# Vol 17, No 2 (2013)

**Year:**2013**Articles:**31**URL:**https://journals.eco-vector.com/1991-8615/issue/view/1250

### In Memory of Dyuis D. Ivlev

**Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences**. 2013;17(2):9-12

9-12

### The Laplace’ quasi-operator in quasi-Sobolev spaces

#### Abstract

The quasi-Sobolev spaces notion introduced in the article is based on the quasinorms concept. Completeness of these spaces on the appropriate quasi-norms is proved and the continuous embedding of these spaces is shown in the work. Also Laplace’ and Green’s quasi-operators concepts are introduced; it is shown that these quasi-operators are toplinear isomorphisms.

**Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences**. 2013;17(2):13-16

13-16

### Application of methods of the perturbation theory to problem of equally-stressed reinfocing of bending metal-composite plates in conditions of steady-state creep

#### Abstract

The problem of equally-stressed reinforcing of bending metal-composite plates in conditions of steady-state creep, is solved by the help of methods of the perturbation theory. The opportunity of existence of several alternative solutions of a considered problem which can be reliably determined using the developed algorithm is shown. Concrete projects are constructed for equally-stressed reinforcing doubly connected plates with different density of reinforcing on an internal contour.

**Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences**. 2013;17(2):17-35

17-35

### Influence of hostile alkaline environment on strength properties of technical fibers

#### Abstract

We consider questions connected with strength properties of continuous ﬁbers from basalt, carbon and ﬁbreglass under the inﬂuence of hostile alkaline KOH; environment in researches were carried out on plaits, having 4000 threads of continuous ﬁber. The inﬂuence of hostile environment on strength properties of ﬁber and on its structure of surface layer is shown.

**Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences**. 2013;17(2):36-41

36-41

### Piezomechanical properties of magneto electric composites with Maxwell–Wagner relaxation

#### Abstract

The numerical calculation and the analysis of inﬂuence on the real and imaginary parts of effective piezoelectric and piezomagnetic factors of magnetoelectric piezocomposite (is PVF with unidirectional ferrite ﬁbers) of size of ﬁlling by ﬁbers and of frequency of the enclosed electric ﬁeld taking into account Maxwell–Wagner relaxation are carried out.

**Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences**. 2013;17(2):42-49

42-49

### Software system for simulation of study of queuing system with heterogeneous servers and independent queues

#### Abstract

Software package for simulation of study and automated visualization of the state orgraph of queuing system with heterogeneous servers and independent limited queues is described. The base of the algorithm is the method of description of such queues with the use of Mealy ﬁnite-state machines.

**Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences**. 2013;17(2):50-57

50-57

### Artificial neural network with modulation of synaptic coefficients

#### Abstract

The model of neural network based on artiﬁcial neuron with dynamic synaptic weights was constructed. As main model processes for changing the synaptic weights were chosen: weakening of a synaptic weight in the absence of synapse stimulation, and modulation of synapse with synchronous irritation of some other synaptic junction.

**Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences**. 2013;17(2):58-71

58-71

### Coalition decision support system designing

#### Abstract

We describe the main stages of designing and development of the coalition decision support system (DSS). The article includes the requirements to the model, the model description in the form of tuple structures, algorithm of multi-agent simulation, the program complex of the DSS and its implementation. The conclusion is made about the ﬁeld of application of the developed DSS.

**Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences**. 2013;17(2):72-79

72-79

### Error analysis of method of integral characteristics measurement caused by the deviation of signals form harmonic model

#### Abstract

The new method of measurement of integral characteristics on instant values of the harmonic signals divided both in space and in time is considered. Results of the analysis of method error because of a deviation of real signal from harmonic model are contained.

**Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences**. 2013;17(2):80-84

80-84

### Physical and technological aspects of laser heat treatment of working surfaces of linear large sized products

#### Abstract

Physical and technological peculiarities of a laser heat-treatment of working surfaces of linear large sized products were studied on the example of a guillotine shears knifes for the purpose of its wear-resistance increase.

**Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences**. 2013;17(2):85-90

85-90

### Conditions of separability of weight factors from the sums with members of sequences of two aspects

#### Abstract

Representation of conditions of separability of integer weight factors from the sequences organizing a basis of enciphering is described. Two aspects of such sequences are considered: a geometrical progression and sequence with equal powers of natural numbers. These sequences of constant signs and alternating sequences are used when generating the relative summarized residuals, expression of each of which is located in a central part of a double inequality. Deﬁnition of conditions of separability involving the residual sequence — a geometrical progression is made with reference to its common ratio, and conditions of separability involving the the residual sequence containing equal powers of natural numbers, are found using the accompanying function introduced with reference to integer arguments of formed values of relative summarized residuals.

**Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences**. 2013;17(2):91-100

91-100

### Prospects of metamathematical structures in science

#### Abstract

The paper deals with metamathematical structures based on Malcev’s concept of algebraic systems. This approach allows us to extend this concept on systems of physical objects having physical interactions and without such interactions. It is shown, that these extended metamathematical structures can be used in rigorous (scientific) version of metaphysics including its axiomatic, as well as in the theory of evolutionary systems. The formal representation of the latter is differed from that of algebraic systems in mathematics.

**Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences**. 2013;17(2):101-110

101-110

### On convergence of the iterative process for the third order pseudo-parabolic equation with nonlocal boundary value conditions in a multidimensional domain

#### Abstract

In this paper the nonlocal boundary value problem for the pseudo-parabolic equation of the third-order in a multidimensional domain is considered. Using an iterative method, the solving process of the nonlocal boundary value problem is reduced to solving the series of some local problems. An a priori estimate for the convergence of the iterative method in the norm $W_2^1(G)$ is obtained.

**Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences**. 2013;17(2):113-119

113-119

### Stability of solution of one nonlinear initial-boundary problem of aeroelasticity

#### Abstract

The dynamic stability of an elastic element of the channel wall under the subsonic stream of an ideal compressible ﬂuid (gas) is studied. Determination of the stability of an elastic body corresponds to the concept of stability of dynamical systems by Lyapunov. The sufficient conditions for stability are obtained. Conditions impose limitations on the speed of the uniform stream of gas, compressed (tensile) element of efforts, the elastic element stiffness and other parameters of the mechanical system.

**Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences**. 2013;17(2):120-126

120-126

### Rolling regime in the Higgs model with friction

#### Abstract

The Higgs model with friction is considered. The hyperbolic analog of the KrylovBogoliubov averaging method is used to obtain an approximate solution. The obtained solution is compared to a numerical solution of the considered equation.

**Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences**. 2013;17(2):127-130

127-130

### The eigenfunctions of curl, gradient of divergence and stokes operators. Applications

#### Abstract

We consider the spectral problems for curl, gradient of divergence and Stokes operators. The eigenvalues are deﬁned by zeroes of half-integer order Bessel functions and derivatives thereof. The eigenfunctions are given in an explicit form by half-integer order Bessel functions and spherical harmonics. Their applications are described. The completeness of eigenfunctions of curl operator in $L_2 (B)$ is proved.

**Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences**. 2013;17(2):131-146

131-146

### Cyclic loading of three-layer beam in a temperature field

#### Abstract

The deformation of three-layer elastoplastic beam under the cyclic loading in a temperature ﬁeld is considered. For the description of kinematics of asymmetrical on the package thickness beam the hypotheses of broken normal are accepted. The method of solving the corresponding boundary-value problems is given. The analytical solutions of thermoelasticity and thermo-elasto-plasticity problems under the direct and reverse loading are received. The numeric analysis is conducted.

**Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences**. 2013;17(2):147-155

147-155

### Asymptotic methods of nonlinear fracture mechanics: results, contemporary state and perspectives

#### Abstract

In the paper the brief review of the important results of nonlinear fracture mechanics recently obtained by the asymptotic methods and perturbation techniques is given. The asymptotic solutions of the whole class of crack problems are discussed. Applications of the asymptotic analysis for crack problems of nonlinear fracture mechanics such that crack tip ﬁelds in damaged medium, fatigue crack growth problems in damaged medium, nonlinear eigenvalue problems arising from fracture mechanics analysis, nonlinear eigenvalue analysis including higher order terms are elucidated.

**Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences**. 2013;17(2):156-168

156-168

### Atom-field entanglement for Jaynes–Cummings model with an intensity-depend coupling

#### Abstract

We investigate the evolution of a quantum system described by the two-atom Jaynes–Cummings model with an intensity-dependent couplings by displaying the linear atomic entropy and the asymptotic behavior of state vector. The possibility of the system being initially in a pure disentangled state to revive into this state during the evolution process is shown. Conditions and times of disentanglement are derived.

**Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences**. 2013;17(2):169-176

169-176

### Entanglement induced by two-mode thermal noise taking into account the dipole-dipole interaction and atomic coherence

#### Abstract

The entanglement of two two-level atoms with the nondegenerate two-photon transitions interacting with two-mode thermal ﬁeld in lossless cavity has been considered. The possibility of entanglement degree growth in the presence of an atomic coherence and direct dipole-dipole interaction of atoms has been derived.

**Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences**. 2013;17(2):177-184

177-184

### The influence functional method to the description of the dynamics of quantum systems interacting with the laser radiation

#### Abstract

The description of interacting multilevel quantum system and quantum electromagnetic ﬁeld in terms of statistical density matrix is considered in path integral approach. The statistical operator and probability transitions of quantum system are represented as mean of electromagnetic ﬁeld inﬂuence functional. The inﬂuence functionals are deﬁned for speciﬁc models of electromagnetic ﬁeld. The explicit form for singleand multimode electromagnetic ﬁeld is concretized in cases when initial state of the ﬁeld is represented by vacuum and pure coherent.

**Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences**. 2013;17(2):185-192

185-192

### Solitons and the generalized Cole–Hopf substitutions

#### Abstract

This paper examines the relationship between the method of the inverse problem and the method of generalized Cole-Hopf substitutions. The relationship between these methods is established by comparing the method of Darboux transformations and the method of Cole-Hopf substitutions. Concrete examples of using such a relationship are given. Some new examples of the integrable equations are considered.

**Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences**. 2013;17(2):193-199

193-199

### Representation of Friedmann equation solution in form of generalized Dirichlet series

#### Abstract

The cosmological Friedmann equation for the Universe, ﬁlled by scalar ﬁeld with the quadratic potential, is reduced to the system of two ﬁrst-order equations, one having the separable variables. The boundary-value problem with data at inﬁnity is formulated for the second equation. The solution of this problem is represented in form of generalized Dirichlet series. The existence of classical solution in this form at the neighborhood of inﬁnity is proved.

**Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences**. 2013;17(2):200-205

200-205

206-214

### On the hartman effect and velocity of propagating the electromagnetic wave in the tunneling process

#### Abstract

A new approach to the problem of scattering the plane electromagnetic TE wave on a homogeneous dielectric layer is presented, which does not predict, unlike the standard model, the Hartman effect for the tunneling time in the case of scattering the TE wave in the regime of a frustrated total internal refection (FTIR). The basic idea of this approach is that a correct deﬁnition of the tunneling velocity and time is possible if only the dynamics of both its subprocesses — transmission and reﬂection — is known at all stages of the scattering process investigated. It is shown that the Wigner (group) tunneling time was introduced without taking into account of this requirement, and, as a consequence, both this characteristic itself and the associated with it Hartman effect have no relation to transferring the light energy through the layer. The dwell transmission time, which is directly related to it, does not lead to the Hartman effect.

**Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences**. 2013;17(2):215-222

215-222

### Accretion of dark energy onto black holes

#### Abstract

The stationary accretion of dark energy onto black holes is studied. General expressions are derived for the accretion rate of an ideal ﬂuid with an arbitrary equation of state and for scalar ﬁelds. The black hole mass was found to decrease for the accretion of phantom energy with p + ρ < 0. We also study the back reaction of accreting matter onto the metrics of a black hole in a perturbative way. The general expressions for corrections to the metric coefficients are found.

**Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences**. 2013;17(2):223-227

223-227

### Photons as carriers of ultra-high energy in cosmic space

#### Abstract

Absorbing process of ultrahigh-energy gamma-quanta in a cosmic space is investigated. It is shown that the main absorbing mechanism is the reactions arising at collisions of cosmic-ray photons with microwave and radio background ones. Estimate of the mean free path of a photon for diﬀerent energies gives evidence that gamma-quanta with energies E > 1019 eV running from Active Galactic Nuclei seem to reach the Earth vicinity. This result is in agreement with the recent observations of extensive air shower array experiments realized by AGASA and Yakutsk.

**Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences**. 2013;17(2):228-232

228-232

### Effective Higgs potential in Next-to-Minimal Supersymmetric Standard Model

#### Abstract

Higgs sector of the Next-to-Minimal Sypersymmetric Model with CP violation in superpotential and in in the soft supersymmetry breaking sector is considered. One-loop corrections to effective potential parameters were calculated and incorporated to the evaluation of neutral Higgs bosons masses.

**Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences**. 2013;17(2):233-242

233-242

### Construction of the electromagnetic current operator in different forms of Poincaré-invariant quantum mechanics

#### Abstract

In an approach of the Poincaré-invariant quantum mechanics in a modiﬁed relativistic impulse approximation performed construction of the operator of the electromagnetic current for different forms of dynamics (instant form, point form and dynamics of the light-front). The current operator is constructed according to the conditions of Lorentz covariance and conservation. It is shown that the analytical expressions for the form factor are identical in all forms of dynamics. Numerical calculations of the pion form factor with the wave function obtained by the variational method are in good agreement with experiment.

**Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences**. 2013;17(2):243-249

243-249

### Higgs boson production at the lhc in the framework of Regge limit of quantum chromodynamics

#### Abstract

In the framework of the L. N. Lipatov Reggeized Partons Theory we consider production of scalar Higgs boson H of the Standard Model and pseudoscalar Higgs boson A of the Minimal Supersymmetric Standard Model in the Reggeized gluon fusion at the energy range of the Large Hadron Collider. Working in the leading order approximation in the strong coupling constant $\alpha_s$ we take into account contributions from $t$and $b$-quark in the loop integrals. We have calculated transverse momentum boson spectra and total cross sections as a function of boson mass. The obtained results agree with predictions which have been obtained earlier in the collinear Parton Model with the next to leading order in $\alpha_s$ corrections and all-order resummation of large logarithmical corrections.

**Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences**. 2013;17(2):250-258

250-258

### The effect of the mass transfer along the cosmic string

#### Abstract

The caption of massive quantum particle by the inﬁnite string is considered. It is demonstrated that the appearance of the cuspidal point on the string leads to the collapse of particle wave function in this point.

**Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences**. 2013;17(2):259-266

259-266