Vol 15, No 4 (2011)

Articles
75th Anniversary of Yuriy P. Samarin's Birthday
Radchhenko V.P., Saushkin M.N.
Abstract
Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences. 2011;15(4):8-12
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In Memory of Ivan S. Volkov, Rector of the Kuibyshev Polytechnical Institute
Barsova A.A.
Abstract
Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences. 2011;15(4):13-17
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On one optimal control problem with a penalty functional in general form
Manakova N.A., Dylkov A.G.
Abstract
The sufficient conditions for the existence of optimal control over solutions of the initial-finish value problem for the linear equation with a penalty functional in general form are found.
Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences. 2011;15(4):18-24
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Nonlocal problem for a equation of mixed type of third order with generalized operators of fractional integro-differentiation of arbitrary order
Repin O.A., Kumykova S.K.
Abstract
The unique solvability of internally boundary value problem for equation of mixed type of third order with multiple characteristics is investigated. The uniqueness theorem is proved with the restrictions on certain features and different orders of fractional integro-differentiation. The existence of solution is equivalent reduced to a Fredholm integral equation of the second kind.
Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences. 2011;15(4):25-36
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Damping problem for the hyperbolic equation with mixed derivative
Kozlova E.A.
Abstract
The boundary control problem for the hyperbolic equation with mixed derivative was considered in the rectangular region. The control functions were constructed in an explicit form. The conditions of controllability for initial data were found for different periods of control.
Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences. 2011;15(4):37-42
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Inversion and characterization of some potentials with the densities in lp in the non-elliptic case
Gil A.V., Zadorozhnyi A.I., Nogin V.A.
Abstract
We construct the inversion of generalized Strichartz potentials with singularities of the kernels on a finite union of spheres in Rn with densities from space Lp, 1≤p≤2 and Hardy space H1 in the non-elliptic case, when its symbols degenerate on a set of zero measure in ℝn . We also give the description of these potentials in terms of the inverting constructions.
Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences. 2011;15(4):43-49
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Solution of nonlinear creep problem for stochastically inhomogeneous plane on the basis of the second approximation for small parameter method
Popov N.N., Chernova O.O.
Abstract
The analytical method for nonlinear stochastic creep problem solving for a plane stressed state was developed. Stochasticity was introduced into the determinative creep equation, which was taken in accordance with the nonlinear theory of viscous flow, through a homogeneous random function of coordinates. The problem was solved on the basis of the second approximation for small parameter method in stress tensor components. The main statistical characteristics of the random stress field were calculated. The analysis of the results in the first and second approximations was obtained.
Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences. 2011;15(4):50-58
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Investigation of the effect of technological factors on the residual stresses in fibrous composites
Bitkina E.V., Pidodnya V.G., Bitkina O.V.
Abstract
The method of analysis for stress state of the composite materials and structures subject to thermal and technological influences is considered. The influence of the volume content of composite materials components, the magnitude of the difference between curing temperature and operating temperature, as well as the level of fibers tension on the distribution of residual thermal equivalent stresses in multilayered composite panels is explored.
Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences. 2011;15(4):59-66
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Simulation of creep and fracture of thick-walled non-uniformly heated pipeline under high-temperature hydrogen corrosion
Bubnov S.A., Ovchinnikov I.G.
Abstract
The technique of calculating the creep and fracture of thick-walled pipeline in a relatively high temperature conditions and exposure to hydrogen is considered. The local nature of the problem is provided by the local effects of temperature on the outer surface of the pipe. The case of linear increase of the local zone temperature with time is examined. The theory of accumulation of damages in Yu. N. Rabotnovs form is applied to definition of the moment of destruction.
Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences. 2011;15(4):67-74
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Mathematical modeling of the stress state of reinforced bone tissue of the femoral neck with static load
Radchhenko V.P., Nekhozhin A.V., Matveev A.L.
Abstract
The research of the influence of bone reinforcement on the stress-strain state of bone tissue in the femoral neck is completed. It is shown, that the reinforcement decreases the intensity of the stress-strain state of bone tissue in the most dangerous areas. Recommendations about the procedure of reinforcement, location and geometry of implants are formulated according to these calculations. Results of the current research can justify the methods for preventing hip fractures due to the prior reinforcement in medical practice.
Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences. 2011;15(4):75-81
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Monte-Carlo estimations for powers of Green operator and the first eigenvalue for Dirichlet boundary value problem
Kuznetsov A.N., Rytenkova I.A., Sipin A.S.
Abstract
In this paper, we examine the algorithm for computing the powers of a Green operator and the first eigenvalue for the Dirichlet boundary value problem using Monte-Carlo method. The efficiency of numerical realization of these algorithms is also discussed.
Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences. 2011;15(4):82-92
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Application of the modified boundary element method for the solution of parabolic problems
Fedotov V.P., Nefedova O.A.
Abstract
An algorithm for finding numerically-analytical solution of parabolic problems (diffusion and heat conduction) is proposed. The problem is solved by the proposed algorithm in three steps. At the first step the one-dimensional problem is solved for a base interval of integration. This problem is of independent significance as well as the basis for the second step. At the second step the two-dimensional parabolic problem is considered. Its solution is performed using the modified boundary elements method. At the third step, the method of step-by-step integration over time is used.
Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences. 2011;15(4):93-101
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Recursive parametrical identification of multidimensional linear dynamic systems with local autocorrelated noises in input and output signals
Ivanov D.V., Katsyuba O.A.
Abstract
The recursive algorithm allowing to receive strongly consistent estimates of parameters of multidimensional on an input linear dynamic systems with locally autocorrelated noise in input and output signals is suggested. Numerical examples are included to illustrate the effectiveness of the proposed algorithm.
Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences. 2011;15(4):102-109
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Generalization of coarse-grained models with introduction of three-dimensional space
Nazarov M.N.
Abstract
As a candidate for generalization in the scope of this work we consider any model derived from a system of first order ordinary differential equations for quantities of abstract bulk objects. The main objective of this work is to construct a universal scheme for generalization of such models with introduction of three-dimensional space and regard for migration of objects without switching to partial derivatives.
Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences. 2011;15(4):110-117
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Solution of nondifferentiable optimization problem for object with distributed parameters based on quasi-asymptotic approximate model
Diligenskiy N.V., Efimov A.P.
Abstract
The possibility of approximate quasi-asymptotic models application is considered on an example of the solution of a time-optimal heating problem. To solve an optimal control problem the numerical algorithm has been used on the basis of spline extrapolation of the minimized field at each iteration. It is shown that this approach to the time-optimal control problem can provide with negligible error the determination of maximum admissible accuracy and interval durations for one-, two-, and three- stage control.
Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences. 2011;15(4):118-124
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Spin-wave resonance in ferrospinel films magnetized perpendicular to the surface
Mitlina L.N., Badrtdinov G.S., Velikanova Y.V., Vinogradova M.R., Nikiforova I.V.
Abstract
The resonance properties of ferroshpinel films 20-30 µm thick obtained by chemical transport reactions were considered. Measurements were performed for the perpendicular orientation of the film relative to the external static magnetic field. Along with a uniform additional resonance absorption peaks corresponding to surface exchange spin waves localized at the free surface of the film were found. The constants of the surface anisotropy, the parameters of the spin pinning, the wave numbers of spin-wave modes were determined.
Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences. 2011;15(4):125-133
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Calculation of three- and four-component eutectic system temperature and composition on the basis of two-component systems known characteristics
Afanasieva O.S., Egorova G.F.
Abstract
Procedure of calculation of three- and four-component eutectic system temperature and composition on the basis of two-component systems known characteristics and the initial substances known melting-points is introduced. The suggested empirical formulas show the relationship between temperature and composition and have the average error not exceeding 6% for three- and four-component eutectic systems.
Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences. 2011;15(4):134-145
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Parallel programming software package GraphPlus Templet
Vostokin S.V., Khayrutdinov A.R., Litvinov V.G.
Abstract
The parallel programming automation software package named Graphplus templet is considered. Its design purposes, architecture, efficiency of applying for numerical modeling problems solutions, features against similar approaches are discussed. Composition of the software package is described in details. Programming complexity of the numerical simulation applications coded with help of the software is considered.
Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences. 2011;15(4):146-153
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Mixed problem with integral condition for the hyperbolic equation
Golubeva N.D.
Abstract
In this paper we consider a nonlocal problem with integral condition of the first kind. Existence and uniqueness of a solution of this problem are proved. The proof is based on a priori estimates and auxiliary problem method.
Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences. 2011;15(4):154-159
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Nonlinear equations with weighted potential type operators in Lebesgue spaces
Askhabov S.N.
Abstract
By method of monotone operators, existence and uniqueness theorems are proved for some classes of nonlinear equations with weighted potential type operators in Lebesgue spaces.
Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences. 2011;15(4):160-164
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Application of the generalized integral Laplace transform to solving differential equations
Zaikina S.M.
Abstract
We consider some boundary value problems for parabolic equations. The solutions were obtained with the generalized Laplace integral transform.
Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences. 2011;15(4):165-168
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Modelling of stress-strain state in mandible with osteosynthesis by bone plate
Loginov O.A., Saveliev A.L.
Abstract
A finite element model of mandible by bone plate is proposed. It is shown that presented model can be used for the determination of optimal parameters of plate.
Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences. 2011;15(4):169-172
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Computing of throwing ability of the explosives at cylindric front tossing of metal
Reout I.I., Krivchenko A.L.
Abstract
Calculation methods of copper plate relative front tossing speed by equivalent mass method and the widening speed calculation methods for the copper cylindric confinement are offered. The calculation results were compared with experimental data. The mean-square deviation is less than 3,5 percent.
Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences. 2011;15(4):173-177
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Evaporation of unstable polymer jet in electrospinning
Salkovskiy Y.E.
Abstract
This study is focused on mathematical modeling of drying unstable polymer electrospun jet. The developed model includes nonuniformity of polymer concentration over the jet cross-section due to the evaporation. The parametric study for influence of mass transfer coefficient on jet motion and fiber deposition is performed.
Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences. 2011;15(4):178-182
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Numerical research of static bending of plates at the local influences along complex form curves
Safonov R.A.
Abstract
The numerical solution for the problems of static bending of thin plates by spline collocation method is considered. The local loads of a special type are used as external forces. Their efficiency as the approximation of concentrated loads applied along compound curves is estimated. The results obtained by this method are compared with thos calculated by finite element software.
Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences. 2011;15(4):183-187
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On assessment method of brass as the material for explosively formed penetrator lining
Reout I.I., Krivchenko A.L.
Abstract
The calculation of a front tossing speed of plates by A-IX-1 and Cyclotol-50/50 charges was made on the basis of tossing elements dynamic adiabats. It is shown that as opposed to copper plate the kinetic module for the mass unit is about 4 % higher for tossing the brass plate in case of using A-IX-1 and is about 8 % higher in case of using Cyclotol-50/50.
Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences. 2011;15(4):188-190
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Numerical simulation of modified Perona-Malik equantion in digital image denoising applications
Yudashkin A.A., Zausaev D.A., Ryabtsov I.S.
Abstract
Classical Perona-Malik model is modified and adapted for digital color image filtering. An advantage of the proposed scheme is the use of perceptual color difference metrics to measure the distance between pixels, and the modification of diffusion coefficients calculation formulas. Numerical simulation shows that the proposed scheme has a high quality and performance.
Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences. 2011;15(4):191-194
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Algorithm for lattice model analyzing of information-measuring system structure
Orlov S.P.
Abstract
A lattice model of the structures of developing information-measuring systems is considered. It is shown that this model allows studying the transformation of structures of information-measuring system during the life cycle. To confirm the distributive property of the lattice model the original algorithm of search in it for the sublattices of pentagon and diamond types is proposed.
Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences. 2011;15(4):195-199
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Software development for automating the process of creation database of asteroids orbital evolution
Denisov S.S.
Abstract
This paper describes the software system that automates the process of calculating the asteroids orbital evolution. These applications allow automatically calculating on multiple computers simultaneously. Also the optimization of the algorithms implementation was done.
Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences. 2011;15(4):200-203
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