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.     

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.     

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.     

Majorizing difference schemes for parabolic equations on unstructured grids

Moscow Physico-Technical Institute. Translated from Matematicheskoe Modelirovanie, Published by Moscow University, Moscow, 1993, pp. 105–113.     

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.     

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.     

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.     

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.     

Compression of an orthotropic prism

The formulation and mathematically correct solution of a three-dimensional boundary value problem are given. A numerical calculation is presented for a prism of Canadian spruce and the displacement and stress fields are determined.Presented at a scientific seminar on polymer mechanics held in the Mechanics-Mathematics Department of Moscow State University, February 7, 1968.M. V. Lomonosov Moscow State University. Translated from Mekhanika Polimerov, Vol. 4, No. 5, pp. 810–815, September–October, 1968.     

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.     

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.     

A fortran programming system for computational problems

The article describes an approach to the design of a programming support system for the construction of modular computational programs. The system automates generation of programs for simulation of multiparameter mathematical models. Translated from Chislennye Metody v Matematicheskoi Fizike, Published by Moscow University, Moscow, 1996, pp. 52–57.     

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.     

Synthesized field method in inverse problems of magnetotelluric sounding

A new method is proposed and investigated for solving the inverse three-dimensional problem of magnetotelluric sounding. The method uses the tangential electric field on the Earth's surface, which is synthesized from the known impedance.Translated from Matematicheskie Modeli Estestvoznaniya, Published by Moscow University, Moscow, 1995, pp. 115–121.     

Continuous regularized proximal minimization method

A continuous regularization method based on the proximal method is proposed for minimization problems with an inexact objective function. Sufficient convergence conditions are given, and the regularizing operator is constructed. Translated from Chislennye Metody v Matematicheskoi Fizike, Published by Moscow University, Moscow, 1996. pp. 5–25.     

The attractor of the delayed functional-differential diffusion equation

We consider a class of functional-differential diffusion equations with delay and spatial rotation that arise in nonlinear optics. The existence of a compact global attractor is established for the corresponding discrete dynamic systems. Translated from Chislennye Metody v Matematicheskoi Fizike, Published by Moscow University, Moscow, 1996, pp. 147–152.     

On T. Kato's problem regarding bounded solutions of differential-functional equations

Karaganda State University. M. V. Lomonosov Moscow State University. Translated from Funktsional'nyi Analiz i Ego Prilozheniya, Vol. 24, No. 1, pp. 77–79, January–March, 1990.