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.     

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.     

Contrast structures: Theory and applications

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

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.     

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.     

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.     

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.     

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.     

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.     

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.     

An inverse problem for a system with a moving boundary

The problem of estimating the right-hand side of a nonlinear parabolic equation is considered. A finite-step algorithm based on the model positional control method and the finite element method is proposed. The algorithm is robust to informational noise and computational errors. Translated from Obratnye Zadachi Estestvoznaniya, Published by Moscow University, Moscow, 1997, pp. 23–33.     

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.     

Mathematical modeling of vertical electrical sounding of quasilayered media

The direct solution of the vertical electrical sounding problem is considered for three-dimensional quasilayered media. An efficient fast algorithm is obtained for computing the apparent resistivity curves in the two-dimensional case. A PC implementation of the algorithm is proposed. Translated from Obratnye Zadachi Estestvoznaniya, Published by Moscow University, Moscow, 1997, pp. 123–131.     

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.     

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.     

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.     

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.     

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.