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Sibirskii  Zhurnal  Industrial'noi  Matematiki
2012,  vol. 15,  No 2 (50)

Contents
 

UDC 519.6
Antyufeev V. S.
On the distribution of a random variable

We describe the physical process of particle transport and the standard and modified methods of modeling the mean free path. We also present a probabilistic proof of a modification of the maximum cross-section method.

Keywords: Monte Carlo method, modeling, probability distribution, mean free path, fictitious scattering, jump process.
Pp. 3–10.

Antyufeev Viktor Stepanovich
 Institute of Computational Mathematics and Mathematical Geophysics SB RAS, 6 Lavrent'ev Av., Novosibirsk 630090, Russia.  E-mail: ant@osmf.sscc.ru

 

UDC 519.237.5
Arkashov N. S., Kovalevskii A. P.
A probabilistic model for the prices of apartments

We propose three regression models for the prices of apartments. The residues of regression models are described by Student's distribution. To check for systematic deviations of the residues, we use the maximum of the modulus of the empirical bridge constructed from the remains.

Keywords: logarithmically smoothed responses, stepwise regression, t-distribution, empirical bridge.
Pp. 11–20.

Arkashov Nikolay Sergeevich,
Kovalevsky Artem Pavlovich,
 Novosibirsk State Technical University, 20 Karl Marx Av., Novosibirsk 630092, Novosibirsk State University, 2 Pirogova Str., Novosibirsk 630090, E-mail: nicky1978@mail.ru;  pandorra@ngs.ru

 

UDC 517,583
Belykh V. N.
Algorithms for computing complete elliptic integrals and some related functions

We give new algorithms for computing the complete elliptic integrals of the first and second kinds and some related functions. The algorithms are constructed on the base of rapidly converging power series; the fixed sign of the series guarantees their good conditionality (stability with respect to rounding errors). The algorithms turned out to be flexible and easily adaptable to any specific demands of computing practice.

Keywords: complete elliptic integrals of the first and second kinds, toroidal functions, conical functions.
Pp. 21–32.

Belykh Vladimir Nikitich, 
Sobolev Institute of Mathematics SB RAS, 4, Koptyug Av., Novosibirsk 630090. E-mail: belykh@math.nsc.ru

 

UDC 539.376:517.97
Bormotin K. S.
Inverse optimal control problems in creep theory

We formulate inverse problems of the theory of quasi-static creep in the form of a variational principle and optimal control with constraints on the displacements and stresses and give necessary optimality conditions. In solving specific examples, we find a continuous function of optimal load that depends on two parameters. We construct and numerically implement the method for determining the parameters from given conditions of the problem.

Keywords: inverse creep problem, damagedness, variational principles, multiobjective optimization problem, optimal control.
Pp. 33–42.

Bormotin Konsantin Sergeevich,
 Komsomolsk-on-Amur State Technical University,  27 Lenin Av., Komsomolsk-on-Amur 681013, Russia. E-mail: cvmi@knastu.ru

 

UDC 539.374
Burenin A. A., Kovtanyuk L. V., Ustinova A. S.
Viscometric flow of an incompressible elastoviscoplastic material in the presence of lubricant on the boundary surfaces

Using a large deformations model generalized to the case of viscous properties of materials, we obtain analytic solutions to a number of quasistatic boundary value problems about viscometric flows of an elastoviscoplastic material in the gap between rigid coaxial cylindrical surfaces when, in a neighborhood of one of the rigid cylinders (both interior and exterior), there is a layer of elastic non-Newtonian lubrication and the conditions of rigid solder are fulfilled on the boundary surfaces. We study the conditions of the appearance of a flow in the lubricant layer and in the base material. We indicate the values of the maximum rotation speed under which the flow does not go over the lubricant layer.

Key words: elasticity, viscoplasticity, large deformations, residual stresses.
Pp. 43–55.

