Application of tabulated singular kernels to the analysis of flexible shells made of hereditary materials

The solution of problems of the bending and stability of flexible shells and plates made of materials with hereditary properties involves the use of singular influence functions, for which tables are available. This considerably reduces the volume of computation and makes it comparatively easy to obtain a numerical solution.Moscow Lomonosov State University. Translated from Mekhanika Polimerov, Vol. 4, No. 6, pp. 1089–1093, November–December, 1968.     

Use of the results of auxiliary experiments in solving problems in the linear theory of viscoelasticity

The approximate method of solving problems of the theory of linear viscoelasticity with arbitrary creep and relaxation kernels, proposed in [2], is substantiated and generalized. The essence of this method consists in the approximation of the functions depending on the Laplace — Carson transforms of the mechanical characteristics of a viscoelastic body by means of certain combinations of the transforms of the creep and relaxation kernels. The expressions obtained as a result of the approximation enable the inverse transforms of the unknown functions to be found without difficulty.Moscow Lomonosov State University. Translated from Mekhanika Polimerov, Vol. 4, No. 6, pp. 963–969, November–December, 1968.     

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.     

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.     

Method of successive approximations in the nonlinear theory of viscoelasticity

A method of successive approximations, a generalization of the Il'yushin method of elastic solutions, is proposed for solving problems of the nonlinear theory of elasticity in which the stress-strain relation is given in the form of a time operator Frechet-differentiable in a neighborhood of zero. The nonlinear relaxation kernels are found from the given nonlinear creep kernels for the principal quadratic theory of elasticity. These relations make it possible to formulate the boundary value problem for this theory. By way of illustration the problem of the pressure exerted on a space by a sphere is examined within the framework of the developed theory. The question of the convergence of the method is discussed in relation to the quadratic theory of visco-elasticity.Presented at the Third All-Union Conference on Theoretical and Applied Mechanics, Moscow (January, 1968).Moscow Lomonosov State University. Translated from Mekhanika Polimerov, Vol. 5, No. 2, pp. 236–242, March–April, 1969.     

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.     

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.     

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.     

Polymerization stresses in linear viscoelastic media

It is proposed to use a model of the hereditary type to take into account the stresses developing in the process of polymerization. The effect of the degree of polymerization (cure) on the viscoelastic properties of the material is taken into account by introducing a function analogous to the temperature shift function in time-temperature superposition. In this case the system of equations consists of the above-mentioned system of equations of viscoelasticity, the kinetic equation of the curing process, and the equation of heat conduction with allowance for the presence of sources and variable thermophysical characteristics.M. V. Lomonosov Moscow State University. Translated from Mekhanika Polimerov, Vol. 4, No. 4, pp. 716–723, July–August, 1968.     

The Poincaré—Lyapunov—Liouville—Arnol'd theorem

Moscow State University. Translated from Funktsional'nyi Analiz i Ego Prilozheniya, Vol. 28, No. 2, pp. 67–69, April–June, 1994.     

Number of components of the set of real morsifications ofDµ singularities

Moscow State University. Translated from Funktsional'nyi Analiz i Ego Prilozheniya, Vol. 27, No. 2, pp. 92–95, April–June, 1993.     

Solutions of the Knizhnik—Zamolodchikov trigonometric equation

Moscow State University. Translated from Funktsional'nyi Analiz i Ego Prilozheniya, Vol. 25, No. 4, pp. 69–71, October–December, 1991.     

On the decay of step for the Korteweg—de Vries—Burgers equation

Moscow State University. Translated from Funktsional'nyi Analiz i Ego Prilozheniya, Vol. 26, No. 2, pp. 88–93, April–June, 1992.     

The hyperbolicity of phase curves of a generic polynomial vector field in ℂn

Moscow State University. Translated from Funktsional'nyi Analiz i Ego Prilozheniya, Vol. 28, No. 2, pp. 1–11, April–June, 1994.     

An averaging theorem inC *-Hilbert modules and operators without adjoint

Moscow State University. Translated from Funktsional'nyi Analiz i Ego Prilozheniya, Vol. 28, No. 3, pp. 88–92, July–September, 1994.     

Effect of structural changes in amorphous polymer films on the mechanical properties of coatings

The effect of structure formation on the mechanical properties of amorphous paint films has been investigated. It is shown that the organization of the supermolecular formations affects the internal stresses and adhesion of the film and, moreover, their tensile and impact strengths over a broad temperature interval. Fibrillar and "reticulate" structures give the best mechanical properties.State Scientific-Research and Planning Institute of the Paint Industry, Moscow. L. Ya. Karpov Physicochemical Institute, Moscow. Translated from Mekhanika Polimerov, Vol. 4, No. 5, pp. 771–775, September–October, 1968.     

The Selberg trace formula and Selberg zeta-function for cocompact discrete subgroups of SO+(1,n)

Moscow State University. Translated from Funktsional'nyi Analiz i Ego Prilozheniya, Vol. 26, No. 3, pp. 55–64, July–September, 1992.     

Continuous pseudocharacters on connected locally compact groups are characters

Moscow State University. Translated from Funktsional'nyi Analiz i Ego Prilozheniya, Vol. 27, No. 4, pp. 88–90, October–December, 1993.     

Semicontinuous envelopes,Riemann integral,and uniform distribution inC *-algebras

Moscow State University. Translated from Funktsional'nyi Analiz i Ego Prilozheniya, Vol. 29, No. 4, pp. 57–67, October–December, 1995.