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Sibirskii  Zhurnal  Industrial'noi  Matematiki
2010,  vol. 13,  No 3 (43)

Contents
 

Mikhail Mikhauilovich Lavrent’ev
In Memory of Academician M. M. Lavrent’ev

UDC 548.1:539.1
Garipov R. M.
A Wave Interpretation of the Mössbauer Effect

We find a possible Mössbauer spectrum disregarding the shapes of spectral lines. We determine the spectral shift relative to the zero velocity.

Keywords: gamma rays, 4-crystal.
Pp. 6–12.

Garipov Ravil’ Mukhamedzyanovich
 Lavrent’ev Institute of Hydrodynamics, SB RAS, 4 Acad. Lavrent’ev prospect, Novosibirsk 630090, RUSSIA, E-mail: R.M.Garipov@mail.ru

UDC 514.745.82
Golubyatnikov V. P., Golubyatnikov I. V.
On Multidimensional Models of Gene Networks

We obtain sufficient conditions for the existence of closed trajectories in the odd-dimensional nonlinear dynamical systems that model gene networks with negative feedback.

Keywords:  gene networks, negative feedback, nonlinear dynamical systems, stationary points, periodic trajectories.
Pp. 13–18.

Golubyatnikov Vladimir Petrovich
Golubyatnikov Ivan Vladimirovich
 Sobolev Institute of Mathematics, SB RAS, 4 Acad. Koptyug prospect, Novosibirsk State University, 2 Pirogova str. Novosibirsk 630090, RUSSIA, E-mail: glbtn@math.nsc.ru

UDC 519.237.7
Gol’tyapin V. V.
A Strategy for Seeking a Factor Mapping That Characterizes the Parameters of External Respiration and Oxygen/Carbon Dioxide Exchange

We develop a strategy for seeking a simple factor analysis structure. In this framework we solve factor analysis problems. Basing on the strategy, we construct a factor model that characterizes the parameters of external respiration and oxygen/carbon dioxide exchange. We select three factors to explain the structure of three biophysical activities not observable explicitly: respiratory  rrhythmia, lung efficiency, and oxygen consumption. We refute the hypothesis that external respiration parameters depend on oxygen consumption capacity.

Keywords: factor analysis, factor structure, communality problem, varimax rotation, parameters of external respiration and oxygen/carbon dioxide exchange.
Pp. 19-29.

Gol’tyapin Viktor Viktorovich
Omsk Branch, Sobolev Institute of Mathematics, SB RAS, 13 Pevtsova str. Omsk 640099, RUSSIA, E-mail: goltyapin@mail.ru

UDC 519.68
Kovalev S. P.
A Formal Approach to Aspect-Oriented Modelling of Scenarios

The article deals with formalizing the aspect-oriented approach to software design. We prove that, from the viewpoint of AOP, the best transformations are those that allow the tracing of component embedding into systems. The formalization of AOP is based on the category theory construction of a formal design discipline. In order to describe the traced transformations we introduce the concept of M-initial morphism. By way of application, we consider a formalization of  aspect-oriented  models for scenarios of system behavior as labeled posets. We describe a general method for  formal transformation of aspect-oriented models for dynamical systems into labeled event structures.

Keywords: aspect-oriented approach, traceability, formal design discipline, initial morphism, scenario modelling, labeled event structure.
Pp. 30–42.

Kovalev Sergey Protasovich
Construction and Technology Institute of Computer Engineering, SB RAS, 6 Lavrent’ev prospect, Novosibirsk 630090, RUSSIA, E-mail: kovalyov@nsc.ru

UDC 519.17
Kolmykov V. A.
Investigation of the Stability of Periodic Hydrocarbon Molecules in a Second Approximation  Model.

We consider some classes of periodic weighted graphs and prove that the instability of these graphs is a periodic property. We determine all possible periods. The results can be used in theoretical and mathematical chemistry.

Keywords: hydrocarbons, graph, spectrum.
Pp. 43–50.

