Thomas-Fermi model of a many-particle oscillator

An equation of the Thomas-Fermi type has been obtained and solved numerically for a many-particle oscillator — a system of N electrons in a potential field of a harmonic oscillator. The electron density distribution in the system has been found. An analogous model has been formulated in the theory of atomic nucleus and used to calculate the charge density distribution in⁴⁰Ca in good agreement with the available experimental data.Odessa Hydrometeorological Institute. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 7, pp. 66–72, July, 1992.     

Calculation of alkali-metal dimers on the basis of a model perturbation theory

On the basis of pseudopotential theory, within the framework of a formally accurate model perturbation theory of Rayleigh—Schrödinger type with a zero-approximation inoculating potential, the calculation of some diatomic alkali molecules in homo- and heteronuclear variants LiM (M = Li, Na, K, Rb, Cs, Fr) is considered. A local model potential of Gell-Mann type is adopted as the zero-approximation potential. The calculation results for the energy parameters — in particular, the energy of dissociation — are given; some of these results are obtained here for the first time. The calculation demonstrates the fundamental role of two basic second-order perturbation-theory effects in achieving acceptable accuracy: polarizational interaction of the valence particles through the core; and mutual screening of these particles.     

Calculation and extrapolation of oscillator strengths in Rb-like,multiply charged ions

The oscillator strengths of dipole transitions between energy levels of the lowest configurations of ions of the Rb I isoelectronic sequence with nuclear charge Z=41–46 are calculated on the basis of the model potential method using an energy approach. For certain ions the reported data are published here for the first time. It is shown that the contribution of core polarization to the oscillator strength attains 15% for some transitions.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 1, pp. 89–92, January, 1996.     

Investigation of lactams

2,3,4-Trioxohexahydroazepine 4-phenylhydrazone with a ¹⁵N-labeled atom bonded to the phenyl fragment was obtained in order to establish its structure. It was established by means of the PMR spectra that this substance is a mixture of syn and anti isomers of the hydrazone form. 2,3,4-Trioxohexahydroazepine 3-phenylhydrazone was isolated when an attempt was made to indolize the 4-phenylhydrazone. Both hydrazones react with phenylhydrazine to give the same 2,3,4-trioxohexahydroazepine 3,4-bis(phenylhydrazone). Derivatives involving the carbonyl group were obtained for both hydrazones, and the conditions for their indolization were studied, as a result of which a number of azepino[4,5-b]indole derivatives were synthesized.See [1] for communication 32.Translated from Khimiya Geterotsiklicheskikh Soedinenii, No. 7, pp. 954–960, July, 1979.     

Flow of elasticoviscoplastic thixotropic polymer systems

The necessity and possibility of taking into account the strain-rate dependence of the plastic strength in deriving mathematical models of the flow of heavily filled polymer systems is demonstrated.     

Study of lactams. VII. Synthesis and some reactions of lactim ethers of 3,3-diethyl-5-methylpiperidine-2,4-dione and 3-carbethoxypiperid-2-one

Chemistry of Heterocyclic Compounds -     

Construction of fundamental solutions of two-dimensional problems of the nonstationary theory of elasticity

We propose a method of constructing the images of the fundamental solutions in the space of the Laplace transform with respect to time, leading to simple formulas. The method is illustrated using three dynamical problems: planar deformation for an anisotropic body; flexural vibrations of an anisotropic plate; and vibrations of a shallow isotropic shell of arbitrary Gaussian curvature. Quadrature formulas are given for computing the values of the fundamental solutions. We give a new interpretation and a new method of computing the values of the special functions used in the construction of singular solutions in problems of the static theory of shells. Translated fromTeoreticheskaya i Prikladnaya Mekhanika, No. 23, 1992, pp. 86–92.