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.     

On the polarization interaction between two closely spaced conducting spheres in a uniform electrostatic field

An electrostatic interaction between two separate, grounded, uncharged, perfectly conducting spheres of different radii in a uniform electrostatic field is investigated. It is shown that at a small center-to-center distance of the spheres, the force of the polarization interaction between the spheres depends appreciably more weakly on that distance in comparison to the force of the electrostatic interaction of two elementary dipoles as it should be in view of the interaction between two like polarization charges.     

Fast and Slow Diffusion of Channelized Particles in Transverse Energy Space

The Fokker–Planck-type kinetic equation is constructed with the help of the evolution equation for the transverse energy of channelized particles, which in its turn is derived beyond the framework of perturbation theory proceeding from the condition of nonconcervation of the adiabatic invariant.     

Reception of a Signal with Unknown Duration

The maximum likely and optimal (Bayesian) algorithms for detecting an arbitrary-shaped signal observed against the background of Gaussian white noise and for measuring the duration are synthesized. Exact expressions for the characteristics of the maximum likely algorithms are found. The characteristics of the Bayesian algorithms are obtained using computer simulations.     

Spontaneous formation of a system of highly ordered germanium nanoislands upon epitaxial deposition on profiled (111) silicon substrates under electromigration conditions

Atomic-force microscopy was used to study the surface topography of SiGe structures grown by epitaxial deposition of Ge on profiled Si(111) substrates under electromigration conditions. Systems of highly ordered germanium nanosized islands with dimensions of 10–20 nm and a density of 6×10¹⁰ cm^?2 were obtained. It is shown that the geometrical parameters of self-organizing nanoislands can be controlled by a proper choice of the growth and postgrowth annealing conditions for these structures.     

Synthesis and structures of nitroxyalkyl methylphosphonates

The reactions of ethylene glycol mononitrate and glycerol 1,3-dinitrate with methylphosphonic dichloride afforded new nitroxyalkyl methylphosphonates.     

Synthesis of N-substituted xanthines (review)

The literature on the synthesis of N-substituted xanthines by cyclization, recyclization, and N-substitution is reviewed.Translated from Khimiya Geterotsiklicheskikh Soedinenii, No. 1, pp. 3–27, January, 1991.     

Calculation of regression functions in problems of rejections of gaussian random fields

We study the asymptotics of some regression functions which occur in the study of high rejections of homogeneous Gaussian random fields.Translated from Statisticheskie Metody Otsenivaniya i Proverki Gipotez, pp. 143–148, 1988.