Systematic calculation of molecular vibrational spectra through a complete Morse expansion

We propose an accurate and efficient method to compute vibrational spectra of molecules, based on exact diagonalization of an algebraically calculated matrix based on powers of Morse coordinate. The present work focuses on the 1D potential of diatomic molecules: as typical examples, we apply this method to the standard Lennard‐Jones oscillator, and to the ab initio potential of the H₂ molecule. Global cm^?1 accuracy is exhibited through the H₂ spectrum, obtained through the diagonalization of a 30 × 30 matrix. This theory is at the root of a new method to obtain globally accurate vibrational spectral data in the context of the multi‐dimensional potential of polyatomic molecules, at an affordable computational cost. © 2006 Wiley Periodicals, Inc. Int J Quantum Chem, 2007     

Some non-existence results for critical equations on step-two stratified groups

We discuss a non-existence result for a semilinear sub-elliptic Dirichlet problem with critical growth on half-spaces of stratified groups of step two. Our result improves a recent theorem (N. Garofalo, D. Vassilev, Math. Ann. 318 (3) (2000) 453–516). To cite this article: A. Bonfiglioli, F. Uguzzoni, C. R. Acad. Sci. Paris, Ser. I 336 (2003).     

The physical neutrino current from a duality transformation

With a magnetic-like interpretation of the axial current, the polarization of (massless) neutrinos can be viewed as the result of a constrained duality transformation, set up so as to lead to an electromagnetic-like gauge field interaction.     

Domain decomposition preconditioners of Neumann-Neumann type for hp-approximations on boundary layer meshes in three dimensions

We develop and analyse Neumann–Neumann methods for hpfinite-element approximations of scalar elliptic problems ongeometrically refined boundary layer meshes in three dimensions.These are meshes that are highly anisotropic where the aspectratio typically grows exponentially with the polynomial degree.The condition number of our preconditioners is shown to be independentof the aspect ratio of the mesh and of potentially large jumpsof the coefficients. In addition, it only grows polylogarithmicallywith the polynomial degree, as in the case of p approximationson shape-regular meshes. This work generalizes our previousone on two-dimensional problems in Toselli & Vasseur (2003a,submitted to Numerische Mathematik, 2003c to appear in Comput.Methods Appl. Mech. Engng.) and the estimates derived here canbe employed to prove condition number bounds for certain typesof FETI methods.     

An improved general method for palladium catalyzed alkenylations and alkynylations of aryl halides under microwave conditions

Palladium catalyzed facile method for alkenylation and alkynylation of arylhalides in good to excellent yield under microwave condition is reported.