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.     

Energy flow in negative index materials

From Maxwell's equations, we compute the speed and the direction of propagation of active power refractedfrom air into a negative index material. We prove, both analytically and numerically that the power mayrefract positively even if phase fronts refract negatively. Considerations on the usage of ray optics inproblems involving negative index materials are drawn.     

Axiomatic properties of inconsistency indices for pairwise comparisons

Pairwise comparisons are a well-known method for the representation of the subjective preferences of a decision maker. Evaluating their inconsistency has been a widely studied and discussed topic and several indices have been proposed in the literature to perform this task. As an acceptable level of consistency is closely related to the reliability of preferences, a suitable choice of an inconsistency index is a crucial phase in decision-making processes. The use of different methods for measuring consistency must be carefully evaluated, as it can affect the decision outcome in practical applications. In this paper, we present five axioms aimed at characterizing inconsistency indices. In addition, we prove that some of the indices proposed in the literature satisfy these axioms, whereas others do not, and therefore, in our view, they may fail to correctly evaluate inconsistency.