Irrationalité de Valeurs Associées a l'Exponentielle de Carlitz

Lete and be the Carlitz-module analogues of their usual counterparts. We have proved in [4]-that these elements of are algebraically independent over whenq3. We study here the remaining caseq=2 and prove among other things that 1,e, are linearly independent over .

     

Analysis of several subcycling schemes in partitioned simulations of a strongly coupled fluid-structure interaction

Fluid-structure interaction (FSI) simulations are used extensively to calculate the vibration of structures subjected to an internal or external flow. In the case of partitioned FSI simulations, separate flow and structure solvers are used, which requires some kind of coupling between both. The time step in both solvers is typically taken the same, but this unnecessarily leads to long calculation times when the time step is small due to stability reasons in one of the two solvers. Subcycling, the procedure where the time step of one solver is chosen smaller than the time step used in the other solver, may reduce the computational cost of the FSI simulation. The subcycling procedure can be either explicit or implicit, the latter implying the use of coupling iterations in each time step. Contrary to explicit subcycling, no stability analyses of implicit subcycling schemes are found in the literature. In this paper, the temporal stability of the implicit subcycling procedure is investigated. The one-dimensional flow in an elastic cylindrical tube is studied analytically. The results of this analysis are subsequently compared to a partitioned two-dimensional axisymmetric FSI calculation with implicit coupling between the flow and structure solvers.     

An asymptotic-preserving well-balanced scheme for the hyperbolic heat equationsUn schema « équilibre » et « asymptotic-preserving » pour les equations de la chaleur hyperboliques

We propose here a well-balanced numerical scheme for the one-dimensional Goldstein–Taylor system which is endowed with all the stability properties inherent to the continuous problem and works in both rarefied and diffusive regimes. To cite this article: L. Gosse, G. Toscani, C. R. Acad. Sci. Paris, Ser. I 334 (2002) 337–342.     

Fast intramolecular dynamics of triphenyl phosphite investigated by <Emphasis Type="Bold">2</Emphasis>H NMR

The first analysis of rapid intramolecular motions of triphenyl phosphite by ²H NMR is presented. The fragile slowing down of the primary relaxation is followed by a solid-echo method. The occurrence of a fast reorientation of the phenyl side groups is demonstrated in the supercooled liquid state, identified as a two-fold flip on the basis of simple lineshape simulations. Coexistence of both static and motionally averaged components in “two phase” spectra indicate a broad distribution of correlation times for this relaxation. This dynamical behavior is shown to persist in the glacial phase. Received 28 May 2002 / Received in final form 1st October 2002 Published online 31 December 2002     

Three-component Ugi-Smiles couplings of cyclic imines

Cyclic imines react with isocyanides and electron-deficient phenols to afford N-aryl piperidines and pyrrolidines in good yields (Ugi-Smiles couplings of cyclic imines). The starting imines were formed by oxidation with N-chlorosuccinimide followed by a base-induced dehydrochlorination.     

Walking metals in d8···d8 hetero-bimetallic complexes: an original dynamic phenomenon

In the course of our investigations on polymetallic complexes derived from 1,3-bis(thiophosphinoyl)indene (Ind(Ph(2)P=S)(2)), we observed original fluxional behavior and report herein a joint experimental/computational study of this dynamic process. Starting from the indenylidene chloropalladate species [Pd{Ind(Ph(2) P=S)(2)}Cl](-) (1), the new Pd(II)···Rh(I) hetero-bimetallic pincer complex [PdCl{Ind(Ph(2) P=S)(2)}Rh(nbd)] (2; nbd=2,5-norbornadiene) was prepared. X-ray crystallography and DFT calculations substantiate the presence of a d(8)···d(8) interaction. According to multinuclear variable-temperature NMR spectroscopic experiments, the pendant {Rh(nbd)} fragment of 2 readily shifts in solution at room temperature between the two edges of the SCS tridentate ligand. To assess the role of the pincer-based polymetallic structure on this fluxional behavior, the related monometallic Rh complex [Rh{IndH(Ph(2) P=S)(2)}(nbd)] (3) was prepared. No evidence for a metal shift was observed in that case, even at high temperature, thus indicating that inplane pincer coordination to the Pd center plays a crucial role. The previously described Pd(II)···Ir(I) bimetallic complex 4 exhibited fluxional behavior in solution, but with a significantly higher activation barrier than 2. This finding demonstrates the generality of this metal-shift process and the strong influence of the involved metal centers on the associated activation barrier. DFT calculations were performed to shed light onto the mechanism of such metal-shift processes and to identify the factors that influence the associated activation barriers. Significantly different pathways were found for bimetallic complexes 2 and 4 on one hand and the monometallic complex 3 on the other hand. The corresponding activation barriers predicted computationally are in very good agreement with the experimental observations.