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Étude d'un modèle de fragmentation secondaire pour les brouillards de gouttelettes

In this Note, we first present a model for droplet secondary breakup, in liquid sprays. This model is based on the kinetic theory formalism and uses experimental correlations found in the literature (L.-P. Hsiang, G.M. Faeth, Int. J. Multiphase Flow 19 (5) (1993) 721–735; R. Maxey, J. Riley, Phys. Fluids 26 (4) (1983) 883–889; M. Pilch, C.A. Erdman, Int. J. Multiphase Flow 13 (6) (1987) 741–757) to determine the fragmentation rate and its outcome. We then conduct a mathematical study of the resulting kinetic equation. We prove, under some physically reasonable assumptions, an existence and uniqueness theorem and characterize the long-time behaviour of the solution. To cite this article: G. Dufour et al., C. R. Acad. Sci. Paris, Ser. I 336 (2003).     

A uniform boundedness theorem for locally convex cones

We prove a uniform boundedness theorem for families of linear operators on ordered cones. Using the concept of locally convex cones we introduce the notions of barreled cones and of weak cone-completeness. Our main result, though no straightforward generalization of the classical case, implies the Uniform Boundedness Theorem for Fréchet spaces.

     

Multicriteria tour planning for mobile healthcare facilities in a developing country

A multiobjective combinatorial optimization (MOCO) formulation for the following location-routing problem in healthcare management is given: For a mobile healthcare facility, a closed tour with stops selected from a given set of population nodes has to be found. Tours are evaluated according to three criteria: (i) An economic efficiency criterion related to the tour length, (ii) the criterion of average distances to the nearest tour stops corresponding to p-median location problem formulations, and (iii) a coverage criterion measuring the percentage of the population unable to reach a tour stop within a predefined maximum distance. Three algorithms to compute approximations to the set of Pareto-efficient solutions of the described MOCO problem are developed. The first uses the P-ACO technique, and the second and the third use the VEGA and the MOGA variant of multiobjective genetic algorithms, respectively. Computational experiments for the Thiès region in Senegal were carried out to evaluate the three approaches on real-world problem instances.     

Fourier transforms of Schwartz functions on Chébli-Trimèche hypergroups

The Fourier transform for Schwartz spaces on Chébli-Trimèche hypergroups is studied, leading to results on approximation to the identity for functions and distributions on the half-line. In particular it is shown that the heat and Poisson kernels on the half-line form approximate units in various function spaces. A characterization of the convolution of a tempered distribution and a Schwartz function is also given.