Burenin Anatoly Aleksandrovich,
Kovtanyuk Larisa Valentinovna,
Ustinova Aleksandra Sergeevna,
 Institute of Automatics and Control Processes FEB RAS, 5 Radio Str., Vladivostok 690041, Russia. E-mail: burenin@iacp.dvo.ru; lk@iacp.dvo.ru; ustinova@iacp.dvo.ru

 

UDC 519.635.8:532.616
Voevodin A. F., Grankina T. B.
Mathematical modeling of icethermal regime of fresh and saline water basins

We consider a one-dimensional three-layer model describing the growth of the ice cover of water basins of varying mineralization with account taken of the dependence of the freezing temperature on the salinity and the influence of snow cover. A developed numerical method is described. Examples of calculations are given for real objects (the Novosibirsk Reservoir, Lake Yarkul), a comparison with the measurement data is carried out.

Keywords: icethermics, icethermal regime of water basins, phase transition, Stefan problem, freezing temperature, crystallization, sweep method, implicit finite-difference scheme.
Pp. 56–63.

Voevodin Anatoly Fedorovich
 Institute of Hydrodynamics SB RAS, 15 Lavrent'ev Av., Novosibirsk 630090, Russia
Grankina Tat'yana Borisovna
Novosibirsk Division of the Institute for Water and Environmental Problems, 2 Morskoy Av., Novosibirsk 630090, Russia. E-mail: voevodin@hydro.nsc.ru; grankina@ad-sbras.nsc.ru

 

UDC 519.237.7
Goltyapin V. V.
The uniqueness of an oblique factor structure. An upgraded oblimax method

We formulate and prove theorems that solve the problem of the nonuniqueness of an oblique factor structure and allowing to uniquely choose a sequence of pairs of axes of rotation that provide a maximum value for the oblimax criterion. We develop and propose an upgraded algorithm for the realization of oblimax oblique-angled rotation method including a theoretical substantiation for its use.

Key words: factor structure, rotation problem, oblimax-criterion, varimax-criterion.
Pp. 64–74.

Goltyapin Viktor Viktorovich
 Omsk Division of Sobolev Institute of Mathematics SB RAS, 13 Pevtsov Str., Omsk 640099, Russia. E-mail: goltyapin@mail.ru

 

UDC 519.242.5
Denisov V. I., Timofeev V. S., Hailenko E. A.
Planning of clarifying observations under the controlling of overhead transmission lines from laser scanning data

We present an approach to the planning of clarifying observations of overhead lines. To this end, we process the high-precision data obtained with the use of the technology of laser scanning. We give the results of estimation of the parameters of the generalized lambda distribution of observational errors, which allows us to apply the algorithm for the planning of experiments and obtain the coordinates of the points for the clarifying observations. It is shown that the thus-constructed plans are effective and their application gives a gain in estimation accuracy.

Key words: planning of experiment, Fisher information matrix, generalized lambda-distribution, regression, controlling of overhead transmission lines.
Pp. 75–85.

Denisov Vladimir Ivanovich
Timofeev Vladimir Semenovich
Haylenko Ekaterina Alekseevna
Novosibirsk State Technical University, 20 Karl Marx Av., Novosibirsk 630092. E-mail: ekavka@yandex.ru; netsc@fpm.ami.nstu.ru

 

UDC 517.956.225:517.575
Karachik V. V., Antropova N. A.
On polynomial solutions to the Dirichlet problem for a biharmonic equation in a ball

We find a polynomial solution to the Dirichlet problem for an inhomogeneous biharmonic equation with polynomial right-hand side and polynomial boundary data in the unit ball. We use an explicit representation of harmonic functions in the Almansi formula.

Keywords: biharmonic equation, harmonic polynomials, Dirichlet problem, polynomial solutions, Almansi formula.
Pp. 86–98.

Karachik Valery Valentinovich
Antropova Natal'ya Aleksandrovna
South Ural State University, 76 Lenina Av., Chelyabinsk 454080, Russia  E-mail: karachik@susu.ru

 

UDC 539.214:539.374
Polonik M. V., Rogachev E. E.
On the stationary flow of an incompressible elastoplastic medium in a spherical diffuser

Using a model of large elastic deformations, we consider an incompressible elastoplastic medium in a spherical diffuser with perfectly smooth walls. The assumption adopted of the impossibility of the reversible compressibility of the medium allows us to obtain an exact solution to the boundary value problem.

