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.     

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.     

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.     

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.     

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.     

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.     

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.     

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.     

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.     

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.     

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.     

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.     

Fredholm equations of the first kind

A method is described for solving the Fredholm integral equation of the 1st kind by passage to the moment L-problem. The problem is reduced to a linear programming problem. A bound of the method for a particular normed space is derived. Translated from Obratnye Zadachi Estestvoznaniya, Published by Moscow University, Moscow, 1997, pp. 34–38.     

Investigation of the fiber packing density in a unidirectional composite

Recommendations are made for designing a unidirectional composite with an optimal arrangement of the fibers. The effect of the fiber diameter distribution law on the packing density is investigated.All-Union Scientific-Research Institute of Glass-Reinforced Plastics and Glass Fiber, Moscow. Moscow Institute of Electronic Machine-Building. Translated from Mekhanika Polimerov, No. 3, pp. 538–541, May–June, 1976.     

Monte-Carlo parallelization algorithm

Parallelization of computer algorithms for multidimensional problems of computational physics is considered. The focus is on efficient data processing by computer systems with a large number of concurrent processors, allowing for data exchange time. The computing time is minimized by a Monte-Carlo technique.Translated from Matematicheskie Modeli Estestvoznaniya, Published by Moscow University, Moscow, 1995, pp. 150–156.     

Two-dimensional model of SHF discharge in gases

The formation and evolution of some discharge structures under the action of a convergent HF beam on a dense weakly ionized plasma is analyzed numerically in the framework of the two-dimensional model. A discharge propagation mechanism leading to a stationary state in the two-dimensional case is investigated.Translated from Matematicheskie Modeli Estestvoznaniya, Published by Moscow University, Moscow, 1995, pp. 5–9.