Plymen, C. R. Acad. Sci. Paris, Ser. I 338 (2004).     

Comment établir des conditions nécessaires d'optimalité dans les problèmes de contrôle dont certains arguments sont déviés ?

We give a general idea to state necessary optimality conditions for problems of variational calculus or optimal control problems with deviating arguments. To cite this article: L. Samassi, R. Tahraoui, C. R. Acad. Sci. Paris, Ser. I 338 (2004).     

Convergence of linear finite elements for diffusion equations with measure data

We show here the convergence of the linear finite element approximate solutions of a diffusion equation to a weak solution, with weak regularity assumptions on the data. To cite this article: T. Gallouët, R. Herbin, C. R. Acad. Sci. Paris, Ser. I 338 (2004).     

Spaces of lower semicontinuous set-valued maps

We give a negative answer to Problem 2 posed by R. A. McCoy in his paper [McCoy R. A.: Spaces of lower semicontinuous set-valued maps II, Math. Slovaca 60 (2010), 541–570]. Some topological properties of the space L ^?(X) introduced in [McCOY R. A.: Spaces of lower semicontinuous set-valued maps I, Math. Slovaca 60 (2010), 521–540] equipped with the Vietoris topology are also investigated.     

Fonctions constructibles et intégration motivique II

We extend the formalism of an earlier Note to a global setting for which a theorem on fiber integrals and a Fubini theorem are obtained. We compare our formalism to the previous constructions given by Denef and Loeser. To cite this article: R. Cluckers, F. Loeser, C. R. Acad. Sci. Paris, Ser. I 339 (2004).     

Matrix-theoretical derivations of some results of Borcea–Shapiro on hyperbolic polynomials

We use matrix analysis to give simple proofs of two theorems of Borcea–Shapiro which yield majorization relations between certain hyperbolic polynomials. We also prove a conjecture of Borcea involving majorization and the zeros of polynomials. To cite this article: R. Pereira, C. R. Acad. Sci. Paris, Ser. I 341 (2005).     

Smallest singular value of random matrices with independent columns

We study the smallest singular value of a square random matrix with i.i.d. columns drawn from an isotropic symmetric log-concave distribution. We prove a deviation inequality in terms of the isotropic constant of the distribution. To cite this article: R. Adamczak et al., C. R. Acad. Sci. Paris, Ser. I 346 (2008).     

Accélération de schémas d'intégration temporelle pour les équations différentielles algébriques linéaires

We propose an approach to accelerate implicit schemes associated to linear differential-algebraic equations with constant coefficients. To cite this article: M. Al Sayed Ali, C. R. Acad. Sci. Paris, Ser. I 346 (2008).     

Essential dimension of Abelian varieties over number fields

We show that the essential dimension of a non-trivial Abelian variety over a number field is infinite. To cite this article: P. Brosnan, R. Sreekantan, C. R. Acad. Sci. Paris, Ser. I 346 (2008).     

Totally geodesic Riemannian foliations with locally symmetric leaves

We prove the arithmeticity of totally geodesic Riemannian foliations, with a dense leaf, on complete finite volume Riemannian manifolds when the leaves are isometrically covered by an irreducible symmetric space of noncompact type and rank at least 2. To cite this article: R. Quiroga-Barranco, C. R. Acad. Sci. Paris, Ser. I 342 (2006).     

Un algorithme de Schur pour les fonctions de transfert des systèmes surdéterminés invariants dans une direction

We define an analogue of the Schur algorithm for transfer functions of lossless 2D systems which are invariant with respect to one of the variables. To cite this article: D. Alpay et al., C. R. Acad. Sci. Paris, Ser. I 347 (2009).     

Fonctions rationnelles aux différences à valeurs entières dans les vecteurs de Witt

We transpose Kochen's results on integral valued rational functions over the p-adic numbers to difference rational functions over the Witt vectors with their Frobenius. To cite this article: L. Bélair, C. R. Acad. Sci. Paris, Ser. I 339 (2004).     

Finite time extinction for solutions to fast diffusion stochastic porous media equations

We prove that the solutions to fast diffusion stochastic porous media equations have finite time extinction with strictly positive probability. To cite this article: V. Barbu et al., C. R. Acad. Sci. Paris, Ser. I 347 (2009).     

The elliptic K3 surfaces with a maximal singular fibre

We give the defining equation of complex elliptic K3 surfaces with a maximal singular fibre. Then we study the reduction modulo p at a particularly interesting prime p. To cite this article: T. Shioda, C. R. Acad. Sci. Paris, Ser. I 337 (2003).     

Marches aléatoires sur certains groupes unimodulaires p-adiques

We give central and off-diagonal estimates for the transition kernels corresponding to simple random walks on certain unimodular solvable p-adic groups. To cite this article: S. Mustapha, C. R. Acad. Sci. Paris, Ser. I 340 (2005).     

Effondrement de quotients aléatoires de groupes hyperboliques avec torsion

We show that random quotients of hyperbolic groups with ‘harmful’ torsion collapse at densities smaller than expected. To cite this article: Y. Ollivier, C. R. Acad. Sci. Paris, Ser. I 341 (2005).     

Utilisation des modules de Drinfeld en cryptologie

We present in this Note a new and efficient public-key cryptosystem based on Drinfeld modules. The details will appear elsewhere. To cite this article: R. Gillard et al., C. R. Acad. Sci. Paris, Ser. I 336 (2003).     

Asymptotic modelling of a fluid–structure coupling in the case of a prestressed inflated orthotropic membrane shell

In this Note, we consider an inflated orthotropic linearly elastic generalized membrane shell submitted to an outer surface perturbation. We obtain the strong convergence towards the solution of a well-posed “2D” problem of the mean value in the membrane thickness 2ε of the “3D” scaled displacements, as ε approaches zero. To cite this article: R. Luce et al., C. R. Acad. Sci. Paris, Ser. I 346 (2008).     

Differentiability of the isoperimetric profile and topology of analytic Riemannian manifolds

We show that smooth isoperimetric profiles are exceptional for real analytic Riemannian manifolds. For instance, under some extra assumptions, this can happen only on topological spheres. To cite this article: R. Grimaldi et al., C. R. Acad. Sci. Paris, Ser. I 347 (2009).     

A uniqueness result for monotone elliptic problems

We give here a short proof of the uniqueness of entropy solutions for nonlinear monotone elliptic problems with L¹-data. To cite this article: M.M. Porzio, C. R. Acad. Sci. Paris, Ser. I 337 (2003).