About the singularity criterion in general relativity

The metric in vacuum is found for the case of a spherical charged dust source. It is shown that a dead zone occurs in the vacuum, impenetrable to light or test particles. All singularities resulting from theorems about geodesic lines, are located in the dead zone and do not represent a physical problem for the theory. The infinite-density type singularities may be absent inside matter-filled zone.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 2, pp. 94–99, 1987.     

Density of the set of attractive compacta

A compact set K in a smooth closed manifold M is said to be attractive, if on M there exists a system of differential equations, for which K is an asymptotically stable invariant set. It is proved that the set of attractive compacta is dense and its complement contains a dense set of type G in the space of all compacta of the manifold M endowed with two natural topologies.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 143, pp. 170–175, 1985.     

Some features of solar wind protons, α particles and heavy ions behaviour: The Prognoz 7 and Prognoz 8 experimental results

The paper describes the results of investigations of the solar wind ions, carried out on board the high apogee Prognoz 7 and Prognoz 8 Earth's satellites with the aid of an SKS instrument (USSR) and a Monitor instrument (USSR-SSR). Behaviour of proton and that of components on the front of Earth's bow and interplanetary shock waves were compared by means of the energoanalysis and energy-mass analysis techniques. In several long-term periods of observation the solar wind heavy ions — oxygen, silicon and iron were determined. It enabled us to estimate the solar corona chemical composition and electron temperature.Presented at the 5th General Assembly IAGA/IAMAP August 5–17, 1985, Prague, Czechoslovakia.     

Distribution of a nonstationary electron beam in a dense gas

The problem of the temporal and spatial dependences of the parameters of the action of a modulated fast-electron beam on a dense gas is posed on the basis of the transport equation. The problem is simplified by making it nondimensional and by transforming to the Fokker-Planck approximation. A Green's function formalism is developed for this problem and is used to express the solution of the general nonstationary problem in the form of a convolution of a nonstationary boundary flow with a stationary Green's function. The use of the derived equation is illustrated using as an example the solution of a problem with the simplest stationary Green's function corresponding to the straight-ahead approximation. This approximation is used to consider a general relativistic case with model scattering cross sections. The methods and results of a numerical computer solution of the nonstationary problem of electron retardation in the upper layer of the atmosphere are surveyed.Translated from Trudy Ordena Lenina Fizicheskogo Instituta im. P. N. Lebedeva AN SSSR, Vol. 145, pp. 172–188, 1984.     

Embedded cluster calculation of the Ce3+ impurity in Lu2SiO5 crystals including crystal lattice relaxation and polarization

Results of electronic structure studies of the Ce³⁺ impurity in Lu₂SiO₅ crystals allowing for lattice polarization and relaxation are given. The calculations were performed by the embedded cluster method combining the scattered wave and molecular static methods. The effect of lattice deformation induced by the defect on the results of calculations is discussed. Translated fromZhurnal Strukturnoi Khimii, Vol. 38, No. 6, pp. 1046–1052, November–December, 1997.     

Synthesis of peptides based onβ-(N1-uracilyl)-α-alanine

The synthesis of peptides which include a DL--(N₁-uracilyl)--alanine (DL-willardiine) residue as an N-terminal or C-terminal group was investigated, dipeptides of DL-willardiine with glycine and L-tyrosine were obtained, and DL-willardiyl-DL-willardiine was synthesized; the latter is the simplest representative of the family of monotonic homopeptides which contain, as a repeating side substituent, a natural nucleic base capable of participation in intermolecular interactions of the complementary type.Translated from Khimiya Geterotsiklicheskikh Soedinenii, No. 3, pp. 404–408, March, 1971.     

Relationship between hydration energy of zeolites and cation distribution in their crystals

A method is proposed for calculating the heat of immersion of zeolites in water from data on the composition and density of the zeolite framework. The phenomenon of localization of some of the zeolite cations in the unhydrated crystallographic positions is explained. For ferrisilicates with the ZSM-5 structure, the fraction of iron atoms in the framework has been estimated from data on the energy of hydration.Translated from Teoreticheskaya i Éksperimental'naya Khimiya, Vol. 29, No. 2, pp. 174–179, March–April, 1993.     

Kinetic Aspects of Dimethylamine Hydroxyethylation in the Presence of Water

The kinetics of dimethylamine hydroxyethylation at an ethylene oxide : dimethylamine : water molar ratio of 1 : 3 : (0.1–0.5) was studied in the temperature range 20–50°C. A kinetic model of the reaction, which adequately describes the experimental data, was suggested.__________Translated from Zhurnal Prikladnoi Khimii, Vol. 78, No. 4, 2005, pp. 687–689.Original Russian Text Copyright © 2005 by Danov, Kolesnikov, Efremov, Mezhenin.