Un modèle mathématique de cyclone

The source waves are some particular solutions to genuinely non linear hyperbolic systems with a source term, whose propagation velocity is a constant determined by the roots of this source term. We propose a system of 2 equations on a 2 dimension space, which model the velocity field of the atmosphere near the ground. The source term is made of three parts: a given pressure gradient, a friction or aspiration effect and the Coriolis force. In the case where these parameters are constant, we build a solution which is a constant outside a circular crown. The internal circle represents the eye's wall of the hurricane and corresponds to a share shock wave. The external circle is a set generating the bifurcation which actually models the hurricane. To cite this article: A.-Y. LeRoux et al., C. R. Acad. Sci. Paris, Ser. I 339 (2004).     

Quasi-free divisors and duality

We prove a duality theorem for some logarithmic $\text{D}$-modules associated with a class of divisors. We also give some results for the locally quasi-homogeneous case. To cite this article: F.J. Castro-Jiménez, J.M. Ucha-Enr??quez, C. R. Acad. Sci. Paris, Ser. I 338 (2004).     

Thermodynamic Limit and Proof of Condensation for Trapped Bosons

We study condensation of trapped bosons in the limit when the number of particles tends to infinity. For the noninteracting gas we prove that there is no phase transition in any dimension, but in any dimension, at any temperature the system is 100% condensated into the one-particle ground state. In the case of an interacting gas we show that for a family of suitably scaled pair interactions, the Gross–Pitaevskii scaling included, a less-than-100% condensation into a single-particle eigenstate, which may depend on the interaction strength, persists at all temperatures.     

Stable boundary layers in a diffusion problem with nonlinear reaction at the boundary

We prove the existence of nonconstant stable stationary solutions of an evolution problem with a nonlinear reaction acting on the boundary. These solutions present layers at certain points of the boundary. We also study the behavior of these solutions as the small parameter appearing in the equation approaches zero and show some stability properties of the profiles given by these equilibrium solutions.     

Comparison of Several Calibration Procedures for Glass Electrodes in Proton Concentration

Several reported procedures for calibrating glass electrodes in proton concentration are compared. Some recommendations for non-experts are also given. The examined procedures can be classified into two broad categories, namely: those based on direct potential difference measurements of solutions of known proton concentration and those that use one or several pH standards to calibrate the electrode and subsequently measure the pH of solutions containing known proton concentrations. With a single buffer, the two types of procedures lead to equivalent results. However, if two pH buffers are used, the slope of the calibration graph in proton concentration will differ from the real electrode slope to an extent proportional to the difference between the liquid junction potentials of the two buffers. Therefore, any other method is preferable under these circumstances.     

Principes de grandes déviations pour des processus de « coarse graining »

We improve the Large Deviations Principle satisfied by a Coarse Grained process already analyzed by Boucher, Ellis and Turkington [Ann. Probab. 27 (1999) 297–324]. To cite this article: J. Trashorras, C. R. Acad. Sci. Paris, Ser. I 336 (2003).     

A simple Markov chain structure for the evolution of credit ratings

We focus on continuous Markov chains as a model to describe the evolution of credit ratings. In this work it is checked whether a simple, tridiagonal type of generator provides a good approximation to a general one. Three different tridiagonal approximations are proposed and their performance is checked against two generators, corresponding to a volatile and a stable period, respectively. Copyright © 2007 John Wiley & Sons, Ltd.