On the spectrum of the sum of generators for a finitely generated group

Let Γ be a finitely generated group. In the group algebra ℂ[Γ], form the averageh of a finite setS of generators of Γ. Given a unitary representation π of Γ, we relate spectral properties of the operator π(h) to properties of Γ and π. For the universal representationπ _un of Γ, we prove in particular the following results. First, the spectrum Sp(π _un (h)) contains the complex numberz of modulus one iff Sp(π _un (h)) is invariant under multiplication byz, iff there exists a character such that η(S)={z}. Second, forS ⁻¹=S, the group Γ has Kazhdan’s property (T) if and only if 1 is isolated in Sp(π _un (h)); in this case, the distance between 1 and other points of the spectrum gives a lower bound on the Kazhdan constants. Numerous examples illustrate the results.     

Recherches sur la structure électronique de composés soufrés (méthode L.C.A.O. améliorée)

Improved L.C.A.O. method primitively built for conjugated molecules holding only atoms of second row in the periodic classification is extended to molecules holding atoms of the third row. The application is done for thiophen, thioketones, SO₂ and SO₃. d orbitals are not introduced in this study. Discussion about results shows that d orbitals must be introduced when the sulphur atom is strongly positively charged like in sulphur oxides.     

Anderson localization for multi-dimensional systems at large disorder or large energy

We prove that discrete Schrödinger operators on ^d with a random-potential have almost-surely only pure point spectrum and exponentially decaying eigenfunctions for large disorder or large energy. This is the first proof of localization for multi-dimensional Anderson models.Groupe de recherche 048 du CNRS     

Application of similarity aggregation techniques to a population of paraplegic patients

We studied a population of paraplegic patients in order to give prominence to a possible relationship between the topography of their spinal lesion and the occurrence of special articular diseases (P.O.A.). According to the motor and sensory state of their spinal cord, we first tried to obtain a classification of these lesions (the usual one schematically separates ‘flaccid’ and ‘rigid’ paraplegics). We mainly put the emphasis on this clustering step of the study:

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Reversible dynamics and the macroscopic rate law for a solvable Kolmogorov system: The three bakers' reaction

We investigate a piecewise linear (area-preserving) mapT describing two coupled baker transformations on two squares, with coupling parameter 0c1. The resulting dynamical system is Kolmogorov for anyc0. For rational values ofc, we construct a generating partition on whichT induces a Markov chain. This Markov structure is used to discuss the decay of correlation functions: exponential decay is found for a class of functions related to the partition. Explicit results are given forc=2^–n. The macroscopic analog of our model is a leaking process between two (badly) stirred containers: according to the Markov analysis, the corresponding progress variable decays exponentially, but the rate coefficients characterizing this decay are not those determined from the one-way flux across the cell boundary. The validity of the macroscopic rate law is discussed.     

Pervaporative transport modelling in a ternary system: ethyltertiarybutylether/ethanol/polyurethaneimide

The study deals with the analysis of diffusion and mass transfer modelling during pervaporation in a true ternary system involving a polar liquid mixture (ETBE/EtOH) and a polar block copolymer (polyurethaneimide or PUI). A survey of methods of pervaporative transfer modelling in ternary systems is first developed. From differential permeation experiments carried out with both pure liquids, it appears that both permeants obey a Fickian law. Moreover, the diffusional behaviour is consistent with Long's model, which has thus been assumed for the related ternary system. An extension of the Brun's model is then derived, which takes into account the diffusion coupling as well the significant deviation from sorption ideality. From a practical point of view, the calculated values of fluxes show generally good agreement with the experimental results, although a small deviation occurs for mixtures of low ethanol content. Diffusion coefficients of both pure solvents corresponding to transient or steady state are compared. A very good agreement is found for the aprotic permeant (ETBE). whereas the diffusion coefficient of ethanol in transient state is only the quarter of the value corresponding to steady state. The results are discussed in comparison with related investigations in the literature, involving specific liquid-polymer interactions.     

Efficient combination of task-specific ionic liquid and microwave dielectric heating applied to one-pot three component synthesis of a small library of 4-thiazolidinones

The first report of the use of task-specific ionic liquid as synthetic equivalent of ionic liquid-phase matrice for the preparation of a small library of 4-thiazolidinones is reported in this paper. The starting (ethyleneglycol)ionic liquid-phase is functionalized in good yields with 4-(formylphenoxy)butyric acid by using usual esterification reaction conditions (DCC/DMAP as catalyst). The synthesis of the ionic liquid-phase bound 4-thiazolidinones was performed by a one-pot three-component condensation under microwave dielectric heating. The final cleavage under microwave/catalysis strategy provides the expected 4-thiazolidinones in high purity after flash-chromatography purification. According to the ionic liquid-phase organic synthesis (IoLiPOS) methodology, it was found that optimized reaction conditions were performed by standard analytical methods (NMR, TLC). The ¹H, ¹³C NMR spectrum of some representative 4-thiazolidinones and ionic liquid-phase bound benzaldehyde are also reported.     

The synthesis of DL-1-(hexadecanoyloxy)methyl- and 1-O-hexadecanoyl-inositols as potential inhibitors of phospholipase C

The synthesis of racemic analogues of phosphatidylinositol (PI) and phosphatidylinositol 4,5-bisphosphate (PIP₂) starting from myo-inositol is described. Inositol derivatives with and without homologalion at C(l) and with and without ionic groups (phosphate or sulfate) at C(4) and C(5) were prepared as well as homologated derivatives with deoxy composition at C(2) and/or C(6). In all these compounds, palmitate ester groups were introduced in place of the diacylglyceryl group of PI or PIP₂.     

Mild cleavage of methoxymethyl (MOM) ethers with trimethylsilyl bromide

Trimethylsilyl bromide is an effective reagent for the deprotection of methoxymethyl ethers under mild conditions.