An interior–exterior Schwarz algorithm and its convergenceUn algorithme de Schwarz intérieur–extérieur et sa convergence

In this work we study the solution of Laplace's equation in a domain with holes by an iteration consisting of splitting the problem in an exterior one, around the holes, plus an interior problem in the unholed domain. We show the existence of a decomposition of the solution when the exterior problem is represented by means of a single-layer protential. Also, for the three-dimensional case and with some adjustments for the two-dimensional case, we prove convergence of the method by writing the iteration as a Jacobi iteration for an operator equation and studying the spectrum of the iteration operator. To cite this article: R. Celorrio et al., C. R. Acad. Sci. Paris, Ser. I 334 (2002) 923–926.     

Aberrations theory of a time dependent magnetic field lens

We analyze new forms of aberrations affecting a time dependent magnetic field lens recently proposed. The lens consist of an axially symmetric ellipsoidal solenoid producing a spatially uniform but time pulsating homogeneous field. The dynamics of electrons emitted by some object and injected into this coil shows that this system is capable of focusing a parallel beam or produce images free of geometrical aberrations. The cardinal elements of this lens change periodically in positions and therefore to obtain a stationary image it is necessary to employ a chopped electron beam. Two forms of aberrations originate from the finite duration of the electron pulse and the energy dispersion of the incoming beam (chromatic aberration). Their image degradation effects are quite similar and result from recording different axially displaced images at some fixed stationary plane. We show how, by adjusting the parameters characterizing the magnetic pulse and introducing small apertures that increase the depth of focus, their effects can be reduced or in some cases eliminated. Other forms of instrumental aberrations characteristic of this time dependent magnetic field lens are briefly discussed.     

Determination of lithium in wines by atomic absorption spectrometry

Lithium (10–150 ng ml^?1) in wine is determined by atomic absorption spectrometry by direct nebulization and after digestion with mixed acids. The results of methods are similar. Thirty-four wines from various Spanish provinces are analysed.     

Studies aimed at the synthesis of morphine V an economic approach to (±)-reticuline from 3,4-dihydropapaverine

Regioselective demethylation of 3,4-dihydropapaveraldine ($\text{2}$a) at 7 and 3' positions affords a properly substituted diphenolic key intermidiate ($\text{2}$d) for the synthesis of reticuline and N-norreticuline.     

Why and how to avoid standard kinetic equations I. Principles and band conduction problem

A review of ideas leading to full rejection of any finite or partially-infinite order kinetic equation linearized in external field is given on grounds of the time-convolution Generalized Master Equations (GME). By two examples (two-level and band conduction problem), it is shown how standard kinetic equations result from GME in the lowest order approximations which obscure, however, a direct correspondence with the Kubo linear response theory. Without approximations, on the other hand, the rigorous approach is shown to be fully equivalent with the Kubo results. It is argued and illustrated that usual technical simplicity and seeming physical lucidity of standard theories (connected with the presence of field-independent transfer or scattering rates in the fielddependent linearized theory) are just owing to structural features which are solely due to the lowest order approximations involved. These features (i.e. also the possibility of standard physical interpretation of kinetic phenomena) are proved to disappear completely as far as the theory goes properly to higher orders.     

Three New Polyoxygenated Steroids from Two Species of the South China Sea Gorgonian Muricella flexuosa and Menella verrucosa Brundin

Three new polyoxygenated steroids, muricesteroid ( 1 ), and menellsteroids A ( 2 ) and B ( 3 ), were isolated from two species of the South China Sea gorgonian Muricella flexuosa and Menella verrucosa Brundin , respectively. The structures of these new compounds were elucidated on the basis of extensive spectroscopic analysis, chemical methods and comparison with known related compounds.     

A finite model property for RMImin

It is proved that the variety of relevant disjunction lattices has the finite embeddability property. It follows that Avron's relevance logic RMI _min has a strong form of the finite model property, so it has a solvable deducibility problem. This strengthens Avron's result that RMI _min is decidable. (© 2006 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Unavoidable Traces Of Set Systems

Sauer, Shelah, Vapnik and Chervonenkis proved that if a set system on n vertices contains many sets, then the set system has full trace on a large set. Although the restriction on the size of the groundset cannot be lifted, Frankl and Pach found a trace structure that is guaranteed to occur in uniform set systems even if we do not bound the size of the groundset. In this note we shall give three sequences of structures such that every set system consisting of sufficiently many sets contains at least one of these structures with many sets.