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.     

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.     

The probability function of a generalized poisson distribution and special polynomials

The probability function of a generalized Poisson distribution is written in terms of modified Hermite polynomials of 2nd kind in many variables. Their relationship is established with special polynomials previously derived for this purpose. The properties of the polynomials and the probability function are studied. Translated from Chislennye Metody v Matematicheskoi Fizike, Published by Moscow University, Moscow, 1996. pp. 160–169.     

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.     

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.     

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.     

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.     

Inverse problem of electromagnetic sounding of the shape of a conducting body

The inverse problem of electromagnetic sounding of the shape of a conducting body is considered in the framework of the two-dimensional model with E-polarization, assuming a cylindrical body of an arbitrary cross section embedded in a layered medium. The integral equations are obtained for the case of an ideally conducting body and a body of finite conductivity. The linearization method is applied to obtain an iterative method that finds a correction to the initial shape. Translated from Obratnye Zadachi Estestvoznaniya, Published by Moscow University, Moscow, 1997, pp. 96–103.     

Analysis of the iterative method of solution of integral diffraction equations

The article investigates the convergence of an iterative method of solution of the integral equation for the diffraction problem of an electromagnetic field in a nonabsorbing medium. The convergence region of the iterative process is determined for the diffraction of a plane wave on a dielectric cylinder in a homogeneous space.Translated from Matematicheskie Modeli Estestvoznaniya, Published by Moscow University, Moscow, 1995, pp. 112–114.     

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.     

Axisymmetric excitation of a dielectric torus: Numerical solution

The article considers the mathematical model of a lens antenna in the shape of a homogeneous dielectric torus excited by an axial magnetic dipole. The boundary-value problem for an elliptical differential equation is posed and reduced by the fundamental solution method to an integral equation of 2nd kind over the torus section. A numerical algorithm is proposed, and the numerical results are compared with experimental findings. Translated from Obratnye Zadachi Estestvoznaniya, Published by Moscow University, Moscow, 1997, pp. 109–115.     

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.     

Development of integro-differential methods of parameter determination for a sum of exponential functions

We consider the problem of determination of decay decrements and amplitudes of exponential functions form observations with errors of the sum of these functions on a nonuniform grid. The integro-differential methods proposed by other authors lead to numerically unstable ill-posed problems, and make it impossible to estimate the errors in the results. New approaches are proposed that overcome these difficulties. The effectiveness of the proposed solutions is demonstrated. Translated from Chislennye Metody v Matematicheskoi Fizike, Published by Moscow University. Moscow, 1996, pp. 129–136.     

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 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.     

Some features of viscous gas flow injected into a supersonic stream from the lateral surface of a cylinder

The article presents a procedure and results of numerical analysis of the structure of flow near an elongated cylinder with a spherically blunted nose that moves with a supersonic velocity with local injection of gas from its lateral surface. The analysis is based on the solution of the full Navier-Stokes equations for a compressible gas. Nonstationary fluctuations in the region of the condensation discontinuity are detected in the given range of Mach and Reynolds numbers. Translated from Chislennye Metody v Matematicheskoi Fizike, Published by Moscow University, Moscow, 1996. pp. 119–124.     

Dynamic mechanical properties of multicomponent polymeric compositions

The mechanical relaxation processes in rubber-polymer compositions have been investigated by the forced nonresonance vibration method. A method of evaluating black-filled polymer mixtures with advantages over microscopic methods is proposed.Scientific-Research Institute of the Tire Industry, Moscow. V. I. Lenin Moscow State Pedagogical Institute, Laboratory of Problems in Polymer Physics. Translated from Mekhanika Polimerov, No. 1, pp. 138–141, January–February, 1970.     

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.     

Inverse coefficient problem for a nonlinear differential equation and an iterative solution method

The article considers the determination of the solution-dependent coefficient of a nonautonomous ordinary differetial equation with a parameter. Reduction of the inverse problem to a nonlinear operator equation is used to prove existence and uniqueness theorems and to propose an iterative solution method. Translated from Obratnye Zadachi Estestvoznaniya, Published by Moscow University, Moscow, 1997, pp. 5–17.     

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.