# Vol 16, No 1 (2012)

**Year:**2012**Articles:**31**URL:**https://journals.eco-vector.com/1991-8615/issue/view/1253

### Three-dimensional integro-multipoint boundary value problem for loaded Volterra-hyperbolic integro-differential equations of Bianchi type

#### Abstract

In this paper the combined three-dimensional non-local boundary value problem with integro-multipoint conditions for loaded volterra-hyperbolic integro-differential equation of Bianchi type is explored. The matter of principle is the fact, that the considered equation has discontinuous coefficients which satisfy only some conditions of P-integrability type and boundedness, i.e. the considered hyperbolic differential operator has no traditional conjugate operator. In particular, for example, Riemann function under Goursat conditions for such equation cannot be constructed by classical method of characteristics.

**Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences**. 2012;16(1):8-20

8-20

### On Cauchy problem for system of n Euler-Poisson-Darboux equations in the plane

#### Abstract

The system of Euler-Poisson-Darboux equations is considered, the Cauchy problem is solved for the case of real n×n matrix-coefficient with one real eigenvalue or two complex conjugate eigenvalues with real part in the interval (−1/2, 1/2).

**Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences**. 2012;16(1):21-30

21-30

31-38

### On one problem in an infinity half-strip for biaxisimmetric Helmholtz equation

#### Abstract

Boundary value problem in an inﬁnity half-strip for biaxisymmetric Helmholtz equation is explored. Existence conditions of this problem are gotten with help of Fourier-Bessel series expansion. Uniqueness of solution of this boundary value problem is proved for some parameters values. Lack of uniqueness of solution is proved for some other parameters values.

**Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences**. 2012;16(1):39-45

39-45

### Multiprogrammed stabilization of the equilibrium positions of the quasi-linear time-invariant systems

#### Abstract

In present work, the problem of multiprogrammed stabilization of the equilibrium positions for a quasi-linear system is considered. The equilibrium positions are very important (from the viewpoint of dynamic object simulation) functioning regimes of any dynamic system. The multiprogrammed controls which realized these regimes are constrained as the Hermits interpolating polynomials. In the paper, the theorem on sufficient conditions of the multiprogrammed stabilized control existence is proved and the illustrative example is given.

**Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences**. 2012;16(1):46-51

46-51

### On two special functions, generalizing the Mittag-Leffler type function, their properties and applications

#### Abstract

Two special functions, concerning Mittag-Leffler type functions, are studied. The ﬁrst is the modiﬁcation of generalized Mittag-Leffler function, which was introduced by A. Kilbas and M. Saigo; the second is the special case of the ﬁrst one. The relation of these functions with some elementary and special functions and their role in solving of Abel-Volterra integral equations is indicated. The formulas of the fractional integration and differentiation in sense of Riemann-Liouville and Kober are presented. The applications to Cauchy type problems for some linear fractional differential equations with Riemann-Liouville and Kober derivatives are noticed.

**Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences**. 2012;16(1):52-65

52-65

### Pure bending of beams made of multimodular behavior material under creep conditions

#### Abstract

The problem of pure bending of beams with rectangular and circular cross-section is solved at steady-state creep, taking into account the different characteristics of the material in tension and compression. Constitutive relations for steady-state creep are taken in the form of fractional functions. A comparison of solutions of problems for beams with square and circular cross-section with the same values of the axial moments of inertia is given.

**Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences**. 2012;16(1):66-73

66-73

### Axisymmetric problem for inhomogeneous conical shell

#### Abstract

New analytical solution of the axisymmetric dynamic problem for circular conical shells with inhomogeneous thickness and ﬁnite shear rigidity was developed on the basis of improved theory by generalized method of ﬁnite integral transformations. Arbitrary dynamic load for the shells with rigidly clamped edges is considered. Dissipative forces of viscous resistance are taken into account in the calculation. The stress state as well as dynamic characteristics of the shells depending on the degree of its heterogeneity is analyzed.

**Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences**. 2012;16(1):74-91

74-91

### Modeling of steady creep of 3D reinforced metal-composits with anisotropy of phase materials

#### Abstract

The iteration model describing mechanical behavior of cross-reinforced in the space metal-composites with steady-state anisotropic creep is presented. The comparative analysis of the calculations on diﬀerent structural models of mechanical behavior of cross-reinforced in plane and in space metal-composites with steady-state creep is carried out.

**Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences**. 2012;16(1):92-109

92-109

### Investigation of uniaxial and biaxial loadings of softening materials in endochronic theory of inelasticity

#### Abstract

Uniaxial and biaxial alternating strains of softening materials are explored in the framework of inelastic theory of endochronic type accounting material dilatation. Constitutive relations generalized for large strain domain are proposed. Some simulated examples for demonstration of theory capability are presented.

**Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences**. 2012;16(1):110-115

110-115

### Antiplane deformation of a cylindrically anisotropic elastic rod

#### Abstract

The problem of antiplane deformation of general cylindrical anisotropic material is studied in this paper. Explicit solutions of Dirichlet and Neumann problems are given for a circular domain. The existence of unique weak solution of the Dirichlet problem in a bounded region with a piece-wise smooth boundary is proved.

**Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences**. 2012;16(1):116-122

116-122

### Investigation of the kinetics of physical and mechanical properties of hardened samples made of B95 and D16T alloys due time-temperature expositions and multicycle fatigue tests

#### Abstract

The kinetics of residual stresses and physical and mechanical properties of the hardened air shot-blasting layer of smooth specimens and specimens with semicircular cuts of aluminum D16T and B95 alloys as a result of time-temperature expositions and multicycle fatigue tests is investigated. This research was done for symmetric loading cycle in terms of bending and tension-compression tests and the base of 107 cycles. The growth of increment of the endurance limit of hardened parts with stress concentrators in comparison with non-reinforced specimens is established experimentally and by calculation. It is shown that the time-temperature exposition causes the relaxation of residual stresses and the reduction of increment of the endurance limit. In fact, surface plastic hardening signiﬁcantly affects the growth of microhardness in comparison with samples unhardened. Microhardness decreases to values corresponding to unhardened sample after time-temperature expositions. The surface hardening increases the roughness layer and further time-temperature exposition and fatigue tests have no effect on these parameters. There is agreement between the calculated and experimental data.

**Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences**. 2012;16(1):123-132

123-132

### Analysis of stress state in semicircular profile notches after preliminary surface plastic deformation of solid cylindrical specimens

#### Abstract

The distribution of residual stresses of surface hardened solid cylindrical specimens and specimens with a semicircular notch using the ﬁnite element method is studied. As the initial information the experimentally determined one and / or two components of residual stresses in a hardened layer are used. It is noted that residual stresses redistribution on the stress concentrator is signiﬁcantly affected by the ratio of a notch radius to a zero depth of axial component of residual stresses.

**Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences**. 2012;16(1):133-140

133-140

### Calculation method for frame construction life prediction on the basis of creep and endurance of energy type

#### Abstract

The analytical method of estimation of frame construction life prediction in terms of creep by strain failure criterion is suggested. The linearization of stochastic rheological energy equations, is made, the estimations of uptime under the assumptions on the limit values of creep are obtained. The checking of accordance of the method with the experimental data for the creep of samples made of 12Kh18N10T steel under T = 850 ℃ is implemented. There is agreement between the calculated and experimental data.

**Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences**. 2012;16(1):141-149

141-149

### Mathematical model of viscoelastic softening material with exponential creep kernel

#### Abstract

The variant of mathematical model of uniaxial strain for viscoelastic material with exponential creep kernel is proposed. Lyapunov stability of the solution of the model in case of permanent stress is investigated. The stability region of solutions of mathematical models diﬀerential equations, corresponding to asymptotically restricted creep of material, is established. Instability region of solutions is in accord with appearance of tertiary creep. Relation between stability of solutions by Lyapunov and stability of iterative calculation for numerical solving the system of equations is established. As an illustration the investigation of model problem is quoted.

**Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences**. 2012;16(1):150-156

150-156

### Parametric identification of Cauchy problem for one fractional differential equation

#### Abstract

The method for parametric identiﬁcation of Cauchy problem for a fractional differential equation with fractional differential operator of α ∈ (0, 1) degree according to instantaneous values of experimental observations is suggested. The method is based on computation of mean-square estimations for coefficients of linear parametric discrete model of approximation function. Numerically-analytical investigations have been done, the results let us conclude about high eﬃciency of the method.

**Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences**. 2012;16(1):157-165

157-165

### A mathematical model of heat transfer in apparatus of air cooling of oil

#### Abstract

In this paper the boundary value problem describing the process of unsteady heat transfer in apparatus of air cooling of oil is formulated and solved. Different modes of operation of such heat exchangers are modeled. The analytical solutions of the boundary value problem corresponding to diﬀerent modes of operation of apparatus of air cooling of oil are obtained.

**Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences**. 2012;16(1):166-174

166-174

### The criterion for space-age organization of stand

#### Abstract

A statistical criterion for randomness of spatial tree patterns in stands with account of trees age is proposed. Interpretation of the criterion statistic and numerical experiments on collected spatial data are presented.

**Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences**. 2012;16(1):175-182

175-182

### Neural network training acceleration using NVIDIA CUDA technology for image recognition

#### Abstract

In this paper, an implementation of neural network trained by algorithm based on Levenberg-Marquardt method is presented. Training of neural network increased by almost 9 times using NVIDIA CUDA technology. Implemented neural network is used for the recognition of noised images.

**Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences**. 2012;16(1):183-191

183-191

### Mathematical modeling as a basis for creation of the effective braking system of hydraulic press ram in upper position

#### Abstract

Single-mass mathematical model of hydraulic press ram braking in upper position is considered. The inﬂuence of control valve closing time, its constructive characteristics and coefficient of hydraulic system quality on dynamics of ram braking are analyzed. Practical recommendations on creating effective braking systems of hydraulic press ram in upper position are given.

**Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences**. 2012;16(1):192-197

192-197

### Forced oscillation of piezoceramic cylinder with circumpolarization of material

#### Abstract

The nonstationary elasto-electrodynamics problem for an anisotropic piezoceramic cylinder of ﬁnite size with circumpolarization of material is considered for the case when the tangential stresses and the electric potential inﬂuence on the radial outside of the cylinder as the arbitrary functions of axial coordinate and time. The new closed solution is obtained by the method of expansion in vector eigenfunctions in the form of structural algorithm of ﬁnite transformations. The constructed algorithm allows to determine the eigenfrequencies, stress-strain state of the element, and all the components of the induced electric ﬁeld.

**Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences**. 2012;16(1):198-207

198-207

### Analytical model of vertical oil-water displacement with the account of viscous, capillary and gravity forces

#### Abstract

A mathematical model of water displacement in vertical porous media is presented. The mathematical formulation takes the form of a nonlinear convection-diffusion equation. Its contribution comes from consideration of the three chief forces: viscous, capillary and gravity in oil recovery processes. A numerical model was based on the simulator Schlumberger ECLIPSE ver. 2004a 1. Finally, analytical and numerical results are compared.

**Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences**. 2012;16(1):208-213

208-213

### Economy method for multiple solving of augmented regularized normal system of equations

#### Abstract

In this work, a new numerical algorithm for solving augmented regularized normal system of equations with several regularization parameters is proposed. The computational costs and the required amount of RAM of the proposed algorithm are analyzed. The proposed numerical algorithm is compared with the algorithm based on the singular value decomposition.

**Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences**. 2012;16(1):214-222

214-222

### The update exposition of the components organisig the sum of weighted equal powers

#### Abstract

The sum of the weighted equal powers with natural bases and parameters is organized of components, which are independent or dependent on weight coefficients. Modiﬁcation of components of the ﬁrst aspect uses explicitly expressed products of binomial coefficients, and modiﬁcation of components of the second aspect - products of binomial and weight coefficients. These visible expressions expand possibilities of representation of structure and an order of shaping of the considered sums.

**Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences**. 2012;16(1):223-232

223-232

### Mathematical foundations of metaphysics

#### Abstract

The paper deals with basic prerequisites for axiomatic of rigorous scientiﬁc metaphysics, which continues Aristotles ideas concerning science explaining furniture of the world. Such rigorous metaphysics could explain many global or local properties of various physical systems like proved mathematical theorems explain global and local properties of mathematical objects.

**Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences**. 2012;16(1):233-242

233-242

### Control problem for the hyperbolic equation with the characteristics having the angular coefficients of the same sign

#### Abstract

The boundary control problem for the hyperbolic equation is considered for the case, when the angular coeﬃcients of characteristics have the same sign. The control functions are constructed in an explicit form. The conditions of controllability are found for different periods of control.

**Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences**. 2012;16(1):243-247

243-247

### The analogue of DAlembert formula for hyperbolic differential equation of the third order with nonmultiple characteristics

#### Abstract

The Cauchy problem for the third order hyperbolic differential equation with nonmultiple characteristics is considered. The analogue of DAlembert formula is obtained as a solution that allows describing the propagation of initial displacement, initial velocity and initial acceleration.

**Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences**. 2012;16(1):247-250

247-250

### On number of solutions in eigenvalue problems for elliptic equations with discontinuous nonlinearities

#### Abstract

We study the existence of solutions of eigenvalue problems for elliptic equations of the second order with nonlinearity discontinuous with respect to a phase variable. Using the variational method, we receive the theorems on number of solutions for investigated problems. M. A. Goldshtiks problem on separated ﬂows of incompressible ﬂuid is considered as an appendix.

**Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences**. 2012;16(1):251-255

251-255

256-260

### Modeling and analysis of macroeconomic system dynamics in MATLAB/SIMULINK environment

#### Abstract

The general theory of cyclic processes is examined in an economy. The simulation model of solutions of differential equations describing the cyclic vibrations of business activity and the trend curve of GDP growth is built in MATLAB/Simulink environment. Stability of the system is investigated. The graphic image of solutions of differential equations is brought, the inﬂuence of accelerator power on the dynamics of the economic system is analyzed.

**Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences**. 2012;16(1):261-267

261-267

### Productivity analysis of doubly-periodic systems of production wells

#### Abstract

The article presents a mathematical model, which allows to analyze the productivity of systems of production wells. System of wells is modeled by a ﬂat inﬁnite doubly periodic lattice of point sinks of equal power. Also an analytic representation for the Dietzs shape factor is presented, which agrees with numerical calculations by the method of imaginary producing wells.

**Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences**. 2012;16(1):268-270

268-270