Factorialité de l'anneau des séries de Dirichlet analytiques

We study arithmetical properties of the ring of analytic Dirichlet series. In particular, we prove a theorem of division by several series and we deduce from it that the ring is factorial. To cite this article: F. Bayart, A. Mouze, C. R. Acad. Sci. Paris, Ser. I 336 (2003).     

Moyennes empiriques pour les mosaïques de Voronoi du disque de Poincaré

Let Φ be a stationary ergodic point process with finite intensity of the Poincaré disk. After defining the typical cell associated to the Voronoi tessellation of Φ, we study the convergence of empirical means of this tessellation. Contrary to the Euclidean case, several natural choices of means exist, leading to different behavior. The case where Φ is a Poisson process is more specifically characterized. To cite this article: F. Lips, C. R. Acad. Sci. Paris, Ser. I 342 (2006).     

Une remarque sur l'annulateur du groupe des classes d'idéaux

Using an inequality for the Weil height on an Abelian extension of the rationals and a theorem of Linnik, we prove a lower bound for the index of the annihilator of the ideal class group of a cyclotomic field. This lower bound is exponential in the degree of the field. To cite this article: F. Amoroso, C. R. Acad. Sci. Paris, Ser. I 342 (2006).     

Formes fermées et feuilletages 2-isotropes

In this Note we introduce, for a closed form of any degree, the notion of 2-isotropic foliation, which plays the same role as that of the Lagrangian foliation in the symplectic case. After constructing an affine structure on its leaves we describe the tubular neighborhood of a ‘Lagrangian’ transverse section. To cite this article: F.-J. Turiel, C. R. Acad. Sci. Paris, Ser. I 346 (2008).     

Borne sur l'advection et la hauteur d'eau du problème de shallow-water avec conditions aux limites de Dirichlet

Using some properties of the Hardy spaces, we give a regularity result on the advection term of the shallow-water equations and we show a $L^2$ bound holding up to the boundary on the water height with Dirichlet boundary conditions. To cite this article: F. Flori, P. Orenga, C. R. Acad. Sci. Paris, Ser. I 340 (2005).     

A counterexample to the Gouvêa–Mazur conjecture

Gouvêa and Mazur made a precise conjecture about slopes of modular forms. Weaker versions of this conjecture were established by Coleman and Wan. In this Note, we exhibit examples contradicting the full conjecture as it currently stands. To cite this article: K. Buzzard, F. Calegari, C. R. Acad. Sci. Paris, Ser. I 338 (2004).     

Fonctions constructibles et intégration motivique I

We introduce a direct image formalism for constructible motivic functions. One deduces a very general version of motivic integration for which a change of variables theorem is proved. These constructions are generalized to the relative framework, in which we develop a relative version of motivic integration. To cite this article: R. Cluckers, F. Loeser, C. R. Acad. Sci. Paris, Ser. I 339 (2004).     

Dynamics of multiple degree Ginzburg–Landau vortices

For the two-dimensional complex parabolic Ginzburg–Landau equation we prove that, asymptotically, vortices evolve according to a simple ordinary differential equation, which is a gradient flow of the Kirchhoff–Onsager functional. This convergence holds except for a finite number of times, corresponding to vortex collisions and splittings, which we describe carefully. The only assumption is a natural energy bound on the initial data. To cite this article: F. Bethuel et al., C. R. Acad. Sci. Paris, Ser. I 342 (2006).     

Convergence of the parabolic Ginzburg–Landau equation to motion by mean curvature

We present some new results for the asymptotic behavior of the complex parabolic Ginzburg–Landau equation. In particular, we establish that, as the parameter ε tends to 0, vorticity evolves according to motion by mean curvature in Brakke's weak formulation. The only assumption we make is a natural energy bound on the initial data. In some cases, we also prove convergence to enhanced motion in the sense of Ilmanen. To cite this article: F. Bethuel et al., C. R. Acad. Sci. Paris, Ser. I 336 (2003).     