Key words: elasticity, plasticity, large deformations.
Pp.99–106.

Polonik Marina Vasil'yevna
Institute of Automatics and Control Processes FEB RAS, 5 Radio Str., Vladivostok 690041, Russia
Rogachev Egor Egorovich
Far Eastern Federal University, 8 Sukhanov Str., Vladivistok 690091, Russia E-mail: polonic@iacp.dvo.ru; egor1805@mail.ru

 

UDC 517.95
Rotanova T. A.
On the statements and solvability of the problems on the contact of two plates containing rigid inclusions

We consider problems with an unknown boundary about the contact of two elastic plates situated at an angle to each other. Each of the plates contains a rigid inclusion. The lower plate is deformed in its plane, and the upper plate, in the vertical direction. We establish the solvability and the uniqueness of the solutions to the problems. Assuming sufficient smoothness of the solution for various cases of the location of the rigid inclusions, we obtain a differential statement of the problem equivalent to the variational statement. The equilibrium equations of plates are fulfilled in  nonsmooth domains, and the boundary conditions have the form of equalities and inequalities. We consider the limit case corresponding to the increase of the rigidity parameter of the lower plate to infinity.

Key words: variational inequality, rigid inclusion Kirchhoff–Love plate, contact problem.
Pp. 107–118.

Rotanova Tat'yana Aleksandrovna,
 Institute of Hydrodynamics SB RAS, 15 Lavrentyev Av., Novosibirsk 630090.  E-mail: t.stekina@gmail.com   

 

UDC 519.651:519.652:517.518.85:519.852
Sidorov S. P.
On the error of optimal interpolation by linear shape-preserving algorithms

We consider the problem of optimal linear interpolation by algorithms positive on a cone describing the properties of the shape of the functions being approximated. We show that such linear shape-preserving methods have a negative property connected with the inability to identically approximate algebraic polynomials of at least the given degree. We also show that the estimation of the error of the problem of linear shape-preserving interpolation can be reduced to the problem of conic optimization. This makes it possible to use the duality principle for obtaining an estimate of the error of the shape-preserving interpolation.

Key words: optimal interpolation, shape-preserving approximation, conic programming.
Pp. 119–127.

Sidorov Sergey Petrovich
 Saratov State University, 83 Astrakhanskaya Str., Saratov 410012, Russia.  E-mail: sidorovSP@info.sgu.ru

 

UDC 518.12:519.34
Smelov V. V.
An iterative method for finding solutions to problems of heat conduction and diffusion of particles with discontinuous coefficients of the differential operator of the problem

We propose an iterative method for the implementation of highly accurate approximate piecewise smooth solutions to practical problems of heat transfer, diffusion of elementary particles (in particular, neutrons in a nuclear reactor) in multilayer constructions. We create a practical algorithm basing on two theorems.

Key words: problem with elliptic operator, discontinuous coefficients, piecewise-smooth basis functions, rapidly convergent series, minimization of a quadratic functional.
Pp. 128–138.

Smelov Vladislav Vladimirovich
 Institute of Computational Mathematics and Mathematical Geophysics 6 Lavrentiev Av., Novosibirsk 630090, Russia E-mail: vl.smelov@gmail.com

 

UDC 517.9
Frolenkov I. V., Romanenko G. V.
On the solution of an inverse problem for a multidimensional parabolic equation

We study the inverse problem for a multidimensional parabolic equation with an unknown coefficient at the differential operator of second order with respect to a chosen  variable with the Cauchy data. The initial condition has a special form and is given in the form of the scalar product of two vector-valued functions that depend on different variables. We obtain sufficient conditions for the existence and uniqueness of the solution to an auxiliary direct problem and the initial inverse problem. We use the weak approximation method for the proof.

Key words: inverse problem, approximation, weak approximation method, theorem of existence and uniqueness, partial differential equations, parabolic equation.
Pp. 139–146.

Frolenkov Igor' Vladimirovich,
Romanenko Galina Viktorovna
 Siberian Federal University, 79 Svobodnyi Av., Krasnoyarsk 660041, E-mail: kspk_job@mail.ru; galina.romanencko@yandex.ru

  

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