Une méthode de bandes et une méthode de cellules pour l'évaluation par défaut de la fréquence fondamentale d'une membrane

Summary For the first eigenvalue ₁ of a vibrating membrane, the «method of one-dimensional auxiliary problems» gave the lower bounds (19). We present here two new interpretations of those bounds, by means of cutting the membrane either into infinitesimal strips or else into infinitesimal quadratic cells, and adding positive or negative elastic support on each side of each cut.     

Analytical quality control by solid sampling graphite furnace atomic absorption spectrometry in the production of animal tissue reference materials: bovine liver, teeth, bone, muscle, blood and equine renal cortex

Summary The function of solid sampling graphite furnace atomic absorption spectrometry (SS-GFAAS) in the laboratory-internal preparation, production and standardization of several animal tissue reference materials is described. SS-GFAAS is successfully applied in the production of a bovine liver reference material with a low content of Pb and Cd. The lab-internal production of 5 bovine teeth and 2 bovine bone reference materials illustrates some of the basic problems entailed in the analysis of Pb in osseus matrices and in the production of the reference material itself. In the production of muscle tissue reference material focal or generalized calcification is a serious source of endogenous Pb contamination. This is shown, by way of example, in the calcification of the larval states of Taenia saginata (Cysticercus bovis) in the bovine muscle. Finally, as further examples of the application of SS-GFAAS, the lab-internal production of reference material from bovine blood and equine renal cortex is described.     

Hyperfine interactions in negative parity baryons

The hyperfine interaction between quarks suggested in chromodynamics can, without free parameters, explain the size and pattern of the splittings and the mixing angles observed experimentally in nonstrange, negative parity baryons.     

Production of high circular polarization by ion surface scattering of ferromagnets

From a theoretical analysis we predict large fractions of circular polarization of light emitted by ions scattered from surfaces of ferromagnetic single crystals. Maximum enhancement of circular polarization as compared to surface ion scattering from non-magnetic materials is again expected at grazing incidence. A circular polarization of 89% was estimated for the case of Ar⁺ ions scattered from the (110) plane of a Ni single crystal.     

On an analogue of a conjecture of Gross

The paper is concerned with a problem in the theory of congruence function fields which is analogous to a conjecture of Gross in Iwasawa Theory. Z_p-extensions K_∞/K₀ of congruence function fields K₀ of characteristic p≠2 involving no new constants are considered such that the set S of ramified primes is finite and these primes are fully ramified. Is the set of S-classes invariant under Gal(K_∞/K₀) finite ? Gross' conjecture asserts that a similar question has an affirmative answer for the class of cyclotomic Z_p- extensions of CM-type if S is the set of p-primes and the classes considered are minus S-classes. Using a formula of Witt for the norm residue symbol in cyclic p-extensions of local fields of characteristic p, a necessary and sufficient condition for the validity of the analogue of Gross' conjecture is given for a class of extensions K_∞/K₀. It is shown by examples that the analogue of Gross' conjecture is not always true.     

Error bars and quadratically convergent methods for the numerical simulation of the Hartree-Fock equations

Summary. This paper presents an a posteriori error analysis of the discretization methods used in computational quantum chemistry on the Hartree-Fock equations. Upper and lower bounds for the energy are obtained from any discrete approximation strategy of the solution and the estimator proposed is shown to possess further approximation virtues.     

The kinetics and mechanism of the pyrolysis elimination of methyl 4-bromocrotonate

The pyrolysis of methyl 4-bromocrotonate in the temperature range 300–340°C and pressure range 74–170 torr has been shown to be homogeneous, unimolecular, and to follow a first-order rate law. The reaction was carried out in a static system, seasoned with allyl bromide, and in the presence of the radical chain exhibitor toluene. The rate coefficients are represented by the Arrhenius expression: log k₁(s^?1) = (13.30 ± 0.66) ? (185.2 ± 7.5) kJ mol^?1 (2.303RT)^?1. The carbomethoxy group appears to provide anchimeric assistance in the process of dehydrobromination and lactone products formation. The partial rates for the parallel reaction have been estimated, reported, and discussed. The pyrolysis elimination is explained in terms of an intimate ion pair-type of mechanism.     

Arbres distingués,bi-arbres et théorèmes de relèvement

We introduce the notion of distinguished tree relation and give applications. We prove in ZFC an old conjecture of A.V. Ostrovsky about the image of a Borel space under a compact covering mapping. We also prove that if $\text{?}{}_{\mathrm{\xi +1}}{}^{\mathrm{L}}$ is countable then any compact covering mapping from a Δ¹₁ space onto a Σ⁰_1+ξ+2 or Π⁰_1+ξ+2 space is inductively perfect. The converse of last statement is shown. To cite this article: G. Debs, J. Saint Raymond, C. R. Acad. Sci. Paris, Ser. I 336 (2003).