Actions modérées de schémas en groupes affines et champs modérés

We compare two notions of tameness: one introduced in Chinburg et al. (1996) [4] for actions of affine group schemes and one introduced in Abramovich et al. (2008) [1] for stacks. From this comparison, we deduce results on the structure of inertia groups in these tame situations.     

Famille de schémas implicites uniformément contrôlables pour l'équation des ondes 1-D

We present a parameterized family of finite difference schemes for the exact controllability of the 1-D wave equation. These schemes differ from the usual centered ones by additional terms of order to $h^2$, where h denotes the discretization step in space. Using a discrete version of Ingham's inequality for nonharmonic Fourier series, the spectral properties and dispersion diagrams of the schemes, we determine the parameters leading to a uniform controllability property with respect to h and an optimal stability CFL condition. To cite this article: A. Münch, C. R. Acad. Sci. Paris, Ser. I 339 (2004).     

Schémas en groupe et modules filtrés

Let k be a perfect field of characteristic p > 0. When p ≥ 3, Fontaine has classified p-divisible groups and finite flat commutative p-groups over the Witt vectors W(k) in terms of filtered modules ([9]+[6],[7]). Still assuming p ≥ 3, we extend these classifications over an arbitrary complete discrete valuation ring of unequal characteristic and residue field k by using “generalized” filtered modules. In particular, there is no restriction on the ramification index.     

Correction non linéaire et principe du maximum pour la discrétisation d'opérateurs de diffusion avec des schémas volumes finis centrés sur les mailles

We describe a nonlinear technique which suppresses oscillations appearing in the discretization of diffusion operators with cell-centered finite volume schemes.     

Sur le caractère entropique des schémas de relaxation appliqués à une équation d'état non classique

In this Note, we show that the relaxation scheme theory applied to a non-classical equation of state allows to build in a very easy way a family of entropic schemes. It is very easy to build this kind of scheme because there exists a kinetic model whose fluid limit gives this non-classical equation of state.     

Différentiation des capacités et des intégrales de Choquet

For any subadditive capacity κ on R dominated by a Radon measure, we show that lim κ (χ − δ, χ + ε]/(δ + ε) = d_κ (χ) exists for a.a. χ, as δ + ε → 0. Moreover, the Choquet integrals of any positive mesurable g satisfy

     

Correction non linéaire et principe du maximum avec des schémas hybrides pour la discrétisation dʼopérateurs de diffusion

We describe a nonlinear technique to eliminate oscillations appearing in the discretization of diffusion operators with hybrid schemes.     

Equirépartition des coefficients de Fourier des fonctions L de carrés et de cubes symétriques

Dans ce travail, on étudie l’équirépartition et l’équirépartition harmonique des coefficients de Fourier des fonctions L de carrés et de cubes symétriques d’une forme primitive.     

Schémas de type Godunov entropiques et positifs pour la dynamique des gaz et la magnétohydrodynamique lagrangiennes

Entropic and positive Godunov-type schemes are constructed for gas dynamics and magnetohydrodynamic equations in Lagrangian coordinates. These schemes are natural extension of already known Roe schemes.     

Pavages auto-affines, opérateurs de transfert et critères de réseau dans ℝ d

Resumé Nous applíquons les résultats de [2] à la construction d'analyses multirésolutions et en particulier à l'étude de pavages auto-affines de ^d . Nous montrons qu'une tuile auto-affine, construite à partir d'une matrice dilatante à coefficients entiers, permet de paver ^d par translation par les éléments d'un réseau.

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We applied results from [2] to multiresolution analysis and to lattice tilings of ^d with self-affine tiles.

     

Mauvaise réduction des variétés de Drinfeld et correspondance de Langlands locale

Sans résumé Oblatum 28-XII-1998 & 3-V-1999 / Published online: 5 August 1999     

Catégories prémodulaires, modularisations et invariants des variétés de dimension 3

An abelian k-linear semisimple category having a finite number of simple objects, and endowed with a ribbon structure, is called premodular. It is modular (in the sense of Turaev) if the so-called S-matrix is invertible. A modular category defines invariants of 3-manifolds and a TQFT ([T]). When is it possible to construct a modularisation of a given premodular category, i.e. a functor to a modular category preserving the structures and ‘dominant’ in a certain sense? It turns out (2.3) that this amounts essentially to making ‘transparent’ objects trivial. We give a full answer to this problem in the case when k is a field of char. 0 (as well as partial answers in char. p): under a few obvious hypotheses, a premodular category admits a modularisation, which is unique (th. 3.1, and cor. 3.5 in char. 0) The proof relies on two main ingredients: a new and very simple criterion for the S-matrix to be invertible (1.1) and Deligne's internal characterization of tannakian categories in char. 0 [D]. When simple transparent objects are invertible, the criterion is simpler (4.2) and the modularisation can be described more explicitly (prop. 4.4). We conclude with two examples: the premodular categories associated with quantum and at roots of unity; in the first case, we obtain modular categories which were built independently by C. Blanchet [B]; in the second case, we obtain modularizations in all the cases where Y. Yokota [Y] found Reshetikhin-Turaev invariants of 3-manifolds, thereby improving as well as explaining Yokota's results.

Re?u le: 14 juillet 1998 / version définitive: 28 mars 1999     

Sur la série de dirichlet et la série de facultés

Sans résumé Extrait d'une lettre à M. N. E.N?rlund.     

Vitesses maximales de décroissance des erreurs et tests optimaux associés

Summary Under reasonable conditions on , both errors of the tests that the law of a sample of size n belongs to , go to zero like exp[–n] and exp[– n]. We shall determine the best possible values for and and give a construction of sequences of tests for which the errors decrease with such an optimal rate.

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Je tiens à remercier tout particulièrement G. Tusnády pour de nombreuses et très utiles suggestions et critiques concernant une première version de cet article.     

Intersection de sous-groupes et de sous-variétés I

We study the intersection of a subvariety X of an abelian variety A over with the union of all the algebraic subgroups of A of given dimension d. Our main result states that if we remove a suitable exceptional subset from X and if d is small enough then the intersection enjoys a Northcott-like property: the points of bounded height on it form a finite set. The condition on d involves only the dimension of X and the structure of A up to isogenies. We show how it can be weakened if we assume certain conjectures in the direction of an abelian version of Lehmer's problem. The theorem is especially meaningful when X is a curve since it is then possible to bound the height and hence to prove finiteness of the set under consideration. This generalises the result of E. Viada on powers of elliptic curves and is analogous to work of E. Bombieri, D. Masser and U. Zannier on tori, whose general strategy we follow.