Cylindricity of tangent bundles of strongly parabolic metrics and strongly parabolic surfaces

It is proved that if the intrinsic zero-index of the Sasaki metric of a tangent bundleTM ⁿ isk, thenk is even andM ⁿ is the metric product of a Riemannian manifoldM ^n–k/2 by a Euclidean spaceE ^k/2, whileTM ⁿ is the metric product ofTM ^n–k/2 byE ^k . An expression is obtained for the second fundamental forms of the imbeddingTF ^l TM ⁿ in terms of the second fundamental forms of the imbeddingF ^l M ⁿ and the curvature tensor ofM ⁿ . It is proved thatTF ^l is totally geodesic inTM ⁿ if and only ifF ^l is totally geodesic inM ⁿ .Translated from Ukrainskií Geometricheskií Sbornik, Issue 28, 1985, pp. 12–32.     

Non-steady state homogeneous nucleation in glass-forming systems: Dimensionless kinetic equation

The kinetic equation of the classical homogeneous nucleation theory is rewritten in dimensionless form and it is shown that the numerical computation of the dimensionless kinetic equation is approximately 20 times faster in comparison with the original kinetic equation. The results are compared with known analytical results and with previous numerical results in the case of the constant and variable temperature for the model Li₂O.2 SiO₂ melt. It is shown, e.g., that under non-isothermal conditions the nucleation rate is greater than the quasistationary nucleation rate and the cluster distribution function is greater than the corresponding quasiequilibrium cluster distribution function.     

Sensitivity of hydrodynamic system of the Obukhov type

The paper deals with the regime of advanced Bénard instabilities (described usually by the Lorenz system) in a more general system formulated firstly by Obukhov. It has been shown that triplet co-operation leads to characteristic courses where some new regularities occur.     

Influence of metastable-metastable collisions on electron distribution function in afterglow

The time dependence of the electron distribution function in helium afterglow, for pressures of 60–260 Pa, is calculated for the case in which metastable-metastable reactions are present. The time variation of the shape of the distribution function shows that careful consideration must be made of the time derivative of the distribution function in the Boltzmann equation for the calculation of the rate constant of such reactions from experimentally determined distribution function.     

Softening during and after the hot deformation of the AISI 321 steel with respect to practical applications

The softening processes during and after the hot deformation (850–1180 C) in AISI 321 stainless steel were studied with respect to true strains _D and true strain rates . The analysis of deformation curves indicates the occurrence of dynamic recrystallization for values of Zener-Hollomon parameterZ10¹⁵ s^–1. The retardation of static recrystallization by fine Ti(N, C) precipitates is documented by microstructure studies and by variations of annealing conditions.     

Scalar gluonium candidates and the radiativeJ/ψ decays

We discuss productions of scalar gluonium candidates in the radiativeJ/ decays. The branching ratios of such productions are estimated on the basis of the Euler-Heisenberg effective Lagrangian for gluon-photon couplings. We mention that these estimates cannot be expected to be accurate to better than within a factor 2. We show that the radiativeJ/ decays probably invalidate gluoniumgg interpretation of the GAMS meson F₀(1590) and a narrow 0⁺⁺ stateS lying below 1 GeV. However, a possible wide scalar effective gluonium candidate(920) is shown not to be excluded by the data on the decayJ/. We also find that the experimental data about radiativeJ/ decays presumably agree with a recently suggested interpretation of F₀(1590) as being approximately a half-and-half mixture of pure 0⁺⁺ gluoniumgg andSU(3)_f singlet quarkoniumq¯q states.     

Asymmetry and magnetism in bis(oximato)-bridged heterobimetallic compounds: a computational approach

A density functional study of exchange coupling was carried out for a series of heterobinuclear oximato-bridged transition metal complexes. Model calculations were used to examine the influence of the electronic configuration of the metal atoms on the coupling constants. This analysis was complemented by a study of the variation of the coupling constant with the most usual structural distortions within this family of compounds. The influence of the nature of the terminal ligands as well as that of the symmetry on the bridge were also investigated.     

PPP-Berechnungen und Vergleich der Elektronenspektren von iso-π-elektronischen Sauerstoff-, Stickstoff-, Schwefel- und Selenheterocyclen

Zusammenfassung 42 Heterocyclen, die sich formal von alternierenden und nichtalternierenden Kohlenwasserstoffen durch Ersatz einer Doppelbindung durch die Heteroatome Sauerstoff, Stickstoff, Schwefel und Selen ableiten, werden nach dem Pariser-Parr-Pople-Verfahren berechnet und ihre Spektren im nahen Ultraviolett und Sichtbaren beschrieben. Schwefel und Selen werden dabei im LCAO-MO-Verfahren nach dem p-Modell behandelt. In den meisten Fällen können die Berechnungen nicht nur die spektralen Charakteristika gut wiedergeben, sondern auch Beziehungen in den Spektren iso--elektronischer Verbindungen gleicher Struktur verständlich machen. Berechnungen an kationischen Stickstoffheterocyclen führten dann zu falschen Ergebnissen, wenn die Stickstoffparameter vom Pyrroltyp übernommen werden.

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PPP-calculations and comparison of electronic spectra of iso--electronic oxygen, nitrogen, sulfur, and selenium heterocycles

42 heterocyclic compounds, formally derived from alternant or nonalternant hydrocarbons by replacing a C=C group by an oxygen, nitrogen, sulfur or selenium atom, are studied by the Pariser-Parr-Pople-type of calculation. By means of these results the near ultraviolet and visible spectra are described. The sulfur and the selenium atoms are treated in the LCAO-MO-method using the p-model. In most cases spectral features are not only well reproduced, but interrelations of the spectra of iso--electronic compounds, possessing analogous structures are interpreted, too. On calculating cationic nitrogen heterocycles using parameters of pyrrol type nitrogen results are unsatisfactory.

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Résumé 42 composés hétérocycliques, formellement dérivés d'hydrocarbures alternants ou non alternants par remplacement d'un groupement C=C par un atome d'oxygène, d'azote, de soufre ou de sélénium, sont étudiés par la méthode de Pariser-Parr-Pople. Les résultats obtenus permettent de décrire le spectre U.V. proche et visible. Soufre et sélénium sont traités en utilisant le modèle p. Dans la plupart des cas les caractères spectraux sont non seulement correctement reproduits, mais les relations entre les spectres des composés iso--électroniques à structures analogues peuvent être interprétées. Les calculs concernant les heterocycles à azote cationique sont insatisfaisants lorsqu'ils sont effectués avec des paramètres de l'azote du type pyrrole.

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Anmerkung: Die Arbeit wurde in dem von Prof. Dr. R. Mayer geleiteten Schwefelarbeitskreis der TU Dresden durchgeführt.