Kolmykov Vladislav Alekseevich
Voronezh State University, 1 University square, Voronezh 394006, RUSSIA, E-mail: kolmykov@math.vsu.ru

UDC 541.124:541.126:517.9
Kononenko L. I.
A Parameterization of the Slow Curve in a Chemokinetics Problem

We give an example of parameterization of the slow curve taken from a singularly perturbed  system of the ODE describing catalytic oxidation.  

Keywords: singular perturbations, slow integral manifolds, parameterization of a curve.
Pp. 51–57.

Kononenko Larisa Ivanovna
 Sobolev Institute of Mathematics, SB RAS, 4 Acad. Koptyug prospect, Novosibirsk State, University, 2 Pirogova str., Novosibirsk 630090, RUSSIA.

UDC 517.977:517.929
Korobov A. A.
On Pointwise Complete Pairs of Linear Transformations

We prove the pointwise completeness of an nth order constant-coefficient system under the  assumption that the matrices of the system split into same-size square blocks so that the collection of all blocks embeds into a finite dimensional associative division algebra; the block rank of the passive matrix is at most 2.

Keywords: pointwise completeness, of a system of ODE with delay.
Pp. 58–67.

Korobov Aleksey Aleksandrovich
 Sobolev Institute of Mathematics, SB RAS, 4 Acad. Koptyug prospect, Novosibirsk 630090, RUSSIA, E-mail: korobov@math.nsc.ru 

UDC 512.54
Kuznetsov A. A., Filippov K. A.
On an Involutive Automorphism of the Burnside Group B0(2,5)

We study the centralizer of the involutive automorphism of the Burnside group B0(2,5) taking the generators of B0(2,5) to their inverses. We find generators for the centralizer and compute its order, solvability length, and nilpotency length.

Keywords: Burnside problem.
Pp. 68–75.

Kuznetsov Aleksandr Alekseevich
Siberian State Air and Space University, 31 Gazety «Krasnoyarsky rabochy» prospect, Krasnoyarsk 660014, RUSSIA, alex_kuznetsov80@mail.ru
Filippov Konstantin Anatol’evich
Krasnoyarsk State University of Agriculture, 90 Mira prospect, Krasnoyarsk 660049, RUSSIA, filippov_kostya@mail.ru

UDC 519.6:537.84
Latyshev A. V., Tereshina T. V., Yushkanov A. A.
An Analytic Solution of the Vlasov–Maxwell equations in the Skin Effect Problem with Electron-Electron Collisions

We solve the skin effect problem analytically in the case that electron-electron collisions start affecting the properties of a Maxwell plasma. We apply a two-parameter kinetic equation to take  these collisions into account. We find analytic expressions for the electric field, electron  distribution, and impedance accounting for the collisions. We analyze impedance near the plasma resonance.

Keywords: mirror scattering, impedance, two-parameter kinetic equation, skin effect, plasma resonance.
Pp. 76–85.

Latyshev Anatoliy Vasil’evich
Tereshina Tat’yana Viktorovna
Yushkanov Aleksandr Alekseevich
Moscow Region State University, 10a Radio str., Moscow 105005, RUSSIA, E-mail: avlatyshev@mail.ru; tv_nikitina@mail.ru; yushkanov@inbox.ru

UDC 517.97
Mamadaliev N.
On a Linear Pursuit-Evasion Problem with Delay

We obtain sufficient conditions for the solvability of pursuit-evasion problems under geometric and  ntegral constraints on the pursuer and evader controls respectively. The results develop and generalize a series of known sufficient conditions of pursuit-evasion theory. Our sufficient conditions differ from the previous results for equations with delay.
Pp. 86–100.

Mamadaliev Numanzhon
 Uzbekistan National University, Vuzgorodok, Tashkent 100174, UZBEKISTAN, E-mail: M_numana59@mail.ru

UDC 533.6.011.51
Markovsky A. I.
The Steady Output of a Well Opening Up Two Gas-Bearing Strata

We consider a mathematical model of high pressure gas flow in a gasodynamic system consisting of a vertical borehole and two horizontal gas-saturated porous strata. The real gas factor is regarded as a known function of pressure. We solve the problem of calculating the total well and strata production rates as functions of pressure at the wellhead.

