Contents of Volume 26 (2004)

Volume Contents

Contents of Volume 26 (2004)     

Relations Between Some Dimensions of Semimodular Lattices

The aim of this paper is to present relations between Goldie, hollow and Kurosh-Ore dimensions of semimodular lattices. Relations between Goldie and Kurosh-Ore dimensions of modular lattices were studied by Grzeszczuk, Okiski and Puczyowski.     

Quantization of Alternative Hamiltonians

We investigate quantum mechanical implications of canonically inequivalent Hamilton formulations of the Newtonian dynamics. Generated alternative quantizations, being noncanonical, are consistent with the same equations of motion, i.e., they satisfy E.Wigner's principle of quantization. As illustration we consider a noncanonical one-dimensional harmonic oscillator.     

Unexpected Hofmann elimination in the benzophenone-(phenylthio)acetic tetrabutylammonium salt photoredox system

The triplet state of benzophenone was quenched by the tetrabutylammonium salt of (phenylthio)acetic acid in acetonitrile solutions. The quenching event, following laser flash photolysis, resulted in the formation of a transient ion pair consisting of the benzophenone radical anion and the tetrabutylammonium cation. Subsequently this ion pair decays with the quaternary ammonium cation undergoing a Hofmann elimination to form butane-1 and tributylamine, which were detected in steady-state irradiation. This appears to be the first report of an ion pair consisting of a benzophenone radical anion and an organic cation (nonradical), in addition to the first report of a photoinduced Hofmann elimination in quaternary ammonium ions.     

Ionic disparity of identical molecules in polymorphs

[structure: see text] Formation of ionic pairs of identical molecules, extremely common in Nature but exceptional for diffractometric observations in the crystalline state, has been found in one of two polymorphs of a nucleobase analogue, 4,6-pyrimidinedione (1). The occurrence of the neutral and ionic polymorphs of 1 in many respects resembles neutral-ionic transitions of electon-donor/acceptor complexes. The ionization affects the reactivity of 1 and illustrates general properties of H-tautomers with low-disproportionation energy.     

The Structure of the (Outer) Automorphism Group of a Bieberbach Group

Referring to Tits alternative, we develop a necessary and sufficient condition to decide whether the normalizer of a finite group of integral matrices is polycyclic-by-finite or is containing a non-Abelian free group. This result is of fundamental importance to conclude whether the (outer) automorphism group of a Bieberbach group is polycyclic-by-finite or has a non-cyclic free subgroup.     

Separated sequences in nonreflexive Banach spaces

We prove that there is 1$"> such that the unit ball of any nonreflexive Banach space contains a -separated sequence. The supremum of these constants is estimated from below by and from above approximately by . Given any 1$">, we also construct a nonreflexive space so that if the convex hull of a sequence is sufficiently close to the unit sphere, then its separation constant does not exceed .

     

Comments on the geometric approximation to the second-order perturbed energies

It is shown that the ideas similar to those behind the ordinary geometric approximation can be efficiently used to speed up the convergence of the coupled Hartree-Fock iterative procedure in the density matrix formalism. The formulation of the geometric approximation in the case of multiple perturbation is also considered and an alternative second-order energy formula is proposed. The validity of the upper bound formula for the error of the geometric approximation denied by Burrows, is discussed.     

Self-consistent perturbation theory

The density matrix form of Hartree-Fock perturbation theory is developed for the case in which the basis functions themselves are perturbation-dependent. Energy expressions are derived, through second order, for both single and double perturbations.

The theory is applied in the calculation of electric dipole polarizabilities and hyperpolarizabilities for atoms (He, Be) and molecules (H₂, LiH), with excellent results. The high computational efficiency of the method is discussed and possibilities of further development are outlined.     

On the universality of Einstein equations

It is proved that a Lagrangian field theory based on a linear connection in space-time is equivalent to Einstein's general relativity interacting with additional matter fields.