Action des bromures de perfluoroalkylmagnésiums sur les aldéhydes α,βéthyléniques

Perfluoroalkylmagnesium bromide, C_nF_2n+1MgBr (n = 2, 6, 8), reacts with α,β-unsaturated aldehydes to give allylic alcohols as the sole products. No attack on the β-carbon atom of the carbonyl was detected, even when the reaction was carried out in the presence of CuCl. Part of the Grignard reagent decomposes to trans-R_FCFCFBr and trans-R_FCFCFI. Neither a mechanism involving dissociation into R⁺_F MgX^- nor the formation of a carbene intermediate is capable of explaining the thermal decomposition of the Grignard reagent.     

Access to 2-fluoroacrylates and their 3-chloro derivatives by chemical hydrogenolysis of 3,3-dichloro-2-fluoroacrylates

The formation of 3-chloro-2-fluoroacrylates 2 and 2-fluoroacrylates 3 by hydrogenolysis of 3,3-dichloro-2-fluoroacrylates 1 was studied by using Bu₃SnH, zinc, the sodium sulphite/sodium formate mixture or iron pentacarbonyl in the presence of a hydrogen donor (Et₃SiH or CH₃OH). The two last couples can be used to prepare the 3-chloro derivatives 2, whereas for the preparation of the 3,3-dihydro derivatives 3, zinc is the most appropriate reducing agent. Keywords: 2-Fluoroacrylate; 3-Chloro-2-fluoroacrylate; 3,3-Dichloro-2-fluoroacrylate; Tributyltin hydride; Zinc; Sodium sulphite; Sodium formate; Iron pentacarbonyl; NMR spectroscopy; IR spectroscopy     

On solving a D.C. programming problem by a sequence of linear programs

We are dealing with a numerical method for solving the problem of minimizing a difference of two convex functions (a d.c. function) over a closed convex set in ⁿ . This algorithm combines a new prismatic branch and bound technique with polyhedral outer approximation in such a way that only linear programming problems have to be solved.Parts of this research were accomplished while the third author was visiting the University of Trier, Germany, as a fellow of the Alexander von Humboldt foundation.     

X-ray determination of the mean amplitudes of vibration and debye temperatures of some rare earth monochalcogenides

The x-ray diffraction intensities of Bragg reflections have been measured at room temperature for thulium selenide, samarium sulphide, samarium selenide and samarium telluride. On the basis of a common amplitude approximation, the Debye-Waller factor, the mean amplitude of vibration and the Debye temperature have been evaluated. The values of the Debye temperatures and mean amplitudes of vibration are 176±16°K, 0·185 ± 0·017 Å (TmSe), 155 ± 7°K, 0·244 ± 0·012 Å (SmS), 153 ± 14°K, 0·221 ± 0·020 Å (SmSe) and 151 ± 20°K, 0·204 ± 0·027 Å (SmTe).     

A new simplicial cover technique in constrained global optimization

A simplicial branch and bound-outer approximation technique for solving nonseparable, nonlinearly constrained concave minimization problems is proposed which uses a new simplicial cover rather than classical simplicial partitions. Some geometric properties and convergence results are demonstrated. A report on numerical aspects and experiments is given which shows that the most promising variant of the cover technique can be expected to be more efficient than comparable previous simplicial procedures.     

Low-temperature photoluminescence spectra of highly excited quantum wires

Optical spectra of highly excited quantum wires at low temperatures have been studied within the dynamical screening approximation. We found a strong Fermi-edge singularity (FES) in the photoluminescence spectra. The spectral shape and FES intensity strongly depend on temperature in agreement with recent experimental results.     

Exciton interaction potential in polar crystals

The problem whether polaron effects can lead to a repulsive barrier in the exciton interaction potential is reinvestigated, because this effect is crucial for the possibility of a Bose-Einstein condensation of excitons (rather than of excitonic molecules). The energy for two excitons is calculated accurately as a function of their mean distance in the case of a heavy hole mass by using an integral expansion method of molecular physics. The resulting interaction potential shows for certain polaron radii a very weak repulsive barrier. Taking into account corrections to the Haken potential which have been introduced by Pollmann and Büttner, it is shown that the interaction potential between two excitons in the relative singlet state is always attractive, so that the exciton system is also in polar materials unstable against exciton molecule formation.This is a project of the Sonderforschungsbereich Frankfurt/Darmstadt, financed by special funds of the Deutsche Forschungsgemeinschaft     

A new algorithm for solving the general quadratic programming problem

For the general quadratic programming problem (including an equivalent form of the linear complementarity problem) a new solution method of branch and bound type is proposed. The branching procedure uses a well-known simplicial subdivision and the bound estimation is performed by solving certain linear programs.