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)     

Une nouvelle méthode de raffinement de maillage spatio-temporel pour l'équation des ondes

In the present Note we introduce an extension of the conservative space–time mesh refinement method presented by Fouquet et al. We also propose a post-treatment of the solution that reduces the spurious phenomena due to the non-conformity between the time meshes. A reinterpretation of the equations in terms of new unknowns leads to a new scheme with second order consistent coupling equations. Numerical experiments in 2D and a plane wave analysis for the 1D model show that the method is second order accurate for an arbitrary refinement. To cite this article: J. Rodríguez, C. R. Acad. Sci. Paris, Ser. I 339 (2004).     

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.     

Hamiltonian N2‐locally connected claw‐free graphs

A graph G is N₂‐locally connected if for every vertex ν in G, the edges not incident with ν but having at least one end adjacent to ν in G induce a connected graph. In 1990, Ryjá?ek conjectured that every 3‐connected N₂‐locally connected claw‐free graph is Hamiltonian. This conjecture is proved in this note. © 2004 Wiley Periodicals, Inc. J Graph Theory 48: 142–146, 2005     

Elliptic equations with BMO coefficients in Reifenberg domains

The inhomogeneous Dirichlet problems concerning divergence form elliptic equations are studied. Optimal regularity requirements on the coefficients and domains for the W^1,p theory, 1 < p < ∞, are obtained. The principal coefficients are supposed to be in the John‐Nirenberg space with small BMO seminorms. The domain is a Reifenberg domain. These conditions for the W^1,p theory not only weaken the requirements on the coefficients but also lead to a more general geometric condition on the domains. In fact, these domains might have fractal dimensions. © 2004 Wiley Periodicals, Inc.     

Supercritical CO2 as a superior solvent for the cyclization of diallylmalonate catalyzed by palladium-containing zeolites

Palladium-containing zeolites catalyze the cycloisomerization of diethyl diallylmalonate to dimethylcyclopentenes. When the reaction is carried out in toluene, the performance of the palladium catalyst depends on the pore size of the zeolites. At 60 °C, palladium adsorbed on large pore size Beta zeolite (pore size ∼7.4 Å) is more active than medium pore size ZSM-5 (pore size ∼5.4 Å). This lower activity of ZSM-5 compared to Beta is attributable to the restricted diffusion of reagent and products through the ZSM-5 channels as compared to Beta zeolite. However, due to the gas-like diffusion characteristic of the supercritical state, the activity of ZSM-5 increases and becomes identical to that of Beta zeolite using supercritical CO₂ as medium.