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Sibirskii Zhurnal Industrial'noi Matematiki
2013, vol. 16, No 1 (53)
Contents
Akinshin A.A.; Golubyatnikov V.P.; Golubyatnikov I.V.
On some many-dimensional models of the functioning of gene networksWe obtain a sufficient condition for the nonuniqueness of cycles in some nonlinear dynamical systems considered as models of the functioning of gene networks. Some constructive methods of determination of these cycles and invariant surfaces containing these cycles are described as well.
Key words: Nonlinear dynamical systems, gene networks models, phase portraits, invariant domains, stationary points, cycles.
P. 3–9.Akinshin Andrey Alexandrovich
I.I. Polzunov Altay state technical university, 46, Lenin avenue, 656038, Barnaul, Russia
Golubyatnikov Vladimir Petrovich
Golubyatnikov Ivan Vladimirovich
Sobolev Institute of Mathematics of the SD RAS, 4, Koptyug avenue, 630090, Novosibirsk, Russia email: andrey.akinshin@gmail.com; glbtn@math.nsc.ru; ivan.golubyatnikov@gmail.com
Dementyeva E.V.; Karepova E.D.; Shaidurov V.V.
Recovery of a boundary function from observation data for the surface wave propagation problem in an open basinThe iterative numerical method of recovery of the unknown boundary function describing the ocean influence on the open boundary of a computational domain is proposed. The algorithm is based on the method for solving inverse problems by adjoint equations and optimal control methods. The algorithm is tested on a model problem for the basin of the Sea of Okhotsk.
Key words: shallow water equations, finite element method, inverse problem.
P. 10–20.Dementyeva Ekaterina Vasilyevna
Karepova Evgeniya Dmitryevna
Shaidurov Vladimir Viktorovich
Institute of Computational Modeling of the SDRAS Akademgorodok, 660036, Krasnoyarsk E-mail: e.d.karepova@icm.krasn.ru; E-mail: shidurov@icm.krasn.ru
Dudko O.V.; Lapteva A.A.
On the propagation of perturbations along an incompressible elastic medium with multimodulus shear resistanceUnder study the features of the propagation of boundary perturbations in the multimodulus incompressible elastic medium with a different resistance to shear stress applied in opposite directions. For the case of plane waves the one-dimensional boundary value problems of a shock shift by the boundary of the halfspace are solved. We show that some piecewise-linear multimodulus incompressible elastic medium nonlinear wave processes (strong and weak breaks, moving as a rigid body layers) can arise.
Keywords: incompressibility, multimodulus, elasticity, one-dimensional shear, dynamic deformation.
P. 21–28.Dudko Olga Vladimirovna
Lapteva Anastasiya Alexandrovna
Institution of Russian Academy of Sciences
Institute of Automation and Control Processes of Far-Eastern Branch of RAS
690041, Vladivostok, Radio st., 5 E-mail: dudko@iacp.dvo.ru; lanastal@mail.ru
Zagoruiko N.G.; Borisova I.A.; Kutnenko O.A.; Duybanov V.V.
Constructing the compressed description of dataset by the function of rival similarityWe argue that the general aim of data mining consists in constructing some simplified compressed description of information. The Function of rival similarity (FRiS-function) is proposed as a new ternary similarity measure between objects instead of a binary one. Quantitative estimation of the compactness of datasets, basing on FRiS-function, allows constructing new more effective compressing algorithms of data mining. Some examples are described of the algorithms testing on real and model tasks.
Keywords: data mining, function of rival similarity, pattern recognition, objects censoring, feature selection.
P. 29–41.Zagoruiko Nikolay Grigorievich
Borisova Irina Artemovna
Kutnenko Olga Andreevna
Duybanov Vladimir Vladimirovich
Sobolev Institute of Mathematics of the SDRAS
Novosibirsk State University
Design Technological Institute of Digital Techniques SD RAS
pr. Akad. Koptyuga 4, Novosibirsk, 630090 Russia E-mail: zag@math.nsc.ru; biamia@mail.ru; olga@math.nsc.ru; vladimir.dyubanov@gmail.com
Zadorin A.I.; Tikhovskaya S.V.
A two-grid method for a nonlinear singular perturbation boundary value problem on the Shishkin schemeUnders consideration is some boundary value problem for a second order nonlinear singular perturbation ordinary differential equationd.An upwind scheme on the Shishkin mesh is applied. We use the Newton and Picard methods to resolve the difference schemeare investigated. To decrease number of arithmetical operations we use the two-grid method. Application of the Richardson extrapolation is shown to give almost second order accuracy of the difference scheme. The results of some numerical experiments are discussed.
