The Leray–Schauder degree is defined for mappings of the form I − C, where C is a compact mapping from the closure of an open bounded subset of a Banach space X into X. Since the fifties, a lot of work has been devoted in extending this theory to the same type of mappings on some nonlinear spaces, and in extending the class of mappings in the frame of… (More)
au cours de la seconde moitié du XXèmesì ecle, " Dedicated with deep respect to the memory of Jean Leray. INTRODUCTION The theory of Navier-Stokes equations (NSE) constitutes a central problem in contemporary mathematical physics. These equations are a physically well accepted model for the description of very common phenomena, and much effort has been… (More)
OBJECTIVES It is still debated if pre-existing minority drug-resistant HIV-1 variants (MVs) affect the virological outcomes of first-line NNRTI-containing ART. METHODS This Europe-wide case-control study included ART-naive subjects infected with drug-susceptible HIV-1 as revealed by population sequencing, who achieved virological suppression on first-line… (More)
For a class of singular Sturm-Liouville equations on the unit interval with explicit singularity a(a+1)/x 2 , a ∈ N, we consider an inverse spectral problem. Our goal is the global parametrization of potentials by spectral data noted by λ a , and some norming constants noted by κ a. For a = 0 and 1, λ a × κ a was already known to be a global coordinate… (More)
(Proceedings of the colloquium dedicated to the memory of Jean Leray, Nantes, 2002) On the 17th and 18th of June 2002 the Laboratory of Mathematics of Nantes University (supported by CNRS) has organized a meeting to celebrate the memory of Jean Leray. At this opportunity the Laboratory took the name Laboratoire Jean Leray. This volume starts with the… (More)
We prove the weak consistency of the posterior distribution and that of the Bayes estimator for a two-phase piecewise linear regression mdoel where the break-point is unknown. The non-differentiability of the likelihood of the model with regard to the break-point parameter induces technical difficulties that we overcome by creating a regularised version of… (More)
Â la mémoire du profond mathématicien polonais JULES SCHAUDER, victime des massacres de 1940.
In order to improve the time/precision ratio of the simulation calculations, we investigate a multi-scale technique for the resolution of the reactor kinetics equations. We choose to focus on the mixed dual diffusion approximation and the Quasi-Static method. We introduce a space dependency for the amplitude function which only depends on the time variable… (More)