Calcul de lʼespérance de la solution dʼune EDP stochastique unidimensionnelle à lʼaide dʼune base réduite

In this Note, we present an efficient method to approximate the expectation of the response of a one-dimensional elliptic problem with stochastic inputs. In conventional methods, the computational effort and cost of the approximation of the response can be dramatic. Our method presented here is based on the Karhunen–Loève (K-L) expansion of the inverse of the diffusion parameter, allowing us to build a base of random variables in reduced numbers, from which we construct a projected solution. We show that the expectation of this projected solution is a good approximation, and give an a priori error estimate. A numerical example is presented to show the efficiency of this approach.     

Sur lʼusage de la formule de Cauchy–Binet dans les démonstrations de convergence de lʼalgorithme QR tri-diagonal avec décalages

Using the Cauchy–Binet formula, one shows that it is possible to simplify the convergence proofs of the tridiagonal QR algorithm with shifts due to Wilkinson (1968) [12], Hoffmann–Parlett (1978, 1998) [3], [7], and Jiang–Zhang (1985) [4], including the quadratic or cubic convergence results.     

Tests dʼadéquation à la mesure de Haar,identité de duplication de Watson et représentations dʼun groupe compact

We use the theory of compact groups representations in building goodness-of-fit tests for the Haar probability measure. An interpretation of a duplication identity already known for the celebrated circular test of G. Watson is given in terms of representation theory.     

Principes de grandes déviations pour l’estimateur à noyau de la densité de probabilité

We establish pointwise and uniform large deviations principles for nonparametric kernel density estimators. The estimates are based on sequences of independent and identically distributed real random variables.     

Estimation de la fonction de régression pour variable explicative et réponse fonctionnelles dépendantes

We consider a kernel estimate of the regression when the response variable is in a Banach space and the explanatory variable takes its values in a semi-metric space. Our main result states the almost complete convergence (with rate) of the constructed estimate when the sample considered is a β-mixing sequence.     

Résultats de convergence presque sûre pour l’estimation et la prévision des processus linéaires hilbertiens

Motivated by the prediction of certain types of continuous time processes, we study, here the estimation and the prediction of hilbertian linear processes. Only results about almost sure convergence are given.     

Une méthode de décomposition en temps avec des schémas dʼintégration réversible pour la résolution de système dʼéquations différentielles ordinaires

We propose a time domain decomposition method that breaks the sequentiality of the integration scheme for systems of ODE. Under the condition of differentiability of the flow, we transform the initial value problem into a well-posed boundary values problem using the symmetrization of the interval of time integration and time-reversible integration scheme. For systems of linear ODE, we explicitly construct the block tridiagonal system satisfied by the solutions at the time sub-intervals extremities. We then propose an iterative algorithm of Schwarz type for updating the interfaces conditions which can extend the method to systems of nonlinear ODE.     

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.     

Résolution du problème de Dirichlet pour lʼéquation du Jacobien prescrit via lʼéquation de Monge–Ampère

We give an alternative proof, based on the Monge–Ampère equation, of Dacorogna and Moser?s result (Dacorogna and Moser, 1990) [4] on the solvability with optimal regularity of the Dirichlet problem for the prescribed Jacobian equation.     

Sur la définition de la probabilité

Sans résumé     

Nouvelle démonstration du principe de correspondance de Cayley et Brill,et méthode à la détermination des coïncidences de correspondances algebriques sur une courbe d'un genre quelconque.

Sans résumé     

Un théorème de décomposition pour les polaires génériques d'une courbe plane

In this Note we state a decomposition theorem into bunches of branches (i.e. analytically irreducible germs) for the generic polar curves of a reduced germ of a plane analytic curve, with equation ƒ(x, y) = 0. They are the curves with equation ∂f(x, y)/∂yτ∂f(x, y)/∂x = 0 with generic τ. All the branches of the same bunch have the same contact with each branch of C. A number of the first terms of the Puiseux expansion of each branch of the polar is therefore independent of τ; this number depends only on the bunch to which the branch belongs. This generalizes results of H.J.S. Smith [8], M. Merle [7] (where C is a branch), E. Casas [1], F. Delgado [2]. We show by an example that it is also optimal. We have shown elsewhere that it implies the results of Lê-Michel-Weber [6].     

Martingales et grandes déviations pour les arbres binaires de recherche

We establish almost sure and in mean large deviations theorems for the leaf structure of binary search trees (b.s.t.). To this end, a parameterized family of martingales is introduced. This family also allows us to have asymptotic results on the number of final leaves of a b.s.t.     

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.