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.     

Hierarchy of interactions and mass relations in asymptotically free E6 model of unified interactions

The hierarchy of gauge interactions within the E₆ model is proved, and the vector and spinor field masses are obtained. The mass spectrum of the charged W-bosons is found, and the mass scale is fixed so that the mass of the lightest of them is about 70 GeV. The lepton spectroscopy is studied and a new charged lepton, with mass of order 4–8 GeV is predicted. For the low-energy phenomenology, the model may be considered as a theory of 6 flavoured quarks and 4 charged leptons, each with its neutrino. Being 4-component the neutrinos are massive except for the ν_e (m_νe = 0, exactly) and ν_μ (m_νμ ≈ 0, approximately) particles. The problem of the “superfluous” particles which as a rule accompanies the asymptotic freedom in such theories is also briefly discussed.     

Low-energy pion-nucleus potential in the extended tree-level model for the pion-nucleon interaction

Starting from the extended tree-level model for the πN interaction [1] (hereafter ETLM) we demonstrated that the observed local pion-nucleus repulsion arises from the reduction of baryon masses in nucleus due to strong scalar nuclear field [2]. This is rather convincing argument in favour of nuclear relativism because such repulsion has no explanation within the traditional nonrelativistic approach to nucleus.