Phase transfer catalysis: some recent applications in organic synthesis

A survey dealing with the use of anhydrous potassium carbonate as an efficient base for promoting organic reactions under solid–liquid phase transfer catalysis (SL-PTC) conditions is reported. In particular, the generation in situ of trifluoro- and trichloroacetamidide, and reactions of these azaanions with 2-bromocarboxylic esters and epoxides, affording protected α-amino acids and β-amido alcohols, respectively, are described. The reduction of allylic nitroderivatives with CS₂ to oximes or nitriles under SL- and liquid–liquid PTC (LL-PTC) is also presented. Finally, new preparation methods and a study of the reactivity of quaternary onium fluorides, hydrogendifluorides and dihydrogentrifluorides, together with the use of dihydrogentrifluorides as hydrofluorinating agents under SL-PTC conditions, are reported.     

On the eigenvalues of a class of saddle point matrices

We study spectral properties of a class of block 2 × 2 matrices that arise in the solution of saddle point problems. These matrices are obtained by a sign change in the second block equation of the symmetric saddle point linear system. We give conditions for having a (positive) real spectrum and for ensuring diagonalizability of the matrix. In particular, we show that these properties hold for the discrete Stokes operator, and we discuss the implications of our characterization for augmented Lagrangian formulations, for Krylov subspace solvers and for certain types of preconditioners. The work of this author was supported in part by the National Science Foundation grant DMS-0207599 Revision dated 5 December 2005.     

FIR Laser Lines from CH3OD: A Review

The methanol isotopic species CH₃OD has also proved to be an efficient and powerful medium to generate radiation in the far infrared (FIR) region. After the critical review of 1994, six papers have been published dealing with new FIR laser lines from this molecule. As a consequence of the use of wide tunability waveguide CO₂ lasers as well as a new pulsed CO₂ laser operating at hot and sequential bands, as of optical pumping sources, the total number of the FIR laser lines increased from 122 in 1994 to 227 today. In this communication we present an updated and complete catalogue of FIR laser lines generated from CH₃OD. Information on wavelength, offset, relative polarization, intensity, and optimum operation pressure is generally available.