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.     

Preparation of Re(I)- and (99m)Tc(I)-metallocarboranes in water under weakly basic reaction conditions

A new method for the preparation of Re- and (99m)Tc-metallocarboranes in water under mild reaction conditions was developed. Three nido-carborane ligands were reacted with [Re(CO)(3)Br(3)](2)(-) in the presence of aqueous potassium fluoride to give the corresponding eta(5)-Re(CO)(3)-carborane complexes. The use of KF as a base afforded the desired Re-metallocarboranes in good yields while avoiding the formation of Re clusters, which are byproducts commonly observed when reactions are carried out in the presence of strong aqueous bases. The reaction was also performed at the tracer level producing the first (99m)Tc-carborane complex, which was isolated in 80% radiochemical yield following a simple Sep-Pak purification process. The resulting organometallic complex was stable to cysteine and histidine challenges for more than 24 h.     

The role of additional solvents in transition metal complex catalyzed asymmetric reductions in ionic liquid containing systems

When ionic liquids (ILs) are employed as solvents for transition metal complex (TMC) catalyzed reductions, a second solvent can be added to increase the efficiency of the catalytic cycle and the solubility of the reactant in the IL phase. Two industrially relevant asymmetric hydrogenations, the enantioselective reductions of methyl 2-acetamidoacrylate with Rh-EtDuPHOS and methyl acetoacetate with Ru-BINAP, were performed in different catalytic systems including 1-butyl-3-methylimidazolium hexafluorophosphate/ tetrafluoroborate as ILs. Product separation and TMC recycling was performed by extracting the product from the reaction mixture. This can be accomplished by cooling the system, by adding an excess of the second solvent or by adding a third solvent. A high solubility of the second solvent in the IL catalytic phase favors the reaction activity, but can induce leaching of the IL and TMC.     

Complexes acetyleniques de titane(II). Reactivite vis-a-vis de l'hydrogene moleculaire: Une nouvelle approche du titanocene

¹³C NMR measurements were performed on [Re₃(μ-H)₃(CO)₁₀]^2? at various temperatures and field strengths. Selective decoupling allowed assignments of the carbonyl resonances. Spin-lattice relaxation time measurements indicated that two mechanisms, scalar coupling and chemical shielding anisotropy, contribute to the relaxation of carbon-13. Variable temperature experiments revealed that more than one mechanism is responsible for the fluxional behaviour.     

Synthesis of thienothiazocinoisoindolediones and thienothiazinoisoindolones from mercaptothiophenes and chloromethylphthalimide

2-Thienylthiomethylphthalimides 3a,b were synthesized by action of Chloromethylphthalimide on 2-or 3-mercaptothiophene. Reduction of 3a,b and Wittig reaction using carbethoxycarbonyltriphenyl-phosphorane gave the corresponding acetic acids 5a,b which cyclized under Friedel and Crafts conditions to lead the thienothiazocinoisoindolediones 6a,b. Thienothiazinoisoindolones 7a,b were obtained from hydroxyisoindolones derivatives 4a,b in acid conditions via an acyliminium ion.     

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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New butenolides in plantlets of Virola surinamensis (Myristicaceae)

A phytochemical investigation in plantlets of the Brazilian medicinal tree Virola surinamensis resulted in the isolation and structural determination of four new compounds: 3-hydroxy-4-methyl-2-(11'-piperonyl-n-undecyl)-butenolide; 3-hydroxy-4-methyl-2-(7'-piperonyl-n-heptyl)-butanolide; 9'-(3,4-methylenedioxy-phenyl)-nonanoic acid and 13'-(3,4-methylene-dioxyphenyl)-tridecanoic acid. Thirteen compounds previously isolated from seeds and adult plants were also reported.     

PM3 semi-empirical study of stereoelectronic effects in the Baeyer-Villiger reaction

The Baeyer-Villiger reaction of polymethoxybenzaldehydes with peroxysuccinic acid (PSA) is studied theoretically. The semi-empirical SCF-MO/PM3 method has been used to study the reaction and to calculate the energy profiles. In addition, heat of formation computations and bond order analyses of the transition species along the reaction coordinates have been performed and are interpreted qualitatively in terms of electron flow through the system during aryl migration. Our results support the hypothesis that the second step is a concerted reaction. Our data support a definite effect of the substituent on the aryl migration. The theoretical predictions are in good agreement with experimental results.     

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.