Sur les immeubles triangulaires et leurs automorphismes

Résumé  Les travaux de J. Tits ont conduit à la classification complète des immeubles euclidiens de dimension supérieure ou égale à 3. L’ensemble de ces immeubles à isomorphisme près est dénombrable et paramétré par les corps locaux qui leur correspondent. Dans cet article nous nous intéressons aux immeubles triangulaires, qui sont euclidiens de dimension 2 et pour lesquelles une paramétrisation analogue est impossible. Nous construisons une lamination Λ sur un espace topologique localement compact séparé, dont l’espace des feuilles est l’ensemble des immeubles triangulaires à isomorphisme près. On considère ainsi les immeubles triangulaires comme points d’un espace dont Λ est une désingularisation naturelle. Nous établissons des résultats de chirurgie sur les immeubles triangulaires à données locales fixées. Ils entra?nent par exemple que Λ est topologiquement transitive. Nous montrons qu’un immeuble triangulaire générique au sens de Baire a un groupe d’automorphismes trivial et qu’il contient toutes les géométries locales possibles. L’espace des immeubles triangulaires à isomorphisme près est un nouvel exemple d’espace non commutatif. Le second auteur a été en partie financé par JSPS.     

Simulation numérique directe de l'influence de la forme aval d'une plaque séparatrice sur une couche de mélangeDirect-numerical simulation of the splitting-plate downstream-shape influence upon a mixing layer

In this Note, we present direct numerical simulation results of a spatial mixing layer generated behind an upstream plate separating two boundary layers. The effect of the shape of the trailing edge of the plate is considered through comparisons between flows obtained from a bevelled or a blunt plate. In the former case, a spatial mixing layer consistent with previous experimental and numerical observations is obtained. In the latter case, the self-excited state that establishes in the near wake region dominates primary and secondary instability mechanisms while understating the importance of inflow perturbations. This behaviour is interpreted in terms of convective or absolute instability. The effects on turbulent statistics are also discussed. To cite this article: S. Laizet, E. Lamballais, C. R. Mecanique 334 (2006).     

On the maslov index

In this paper we give four definitions of Maslov index and show that they all satisfy the same system of axioms and hence are equivalent to each other. Moreover, relationships of several symplectic and differential geometric, analytic, and topological invariants (including triple Maslov indices, eta invariants, spectral flow and signatures of quadratic forms) to the Maslov index are developed and formulae relating them are given. The broad presentation is designed with a view to applications both in geometry and in analysis. © 1994 John Wiley & Sons, Inc.     

SG1 based alkoxyamines as radical initiators for the synthesis of lactones and lactames

Recently, it has been shown that alkoxyamines can be used as radical initiators in tin-free radical chemistry. Thus, it prompted us to develop the preparation of highly valuable alkoxyamines via ionic chemistry and the radical cyclization was triggered by thermal initiation. Following that procedure, bicyclic, spiro and eight-membered lactones were easily prepared in good yields with very high stereoselectivity.     

Méthode d'homogénéisation auto-cohérente en calcul à la ruptureSelf-consistent homogeneization method in yield design

This work is aimed towards determining the macroscopic strength criterion of a heterogeneous material with a random microstructure. We use the self-consistent concept by considering a reference material, which is of same nature as the constituents of the heterogeneous material. We deduce that the estimates of the macroscopic strength domain are the solutions to self-consistent equations and we give their derivation procedure. To cite this article: S. Turgeman, B. Guessab, C. R. Mecanique 330 (2002) 623–626.     

Computational Studies on Intramolecular Cycloadditions of Azidoenynes and Azidobutenenitriles to Give 6H‐Pyrrolo[1,2‐c][1,2,3]triazoles and 5H‐Pyrrolo[1,2‐d]tetrazoles

Energetics of intramolecular cycloadditions of azidoenynes and azidobutenenitriles to give 6H‐pyrrolo[1,2‐c][1,2,3]triazoles and 5H‐pyrrolo[1,2‐d]tetrazoles have been calculated at the B3LYP/6.311++G(3df,3pd) level of theory in ideal gas and in H₂O as solvent. Stabilities of the corresponding anions, tautomers, and isomers are discussed. Transition states of the cyclization of parent compounds are determined at the same level of theory.     

Competitive Gold‐Promoted Meyer–Schuster and oxy‐Cope Rearrangements of 3‐Acyloxy‐1,5‐enynes: Selective Catalysis for the Synthesis of (+)‐(S)‐γ‐Ionone and (−)‐(2S,6 R)‐cis‐γ‐Irone

We report a simple, highly stereoselective synthesis of (+)‐(S)‐γ‐ionone and (‐)‐(2S,6R)‐cis‐γ‐irone, two characteristic and precious odorants; the latter compound is a constituent of the essential oil obtained from iris rhizomes. Of general interest in this approach are the photoisomerization of an endo trisubstituted cyclohexene double bond to an exo vinyl group and the installation of the enone side chain through a [(NHC)Au^I]‐catalyzed Meyer–Schuster‐like rearrangement. This required a careful investigation of the mechanism of the gold‐catalyzed reaction and a judicious selection of reaction conditions. In fact, it was found that the Meyer–Schuster reaction may compete with the oxy‐Cope rearrangement. Gold‐based catalytic systems can promote either reaction selectively. In the present system, the mononuclear gold complex [Au(IPr)Cl], in combination with the silver salt AgSbF₆ in 100:1 butan‐2‐one/H₂O, proved to efficiently promote the Meyer–Schuster rearrangement of propargylic benzoates, whereas the digold catalyst [{Au(IPr)}₂(μ‐OH)][BF₄] in anhydrous dichloromethane selectively promoted the oxy‐Cope rearrangement of propargylic alcohols.     

Formation of the Main Cores Present in Natural Products by Tandem Additions

A rapid route to 5,5‐ and 5,6‐ bicyclic systems is provided by an 1,3‐alkyl‐shift process mediated by a hypervalent iodine reagent on aromatics. The structures obtained contain several unsaturations with different behaviors and reactivities. Such diversity allows further elaborations for the rapid formation of compact systems present in a variety of natural products. The potential for further transformations has been demonstrated by performing a double Michael addition. This cyclization process is regio‐ and stereoselective due to the presence of a former benzylic substituent. Furthermore, an extension of this approach has been accomplished on indole derivatives.     

A Bistable Microelectromechanical System Actuated by Spin-Crossover Molecules

We report on a bistable MEMS device actuated by spin-crossover molecules. The device consists of a freestanding silicon microcantilever with an integrated piezoresistive detection system, which was coated with a 140 nm thick film of the [Fe(HB(tz)₃)₂] (tz=1,2,4-triazol-1-yl) molecular spin-crossover complex. Switching from the low-spin to the high-spin state of the ferrous ions at 338 K led to a reversible upward bending of the cantilever in agreement with the change in the lattice parameters of the complex. The strong mechanical coupling was also evidenced by the decrease of approximately 66 Hz in the resonance frequency in the high-spin state as well as by the drop in the quality factor around the spin transition.     

Biomimetic synthetic studies on lactonamycin: an expedient synthesis of dihydroxy-isoindolinone-carboxylates

The synthesis of dihydroxy-isoindolinone-carboxylates from a dioxinone keto-ester and N-protected sarcosine without the use of phenolic protection is described. Base-induced aromatization of the dioxinone diketo-ester followed by lactamization furnished the desired dihydroxy-isoindolinone moiety, which could be used as an EF-ring precursor toward the synthesis of lactonamycin.