On the spectral picture of an irreducible subnormal operator II

In this paper we show that the spectral picture of an irreducible subnormal operator may be arbitrarily prescribed subject only to certain natural necessary conditions. This completes work begun by the second author.

     

Inelastic collisions between 4He and H2: Study of dynamical approximations

We report a detailed study of the convergence and accuracy of HeH₂ rotationally and ro-vibrationally inelastic cross sections, determined within both the coupled states (CS) and effective potential (EP) formalisms. Two different potential surfaces were used. CS total cross sections appear insensitive to the specific choice of centrifugal barrier. Although the CS results are more accurate, the EP method reproduces the important qualitative features of the various inelastic processes. In addition, with the counting-of-states correction, the EP cross sections for ro-vibrationally inelastic transitions out of low-lying rotational levels agree with the CS values to within a factor of two, with only few exceptions.     

Direct conversion of N-methoxy-N-methylamides (Weinreb amides) to ketones via a nonclassical Wittig reaction

[reaction: see text] N-Methoxy-N-methylamides (Weinreb amides) are converted efficiently into ketones by reaction with alkylidenetriphenylphosphoranes and in situ hydrolysis of the product.     

Equivalence and conservation rules for the total integral cross section in molecular collisions

The rule of conservation of the total integral cross section o_Tj) is described in a general way using the opacity function. An equivalence rule which states that at the same initial kinetic energy, the total integral cross section from the initial state j is equal to that from the initial state j, i.e., o_Tj) is also presented. Both rules are demonstrated with numerical examples in the He + H₂ collision system and counter-examples are also presented. Possible uses of the rules in the inversion of the intermolecular surface and as an experimental tool are also discussed.