Key words: nonlinear differential equation, singular perturbation, Shishkin mesh, difference scheme, iterative method, two-grid method, Richardson extrapolation.
P. 42–55.Zadorin Alexander Ivanovich
Tikhovskaya Svetlana Valer'evna
Omsk Deaprtment of the Sobolev Institute of Mathematics of the SDRAS 13, Pevtsova str. 644099, Omsk, E-mail: zadorin@ofim.oscsbras.ru; s.tihovskaya@yandex.ru
Kovtanyuk L.V.; Panchenko G.L.
Nonisothermic deformation of the elastoviscoplastic flat heavy layerThe solution is given of the thermoelasticoplastic problem about slide of a heavy layer from an inclined plane under heating. The creep effect is stipulated to the development of a viscoplastic flow at the cost of a dependence from the temperature of the material layer yield strength. Within the theory of large deformations the law of the propagation of elastoplastic boundary is indicated, stresses, strains and strain rates are calculated both in the area of thermoelastic deformation and in the area of flow.
Keywords: elasticity, plasticity, viscosity, thermal conductivity, large deformation.
P. 56–65.Kovtanyuk Larisa Valentinovna
Institute of Russian Academy of Sciences Institute of Automation and Control Processes Far Eastern Branch of RAS Radio Street, 5 690041 Vladivostok
Panchenko Galina Leonidovna
Vladivostok State University Economics and Service Gogolya Street, 41 690014 Vladivostok E-mail: lk@iacp.dvo.ru; panchenko.21@yandex.ru
Likhoshvai V.A.; Fadeev S.I.
On the shift of a regulatory signal in models of matrix synthesisThe paper deals with the limiting properties of the matrix synthesis models thattake into account the phenomenon of branching and an unspecified number of intermediate stages. Numerically, it is shown that with unlimited increase in the number of intermediate stages, the shift on observed of the control signal along the chain synthesis. Also, compression of the control function, is inversely proportional to the branching ratio. If branching is absent, the hypothesis is proved by analogy with the available limit theorems.
Keywords: mathematical biology of the gene, matrix synthesis, a system of ordinary differential equations, retarded arguments, shift of regulatory signal, implicit scheme.
P. 66–74.Likhoshvai Vitaly Alexandrovich
Institute of Cytology and Genetics of the SDRAS Acad. Lavrentiev Ave., 10
Novosibirsk State University
Fadeev Stanislav Ivanovich
Sobolev Institute of Mathematics of the SDRAS Acad. Koptyug Ave., 4
Novosibirsk State University Pirogova Str., 2 630090 Novosibirsk E-mail: likho@bionet.nsc.ru; fadeev@math.nsc.ru
Mehraliyev Y.T.
Inverse problem of the boussinesq-love equation with an extra integral conditionThe paper addresses an inverse boundary value problem for the Boussinesq–Love equation with an extra integral condition of the first kind. The problem is firstly reduced to the problem that is in a sense equivalent to the original. Then, the Fourier method is applied, reducing the problem to solution of a system of integral equations. The existence and uniqueness of the latter equation is proved by the contraction mapping principle, which also yields the unique solution of the equivalent problem. Using equivalence, we finally prove the unique existence of a classical solution of the problem under consideration.
Key words: inverse boundary problem, Boussinesq–Love equation, Fourier method, classical solution.
p. 75–83.Mehraliev Yashar Topush oqli
Baku State University Z. Khalilov str., 23 Azerbaijan, AZ1148 Baku E-mail: yashar_aze@mail.ru
S. N. Postovalov, E. A. Naumova
Comparative analysis of the power of goodness-of-fit tests for composite hypotheses in dependence on the estimation method
The results are presented of the power comparison of the Kolmogorov, Cramer–von Mises–Smirnov and Anderson–Darling goodness-of-fit tests for composite hypotheses, depending on the method of parameter estimation. They demonstrate that the maximal power of the tests is achieved by using the maximum likelihood estimation method has the maximal power of tests inn estimating the scale parameter and evaluating both parameters of the normal distribution law. The power is higher atL -estimates in the case of the shape parameter of the Weibull distribution law. In estimating the shift parameter, the maximum power is observed in the case of the minimal distance method minimizing the relevant test statistic.
Keywords: goodness-of-fit test, test power, maximum likelihood estimation method, minimum distance method, composite hypothesis.
P. 84–94.Postovalov Sergey Nikolaevich
Naumova Elena Andreevna
Novosibirsk State Technical University 20 Prospekt K. Marksa 630073 Novosibirsk, Russia E-mail: postovalov@ngs.ru; elena.naymova@gmail.com
Starovoitov V.N.
