Heat propagation in linear and nonlinear media with strongly nonstationary properties

We consider a first boundary-value problem in a quadrant of the plane for a second-order linear parabolic equation with two independent variables. The boundary function may increase along with the time variable. We show that the solution remains bounded at interior points when the highest-order coefficient decreases sufficiently rapidly or when the lowest order coefficients, having appropriate signs, increase sufficiently rapidly. Similar results are established for certain quasilinear nonuniformly parabolic equations. Examples are constructed showing the accuracy of the results obtained.Translated from Trudy Seminara im. I. G. Petrovskogo, No. 12, pp. 137–148, 1987.     

Solid-state lasers mode-locked by nonlinear and external linear frequency shift

A new mechanism of the ultrashort pulse formation in solid-state lasers has been investigated. It was shown that linear frequency shift of the pulse from the centre of the luminescence band along with the self-phase modulation creates the conditions for the generation of stable symmetrical ultrashort pulses in the presence of external low-frequency modulation.     

Issue of the spherically symmetric static vacuum metric in the relativistic theory of gravity

The spherically symmetric vacuum metric in the relativistic theory of gravity is analyzed numerically. It is found that there is no deviation of the numerical solution from that of general relativity except in the near-horizon range. The solution obtained has the well-established analytical asymptotics for both the near-and far-horizon limits. It satisfies the causality principle and does not impose a lower limit on the graviton mass.      

Longitudinal static spin susceptibility of the Heisenberg ferromagnet at T < Tc

An interpolation formula for the longitudinal static susceptibility of the Heisenberg ferromagnet is derived. The result is shown to have correct temperature and magnetic field dependencies at low temperatures as well as in the vicinity of the Curie point.     

Stability in the mean of the characterization of queueing models

Translated from Problemy Ustoichivosti Stokhasticheskikh Modelei — Trudy Seminara, pp. 67–75, 1985.     

Solving two-Level variational inequality

An approach to solving a mathematical program with variational inequality or nonlinear complementarity constraints is presented. It consists in a variational re-formulation of the optimization criterion and looking for a solution of thus obtained variational inequality among the points satisfying the initial variational constraints.This research was supported by the Russian Fundamental Research Foundation, Grant No. 93-012-842     

The dating of Ptolemy's Almagest based on the coverings of the stars and on lunar eclipses

This paper is a natural extension and continuation of the authors' studies of the astronomical dating problem of Ptolemy's famous Almagest. In previous papers, the authors suggested and developed a new geometrical-statistical method for dating ancient star catalogues. This method was then applied to Ptolemy's Almagest. The results obtained do not confirm the traditional dating of the Almagest (2nd century AD or 2nd century BC) but shift it to the epoch AD 600–1300. In this paper, we extend our analysis to other parts of the Almagest and study the dating problem for series of lunar eclipses described in the Almagest and for the covering of stars by planets. The results obtained completely agree with our previous results and give the same time interval, AD 600–1300.     

Amplifier module of the “Del'fin” facility for thermonuclear plasma heating

The construction principle and the applicable system are considered for the highpower laser amplifier module of the “Del'fin” facility, intended for spherical heating of thermonuclear targets. Results are presented of investigations of the radiation parameters of the amplifier module under various operating regimes. The system for focusing the laser radiation on the target surfaces is described and the results of experiments on plasma heating by radiation of three composite laser beams, at a laser energy level up to 1 kJ at a flux density up to 10¹⁴ W/cm², are analyzed.