# Vol 15, No 2 (2011)

**Year:**2011**Articles:**39**URL:**https://journals.eco-vector.com/1991-8615/issue/view/1256

### Some new generalized integral transformations and their application in differential equations theory

#### Abstract

We present new integral transforms, generalized the classical Laplace, Stieltjes and Widder integral transforms in the potential theory. The (τ, β)-generalized confluent hypergeometric functions are the kernels of these integral transforms. Inverse formulas for new integral transforms are proved. Relations of the Parseval-Goldstein type are established. Some examples of applications of the new integral transforms are given.

**Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences**. 2011;15(2):8-16

8-16

### Estimates for some convolution operators with singularities of their kernels on spheres

#### Abstract

In the framework of Hardy spaces H p , we study multidimensional convolution operators whose kernels have power-type singularities on a finite union of spheres in Rn. Necessary and sufficient conditions are obtained for such operators to be bounded from Hp to Hq, 0 < p ≤ q < ∞ from H p to BMO, and from BMO to BMO.

**Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences**. 2011;15(2):17-23

17-23

### On the numerical solution convergence of optimal control problems for Leontief type system

#### Abstract

This article contains proving the convergence of numerical solving of optimal control problem for degenerate linear systems of ordinary differential equations with constant coefficients. Considering different appendixes of such systems, they belong to Leontief type system, as in the first time such systems were investigated as a dynamic Leontief input-output model with noninvertible operator on derivative. By using the initial condition of Showalter-Sidorov we gain an ability to extend the range of practical applicability for this model. The article includes existence and uniqueness theorem of numerical solution of investigated problem, his kind, and results of numerical experiment for dynamic input-output model, which was offered by W. Leontief.

**Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences**. 2011;15(2):24-33

24-33

### On solvability of a inverse problem for hyperbolic equation with an integral overdetermination condition

#### Abstract

In this paper we study an inverse problem with an integral overdetermination condition for a hyperbolic equation with an unknown coefficient in equation. The existence and uniqueness of a solution is proved with the help of an a-priory estimate and Galyorkin procedure.

**Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences**. 2011;15(2):34-39

34-39

### On a non-local boundary value problem for loaded differential equation with characteristic form of variable sign

#### Abstract

Non-local boundary value problem for loaded equation of parabolic type with the sign- variable characteristic form is solved. Common representation of solution is constructed. The theorems of common representation, existence and uniqueness of solution for boundary value problems set in rectangular domain are proved.

**Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences**. 2011;15(2):40-45

40-45

### Numerical calculation for limit values of control parameters in the problem about extension with torsion for special sample in the framed structure

#### Abstract

The numerical procedure for computation of the loads limit values was considered in this article. This loads apply to discrete gradient mechanical systems. Part of their elements can work at loss of strength stadium already. Methodic was shown for example of the problem about extension with torsion in the framed structure for special sample from nonlinear material. Properties of this material are defined by non-convex potential. This potential describe steady stats (strengthening) and non-steady (loss of strength) of the material. This calculating scheme allow don't solve nonlinear equilibrium equations with gradually increase of loads and test of the stiffness for any equilibrium for definition of loads values, which act the structure accident.

**Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences**. 2011;15(2):46-52

46-52

### Wavenumbers of type III thermoelastic waves in a long waveguide under sidewall heat interchanging

#### Abstract

The paper presents a study of wavenumbers of coupled harmonic thermoelastic waves propagating via an infinite circular cylinder for higher azimuthal order. Heat interchanging between sidewall of the waveguide and environment is assumed. The analysis is carried in the frameworks of coupled generalized thermoelasticity theory of type III (GNIII-thermoelasticity). This theory synthesizes thermodiffusion and wave mechanisms of heat transfer in solids including as limiting cases both the theories: classical thermoelasticity (GNI/CTE) and the theory of hyperbolic thermoelasticity (GNII). The latter permits field-theoretic formulation and leads to the field equations of hyperbolic analytical type. The two principal problems: separation of 32 independent single-valued square radicals involved in the frequency equation and more accurate computation of the real-valued wavenumbers are resolved and discussed.

**Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences**. 2011;15(2):53-61

53-61

### On some properties of equal-stress problem solution reinforcement bending the metal-composite plates working in steady creep conditions A. P. Yankovskii

#### Abstract

Solution of a stress condition of stochastic heterogeneous plate problem was obtained on the basis of statistic linearization of determinative creep equation and by using a method of spectral representation of random functions. Stochasticity is introduced into determinative creep equation by random function of two variables. It was proved, that stochastic nonhomogeneities of material can lead to signiﬁcant ﬂuctuations of stress ﬁelds.

**Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences**. 2011;15(2):62-73

62-73

### Multipoint moment functions of structural properties for polydisperse composites

#### Abstract

The stochastic boundary-value problem of elasticity theory for two-phase polydisperse composites is stated. The solution method with using high order moment functions is described. Algorithm of synthesis of n-order moment functions for 3D structures is presented. Approximating expression for moment functions is suggested. Examples of calculation of high-order moment functions for polydisperse structures are given.

**Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences**. 2011;15(2):74-82

74-82

### Elastic stresses in a plane with a thin piecewise-homogeneous inclusion

#### Abstract

The elastic plate composed of two semi-inﬁnite plates connected one with other through a thin elastic piecewise-homogeneous inclusion is considered. Stress state in the plates under the action applied to them concentrated forces is studied. The stresses on the lines of contact are found and their behavior near point of changing the inclusion rigidity is studied.

**Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences**. 2011;15(2):83-88

83-88

### Solution parallelization of softening plasticity problems

#### Abstract

Parallelization of deformation-damage coupling boundary value problem solution is considered. In deﬁnition the equations of the strength we used the principle of equivalence of deformations in a real and relatively undamaged structures. Principle of real and hypothetical undamaged structure strain equivalence is applied. An iterative procedure characterized by successive solutions of plasticity and damage problems at each iteration step, is proposed. The approach to parallelization of softening plasticity boundary value problem solution is based on the conception of generalized nonlinear structural models and on the method of decomposition.

**Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences**. 2011;15(2):89-100

89-100

### Numerical modeling of structural fracture processes for granular composites with isotropic elements of structure

#### Abstract

Presents the results of numerical modeling of deformation processes, and processes of micro- and macrodestruction for granular composites. Detail discussed failure mechanisms at the structural level. Detected the eﬀect of self-sustaining fracture.

**Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences**. 2011;15(2):101-106

101-106

### Substructure and magnetic properties of single-crystal spinel ferrites films

#### Abstract

The results of the study of static and dynamic magnetic properties of single-crystal spinel ferrites ﬁlms. It is shown that the magnetic properties of ﬁlms depend on the chemical composition, degree of structural defects and technological conditions of synthesis. We conclude that decreasing the cooling rate of the ﬁlms on the synthesis temperature may change the valence of iron that signiﬁcantly aﬀects the magnetic parameters of the ﬁlms.

**Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences**. 2011;15(2):107-115

107-115

### Numerical modelling of major planets movement on the new interaction principle basis

#### Abstract

Numerical integration of the equations of movement of major planets, on the basis of a new principle of interaction is spent. Elements of orbits of major planets on large time interval (1602-2200) are calculated. Results of calculations are compared with elements of the orbits deﬁned according to coordinates and speeds by numerical theory DE405. It is shown that elements of orbits of the exterior planets, found on new algorithm, will well be coordinated with dates DE405. For internal planets Venus, the Earth and Mars have insigniﬁcant discrepancies in secular oﬀsets of perihelions in comparison with dates DE405.

**Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences**. 2011;15(2):116-122

116-122

### Thermodynamic research of aluminium-ferric thermit combustion

#### Abstract

The paper describes the main results of thermodynamic calculations of aluminoferric themit combustion reaction, including combustion reaction of thermit, pelletized with cellulose nitrate. Based on the calculations results, the presence of gas phase during combustion is approved. The reason of gas phase presence is determined, what allowed to develop recommendations of its reducing. The eﬀect of cellulose nitrate on thermit combustion reaction temperature is also estimated.

**Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences**. 2011;15(2):123-128

123-128

### Preface

**Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences**. 2011;15(2):131-132

131-132

### Entanglement in two-atom model with degenerate Raman transitions

#### Abstract

The peculiarities of atom-ﬁeld entanglement in the model of two nonidentical atoms interacting with one-mode coherent electromagnetic ﬁeld in lossless cavity via degenerate two-photon Raman transitions have been investigated. The times of atoms and ﬁeld states disentanglement have been calculated on the basis of time-dependent wave function behavior and the linear atomic entropy concept.

**Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences**. 2011;15(2):135-141

135-141

### Matrix method of calculating the rescattering wave in a periodic structure

#### Abstract

The method of recursive calculation of the characteristic matrix of the layered structure is developed. Analytical solutions for the matrix of second, third and fourth order describing the propagation of waves in periodic structures are found.

**Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences**. 2011;15(2):142-148

142-148

### Extension of the Lorentz symmetry up to conformal in the limit of ultrahigh energies

#### Abstract

The group-theoretical justiﬁcation is presented for the original approach by Kirznits and Chechin which allows for the primary protons of ultra-high energy cosmic rays to overcome the energetic limit (about 50 EeV) of Greisen-Zatsepin-Kuzmin remaining in the scope of the usual ideas about the nature of the extra-galactic sources of the cosmic rays. It is shown that the explicit form of the factor deforming the Lorentz invariant in the energy-momentum space may be found on the grounds of the approximate transition from Lorentz symmetry to the conformal values of the Lorentz-factor of the order 1010÷1011.

**Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences**. 2011;15(2):149-154

149-154

### Some topics in dynamics and control of open quantum systems

#### Abstract

This work reviews several topics in the non-equilibrium dynamics and control of open quantum systems, including the dynamics in the weak coupling and low density regimes, incoherent control and universal Kraus maps.

**Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences**. 2011;15(2):155-161

155-161

### Johansen-Sornette hierarchical model of financial crashes and its ultrametric generalization

#### Abstract

We consider the hierarchical model of ﬁnancial crashes introduced by A. Johansen and D. Sornette which reproduces the log-periodic power law behavior of the price before the critical point. In order to build the generalization of this model we introduce the dependence of an inﬂuence exponent on an ultrametric distance between agents. Much attention is being paid to a problem of critical point universality which is investigated by comparison of probability density functions of the crash times corresponding to systems with various total numbers of agents.

**Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences**. 2011;15(2):162-169

162-169

### The Faddeev equation and location of the essential spectrum of a three-particle model operator

#### Abstract

In this paper a model operator H associated to a system of three-particles on a lattice is considered. The location of the essential spectrum of H is described by the spectrum of channel operators. The Faddeev type equation for the eigenvectors of H is obtained.

**Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences**. 2011;15(2):170-180

170-180

### Some spectral properties of a generalized Friedrichs model

#### Abstract

We consider self-adjoint generalized Friedrichs model h(p), p ∈ T3 (T3 is the threedimensional torus), in the case where the parameter functions w1 and w2 of this operator has the special forms. These functions has non-degenerate minimum at the several different points. Threshold effects for the considering operator are studied depending on the minimum points of w2.

**Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences**. 2011;15(2):181-188

181-188

### The problem with integral condition for one space analog of hyperbolic type equation degenerated on coordinate planes

#### Abstract

For the full equation of the third order in a three-dimensional Euclidean space the boundary value problem with interface on non-characteristic plane in the area limited by planes of a singularity of the equation factors is solved.

**Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences**. 2011;15(2):189-193

189-193

### On representation of Parseval frames

#### Abstract

This paper investigates properties of Parseval frames in ﬁnite dimensional vector spaces, namely, the possibility of representing some frames as sums of others. A new approach in constructing arbitrary Parseval frames and the decomposition arbitrary frame into the sum are described. Besides there is a number of special properties of equiangular tight frames.

**Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences**. 2011;15(2):194-199

194-199

### On the dynamics of the quantum states set for a system with degenerated Hamiltonian

#### Abstract

We study the sequence of regularizing Cauchy problem as the elliptic regularization of Cauchy problem for Schrodinger equation with discontinuous and degenerated coefficients. The necessary and sufficient conditions of the convergence of the regularizing dynamical semigroups sequence are presented. If the convergence is impossible then divergent sequence of the regularizing quantum states is considered as the stochastic process on the measurable space of regularizing parameter endowing with ﬁnite additive measure. The expectation of this stochastic process deﬁnes the averaging trajectory in the space of quantum states. It was obtained the condition on the ﬁnite additive measure such, that averaging trajectory can be deﬁned by its values in two instants with the help of solving the variational problems.

**Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences**. 2011;15(2):200-220

200-220

### The exact cosmological solutions for tachyon fields

#### Abstract

The application of the method of super-potential to the solution of the problems of cosmology with the tachyon ﬁelds is examined. The classes of exact solutions are found and the periods of time with the predominance of dark energy are established.

**Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences**. 2011;15(2):221-226

221-226

### Spherically-symmetric non-linear sigma model: the exact solutions obtained with isometrical embedding method

#### Abstract

The method to generate exact cosmological solutions in the frame of the sphericallysymmetric non-linear sigma model is oﬀered in the present paper. This method is based on the isometrical embeddings of the target space (non-linear sigma-model ﬁelds chiral space) into space-time. Also the method of application to two- and three-component chiral spaces embedded into space-time was considered. The exact cosmological solutions were obtained in the frame of the several special cases of the two- and three-component spherical-symmetric non-linear sigma-model. The obtained cosmological solutions were also investigated.

**Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences**. 2011;15(2):227-234

227-234

### On the compatibility of the corpuscular and wave properties of a particle in the two-slit experiment

#### Abstract

A new quantum-mechanical model of the two-slit experiment is presented, in which the wave properties of a particle are compatible with its corpuscular ones. The model is based on the idea which also underlies our previous model of a one-dimensional completed scattering. Its essence is that quantum processes, in which the systems state represents a coherent superposition of microscopically distinct substates (CSMDS), must be considered as complex random processes consisting of alternative subprocesses. Only with a new approach to CSMDSs quantum theory admits a consistent statistical interpretation and becomes free from the paradoxes associated at present with CSMDSs.

**Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences**. 2011;15(2):235-242

235-242

### Problems with laplace operator on topological surfaces

#### Abstract

This work highlights the problems related to the Laplace operator on topological surfaces such as Mobius strip, Klein bottle and torus. In particular, we discuss oscillations on the surface of the Mobius strip, eigenfunctions and eigenvalues of the Laplace operator on the surface of the Klein bottle, as well as behavior of a charged particle on the torus.

**Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences**. 2011;15(2):243-250

243-250

### Functional Laplace operator on a p-adic space and Feynman-kac and Feynman formulas

#### Abstract

Homogeneous closed PDO are constructed which are analogous to the powers of (absolute value of ) inﬁnite dimensional Laplacian and acting in Banach spaces of complexvalued functions deﬁned on function spaces over a ﬁeld of p-adic numbers. For elements of semigroups, for which these PDOs are generators, Feynman formulas and Feynman-Kac ones are obtained.

**Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences**. 2011;15(2):251-259

251-259

### Photonic communications in biological systems

#### Abstract

The mechanism of communications between distant bio-systems by means of optical and UV photons is studied. In the proposed model the bio-systems perform such communications radiating the photons in form of short periodic bursts, which were observed experimentally for ﬁsh and frog eggs. In this case the communication algorithm can be similar to the exchange of binary encoded data in the computer nets via the noisy channels. The analysis of experimental data on the radiation of ﬁsh eggs conﬁrm our hypothesis and reveals the main features of signal encoding.

**Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences**. 2011;15(2):260-265

260-265

### On solutions of integro-differential equations in dynamic problem of one aeroelastic system "tandem" type

#### Abstract

A mathematical model of the dynamical system of the two elastic tandem type plates, ﬂowing along of the subsonic ﬂow of gas (ﬂuid) is proposed. The solution of aerohydrodynamic part of problem based on the methods of complex variable functions theory is given. The bound system of the equations allowing to investigate the plates dynamic is obtained. The numerical-analytical method of solution of this equation is offered.

**Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences**. 2011;15(2):266-271

266-271

### Modeling of temperature dependencies in the problem of hydrogen permeability

#### Abstract

Processes of hydrogen transfer through the membrane with a presence of desorption are considered. The temperature dependencies of outlet ﬂux and permeability factor, that are based on the relations between the rates of diﬀusion and surface processes, are modelled.

**Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences**. 2011;15(2):272-277

272-277

### Non-stationary problems of the dynamics of stepped section plates and rotation cylindrical shells

#### Abstract

The technique of exact non-stationary dynamic calculation of compound designed systems of in steps-variable thickness a method initial parameters is oﬀered. The settlement scheme considers displacement of median surfaces of interfaced elements. As an example calculation of base plate of a dam GES and matrices of explosive punching is resulted at pulse inﬂuence.

**Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences**. 2011;15(2):278-288

278-288

### On some classes of solutions of aerohydromechanic equations

#### Abstract

The article gives a review of the method of constructing parametric solutions of polynomial form for systems of partial diﬀerential equations and its application to some aerohydromechanic equations. For example the parametric solutions are constructed and their classiﬁcation is carried out for the system of equations, describing the plane ﬂows of the ideal gas with the constant entropy. Particularly, the solutions of simple wave type are demonstrated. Also the solutions of transonic equations, describing ﬂows of gas with local supersonic zones in Laval nozzles are obtained.

**Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences**. 2011;15(2):289-294

289-294

### Simulation of crack growth in a granular material

#### Abstract

A model describing the process of destruction of granular materials was developed. The regularities of formation and development of cracks in discrete environment were determined. The results of numerical calculation of stress intensity factors of the ﬁrst kind, taking into account the elastic characteristics of grain boundary core are presented.

**Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences**. 2011;15(2):295-299

295-299

### On wavenumbers of plane harmonic type I thermoelastic waves of microrotation

#### Abstract

The present paper is researching the propagation of plane harmonic GNI-thermoelastic waves of microrotation by the coupled system of linear micropolar equation of motion and heat transport. The study incorporates the investigation of weak discontinuities propagating in CTMPE media by the Thomas-Hadamard technique.

**Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences**. 2011;15(2):300-305

300-305

### Stability of disk motion on the rheological ground

#### Abstract

In this paper a new mathematical model of the disk motion on the basis of the Kelvin body is constructed. Accepting the hypothesis of a point contact with the drive base, a system of diﬀerential equations of the disk motion is derived in the form of modiﬁed Chaplygin equations involving generalized rheological response force, as well as three stationary constraint equations, two of which are nonholonomic. The analysis of the drive permanent movements stability was carried out. It is shown that the rectilinear motion of the disk and spinning around a vertical diameter are unstable in relation to the nutation angle θ.

**Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences**. 2011;15(2):306-312

306-312