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Sibirskii Zhurnal Industrial'noi Matematiki
2010, vol. 13, No 1 (41)
Contents
UDC 517.956.3:533.6.011
Blokhin A. M., Anufriev I. A.
The Well-Posedness of the Linearized Problem of a Supersonic Stream over a Wedge under Arbitrary PerturbationsUsing dissipative energy integrals, we study the well-posedness of the linearized mixed problem of a stream over a wedge.
Keywords: gas dynamics, hyperbolic systems, dissipative energy integrals, well-posedness, linear problem, shock waves.
Pp. 3–17.Blokhin Aleksandr Mikhailovich
Anufriev Ivan Aleksandrovich
Sobolev Institute of Mathematics, SB RAS, 4 Acad. Koptyug prospekt
Novosibirsk State University, 2 Pirogova str. Novosibirsk 630090 E-mail: Blokhin@math.nsc.ru; chrono@gorodok.net
UDC 333.1:519.86
Vasil'ev V. A., Suslov V. I.
Edgeworth Equilibrium in a Model of Interregional Economic RelationsWe introduce an analog of Edgeworth equilibrium for a class of multiregional economic systems. We analyze the game-theoretic aspects of the coalition stability of regional development plans and establish a rather general existence theorem for Edgeworth equilibria. We discuss the questions of coincidence of the set of these equilibria with fuzzy kernel and the set of Walras equilibria of the multiregional systems under study. The methods used rest on systematically accounting for the polyhedrality of the sets of balanced coalition plans of the models under consideration.
Keywords: model of a multiregional system, k-partitioning of a model, Edgeworth equilibrium, fuzzy Q-kernel, Walras equilibrium.
Pp. 18–33.Vasil'ev Valery Aleksandrovich
Sobolev Institute of Mathematics, SB RAS, 4 Acad. Koptyug prospekt, E-mail: vasilev@math.nsc.ru;
Suslov Viktor Ivanovich
Institute of Economics and Industrial Engineering, SB RAS, 17 Lavrent'ev prospekt, Novosibirsk 630090, E-mail: suslov@ieie.nsc.ru
UDC 517.988.8
Vinogradova P. V.
On a Numerical Method for Solving the Cauchy Problem for an Operator Differential EquationWe study a projection-difference method for solving the Cauchy problem for an operator differential equation in a Hilbert space with the principal selfadjoint operator A(t) and the subordinate linear operator K(t). For approximation equations constructed with the Faedo–Galerkin method we discretize with respect to time using the Crank–Nicolson scheme. We estimate the errors of approximate solutions and the errors for fractional powers of the principal operator A(t). We apply the method to solving an initial boundary value problem.
Pp. 34–45.Vinogradova Polina Vital'evna
Far-Eastern State University of Transportation, 7 Seryshev str. Khabarovsk 680021, E-mail: vpolina17@hotmail.com
UDC 338.4.01
Gusev V. B.
Productivity and Stability Conditions for Reproduction ModelsWe study equilibrium conditions for multile goods production models. We give an optimization formulation of equilibrium conditions, as well as indicators of productivity and stability of the technological loop with respect to the varying production parameters. We consider a feedback mechanism for maintaining a dynamic equilibrium.
Keywords: multiple sector model balancing manufacturing cycle parameters, equilibrium conditions, productivity, optimizing output regulator
Pp. 46–54.Gusev Vladislav Borisovich
Trapeznikov Institute of Control Problems, RAS, 65 Profsoyuznaya str. Moscow 117997. E-mail: gusvbr@ipu.ru
UDC 517:531:511.225
Gutman A. E., Kutateladze S. S., Reshetnyak Yu. G.
Cofinite Numbers, Nonstandard Analysis, and MechanicsWe show the mathematical insignificance of the versions of nonstandard analysis proposed by A. F. Revuzhenko.
Keywords: nonstandard analysis, Revuzhenko, pseudoscience.
