Preparation and wittig reactions of organotrifluoroborato phosphonium ylides

[reaction: see text] Potassium [(trifluoroboratophenyl)methyl]triphenylphosphonium chlorides have been prepared from the corresponding benzyl chlorides and PPh3. In the presence of 1.2 equiv of K2CO3 and various aldehydes, these mixed salts are easily converted to the corresponding unsaturated organotrifluoroborates via the intermediate phosphorus ylides. A protocol for a one-pot transformation has also been developed.     

Pseudospin and spin symmetry in Dirac-Morse problem with a tensor potential

Under the conditions of the pseudospin and spin symmetry, approximate analytical solutions of the Dirac-Morse problem with Coulomb-like tensor potential are presented. The energy eigenvalue equations are found and corresponding radial wave functions are obtained in terms of confluent hypergeometric functions. The energy eigenvalues are calculated numerically in the absence and presence of the tensor potential. We also investigate the contribution of the potential parameters to the energy splitting of the pseudospin and spin doublets.     

Klein–Gordon and Dirac Equations with Thermodynamic Quantities

We study the thermodynamic quantities such as the Helmholtz free energy, the mean energy and the specific heat for both the Klein–Gordon, and Dirac equations. Our analyze includes two main subsections: (1) statistical functions for the Klein–Gordon equation with a linear potential having Lorentz vector, and Lorentz scalar parts (2) thermodynamic functions for the Dirac equation with a Lorentz scalar, inverse-linear potential by assuming that the scalar potential field is strong (A ? 1). We restrict ourselves to the case where only the positive part of the spectrum gives a contribution to the sum in partition function. We give the analytical results for high temperatures.     

Refinements of the generalised trapezoid and Ostrowski inequalities for functions of bounded variation

Refinements of the generalised trapezoid and Ostrowski inequalities for functions of bounded variation are given. Applications for the trapezoid and mid-point inequalities are also provided. Received: 19 May 2008     

Copper-catalyzed oxaziridine-mediated oxidation of C-h bonds

The highly regio- and chemoselective oxidation of activated C-H bonds has been observed via copper-catalyzed reactions of oxaziridines. The oxidation proceeded with a variety of substrates, primarily comprising allylic and benzylic examples, as well as one example of an otherwise unactivated tertiary C-H bond. The mechanism of the reaction is proposed to involve single-electron transfer to the oxaziridines to generate a copper-bound radical anion, followed by hydrogen atom abstraction and collapse to products, with regeneration of the catalyst by a final single-electron transfer event. The involvement of allylic radical intermediates was supported by a radical-trapping experiment with TEMPO.