Numerical analysis of the eigenfrequency spectrum of shells of revolution

M. V. Lomonosov Moscow State University, Institute of Mathematical Modeling of Russian Academy of Sciences, Moscow. Translated from Matematicheskoe Modelirovanie, Published by Moscow University, Moscow, 1993, pp. 19–24.     

Stabilization of uncertain systems on rings

M. V. Lomonosov Moscow State University. Translated from Matematicheskoe Modelirovanie. Published by Moscow University, Moscow, 1993, pp. 279–295.     

Contrast structures: Theory and applications

M. V. Lomonosov Moscow State University. Translated from Matematicheskoe Modelirovanie, Published by Moscow University, Moscow, 1993, pp. 63–67.     

Development and analysis of a mathematical model of the Earth's upper atmosphere

Tomsk State University. Translated from Matematicheskoe Modelirovanie, Published by Moscow University, Moscow, 1993, pp. 122–138.     

Functional models for representations of current algebras and semi-infinite Schubert cells

Moscow Mathematical Institute. Independent Moscow University. Translated from Funktsional'nyi Analiz i Ego Prilozheniya, Vol. 28, No. 1, pp. 68–90, January–March, 1994.     

Multigrid method as an accelerating procedure for solving systems of linear algebraic equations with a dissipative matrix

Rostov State University. Translated from Matematicheskoe Modelirovanie, Published by Moscow University, Moscow, 1993, pp. 45–52.     

Hadamard's problem and coxeter groups: New examples of Huygens' equations

Moscow Physical Technical Institute. Moscow State University. Translated from Funktsional'nyi Analiz i Ego Prilozheniya, Vol. 28, No. 1, pp. 3–15, January–March, 1994.     

Changes in the supermolecular structure and physico-mechanical properties of a polycarbonate subjected to supplementary heat treatment

The possibility of modifying the supermolecular structure of polycarbonate by suitable supplementary heat treatment is demonstrated. An improvement in the physico-mechanical and service properties controlled by the supermolecular structure of the polycarbonate is noted.Departmental Plastics Laboratory, Ministry of the Machine-Tool and Tool Industry of the USSR, Moscow. Moscow Mendeleev Chemical Engineering Institute. State Scientific-Research Institute of Machine Science, Moscow. Translated from Mekhanika Polimerov, Vol. 5, No. 2, pp. 347–349, March–April, 1969.     

Some features of the thermodynamics of nonlinear classical systems

We derive the thermodynamic characteristics of an ideal gas of diatomic molecules with a nonlinear interatomic interaction, solving the problem for a wide class of potentials on the classical level, which is permissible for relatively high temperatures. The nonlinearity of the interaction can yield some characteristic properties of the gas. Moscow State Institute of Radio Engineering, Electronics, and Automatics (Moscow Technical University), Moscow, Russia Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 125, No. 2, pp. 315–325, November, 2000.     

Galerkin method for the linear-radiator integral equation

The article examines the general Galerkin method scheme for the singular integral equation in the problem of radiation from a finite-thickness linear radiator. Translated from Obratnye Zadachi Estestvoznaniya, Published by Moscow University, Moscow, 1997, pp. 150–158.     

Stability of implicit schemes on nonuniform grids

Implicit finite-difference approximations of the quasilinear conservation law are considered. Issues of stability and convergence are discussed, and an accuracy bound is obtained.Translated from Matematicheskie Modeli Estestvoznaniya, Published by Moscow University, Moscow, 1995, pp. 157–161.     

An algorithm for the constrained extremum problem

An algorithm is proposed to find the constrained minimum of a function. The algorithm uses differential equations that incorporate the problem constraints as singular manifolds. Translated from Obratnye Zadachi Estestvoznaniya, Published by Moscow University, Moscow, 1997, pp. 48–51.     

Modified Navier-Stokes equations for finite-difference computation of viscous flows

The classical Navier-Stokes model is modified so as to increase its accuracy. A system of third-order differential equations is proposed describing viscous flow of liquids and gases. Translated from Obratnye Zadachi Estestvoznaniya, Published by Moscow University, Moscow, 1997, pp. 189–198.     

Nicolai Nicolaevich Luzin and the Moscow school of the theory of functions

Shortly before the revolution of 1917, four papers written by participants in N. N. Luzin's analysis seminar at Moscow University appeared in the Comptes Rendus of the Paris Academy of Sciences. The publication of these papers--written by A. Ya. Khinchin, D. E. Menshov, P. S. Aleksandrov and M. Ya. Suslin--and Luzin's monograph, The Integral and Trigono-metric Series 1915, marked the emergence of Moscow University as a center of research in the theory of functions of a real variable. This paper describes Luzin's early mathematical education at Moscow University and the three year period he spent abroad (mainly in Paris) where he wrote a series of papers whose results form the core of his influential and widely praised monograph. Finally, we will show how Luzin's ideas formed the basis for the early investigations of a series of young Moscow mathematicians.     

A difference spline scheme for navier-stokes equations in natural variables

A difference scheme is proposed for solving Navier-Stokes equations in “veiocity-pressure” variables. It is constructed using one-dimensional discrete parabolic splines. The monotonizing properties of the scheme are investigated with prototype problems. Translated from Chislennye Metody v Matematicheskoi Fizike, Published by Moscow University, Moscow, 1996, pp. 33–38.     

Spectral asymptotics of non-self-adjoint elliptic systems of differential operators in bounded domains

Mathematical Institute with Computation Center, Academy of Sciences of the Tadzhik SSR. M. V. Lomonosov Moscow State University, Moscow. Translated from Funktsional'nyi Analiz i Ego Prilozheniya, Vol. 24, No. 1, pp. 64–66, January–March, 1990.     

Equilibrium conditions for multilayered anisotropic viscoelastic plates in a complex state of stress

Systems of linear differential-difference equations describing the complex state of stress of multilayered viscoelastic and elastic plates are obtained.Moscow Institute of Electronic Machine Building; All-Union Scientific-Research Institute of Glass-Reinforced Plastics and Glass Fiber, Moscow Region. Translated from Mekhanika Polimerov, No. 2, pp. 281–288, March–April, 1973.     

Moscow spaces and selection theory

A well-known result on Moscow spaces states that every Gδ-dense subset of a Moscow space X is C-embedded in X. We present here the selection version of this result and also (by means of two different approaches) we use selection theory to characterize the open bounded subsets of a uniform space (X,U) in the case when its completion is a Moscow space.     

Dependence of the dynamic strength of a glass-reinforced plastic on the mechanical and geometric parameters of its components

The dependence of the dynamic strength of a glass-reinforced plastic on the mechanical and geometric parameters of its components is investigated.Moscow Institute of Electronic Machine-Building; All-Union Institute of Glass-Reinforced Plastics and Glass Fiber, Moscow Oblast'. Translated from Mekhanika Polimerov, No. 2, pp. 366–370, March–April, 1974.     

Nonsteady deformation of SKN-18 rubber

In certain polymers, in certain conditions of temperature and deformation, orientation processes predominate over processes of thixotropic structural breakdown.Scientific-Research Institute of Rubber and Latex Goods, Moscow. V. I. Lenin Moscow State Pedagogical Institute. Translated from Mekhanika Polimerov, No. 2, pp. 350–351, March–April, 1974.