Pp. 55–58.Gutman Aleksandr Efimovich
Kutateladze Semen Samsonovich
Reshetnyak Yury Grigor'evich
Sobolev Institute of Mathematics, SB RAS, 4 Acad. Koptyug prospekt, Novosibirsk 630090, E-mail: sskut@math.nsc.ru
UDC 519.95
Zagoruiko N. G., Borisova I. A., Dyubanov V. V., Kutnenko O. A.
A Quantitative Measure of Compactness and Similarity in Competitive SpaceWe describe similarity measures among objects in metric and competitive spaces. We propose a competitive similarity function as a similarity measure used in classification and pattern recognition problems. This function enables us to construct some efficient algorithms for solving all main data mining problems, to obtain quantitative estimates for the compactness of images and the informativeness of trait spaces, and to construct easily interpretable decision rules. The method applies to problems with arbitrary numbers of images and characters of their distributions, and can also be used for solving poorly conditioned problems.
Keywords: similarity measure, pattern recognition, compactness, informativeness.
Pp. 59–71.Zagoruiko Nikolay Grigor'evich
Borisova Irina Artemovna
Dyubanov Vladimir Vladimirovich
Kutnenko Olga Andreevna
Sobolev Institute of Mathematics, SB RAS, 4 Acad. Koptyug prospekt, Novosibirsk 630090. E-mail: zag@math.nsc.ru
UDC 519.65
Nazarov V. G.
Determining the Chemical Composition of an Inhomogeneous Body by Multi-Energy RadiographyWe consider the question of determining the chemical composition of an inhomogeneous body consisting of several homogeneous parts using multi-energy radiography. The interior structure of the body is assumed known. At the first stage of the solution the body is illuminated by collimated X-ray beams along a collection of specifically chosen directions at a prescribed set of energies, and by solving systems of linear algebraic equations we find the values of attenuation coefficients in each homogeneous part of the body. Then under certain additional assumptions we find the possible chemical composition of these parts. We analyze the effect of measurement errors on the quality of the solution. We illustrate the results with particular simulations. The proposed method can be used in the nondestructive control of products, customs control, and medicine.
Keywords: radiation transfer equation, X-ray tomography, numerical method for determining the chemical composition of a medium.
Pp. 72–83.Nazarov Vasiliy Gennadievich
Institute of Applied Mathematics, FEB RAS, 7 Radio str. Vladivostok 690041 E-mail: naz@iam.dvo.ru
UDC 519.622
Novikov E. A.
An Additive Third Order Method for Solving Rigid Nonautonomous ProblemsWe construct an additive method of the third order of accuracy for solving rigid nonautonomous problems. We obtain inequalities for controlling the precision of calculations and stability of the numerical algorithm. We include the results of some simulations.
Keywords: rigid problems, additive method, control of precision and stability.
Pp. 84–95.Novikov Evgeniy Aleksandrovich
Institute of Numerical Modeling, SB RAS. Akademgorodok Krasnoyarsk 660036 E-mail: novikov@icm.krasn.ru
UDC 532.517.4:536.25
Palymsky I. B.
A Numerical Method for Simulating Three-Dimensional ConvectionWe consider the three-dimensional convection of a fluid in a rectangular parallelepiped with isothermic horizontal boundary free from tangent stresses and heated from below. We propose a special spectral difference numerical method for calculating an approximation of the second order in space and the first order in time. Linear analysis of this numerical method showed that the method predicts correctly (with a good quantitative fit in the long wavelength range and a qualitative fit in the short wavelength range) the spectral characteristics of the differential problem for practical values of mesh sizes in time, space, and overcriticity. For testing we simulated two- dimensional cylindrical and turbulent Rayleigh–Benard convection for the supercriticity equal to 2.2 and 950 and the Prandtl number equal to 10.
Keywords: modeling, hydrodynamics, convection, heat transfer, turbulence, stochasticity.
