Primitive du cocycle de Maslov généralisé

Résumé Soit un espace hermitien symétrique de type tube, de frontière de Shilov S. Nous décrivons une réalisation du revêtement universel de S. Nous construisons ensuite sur une primitive du cocycle de Maslov généralisé. C’est l’analogue de l’indice de Souriau pour la variété lagrangienne. Une variante de cette construction généralise l’indice d’Arnold-Leray-Maslov. Enfin, nous utilisons cette primitive pour généraliser la notion de nombre de rotation symplectique.     

Équations du filtrage non linéaire de la prédiction et du lissage

We establish equations of non linear filtering, prediction (extrapolation) and smoothing (interpolation) in the case where the signal is a non degenerate diffusion process, and the observation is a noisy functional of the signal. We consider both the case of observation noise correlated with the signal, and the opposite case where we establish “robust” form of the equations. We study finally the case of unbounded coefficients, and the case where there is a feedback from the observation to the signal.     

Sur l'intégration approchée d'équations du type parabolique

Zusammenfassung Es wird in dieser Arbeit die stochastische Methode der Fahlerauswertung auf Näherungslösungen durch Differenzenmethoden für die Wärmeleitungsgleichung behandelt. Die Methode erlaubt die Genauigkeit der verschiedenen Differenzenmethoden zu vergleichen sowie den Einfluss der Schrittlägen in den beiden Varaiblen abzuschätzen.

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Institut de mathématiques appliquées de l'Ecole polytechnique de l'Université de Lausanne. Etude subventionnée en partie par le Fonds national de la recherche scientifique.M. W. Liniger, math. dipl., a contribué dans une importante mesure à l'élaboration de ce travail et aux calculs numériques.     

Loi fonctionnelle du logarithme itéré pour les incréments du processus des espacements

Let a_n(l): 0 ≤ /denote the reseated empirical process based upon uniform spacings. Let {h_n, n ≥ 1 } be a sequence decreasing to 0. Under appropriate conditions on h_n. We give a functional lnw of the iterated logarithm for the set of increment functions {a_n (l + h_n.) — a_n(l): 0 ≤ / ≤ 1 -h_n}.     

Régularité du rayon hyperbolique

Let $\text{Ω?}\text{R}{}^2$ be a bounded domain of class $\text{C}{}^{\mathrm{2+\alpha }}\text{,}\text{0<α<1}$. We show that if u is the maximal solution of Δu=4exp(2u), which tends to +∞ as $\text{(x,y)→?Ω}$, then the hyperbolic radius v=exp(?u) is of class C^2+α up to the boundary. The proof relies on new Schauder estimates for Fuchsian elliptic equations. To cite this article: S. Kichenassamy, C. R. Acad. Sci. Paris, Ser. I 338 (2004).     

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.     

Théorie du potentiel pour des opérateurs elliptiques non linéaires du second ordre à coefficients discontinus

Let a open subset of ⁿ , n3, and an open. Existence and unicity are proved for the Dirichlet problem

Une généralisation du théorème de Kobayashi-Ochiai

We establish relations between the growth of non-degenerate holomorphic maps \(\varphi\) from \({\mathbb{C}}^n\) to X, an n-dimensional compact Kähler manifold, and the positivity of the canonical bundle of X. The general principle is that the growth increases with this positivity. In the extreme case where X is of general type, such maps do not exist, a result of Kobayashi-Ochiai. In the other extreme, if the growth is sufficiently slow (see theorem 1), we show that X is uniruled if projective. K. Kodaira obtained the weaker property that X has no nonzero pluricanonical forms. Our results interpolate between, and include, these two extreme cases.     

Théorèmes du type Ingham et application à la théorie du contrôle

Ingham [4] improved a previous result of Wiener [10] on nonharmonic Fourier series. Modifying his weight function we obtain optimal results improving several earlier theorems of Kahane [7], Castro and Zuazua [2] and of Jaffard, Tucsnak, and Zuazua [5]. Then we apply these results to simultaneous observability problems.     

Une interprétation du théorème de colonnetti

Summary Considering an elastic-plastic continuum, the plastic deformations of which are given, it is prooved in a general way thatColonnetti's function (4), where ( _x , ..., _xy , ...) is the stress tensor, ( ) the plastic-strain tensor and the elastic potential energy, differs only by a constant value from the fictitious strain energy evaluated from the total strain as if it were purely elastic. Consequently, both functions are simultaneously minima andColonnetti's theorem can be rephrased in terms of fictitious (elastic) strain energy.     

Sous-Groupes Algébriques du Groupe de Cremona

We give a complete classification of maximal algebraic subgroups of the Cremona group Bir() and provide algebraic varieties that parametrize the conjugacy classes.

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Résumé  Résumé Nous donnons une classification complète des sous-groupes algébriques maximaux du groupe de Cremona Bir() et explicitons les variétés qui paramètrent les classes de conjugaison.

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Soutenu par le fonds national suisse de la recherche scientifique (FNRS).     

Transformation de Lévy et zéros du mouvement Brownien

In this paper, it is shown that the iterated Lévy transforms ( ⁿ ) of a standard Brownian motion , so defined:

Proprieétés du degré des morphismes de Belyi

Properties of the degree of Belyi functions. A famous theorem of Belyi characterizes the curves defined over a number field by the existence of an element of its function field with certain ramification properties. In this article we are interested in the degree of these functions. We define the Belyi degree of a curve defined over a number field and the Belyi degree of a point on such a curve. We prove finiteness results concerning these invariants. We give an explicit upper bound for the Belyi degree of a point on the projective line, depending on the height and on the degree of its field of definition.     

Etudes de certaines propriétés optiques du corps solide

Ohne Zusammenfassung