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.     

Synthesis and photophysical properties of meso-substituted bisporphyrins: comparative study of phosphorescence quenching for dioxygen sensing

The 4,6-bis(10-mesityl-5,15-di-p-tolylporpyrinyl)dibenzothiophene (H4DPSN) free base was obtained in five steps from commercially available materials. The metalation of DPSN2- with zinc(II), copper(II), and palladium(II) led to three new homobimetallic systems, (Zn)2DPSN, (Cu)2DPSN, and (Pd)2DPSN, respectively. The cofacial structures of these molecules offer the possibility of having dioxygen molecules inside the cavity for a period of time, allowing dynamic (collisional) phosphorescence quenching to be more efficient. The bimolecular excited-state deactivation rate constant for deactivation by dioxygen (kQ: (Pd)2DPB, 2.98x10(9); (Pd)2DPSN, 3.99x10(9); (Pd)2DPX, 6.94x10(9); (Pd)TPP, 8.95x10(9); (Pd)2DPS, 8.95x10(9) M-1 s-1) of (Pd)2DPSN, which exhibits an intense phosphorescence at 699 nm, was compared to those observed for (Pd)TPP, (Pd)2DPS, (Pd)2DPX, and (Pd)2DPB (TPP2-=tetraphenylporphyrin dianion, DPS4-=4,6-bis[5-(2,8,13,17-tetraethyl-3,7,12,18-tetramethylporphyrinyl)]dibenzothiophene tetraanion, DPX4-=4,5-bis[5-(2,8,13,17-tetraethyl-3,7,12,18-tetramethylporphyrinyl)]-9,9-dimethylxanthene tetraanion, and DPB4-=1,8-bis[5-(2,8,13,17-tetraethyl-3,7,12,18-tetramethylporphyrinyl)]biphenylene tetraanion). These collision-induced deactivation data were interpreted by estimating a series of physical parameters such as the surface area and bisporphyrin radii, the diffusion coefficient of the bismacrocycles, and the theoretical deactivation efficiency for the five compounds addressing the role of steric hindrance of the macrocycles on each other and the aryl groups at the meso positions. For sensing purposes, (Pd)2DPX is characterized by a Stern-Volmer constant kSV of 2.91x10(6) M-1, placing the lower detection limit for [O2] in solution at 0.58 ppm, which is better than that for (Pd)TPP (kSV=2.31x10(6) M-1; lower detection limit of 0.73 ppm), the classically used monoporphyrin complex.     

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.     

Adding water to sugar: a spectroscopic and computational study of alpha- and beta-phenylxyloside in the gas phase

The gas phase structures of phenyl alpha- and beta-d-xylopyranoside (alpha- and beta-pXyl) and their mono-hydrates have been investigated using a combination of resonant two-photon ionization (R2PI), ultra-violet hole-burning and resonant infrared ion dip spectroscopy, coupled with density functional theory (DFT) and ab initio computation. The hole-burning experiments indicate the population of a single conformer only, in each of the two anomers. Their experimental and calculated infrared spectra are both consistent with a conformational assignment corresponding to the computed global minimum configuration. All three OH groups are oriented towards the oxygen atom (O1) on the anomeric carbon atom to form an all trans(ttt) counter-clockwise chain of hydrogen bonds. The mono-hydrates, alpha- and beta-pXyl(H(2)O) each populate two distinct structures in the molecular beam environment, with the water molecule inserted between OH4 and OH3 or between OH3 and OH2 in alpha-pXyl(H2O), and between OH2 and O1 in either of two alternative orientations, in beta-pXyl(H2O). In all of the mono-hydrated xyloside complexes, the water molecule inserts into the weakest link of the sugar molecules' hydrogen-bonded chain of hydroxy groups, creating a single extended chain, strengthened by co-operativity. The all-trans configuration of the xylose moiety is retained and the mono-hydrate structures correspond to those calculated to lie at the lowest relative energies.     

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:

相似文献   

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.