Propriétés statistiques des entiers friables

Let Ψ(x,y) (resp. Ψ_m(x,y)) denote the number of integers not exceeding x that are y-friable, i.e. have no prime factor exceeding y (resp. and are coprime to m). Evaluating the ratio Ψ_m(x/d,y)/Ψ(x,y) for 1≤slantd≤slantx, m≥slant 1, x≥slant y≥slant 2, turns out to be a crucial step for estimating arithmetic sums over friable integers. Here, it is crucial to obtain formulae with a very wide range of validity. In this paper, several uniform estimates are provided for the aforementioned ratio, which supersede all previously known results. Applications are given to averages of various arithmetic functions over friable integers which in turn improve corresponding results from the literature. The technique employed rests mainly on the saddle-point method, which is an efficient and specific tool for the required design.2000 Mathematics Subject Classification: Primary—11N25; Secondary—11K65, 11N37     

Un principe d'invariance relatif à un processus généralisant le mouvement brownien N-dimensionnel

We prove that the generalized random walks associated to a root system R in $\text{R}{}^{\mathrm{N}}$ and a nonnegative multiplicity function k defined on R, converge in distribution (if suitably normalized) to a Markov process with càdlàg trajectories and infinitesimal generator a differential-difference operator on $\text{R}{}^{\mathrm{N}}$ which generalizes the usual Laplacian. To cite this article: L. Gallardo, L. Godefroy, C. R. Acad. Sci. Paris, Ser. I 338 (2004).     

Tomographic reconstruction using heuristic Monte Carlo methods

A tomographic reconstruction method based on Monte Carlo random searching guided by the information contained in the projections of radiographed objects is presented. In order to solve the optimization problem, a multiscale algorithm is proposed to reduce computation. The reconstruction is performed in a coarse-to-fine multigrid scale that initializes each resolution level with the reconstruction of the previous coarser level, which substantially improves the performance. The method was applied to a real case reconstructing the internal structure of a small metallic object with internal components, showing excellent results.     

A remark on divisibility of definable groups

We show that if G is a definably compact, definably connected definable group defined in an arbitrary o‐minimal structure, then G is divisible. Furthermore, if G is defined in an o‐minimal expansion of a field, k ∈ ? and p_k : G → G is the definable map given by p_k (x ) = x^k for all x ∈ G , then we have |(p_k )^–1(x )| ≥ k^r for all x ∈ G , where r > 0 is the maximal dimension of abelian definable subgroups of G . (© 2005 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

On Non-Continuous Dirichlet Processes

We introduce here some Itô calculus for non-continuous Dirichlet processes. Such calculus extends what was known for continuous Dirichlet processes or for semimartingales. In particular we prove that non-continuous Dirichlet processes are stable under C ¹ transformation.     

Conservation de la charge dans les codes PIC

This Note introduces a new integral form of the charge and current deposition scheme given in 1992 by Villasenor and Buneman, which permits the conservation of charge in PIC codes. This integral form extends directly to higher order spline shape factors, whose use produces less numerical noise. We thus get a discrete charge conserving method for high order shape factors. This method extends easily to nonuniform Cartesian grids for first order shape factors. To cite this article: R. Barthelmé, C. R. Acad. Sci. Paris, Ser. I 341 (2005).     

Spectrofluorimetric Method for the Determination of Aluminum with Alizarin Red PS

 A simple and direct spectrofluorimetric method has been developed for the determination of aluminum using alizarin red PS (1,2,4-trihydroxy 9,10-anthraquinone-3-sulfonic acid). The method is based on the strong fluorescence (480/564 nm) of Al³⁺ and alizarin red. Experimental parameters such as pH, concentration of the ligand, ionic strength of the solution, reaction time and temperature were optimized in order to maximize the analytical signal. Interferences of several ions (anions and cations) were studied and evaluated. The linear range of the method extends from 3 to 100 μg L⁻¹. Limit of detection (3s_b) was 0.9 μg L⁻¹. The method was tested with a silicate certified reference material. Interferences were eliminated by a liquid extraction with cupferron. Author for correspondence. E-mail: aucelior@rdc.puc-rio.br Received September 10, 2002; accepted January 15, 2003 Published online May 5, 2003     

Loading aircraft for military operations

In this paper, we describe an aircraft loading problem submitted by the French military agency (DGA) as part of a more general military airlift planning problem. It can be viewed as a kind of bi-dimensional bin-packing problem, with heterogeneous bins and several additional constraints. We introduce two-phase methods for solving this NP-hard problem. The first phase consists in building good initial solutions, thanks to two fast algorithms: a list-based heuristic and a loading pattern generation method. Both algorithms call a constraint-based subroutine, able to determine quickly if the items already loaded can be reshuffled to accommodate a new object. The second phase improves these preliminary solutions using local search techniques. Results obtained on real data sets are presented.     

Automorphisms with only infinite orbits on non-algebraic elements

 This paper generalizes results of F. K?rner from [4] where she established the existence of maximal automorphisms (i.e. automorphisms moving all non-algebraic elements). An ω-maximal automorphism is an automorphism whose powers are maximal automorphisms. We prove that any structure has an elementary extension with an ω-maximal automorphism. We also show the existence of ω-maximal automorphisms in all countable arithmetically saturated structures. Further we describe the pairs of tuples (ˉa,ˉb) for which there is an ω-maximal automorphism mapping ˉa to ˉb. Received: 12 December 2001 / Published online: 10 October 2002 Supported by the ``Fonds pour la Formation à la Recherche dans l'Industrie et dans l'Agriculture' Mathematics Subject Classification (2000): Primary: 03C50; Secondary: 03C57 Key words or phrases: Automorphism – Recursively saturated structure