Convergence de l'estimateur à noyau des k plus proches voisins en régression fonctionnelle non-paramétrique

This note focuses on the k nearest neighbor method when one regresses a real random variable on a functional random variable (i.e. valued in an infinite-dimensional space). More precisely, we consider a kernel estimator of the regression based on a local bandwidth using exactly the k nearest neighbors. Although it is frequently used in functional data analysis, this method has not given any theoretical result so far. The aim of this Note is to show the pointwise almost-complete convergence of the k nearest neighbor kernel estimator in nonparametric functional regression. To cite this article: F. Burba et al., C. R. Acad. Sci. Paris, Ser. I 346 (2008).     

New constructions of perfectly matched layers for the linearized Euler equations

Based on a PML for the advective wave equation, we propose two PML models for the linearized Euler equations. The derivation of the first model can be applied to other physical models. The second model was implemented. Numerical results are shown. To cite this article: F. Nataf, C. R. Acad. Sci. Paris, Ser. I 340 (2005).     

Espaces productivement de FréchetProductively Fréchet spaces

The class of topological spaces whose product with every strongly Fréchet space is also Fréchet is characterized internally. This solves a long standing problem. To cite this article: F. Jordan, F. Mynard, C. R. Acad. Sci. Paris, Ser. I 335 (2002) 259–262.     

Un résultat de consistance pour des SVM fonctionnels par interpolation spline

This Note proposes a new methodology for function classification with Support Vector Machine (SVM). Rather than relying on projection on a truncated Hilbert basis as in our previous work, we use an implicit spline interpolation that allows us to compute SVM on the derivatives of the studied functions. To that end, we propose a kernel defined directly on the discretizations of the observed functions. We show that this method is universally consistent. To cite this article: N. Villa, F. Rossi, C. R. Acad. Sci. Paris, Ser. I 343 (2006).     

Description chirurgicale des revêtements ramifiés simples à quatre feuillets de la 3-sphère

Given a simple 4-fold branched covering $\text{p}\text{:M→S}{}^3$, we provide an effective method to find a surgery presentation of M. To cite this article: F. Harou, C. R. Acad. Sci. Paris, Ser. I 336 (2003).     

Bifurcation and forced symmetry breaking in Hamiltonian systems

We consider the phenomenon of forced symmetry breaking in a symmetric Hamiltonian system on a symplectic manifold. In particular we study the persistence of an initial relative equilibrium subjected to this forced symmetry breaking. We see that, under certain nondegeneracy conditions, an estimate can be made on the number of bifurcating relative equilibria. To cite this article: F. Grabsi et al., C. R. Acad. Sci. Paris, Ser. I 338 (2004).     

Backward volume contraction for endomorphisms with eventual volume expansion

We consider smooth maps on compact Riemannian manifolds. We prove that under some mild condition of eventual volume expansion Lebesgue almost everywhere we have uniform backward volume contraction on every pre-orbit of Lebesgue almost every point. To cite this article: J.F. Alves et al., C. R. Acad. Sci. Paris, Ser. I 342 (2006).     

On localization for the Schrödinger operator with a Poisson random potential

We prove exponential localization for the Schrödinger operator with a Poisson random potential at the bottom of the spectrum in any dimension. We also prove exponential localization in a prescribed interval for all large Poisson densities. In addition, we obtain dynamical localization and finite multiplicity of the eigenvalues. To cite this article: F. Germinet et al., C. R. Acad. Sci. Paris, Ser. I 341 (2005).     

Affability of Euclidean tilings

We prove that every minimal equivalence relation on a Cantor set arising from the continuous hull of an aperiodic and repetitive Euclidean tiling is affable. To cite this article: F. Alcalde Cuesta et al., C. R. Acad. Sci. Paris, Ser. I 347 (2009).     

Un modèle non-linéaire de prolifération cellulaire : extinction des cellules et invariance

This Note analyses a nonlinear age-maturity structured system which arises as a model of the blood cellular production in the bone marrow. The resulting model is a nonlinear first-order partial differential equation in which there is a distributed temporal delay and a retardation in the maturation variable. We prove that uniqueness of solutions depends only on small maturity cells (stem cells) and we give a result of invariance. To cite this article: M. Adimy, F. Crauste, C. R. Acad. Sci. Paris, Ser. I 336 (2003).