Pp. 95–108.Palymsky Igor Borisovich
Modern Humanitarian Academy, Novosibirsk Branch, 71 Vatutina str., Novosibirsk 630064. E-mail: palymsky@hnet.ru
UDC 517.958:57
Pertsev N. V., Tsaregorodtseva G. E.
A Mathematical Model for the Dynamics of a Population Affected by PollutantsWe present a mathematical model for the dynamics of a population whose members are affected by ingested pollutants. We assume that a pollutant decomposition product is harmful for the individua and raises the incidence of their death. We describe the equations of the model and study the properties of their solutions, including the existence and stability of equilibrium states. We obtain conditions for the degeneration of the population and conditions guaranteeing its sustainment at nonzero stationary levels. We include the results of a numerical simulation.
Keywords: population dynamics, nonstationary medium, mathematical model, influence of pollutants.
Pp. 109–120.Pertsev Nikolai Viktorovich
Tsaregorodtseva Galina Evgenevna
Omsk Branch, Sobolev Institute of Mathematics, SB RAS, 13 Pevtsova str., Omsk 644099. E-mail: homlab@ya.ru
UDC 330.115:519.83
Romanovskaya A. N.
Efficient Algorithms for Solving Bank Activity Optimization ProblemsWe consider the two models: the activity of a monopolist bank and the activity of a new bank starting up on the banking services market. Each model involves a multiextremal nonlinear mathematical programming problem. Algorithms for solving these problems rest on those for solving linear programming problems of a special form, for which we give solutions explicitly and count the number of required operations. We prove the existence of a solution for the problem of the activity of a new bank.
Keywords: optimization model, nonlinear programming problem, linear programming problem, effective rate, complexity of solution algorithm, existence theorem for a solution.
Pp. 121–132.Romanovskaya Anastasiya Nikolaevna
Sobolev Institute of Mathematics, SB RAS. 4 Acad. Koptyug prospekt. Novosibirsk 630090. E-mail: nastenar@gmail.com
UDC 517.948
Tanana V. P., Bokov A. V.
On Estimating the Precision of an Approximate Solution to an Inverse Thermodiagnostics Problem with Free BoundaryWe estimate the precision of an approximate solution to an inverse thermodiagnostics problem with free boundary.
Keywords: inverse thermodiagnostics problem, projection regularization method, parameter regularization.
Pp. 133–139.Tanana Viktor Pavlovich
Bokov Aleksandr Viktorovich
South Urals State University, 76 Lenin prospekt, Chelyabinsk 454080, E-mail: tvpa@susu.ac.ru; bokov@susu.ac.ru
UDC 517.95
Chirkunov Yu. A.
Steady-State Oscillations in Continuously Inhomogeneous Medium Described by a Generalized Darboux EquationWe refine the result of Ovsyannikov on the general form of second order linear differential equations with a nonzero generalized Laplace invariant admitting a Lie group of transformations of maximal order with n > 2 independent variables for which the associated Riemannian spaces have nonzero curvature. We show that the set of these equations is exhausted by the generalized Darboux equation and the Ovsyannikov equation. We find the operators acting on the set of solutions inside every one-parameter family of generalized Darboux equations. For the elliptic generalized Darboux equation possessing the maximal symmetry and describing steady-state oscillations in continuously inhomogeneous medium with a degeneration hyperplane, by group analysis methods we obtain exact solutions to boundary value problems for certain domains (generalized Poisson formulas), which in particular can be test solutions in simulating steady-state oscillations in continuously inhomogeneous media.
Keywords: generalized Darboux equation, Ovsyannikov equation, intertwining operators, steady-state oscillations in continuously inhomogeneous medium, generalized Poisson formulas, radiation conditions.
Pp. 140–149.Chirkunov Yury Aleksandrovich
Novosibirsk State Technical University, 20 Karl Marx prospekt, Novosibirsk 630092. E-mail: chr01@rambler.ru