Optimal control of cylinder rotation in a viscous fluidThe paper deals with the axisymmetric problem of optimal boundary control of a mechanical system consisting of two coaxial cylinders and an incompressible viscous fluid filling the area between them. The control parameter is the angular velocity of the outer cylinder. It is required to stop the inner cylinder at a prescribed time with minimal energy cost. The unique solvability of the problem is proved and the optimality system is derived.
Key words: viscous fluid, rigid body, optimal control.
P. 95–104.Victor N. Starovoitov
Lavrentyev Institute of Hydrodynamics of the SDRAS Lavrentyev prospekt 15 Novosibirsk State University Pirogova Str., 2 630090 Novosibirsk E-mail: starovoitov@hydro.nsc.ru
Sukhinin S.V.; Yurkovskiy V.S.
Waves in a homogeneous channel with a periodical chain of thin-wall platesUnder study is propagation of acoustic waves in a uniform rectangular channel with one-dimensional periodic chain of lates on using the group theory of local plane symmetry in the two-dimensional formulation. Dispersion relations are obtained for the modes, orthogonal to plug mode. The pass bands and stop bands of these modes are obtained and the dependence of the waveguide properties on the geometrical parameters of the plates chain are carried out. It is shown that the waveguide properties of the channel with the plates chain for the waves orthogonal to plug mode are significantly better than the waveguide properties of a free channel. The lower bound of the pass band of the waves in channel with plates orthogonal to plug mode lies below than the lower bound of the pass band of the free channel.
Key words: waveguide properties of the channels, one-dimensionally periodic chains of obstacles
P. 106–115.Sergey V. Sukhinin
Vadim S. Yurkovskiy
Lavrentiev institute of hydrodynamics of the SDRAS 15 Lavrentyev pr. 630090 Novosibirsk, Russia, sukhinin@hydro.nsc.ru ; yvs2000@gmail.com
Khasanov N.A.; Sukhinin S.V.
Acoustic eigen oscillations near thin-walled obstacles in an annular cylindrical channelThe articlepresents the analytical and numerical investigations of acoustic eigen oscillations near thin-walled obstacles in a uniform annular cylindrical channel. Acoustical eigen oscillations are described with the help of the Neumann problem for the Laplace operator. Using representation of symmetry groups in the solution space, it is shown that for the large class of thin-walled obstacles in annular channels there always exists a pure point spectrum that is embedded into a continuous spectrum of a self-adjoint extension of the Laplace operator appropriate to the homogeneous Neumann problem. Also we present the results on dependence of eigenfrequencies on the geometrical parameters of thin-walled obstacles in a uniform annular cylindrical channel as well as on the form of eigenfunctions. The influence is also addressed of the geometric characteristics of oscillations on the frequencies, quantity and and form of eigenoscillations.
Key words: acoustic eigen oscillations in unbounded domains, resonance phenomena, spectral properties of Laplace operator.
P. 116–125.Khasanov Nail
Sukhinin Sergey
Lavrentiev institute of hydrodynamics of the SDRAS 15 Lavrentyev pr. 630090 Novosibirsk E-mail: nail_khasanov@mail.ru; sukhinin@hydro.nsc.ru
Shan'ko Yu.V.
Geveralized functionally-invariant nonhomogeneous wave equationWe suggest a definition of generalized functionally invariant solutions of class N of differential equations for sound propagation in a two-dimensional stationary inhomogeneous medium. The conditions are studied on functions of the density and speed of sound under which there are generalized functionally invariant solutions of class 2. The method is presented for constructing exact generalized functionally invariant solutions.
Keywords: inhomogeneous wave equation, generalized functionally invariant solutions, exact solutions.
P. 126–137.Shan'ko Yury Vadimovich
Institute of Computational Modeling of the SDRAS Akademgorodok 660036 Krasnoyarsk E-mail: shy70@mail.ru
Shcherbakov V.V.
On an optimal control problem of thin inclusions shapes in elastic bodiesThe paper concerns an optimal control problem for a 2D elastic body with a thin rigid inclusion and a crack. The thin rigid inclusion is supposed to delaminate and contain a kink. Inequality type boundary conditions are imposed at the crack faces to provide a mutual nonpenetration between the crack faces. The cost functional characterizes the derivative of the energy function with respect to the crack length. The position of the kink is considered as a control function. The main result is the existence of a solution to the optimal control problem. Key words: crack, thin rigid inclusion, nonlinear boundary conditions, optimal control, derivative of energy functional.
P. 138–147.Shcherbakov Victor Victorovich
Lavrentiev's Institute of Hydrodynamics of the SDRAS 15, Prospect Akad. Lavrentyeva 630090 Novosibirsk e-mail: sherbakov87@gmail.com