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.     

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.     

Inverse sounding problem using stabilization of the magnetic field of a loop

We consider the inverse sounding problem for a stratified medium using the variable magnetic field of a loop. A uniqueness theorem and a theorem ensuring stable determination of the integral conductivity of the medium are proved. An algorithm is proposed for the solution of the inverse problem based on a transformation from the time domain to the frequency domain. Translated from Obratnye Zadachi Estestvoznaniya, Published by Moscow University, Moscow, 1997, pp. 87–95.     

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.     

A method for approximate construction of the basic component in the class of functions of bounded variation

The article considers the construction of a stable approximation of the basic component in an experimental spectrum. Conditions of independence and nondegeneracy are introduced for the local resonance nonhomogeneities and the basic component, which is treated as a continuous smooth function whose local variation is substantially less than the variation of the local nonhomogeneities. The problem of approximating the basic component is shown to have a unique solution under these conditions. A stable algorithm is developed for the construction of the basic component. The algorithm is applied to construct the basic component from typical spectrometric data, and the results are compared with other known basic-component fitting methods. Translated from Chislennye Metody v Matematicheskoi Fizike, Published by Moscow University, Moscow, 1996, pp. 137–146.     

An inverse problem of atmospheric radar sounding

The paper considers the problem of determining the velocities of targets in the atmosphere given a set of Doppler spectra produced by continuous Doppler systems. The problem of determining the velocities of particles moving in a closed trajectory (a circle) is examined. A uniqueness theorem is proved for the reconstruction of velocities from two spectra. An algorithm is proposed for determining the sought function, and a numerical experiment is conducted to establish its efficiency.Translated from Matematicheskie Modeli Estestvoznaniya, Published by Moscow University, Moscow, 1995, pp. 162–167.     

An interactive method for parametric identification of the mathematical model of a parachute system using computer graphics

A simple mathematical model of the motion of a parachute system in space is described and an interactive algorithm for parametric identification of the model is proposed. The algorithm selects the model parameters that minimize the deviation of the calculated dependences from experimental observations on the computer graphic monitor.Moscow. Translated from Dinamicheskie Sistemy, No. 10, pp. 106–111, 1992.     

Optimization of modular associative memory

Mathematical models are proposed for optimizing the structure of modular associative memory. Optimal hashing is considered. The optimization problem is solved using a genetic algorithm. Research supported by Ministry of Science grants 201.03.002 and 201.03.003. Translated from Chislennye Metody i Vychislitel'nyi Eksperiment, Moscow State University, pp. 97–106, 1998.     

Application of a genetic algorithm to compute the control of a complex dynamic system

A genetic algorithm is applied to compute the control of a complex dynamic system. Methods are proposed to modify the genetic algorithm so as to adapt it to variation of the objective function. Comparison with dynamic programming results is carried out. The study was supported by the Russian Foundation of Basic Research (grant No. 9607-89110) and Ministry of Science (grants 0201.03.002 and 0201.03.003). Translated from Chislennye Metody i Vychislitel'nyi Eksperiment, Moscow State University, pp. 82–96, 1998.     

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.     

Equilibrium routing strategies in data transmission networks

Search for optimal routing (in the game-theoretical sense) in a packet data transmission network is considered. The proposed method reduces the general problem to a particular problem of routing in ring networks. A fast parallel (distributed) algorithm is constructed, which may be used in network-level data transmission protocols. Translated from Chislennye Metody i Vychislitel'nyi Eksperiment, Moscow State University, pp. 107–123, 1998.     

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.     

Using Richardson's method to construct high-order accurate adaptive grids

An algorithm is proposed to construct a sequence of evolutionary adaptive grids, each consisting of segments of uniform grids compatible with the Richardson extrapolation procedure. The necessary numerical accuracy is achieved by using Richardson's extrapolation method to increase the accuracy of the difference solution and by controlling the nonhomogeneity parameter on passing from one segment to the next. The numerical model used in the article is the diffusion-convection equation, whose solution contains large gradients. Numerical calculations show that the algorithm attains the prespecified accuracy on a nonuniform difference grid. Numerical examples support the universality of the proposed algorithm. High accuracy results can be obtained without changing the structure of the difference schemes approximating the original problem; only the grid spacing has to be changed. Translated from Chislennye Metody v Matematicheskoi Fizike, Moscow State University, pp. 22–36, 1998.     

Did Egyptian scribes have an algorithmic means for determining the circumference of a circle?

It has been at various times proposed in regard to Problem 10 of the Moscow Mathematical Papyrus that Egyptian scribes had developed a computational algorithm by which they could calculate the circumference of a circle of known diameter length. It has also been proposed at various times that the 7:22 ratio between a circle’s diameter and its circumference was known by the Egyptian scribes at a surprisingly early period.The present paper explores currently available evidence that lends support to each of these propositions.     

Integral characteristics in the inverse problem of magnetotelluric sounding

This article examines some aspects of the one-dimensional inverse problem of magnetotelluric sounding. A uniqueness theorem is proved in the presence ofS-surfaces. A numerical algorithm based on transformation formulas is proposed. This research was partially supported by Russian Foundation for Basic Research (grant No. 96-01-00410) and by the State Scientific-Technical Program “Future Information Technologies” (grant No. 0201.06.010). Translated from Chislennye Metody v Matematicheskoi Fizike, Moscow State University, pp. 53–66, 1998.     

Breaking of two-dimensional relativistic electron oscillations under small deviations from axial symmetry

A numerical asymptotic model for the breaking of two-dimensional plane relativistic electron oscillations under a small deviation from axial symmetry is developed. The asymptotic theory makes use of the construction of time-uniformly applicable solutions to weakly nonlinear equations. A special finite-difference algorithm on staggered grids is used for numerical simulation. The numerical solutions of axially symmetric one-dimensional relativistic problems yield two-sided estimates for the breaking time. Some of the computations were performed on the “Chebyshev” supercomputer (Moscow State University).     

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.     

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.