Convergent Star Product Algebras on ‘ax+b’

We define nontempered (exponential growth) function spaces on the Lie group ax+b which are stable under some left-invariant (convergent) star product. The techniques used to achieved the latter come from symmetric spaces geometry and star representation theory.     

Characteristic classes and obstruction theory for infinite loop spaces

The classical extension problem is to determine whether or not a given mapg:AY, defined on a given subspaceA of a spaceX, has an extensionXY. The present paper examines this question in the special case where thek-invariants ofY are cohomology classes of finite order (for instance ifY is an infinite loop space).     

Numerical computation of the electrostatic interaction energy between methanol and the dyad water-imidazole

Summary The electrostatic interaction energy between methanol and the dyad water-imidazole has been computed numerically at three levels of approximation from 3D grids of the charge density of one partner and the electrostatic potential of the other. The minimum positions and energy values thus obtained compare well with those calculated analytically. The numerical procedure is especially interesting for the prediction of the stable conformers.     

Reactions de photoaddition de benzo[b]selenophenes avec l'acetylene dicarboxylate de methyle et avec le dichloro-1,2 ethylene

Photoirradiated in presence of acetophenone, benzo[b]selenophene and its 3-methyl derivative add to dimethyl acetylenedicarboxylate. In each ease, the primary reaction product is unstable and has not been isolated. Photoexeited in its triplet state (the energy of which is in the neighbourhood of 69 $\text{kcal}\text{mole}$) benzo[b]selenophene and its 2- and 3-methyl, 2,3 dimethyl, 3 acetoxy and 2-methyl-3-acetoxy derivatives add to 1,2 dichloroethylene leading to cyclobutanes. Neither cyclo-addition occurs in absence of photosensitiser. Single-crystal X-ray analysis gave the structures of the two adducts of 3-acetoxybenzo[b]selenophene with trans-1,2-dichloroethylene. In both compounds the chlorine atoms are trans.     

Mild electrophilic trifluoromethylation of beta-ketoesters and silyl enol ethers with 5-trifluoro methyldibenzothiophenium tetrafluoroborate

Cyclic and acyclic beta-ketoesters were efficiently trifluoromethylated with 5-trifluoromethyldibenzothiophenium tetrafluoroborate in the presence of a phase-transfer catalyst to afford the corresponding alpha-substituted alpha-trifluoromethyl beta-ketoesters in good to excellent yields. In a second approach, 5-trifluoromethyldibenzothiophenium tetrafluoroborate and tetrabutylammonium difluorotriphenylstannate were used for efficient electrophilic trifluoromethylation of various silyl enol ethers leading to the corresponding alpha-trifluoromethyl ketones in good to high yields.     

SELECTIVE DEGRADATION OF AMINO ACIDS PHOTOSENSITIZED BY TRYPTOPHAN IN POLYPEPTIDE STRUCTURES

Polypeptides containing a basic amino acid close to their single tryptophan residue were irradiated with monochromatic 302 nm radiation. Tryptophan photolysis was monitored by absorption and fluorescence spectroscopy. Amino acid loss was evaluated by amino acid analysis. Only the protonated residues adjacent to tryptophan in the sequence were destroyed upon tryptophan excitation. This reaction is probably due essentially to direct interaction between the excited tryptophan and the neighbouring residue without electron solvation.