The effective rotational hamiltonian for open-shell molecules

A formalism for obtaining the effective rotational hamiltonian for any open-shell molecule is described. This effective hamiltonian is shown to be formed of series of irreducible tensors composed of real and fictitious angular momentum operators. The operations of these tensors may in all cases be restricted to a particular electronic state. Application of such a formalism should be particularly valuable in the interpretation of the high resolution spectra (zero-field microwave, gas-phase electron resonance, etc.) of open-shell molecules, for it follows that the experimental data may always be interpreted without explicit reference to electronic states other than that wherein the spectrum originates. Useful rules are given which determine the relevant orders of tensors in the series and the method is illustrated for the case of a ³Σ diatomic molecule.     

TheK-theory of AF embeddings of the rational rotation algebras

Our main result is the construction of an embedding ofC(T²) into an approximately finite-dimensionalC ^*-algebra which induces an injection onK ₀(C(T²)). The existence of this embedding implies that Cech cohomology cannot be extended to a stable, continuous homology theory forC ^*-algebras which admits a well-behaved Chern character. Homotopy properties ofC ^*-algebras are also considered. For example, we show that the second homotopy functor forC ^*-algebras is discontinuous. Similar embeddings are constructed for all the rational rotation algebras, with the consequence that none of the rational rotation algebras satisfies the homotopy property called semiprojectivity.     

Rapid catalytic transfer reduction of aromatic nitro compounds to hydroxylamines

A general method has been developed for the rapid, metal-catalysed transfer reduction of nitro compounds to N-substituted hydroxylamines.     

Focused cryogenic trapping for dynamic headspace and pyrolytic analysis of polymers on a fused silica capillary column

Focused cryogenic trapping has been used to maximize the high resolution capabilities of fused silica capillary columns during dynamic headspace and pyrolytic polymer analyses. Mass spectrometric detection with data system recording/processing provide sensitive, selective, and rapid results. The techniques described herein demonstrate the power of both dynamic headspace and pyrolytic analyses for troubleshooting applications with complex industrial polymer products.     

Nanovoid relaxation in a series of copolyester glasses under cyclic loading using synchronous PALS

This study examines if correlation between a specific molecular motion and the growth and relaxation of nanovoids, which are precursors to crazes, can be established. A novel technique, positronium annihilation lifetime spectroscopy (PALS) synchronized with cyclic stress, is reported. In this technique the positronium annihilation signal was accumulated in sixteen channels corresponding to sixteen phases of the sinusoidal load, which allowed statistically significant data for nanovoid generation and relaxation due to the fluctuating stress to be accumulated. This technique was applied to a series of copolymers of poly(ethylene terephthalate) (PET) and poly(1,4-cyclohexylenedimethylene terephthalate) (PCT). Previous studies have shown that the cyclohexylene rings in the main chain of PCT actively undergo chair-boat-chair conformational transitions in the glassy PCT at around room temperature. The PET-co-PCT series was also chosen for this study because the crazing stress increases systematically with the cyclohexylene content. The synchronized PALS data are consistent with the hypothesis that transient nanovoids generated by the cyclic stress in polymers containing more cyclohexylene rings relax more readily than those with fewer rings. The results also correlate well with the crazing stress in this series of copolymers. © 2007 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 45: 1410–1417, 2007     

Fréchet differentiability of the solutions of a semilinear abstract Cauchy problem

Sufficient conditions are found under which the solutions z(t;q) of a semilinear abstract Cauchy problem of the form are Fréchet differentiable with respect to the parameter q. An explicit form is provided for the sensitivity equation satisfied by the Fréchet derivative Dqz(t;q).