Principe de grandes déviations uniforme pour l'estimateur de la densité par la méthode des delta-suites

In this Note, we obtain a large deviations principle for the uniform deviation of the delta-sequence density estimator. A general result is stated for any regular delta-sequence and a discussion of hypotheses for the most usual methods is given. Implications of our results in the study of the inaccuracy rate of these estimates with the comparisons of performances of various methods are given. The estimation is based upon sequences of i.i.d. random variables. To cite this article: N. Berrahou, C. R. Acad. Sci. Paris, Ser. I 343 (2006).     

Ionization potentials and geometrical structure of pure and oxygenated barium clusters

In this article, we present results obtained on structures of small bare and oxygenated barium clusters produced by the laser vaporization technique. Contrary to the very weak Ba—Ba binding (0.202 eV), the Ba—O binding is rather strong (5.8 eV). As a consequence, extremely small amounts of oxygen in the cluster source are sufficient to induce the nucleation of oxygenated barium clusters. Surprisingly, at least for substoechiometric systems, Ba_nO_m clusters exhibit the same icosahedral structure as bare clusters do. Mass spectra seem to indicate that replacing a barium atom with a strongly polar BaO molecule does not affect the geometrical structure of the cluster. This aspect is more easily understandable if we assume that the oxygen atom takes place inside the structure of the Ba_n cluster without significant distortions. Ab-initio calculations have been undertaken in order to give a satisfactory account of this hypothesis.     

Hele-Shaw type problems with dynamical boundary conditions

In this paper, we study the nonlinear evolution equation of Hele-Shaw type with dynamical boundary conditions. That is, the equation ut=Δw+f where u∈H(w) and H is the Heaviside function, with boundary condition μ(x,w)t_∂w+k∇w⋅ν=g, where ν denotes the outward normal vector of the fixed boundary of the domain. We prove existence, uniqueness and some qualitative properties of the solution.     

A novel capacitive pressure sensor structure with high sensitivity and quasi-linear responseUne nouvelle structure de capteur de pression capacitif avec haute sensibilitée et réponse quasi-linéaire

This paper describes a new capacitive structure of pressure sensor to increase simultaneously the sensitivity and the linearity of the transducer. This structure contains two capacitors which change in response to pressure, but in opposite senses. To increase even more the sensitivity of each capacitor, the pressure sensitive diaphragm carries a central boss. The optimal position and the length of the boss are also calculated. To cite this article: A. Ettouhami et al., C. R. Mecanique 332 (2004).     

Dirichlet Series and Curious infinite Products

By number-theoretical methods we give a result generalizingthose of J. O. Shallit, one particular case of which reads asfollows: ...=2^–;, where a(n) is equal to 1 if the sum of the digits of n in basetwo is even, and – 1 if this sum is odd. Moreover we provea conjecture of Shallit concerning a way of approximating 2^–     

Theoretical study of the adsorption of silver atoms on the (111) face of silicon

The adsorption of one or many silver atoms on a (111) silicon face (reduced to 61 dangling atomic orbitals) is investigated by means of a self-consistent Hartree–Fock method parametrized from atomic and thermodynamical data. The valley sites (above three Si atoms) are favored over the top sites (above one Si atom). The extrapolation of the results obtained for several structures corresponding to the adsorption of n = 1, 2, 3, 4, 6, and 7 Ag atoms allows us to conclude that the most stable structures correspond: for \documentclass{article}\pagestyle{empty}\begin{document}$ \theta = \frac{1}{3} $\end{document} to linear Ag chains (3 × 1 phase), for \documentclass{article}\pagestyle{empty}\begin{document}$ \theta = \frac{2}{3} $\end{document} to an honeycomb lattice (\documentclass{article}\pagestyle{empty}\begin{document}$ \sqrt 3 \times \sqrt 3 $\end{document} phase), and for θ = 1 to a centred hexagonal lattice (\documentclass{article}\pagestyle{empty}\begin{document}$ \sqrt 3 \times \sqrt 3 $\end{document} phase), the Ag atoms located at the centers of the hexagons being beneath the plan of the hexagons. The adsorption energies corresponding to the various θ are practically equal (ca. 3 eV/Ag). The net charges of Ag atoms are equal to 0.35.     

Unprecedented base effect on the synthesis of chiral phosphinate esters: A new route to P-chiral phosphine oxides of high enantiomeric purity

The stereochemical outcome of the reaction of chiral secondary alcohols with a phosphinyl chloride was found to be highly dependent on the achiral base used. Thus, the reaction of the readily available sugar derived carbinols, 1 and 2, with methylphenylphosphinyl chloride in the presence of triethylamine yields stereoselectively the corresponding Snp-phosphinates 3Sp and 5Sp in 94 and 92% diastereomeric excess (de). Simply changing the base from triethylamine to pyridine affords Rp-phosphinates 4Rp and 6Rp epimers to 3Sp and 5Sp at the phosphinyl phosphorus in 50 and 40% de respectively. These phosphinate esters were found to be good P-chiral transferring intermediates, they react with Grignard reagents under very mild conditions to give the corresponding phosphine oxides. Both enantiomers Sp- and Rp-o-anisylmethylphenylphosphine oxide (PAMPO) as well Sp- and Rp- methylphenylpropyl phosphine oxide were obained enantiomerically pure in high yields     

About macroscopic models of instability pattern formation

Various macroscopic models to describe instability pattern formation are discussed in this paper. They are similar to the Ginzburg–Landau envelope equation, but they can remain valid away from the bifurcation and are based on the technique of Fourier series with slowly varying coefficients. We focus on two questions: the need to take phase changes into account and the boundary conditions to be associated with macroscopic models. The analysis is carried out on the basis of numerical simulations for the problem of a compressed beam on a nonlinear foundation that is quite similar to the well known Swift–Hohenberg equation. The first macroscopic model involves a real envelope so that the phase is assumed to be constant. The second model is also macroscopic and it is a sort of Ginzburg–Landau equation with a complex envelope. The third one follows from a multi-scaled approach with a numerical bridging between the full model near the boundary and a macroscopic model in the bulk.