## Vol 17, No 4 (2013)

**Year:**2013**Articles:**17**URL:**https://journals.eco-vector.com/1991-8615/issue/view/1248

Articles

Varieties of linear algebras of polynomial growth

#### Abstract

The paper is survey of results of investigations on varieties of linear algebras of polynomial growth. We give equivalent conditions of the polynomial codimension growth of a variety of associative algebras, Lie algebras, Leibniz algebras, Poisson algebras, Leibniz-Poisson algebras. It is shown that in the study of varieties of linear algebras of polynomial growth varieties of almost polynomial growth play an important role.

**Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences**. 2013;17(4):7-14

Riemann method for solving non-local boundary value problems for the third order pseudoparabolic equations

#### Abstract

The existence and uniqueness of regular solutions of non-local boundary value problems for the third order pseudoparabolic equations with variable coefficients are proved using the Riemann function method.

**Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences**. 2013;17(4):15-24

On irregular singular curves of Whittaker type systems

#### Abstract

The given work studies the regular and irregular singular curves of special systems of the second order partial differential equations. By the means of rank and antirank, the necessary and sufficient condition for an existence of regular solution, also the ﬁrst and the second necessary condition for an existence of normal-regular solution were established. The types of solutions in the neighborhood of regular and irregular features were deﬁned. The application of two variables special functions was considered.

**Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences**. 2013;17(4):25-33

Optimal control problem for the impulsive differential equations with non-local boundary conditions

#### Abstract

The optimal control problem is investigated, where the state of the controlled system is described by the impulsive differential equations with non-local boundary conditions. The existence and uniqueness of the non-local impulsive boundary problem by fixed admissible controls are proved using the contraction mapping principle. The gradient of the functional is calculated under certain conditions on the initial data. The necessary conditions for optimality of the first order are obtained.

**Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences**. 2013;17(4):34-45

On solvability of a mixed value problem for nonlinear partial differential equation of higher order

#### Abstract

The questions of one valued generalized solvability of mixed value problem for nonlinear partial differential equation with the parabolic operator of arbitrary natural power are studied. The separation of variables is used.

**Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences**. 2013;17(4):46-57

Expansion of multiple series in infinite diagonals

#### Abstract

In this paper a method of summation of double absolutely convergent numerical series was obtained. This method was named the expansion of double numerical series in inﬁnite diagonals. The form of the expansion for symmetric and skew-symmetric general term of double series was established. This expansion was generalized to the case of multiple series. It was called the expansion of multiple numerical series in inﬁnite diagonals for two indices. The expansion of triple series in inﬁnite diagonals for two indices was generalized to the case of three indices.

**Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences**. 2013;17(4):58-65

Stress concentration at a hooked-fiber textile composite layer with local technological defects under biaxial tension on transversal origin

#### Abstract

A new model has been developed to simulate a woven textile composite layer with a polycrystalline matrix. Based on the numerical solution of the boundary-value problem by the ﬁnite-element method, the values of stress concentration caused by local processing defects (break in a ﬁber, closed internal pore) under symmetric biaxial macrodeformation are obtained. The numerical solution by the ﬁnite-element method is received using the part of SALOME-MECA framework, the non-commercial package Code-Aster. The regions of maximum stress disturbance coefficients in the textile composite layer are determined. The cause of marked increase of stress disturbance coefficients is the contact with friction between the ﬁbers of reinforcing skeleton and the shifts are the main mechanisms of polycrystalline matrix damaging. It is shown that application of additional processing operations to ﬁll the formed voids by matrix material can decrease stress concentration and increase the ability of a material to withstand external force loads. The mechanisms responsible for initiation of damages in a polycrystalline matrix are determined.

**Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences**. 2013;17(4):66-75

The application of perturbation method to problem of misaligned tube in conditions of steady-state creep

#### Abstract

The problem of determining the stress-strain state of the thick-walled misaligned tube under internal pressure on steady-state creep is considered. The task linearization with the perturbation method is carried out. The second approximation of this problem is constructed. The effect of misalignment of the tube on the stress-strain state considering the second approximation is analyzed.

**Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences**. 2013;17(4):76-85

Field-theoretic approach for characterization the deformation of multicomponent polycrystalline materials

#### Abstract

Most of inorganic structural materials (metallic alloys, ceramics, minerals etc.) are polycrystalline aggregates, consisted of macroscopically large quantity of single-crystal grains (crystallites). The mechanical behavior of the specimen of polycrystalline material is governed by the physical and mechanical processes in the grains and interaction of the grains. Thus the deformation of polycrystalline material is a cooperative phenomenon typical for condensed matter physics and mechanics of heterogeneous materials. The passing of these processes depends on many parameters, including stress states of individual grains and its evolution during macrodeformation. In this paper we note a mathematical analogy between the equations of the mechanics of heterogeneous polycrystalline materials and the equations of quantum theory of particles scattering. This analogy allows to apply the methods of quantum ﬁeld theory to solution of the equations of solid mechanics for heterogeneous media. We consider the application of Corringa-Kohn-Rostoker method, used in quantum theory for calculating wave function of electrons in metallic alloys, to elasticity of polycrystals. This approach allows, for instance, to calculate probability distribution density function for stresses in grains under arbitrary macrodeformation of polycrystal. Application of the method to classical problem of homogenization gives new formulae for the eﬀective moduli of disordered polycrystalline medium.

**Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences**. 2013;17(4):86-97

Strength characteristics of the proximal femur in conditions of internal force shunting

#### Abstract

The present research describes a method of surgical prophylactic reinforcement of the proximal femur in elderly patients suffering from various diseases that cause degenerative and dysplastic processes in bone (oncology, osteoporosis, cartilage and ﬁbrous dysplasia, etc). These processes cause pathological fractures. Original reinforcement implants (Russian Federation patents number 91845, 98901, 101351, 121725) are installed in the intact bone of the proximal femur to prevent its fractures in case of low-energy trauma, thereby increasing bone strength. Preventive reinforcement technique has a mathematical and economic feasibility. Increasing of the strength of the proximal femur, reinforced by implants from nanostructured titanium, is proved by bench tests.

**Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences**. 2013;17(4):98-106

Optimal honeynet configuration in enterprise computer networks

#### Abstract

The article is devoted to the optimal conﬁguration of honeypots in the enterprise network. It describes the mathematical model of an enterprise computer network with honeypots. The authors analyze the standard ways of setting up honeypot parameters and propose the optimization criterion with regard to the dynamics of the external environment. The optimization problem of conﬁguring decoys is reviewed and the solution of the problem is discussed. Also a procedure of searching optimal honeypot conﬁguration is proposed and recommendations concerning practical appliance of the obtained results are given.

**Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences**. 2013;17(4):107-114

Application of the mathematical models used for estimating the impact probability of asteroids 99942 Apophis and 2011 AG5

#### Abstract

Methods for estimating the impact probability of asteroids 99942 Apophis and 2011 AG5 were implemented. The probability of a collision was assessed using two methods: The Monte Carlo method (statistical experiments), and as a ratio between the interval of values of orbital elements, leading to a collision, and the conﬁdence intervals of orbital elements. It was established that the main contribution to the estimation of the impact probability makes a variation in the semimajor axis. The expected date and the estimate of the probability of collisions of asteroids 99942 Apophis and 2011 AG5 with the Earth were computed.

**Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences**. 2013;17(4):115-121

Non-stationary heat exchange in cylindrical channel at laminar flow of fluids

#### Abstract

Using double integral Laplace–Carson transformation and orthogonal method of Bubnov–Galyorkin, the analytical solution of the non-stationary problem of heat transfer in a cylindrical channel in the laminar ﬂow of ﬂuids was obtained. It has two components: stationary and non-stationary, each part has application only in a certain range of temporal and spatial coordinates. For the stationary Graetz-Nusselt problem on the basis of introduction of the temperature perturbation front and additional boundary conditions it was managed to ﬁnd an analytical solution that allows the assessment of liquid thermal state with small values of spatial variable, directed along the stream ﬂow. It is not possible to obtain such results using the well-known exact analytical methods because of the poor convergence of inﬁnite series of received solutions.

**Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences**. 2013;17(4):122-130

Regression mathematical model of microfinance institutions influence on small and medium enterprises development intensity in Russian Federation regions

#### Abstract

The multidimensional statistical grouping of microﬁnance institutions registered in the territory of the Russian Federation by the type of organizational and legal forms of business is made. The regression econometric model that reﬂects the inﬂuence of the number of microﬁnance institutions on the intensity of development of small and medium-sized businesses in the regions is developed and investigated.

**Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences**. 2013;17(4):131-137

Before getting around to do black hole physics

#### Abstract

The short history is presented of the very notion “black hole”. The global geometry of the general spherically symmetric space-time is described. Einstein equations for spherical gravity are derived. The causal structure of the Schwarzschild black hole is investigated, and it is shown in details how to construct conformal Carter–Penrose diagrams that reveal visually such a structure. The Israel equations for self-gravitating thin shells are obtained and the modiﬁed gravitational Newton’s law is investigated. Very simple and instructive derivation of the Vaidya metrics describing the spherically symmetric gravitating radiation is given. As an application of the theory described above the problem if the real (not virtual) static Schwarzschild observer is solved. The essay is prepared following a series of lectures, read by the author at the Third International Conference “Mathematical Physics and Its Applications” (August 27 — September 1, 2012, Samara, Russia) Translated from Vestn. Samar. Gos. Tekhn. Univ. Ser. Fiz.-Mat. Nauki, 2013, Issue 3(32), Pages 147–184; DOI: 10.14498/vsgtu1230.

**Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences**. 2013;17(4):138-172

Bifurcation sets of extended Higgs potential

#### Abstract

One of the most actual problems in modern particle physics is the problem of the baryon charge evidence in the Universe. In the frameworks of supersymmetric models, phase transitions and catastrophe theory it is possible to describe the baryogenesis. We explored the temperature evolution of Higgs potential with control parameters in the framework of the MSSM, considered the stable minimum conditions and evaluated the area of constrained parameters A, µ, tg β. The sets of model parameters at which the system undergoes a bifurcation are obtained.

**Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences**. 2013;17(4):173-183

Combinatorial representation of the sum of the weighted equal powers of members of an arithmetical progression

#### Abstract

The correctness of equality which gives the combinatorial expression for the sum of the weighted equal powers of members of an arithmetical progression is found out. Such aspect provides usage of double summation of certain algebraic combinations with free and weight components of the given sum. Thus speciﬁed algebraic combinations also include binomial coefficients. Determination of required equality was made with use of comparison of real and hypothetical values.

**Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences**. 2013;17(4):184-191