Sur le problème de descente des formes quadratiques

In this paper, we give some positive answers to a conjecture of B. Kahn on a descent problem for quadratic forms [9].     

Trois Notes sur la théorie des formes

Sans résumé     

Régularité de la loi du maximum de processus gaussiens réguliers

Let X be a real-valued Gaussian process with a one-dimensional parameter. If the sample paths of X are of class C^2k, k integer and if the marginal distributions of X and its derivatives have no degeneracy, then the distribution function of the maximum on a bounded interval is of class C^k. We give a recurrence method allowing to express the derivatives by means of certain implicit formulae.     

Grandes déviations pour des formes quadratiques de processus gaussiens localement stationnaires

We establish large deviations principles for quadratic forms - tapered periodograms integrated over frequencies, a pre-periodogram integrated over time and frequencies, likelihood ratio — of Gaussian locally stationary processes as defined bx Dahlhaus ([3], [4]).     

Solutions du système d'équations différentielles de Hua et intégrales de Poisson-Shilov des fonctions de carré intégrable sur la frontière de Shilov de la boule matricielle de rang deux

We give a characterization of those solutions F of the Hua system of differential equations H_DF(Z) = − (λ² + 4)F(Z) · I, that are Poisson-Shilov integrals of L²-functions on the Shilov boundary of the rank two matrix ball.     

Sur la méthode de Gauss pour le calcul approché des intégrales

Sans résumé     

Un modèle du calcul de Dirac dans la théorie relative des ensembles

The aim of this Note is a new justification of the pertinence of the Dirac calculus (see [1]). We give a model of it in a relatively consistent set theory,the Relative Set Theory (see [2]). We have obtained this result by introducing a derivation of step functions.     

Asymptotique des approximants de Hermite–Padé quadratiques de la fonction exponentielle et problèmes de Riemann–Hilbert

We describe the asymptotic behavior of the polynomials $\text{p,}\text{q,}\text{r}$ of degree n in type I Hermite–Padé approximation to the exponential function, i.e., $\text{p(z)}\text{e}{}^{\mathrm{?z}}\text{+q(z)+r(z)}\text{e}{}^{\mathrm{z}}\text{=}\text{O}\text{(z}{}^{\mathrm{3n+2}}\text{)}$ as z→0. A steepest descent method for Riemann–Hilbert problems, due to Deift and Zhou, is used to obtain strong uniform asymptotics for the scaled polynomials $\text{p(3nz),}\text{q(3nz),}\text{r(3nz)}$ in every domain of the complex plane. An important role is played by a three-sheeted Riemann surface and certain measures and functions defined on it. To cite this article: A. Kuijlaars et al., C. R. Acad. Sci. Paris, Ser. I 336 (2003).     

Leçons sur la viscosité des liquides et des gaz

Monatshefte für Mathematik -     

Théorie de la réduction des formes quadratiques définies positives dans un corps algébriqueK fini

Sans résumé