Metrics of Homogeneous Spaces Admitting (3.1)-Type Complete Sets

A classification has been obtained for spaces which admit complete sets of motion integrals of the (3.1)-type and are spatially homogeneous. The metrics and Killing vectors have been found in explicit form for all types of these spaces. A classification by Bianchi is given for the spaces obtained.     

General-relativistic cosmology with expansion and rotation

A model of an expanding and rotating universe is constructed in the framework of general relativity. The parameters of the model are compared with the fundamental observables and shown to be in good agreement.Kaluzhsk Branch, N. É. Bauman Moscow State Technical University (MGTU). Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 6, pp. 71–77, June, 1993.     

Rotation in cosmology

Cosmological models for a universe with expansion and rotation are considered. In particular, we analyse some effects of the universal rotation on the observational cosmology. It is shown that pure cosmic rotation does not produce neither causality voilations, nor parallax effects, nor anisotropy of the microwave background radiation. It can be detected by studying angular dependence of standard cosmological tests, and is directly measurable via polarization observations. The latter are used to obtain experimental estimates for the direction and value of the rotation of the universeThis essay received the third award from the Gravity Research Foundation, 1991 — Ed.     

The Effect of cis-trans Isomerism on the Electronic-vibrational Structure of the Ground and Excited States and Reactivity of 2-(2-Furyl)- and 2-(2-Thienyl)oxazole

The fluorescent properties, structure, and electronic structure of the ground and excited singlet and triplet electronic states of the cis and trans forms of 4,5-dihydro-2-(2-furyl)oxazole, 4,4-dihydro-2-(2-thienyl)oxazole, 2-(2-furyl)oxazole (FO), and 2-(2-thienyl)oxazole (TO) have been studied. The orbital nature of the lower excited singlet and triplet states has been studied by the semiempirical INDO/S (valence approximation) and PPP/S ( approximation) methods. It was shown that for FO and TO molecules the lower triplet state is of the * type, for which delocalization of the electronic excitation on atoms is characteristic. In the singlet excitation state inversion was observed of the energy levels of the delocalized * states and n* states localized over several bonds (for the free TO and FO molecules the lower excited singlet states S₁* were assigned to * and n* types respectively). Owing to the low position of the T * and T _n* levels relative to the singlet level of * type, the rate constant for intercombination conversion is greater than the rate constant for radiative decay. Consequently an efficient population of the triplet states of the molecules occurs under conditions of electronic-vibrational excitation. The direction of reactions during synthesis was compared with the localization indices in the ground state for electrophilic, nucleophilic, and radical substitution, and also with the excitation localization numbers L for a wide selection of electronically excited states. It was concluded that the change in the structure of the azole molecule on replacing an O atom by an S atom, or on changing from a partially hydrogenated to a heteroaromatic system, was the main reason for the change of all the spectral parameters characterizing the electronic-vibrational or the spin-orbital interaction of the most reactive groups of atoms in the molecular structure.     

Localization of electronic excitation and change in the direction of electrophilic substitution reactions in some phenylazoles, 2-furylazoles, and 2-thienylazole

NMR, IR, UV, and fluorescence spectral data and semiempirical quantum chemical PPP and INDO/S methods were used to refine the electronic structure of several azoles and analyze the change in course of electrophilic aromatic substitution reactions involving addition and dissociation in going from free bases to protonated forms. The electronically excited singlet and triplet states of the protonated forms of the mono- and bicyclic systems studied feature excitation localization different from the free molecules. The results of quantum chemical modelling of the change in the reactivities of these systems are given.Dedicated to Prof. A. Katritzky on his seventieth birthday.Russian International Friendship University, 117302 Moscow. N. D. Zelinskii Institute of Organic Chemistry, Russian Academy of Sciences, 117913 Moscow. Translated from Khimiya Geterotsiklicheskikh Soedinenii, No. 9, pp. 1181–1194, September, 1998.     

The effect of radiation defects in silicon single crystal lattice on the characteristic states of the interstitial muonium atom

Radiation defects are shown experimentally to affect differently the normal and anomalous muonium states in silicon. This evidences essentially different mobilities of the two muonium states in the sample lattice.