Complète intégrabilité singulière

We show that an holomorphic vector field in a neighbourhood of its singular point 0 0 ∈ ℂⁿ is analytically normalizable as soon as it has a sufficiently large number of commuting holomorphic vector fields, a sufficiently large number of formal first integrals, and that a Diophantian small divisors condition related to its linear part is satisfied.     

Un théorème de dualité

Sans résumé Herrn H. Hopf zum sechzigsten Geburtstag gewidmet     

Algèbres de Sobolev Généralisées

We examine the structure of a generalized Sobolev spaces. We also exhibit a class of locally uniformlyA-convex algebras, the unitization of which are not the same type.

     

Homogénéisation d'un problème de capillarité

We study the behavior of the height of a liquid contained in a vertical cylindrical tube where are immerged a periodic distribution (period ɛ) of cylindrical fibers with radius r < ɛ and whose material-liquid coefficient is λ. It is showed that the homogenized problem depends on the limit of λr/ɛ² as (ɛ, λ, r) → (0,0, 0). The second problem is when the border is made of two alternate periodic bands, the first of length r being incrusted in the second of length ɛ − r. Here, the homogenized problem depends on the limit of r/ɛ as (, r) → (0, 0). For this, we use epi-convergence techniques.     

Paramètres algébriques de groupes formels et critères d'isogénie

We generalise G. and D. Chudnovsky's isogeny criterion for elliptic curves over Q to the case of Abelian varieties of dimension g. The proof is bused on an explicit construction of algebraic parameters of their formal groups.     

Modèle électromagnétique d'objet dissimulé

We model propagation of electromagnetic waves in a medium, which is inhomogeneous with a rough layer, and which hides an object. We first get an effective medium, and then we solve the problem by integral equations.     

Espaces homogènes génériquement triviaux

We study the homogeneous spaces of a smooth group G over affine spaces or local k-algebra and gerbs locally banded by a semi-simple group H dèfine over k. In particular we show that every gerb locally banded by H and rationally trivial is trivial, and that an homogeneous space of G with semi-simple isotropy which is rationally trivial is trivial in the Zariski topology. This extends a result of Colliot-Thélène and Ojanguren concerning G-torsors.     

Stabilisation des systèmes bilinéaires homogènes

We deal with the problem of stabilizing the bilinear homogeneous systems. We give sufficient conditions for a bilinear system to be stabilizable with homogeneous feedback of degree zero. The explicit design of the feedback is given.     

Algèbre Pré-Gerstenhaber à homotopie près

This paper is concerned by the concept of algebra up to homotopy for a structure defined by two operations . and $[,]$. An important example of such a structure is the Gerstenhaber algebra (i.e. commutatitve structure with degree 0 and Lie structure with degree ?1). The notion of Gerstenhaber algebra up to homotopy ($G_{\infty }$ algebra) is known: it is a codifferential bicogebra.Here, we give a definition of pre-Gerstenhaber algebra (pre-commutative and pre-Lie) allowing a similar construction for a $\text{pre}{G}_{\infty }$ algebra.Given a structure of pre-commutative (Zinbiel) and pre-Lie algebra and working over the corresponding Koszul dual operads, we will give an explicit construction of the associated pre-Gerstenhaber algebra up to homotopy: it is a bicogebra (Leibniz and permutative) equipped with a codifferential which is a coderivation for the two coproducts.     

Une nouvelle caractérisation des sphères géodésiques dans les espaces modèles

We show that a compact immersed hypersurface of hyperbolic space or an open half-sphere with constant mean curvature and almost constant scalar curvature is a geodesic sphere. To cite this article: J. Roth, C. R. Acad. Sci. Paris, Ser. I 347 (2009).     

Algèbres localement uniformémentA-pseudo-convexes advertiblement complètes

We examine the structure and the spectral properties of locally uniformlyA-pseudo-convex algebras.      

Critères d'ergodicité géométrique ou arithmétique de modèles linéaires pertubés à représentation markovienne

This paper is devoted to some models with a state space representation ( 1 ). Foster-Lyapounov type inequalities due to Tweedie [11], Tuominen and Tweedie [10] describe the conditions under which such a model remains ergodic. The applications are twofold. In the first case we examine an autoregressive model which departs from linearity additively. In the second case, the state space model arises from a sublinear model. In each case conditions that ensure ergodicity are given, with geometric or, possibly, subgeometric rates of convergence to the ergodic measure.     

Problème du bord dans les variétés $q$-convexes et phénomène de Hartogs-Bochner

Résumé.   Soient E un fibré vectoriel holomorphe au dessus d'une variétéq-complète X et M une sous-variété réelle de dimension 2p-1 () de E. Nous montrons que le problème du bord pour M est résoluble si et seulement si M est maximalement complexe. Dans le cas où nous retrouvons le théorème de Harvey et Lawson [17]. Comme conséquence nous obtenons une généralisation du théorème de Hartogs-Bochner pour les applications CR-méromorphesà valeurs dans une variétéq-convexe et une généralisation au cas CR-méromorphe du théorème d'extension de Chazal [5].

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Let E be a holomorphic vector bundle over a -complete manifold X and M be a real submanifold of dimension 2p-1 () of E. We prove that M has a solution to the boundary problem in X if and only if M is maximally complex. In the case , this is a result of Harvey and Lawson [17]. As a consequence, we obtain a generalization of the Hartogs-Bochner theorem for CR-meromorphic maps taking their values in -convex manifolds and a generalization to the CR-meromorphic case of a theorem of Chazal [5].

Received: 27 April 2000 / Published online: 23 July 2001     

Une réciproque générique du théorème Sunada

Let G a compact group of isometries of a closed riemannian manifold(X,m). Sunada proved that if are twofinite almost-conjugated subgroups of G, then and are isospectral. We prove that if G is finite, there exists an open dense set in the set of G-invariant metrics for which the converse ofthis resukt is true. If G is infinite, the situations is more complicated and we obtain some partial results.     

Sur les multiplicités intégrales des systèmes d'équations différentielles non linéaires ayant un petit paramètre

Résumé On expose les résultats principaux deN. Bogolioubov sur la théorie des variétés intégrales pour les équations de type(1.1) et ceux de travaux consacrés a la généralisation et au développement de cette théorie pour les classes plus générales d'équations, contenant un paramètre petit. à Giovanni Sansone pour son 70^me anniversaire     

Régression non paramétrique: une approche générale du problème de sélection automatique de modèle

This Note presents a unifying approach for data-driven model selection in nonparametric regression. Some asymptotic optimality property is presented in a general way that allows applications to many nonparametric smoothers and many model choice problems.     

Modèles semi-factoriels et modèles de Néron

Let S be the spectrum of a discrete valuation ring with function field K. Let X be a scheme over S. We will say that X is semi-factorial over S if any invertible sheaf on the generic fiber X _K can be extended to an invertible sheaf on X. Here we show that any proper geometrically normal scheme over K admits a proper, flat, normal and semi-factorial model over S. We also construct some semi-factorial compactifications of regular S-schemes, such as Néron models of abelian varieties. The semi-factoriality property for a scheme X/S corresponds to the Néron property of its Picard functor. In particular, one can recover the Néron model of the Picard variety ${{\rm Pic}_{X_K/K,{\rm red}}^0}$ of X _K from the Picard functor Pic _X/S , as in the known case of curves. This provides some information on the relative algebraic equivalence on the S-scheme X.