Keywords: gas filtration, supercompressibility, connected strata, well and strata production rate, turn points, Newton's method.
Pp. 101–112.

Markovsky Anatoly Ivanovich
 Institute of Applied Mathematics and Mechanics, National Academy of Sciences, 74 Roza Luxemburg str., Donetsk 83048, UKRAINE, E-mail: markowski@yandex.ru

UDC 539.376
Oleynikov A. I.
Models for the Steady-State Creep of Transversally Isotropic Materials with Different Contraction and Expansion Characteristics

We propose constitutive equations for describing the steady-state creep of transversally isotropic materials with different contraction and expansion properties. We assume that the creep coefficient is independent of  the sample cut-off direction.

Keywords: constitutive equations, steady-state creep, transversal isotropy, multimodulus behavior.
Pp. 113–116.

Oleynikov Aleksandr Ivanovich
Komsomol’sk-on-Amur State Technical University, 27 Lenina prospect, Komsomol’sk-on-Amur 681013, RUSSIA, E-mail: cvmi@knastu.ru

UDC 534.18
Romensky E. I., Sadykov A. D.
On Modelling the Frequency Transformation Effect in Elastic Waves

We give a continual model of an elastic medium with a field of distributed defects and use it to study the frequency transformation effect in elastic waves. By an example of numerical simulation of one-dimensional waves arising under a harmonic action on a layer with defects we demonstrate the possibility of describing frequency transformation in the framework of the  model.

Keywords: elastic waves, frequency transformation, field of distributed defects.  
Pp. 117–125.

Romensky Evgeny Igorevich
Sadykov Asylkhan Dyusembaevich
 Sobolev Institute of Mathematics, SB RAS, 4 Acad. Koptyug prospect, Novosibirsk 630090, RUSSIA, E-mail: evrom@math.nsc.ru; asilkhan@rambler.ru

UDC 517.983.5:517.937
Falaleev M. V., Krasnik A. V., Orlov S. S.
Degenerate High-Order Differential Equations of a Special Kind in Banach Spaces and Their Applications

Using generalized function methods in Banach spaces, we study the solvability of Cauchy problems for third or fourth order differential equations with a Fredholm operator at the highest derivative in the class of distributions with support bounded on the left. In terms of the generalized Jordan structure of the degenerate principal part of these equations we construct fundamental operator functions that correspond to the differential operators and use them to recover generalized solutions, prove  uniqueness pf the latter, and study  relations with the classical solutions. We apply the results to two initial-boundary value problems for nonclassical equations of mathematical  physics. We study the Cauchy–Dirichlet problem for the generalized electric potential equation and the thermoelastic plate equation.

Keywords: Banach spaces, Fredholm operator, Jordan tuples, distributions, fundamental operator functions.
Pp. 126–139.

Falaleev Mikhail Valentinovich
Krasnik Andrey Valer’evich
Orlov Sergey Sergeevich
 Irkutsk State University, 1 Karl Marx str., Irkutsk 664003, RUSSIA, E-mail: mihail@ic.isu.ru

UDC 517.9
Chistyakova E. V.
Nonlocal Solvability Theorems for Systems of Differential-Algebraic Equations for Nonsteady Hydraulic Chains

We prove nonlocal solvability theorems of initial problems for systems of differential-algebraic equations and indicate a criterion for the asymptotic stability of their stationary points. Using these results we study a mathematical model of a nonsteady hydraulic chain.

Keywords: differential-algebraic equation, stationary point, hydraulic chain.
Pp. 140–150.

Chistyakova Elena Viktorovna
 Institute of Systems Dynamics and Control Theory, SB RAS, 134 Lermontova str., Irkutsk 664074, RUSSIA, E-mail: elena.chistyakova@icc.ru

 

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