# Vol 17, No 3 (2013)

**Year:**2013**Articles:**16**URL:**https://journals.eco-vector.com/1991-8615/issue/view/1247

### An anniversary of the journal “Computer optics”

#### Abstract

We summarize the ﬁrst twenty ﬁve years of scientiﬁc publishing “Computer Optics”, analyze its creating pre-conditions and history, and its development by the example of breakthrough articles on the diffractive optics, information optical technologies, image processing. We describe the progress of editorial team and the future development of journal.

**Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences**. 2013;17(3):7-20

7-20

### On a problem with a displacement for a partial differential equation

#### Abstract

The unique solvability of the problem with the generalized operators of fractional integro-differentiation in the boundary condition is investigated for the mixed type equation. The uniqueness theorem for the nonlocal problem is proved. The proof of existence of the problem solution is reduced to the demonstration of solvability of Fredholm integral equation of the second kind.

**Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences**. 2013;17(3):21-28

21-28

### Boundary value problem for mixed type equation of the third order with periodic conditions

#### Abstract

The problem for the equation of the mixed elliptic-hyperbolic type with nonlocal boundary conditions is viewed. This problem is reduced to the inverse problem for elliptichyperbolic equation with unknown right-hand parts. The criterion of the uniqueness is established. The explicit solution is constructed as the sum of orthogonal trigonometric series of the one-dimensional spectral problem eigenfunctions. The argumentation of the series convergence under some restrictions is given. The stability of the solution by the boundary functions is proved.

**Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences**. 2013;17(3):29-45

29-45

### Inverse problem for quazilinear partial integro-differential equations of higher order

#### Abstract

A method of studying an inverse problem for the some classes of quasilinear partial integro-differential equation of the higher order is proposed. A theorem on the existence and uniqueness of the solution of this problem is proved.

**Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences**. 2013;17(3):46-55

46-55

### Construction of Mikusinski operational calculus based on the convolution algebra of distributions. The theorems and the beginning of use

#### Abstract

We consider the Mikusinski operational calculus based on the convolution algebra of distributions $D^{+}$ and $D^{-}$. We state and prove the basic theorems, and give examples of Mikusinski operational calculus using, which demonstrate its additional possibilities, such as extension of solutions to the domain of negative argument values, removing the growth limits of right-hand functions and obtaining the new methods for solving the nonhomogeneous equations with discontinuous right part.

**Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences**. 2013;17(3):56-68

56-68

### Method for nonlinear stochastic problem of creep solving for a plane taking into account damage of the material

#### Abstract

The analytical method for nonlinear stochastic problem of creep solving for a plane taking into account the damage of the material and the third stage of creep is developed. Determinative creep equations are taken in accordance with the energy version of the nonlinear theory of a viscous ﬂow in a stochastic form. Stochasticity of the material is determined by two random functions of coordinates $x_1$ and $x_2$. Linearization of the problem relative to the nominal stress on the basis of small parameter method is produced. The variance of the random stress ﬁelds is found on the hypothesis that processes of creep and damage accumulation are independent. The case when the plane is stretched in two orthogonal directions in proportion to some parameter is given as an example. The provided analysis showed that at the third stage of creep magnitude stress ﬂuctuation is increased relative to the value at the stage in steady-state creep.

**Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences**. 2013;17(3):69-76

69-76

### The stress-strain state of cylindrical sample from alloy D16T under axial tension and torsion creep

#### Abstract

The method for calculation of cylindrical sample rheological deformation and fracture in creep conditions for three types of stress state: tension, pure torsion, the combined effect of tensile load and torque is offered. The procedure is based on the theory of creep and creep rupture strength of energy type. Calculations are performed for all three types of stress state for solid and hollow cylinder tests from aluminum alloy D16T at 250 ℃. Comparison of the calculated data with the corresponding test data for each type of stress state is conducted. It shows the agreement between the calculated and experimental values. The intensiﬁcation of creep and decreasing of creep rupture strength factors after the application of torque to the specimen under the axial tension are established. The substantial redistribution of axial and shear stresses along the radius depending on the time is observed. The estimates of errors of deviation of calculated data from the experimental values are given.

**Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences**. 2013;17(3):77-86

77-86

### Description of creep rupture strength of tensile rod with rectangular and circular cross-section at high temperature air media

#### Abstract

Description of known experimental data on the creep rupture strength of tensile rectangular and circular cross-sections rods at high temperature in air media is considered. Simulation of the creep rupture strength of tensile specimens is based on the Yu. N. Rabotnov’s kinetic theory with two structural parameters — damage and concentration of the chemical elements of the medium in the rod’s material. It has been shown on the basis of experimental data that the scale effect and in particular the relative volume fraction of the surface layer of the rod exposed to the aggressive medium inﬂuence on the characteristics of creep rupture strength.

**Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences**. 2013;17(3):87-97

87-97

### Mathematical modelling of mass-transfer under the evaporation of multicomponent liquids

#### Abstract

The mathematical model of evaporation of multicomponent liquids is developed for open systems with consideration of mass-transfer substances in a liquid phase. Feature of the given model is the mathematical description of one-dimensional evaporation of the multicomponent liquid mixes containing poorly volatile solvent and n of diluted substances. Exact analytical solution of the boundary value problem based on Green’s functions method is received by reduction of the differential equations system with moving boundary of the $n$ diluted substances to the $n$ differential equations with ﬁxed boundary.

**Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences**. 2013;17(3):98-109

98-109

### On one class of analytic solutions of the stationary axisymmetric convection Bénard–Maragoni viscous incompreeible fluid

#### Abstract

The purpose of this work is to ﬁnd solutions for the system of equations Oberbeck– Boussinesq ﬂat convection Bénard–Marangoni a viscous incompressible ﬂuid. In this viscous incompressible ﬂuid the radial component of the temperature gradient may become zero. It is shown that the initial system may be reduced to the system of equations of ordinary differential equations of the eleventh order. We obtain the exact solution at the point of the extremum of the temperature (at zero including Grasgof’s). Integration of equations is carried out in dimensionless variables, which are non-classical way: put the scale factor for each variable, and not by linear characteristic size of the layer. The solution is the initial approximation to the solution of convection Bénard–Marangoni in numbers Grasgof’s, the big zero.

**Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences**. 2013;17(3):110-118

110-118

### Medical-and-biological aspects of laser influence

#### Abstract

The distributions of reﬂection and admission coefficients of a different wave-length radiation by the biological tissues were experimentally studied. A physical basis of the methods of approach to an optimum selection of the laser sources and the conditions of its practical application to solution of the fundamental and applied problems of the medical-and-biological investigations was given.

**Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences**. 2013;17(3):119-128

119-128

### Bilayer mathematical model of human femur neck for research of the stress state after reinforcement with different designs of implants

#### Abstract

A bilayer mathematical model of human femur neck reinforced with implants of various designs is represented. New models of implants are designed. The software for geometric modeling of bone with the implant is developed. The rational geometry for placing implants into the bone tissue to unload the most loaded areas is proposed. A number of boundary value problems for evaluating the stress-strain state in the reinforced femoral neck are solved. It is shown that stress state in the most loaded region in the reinforced construction is considerably less than in the non-reinforced one.

**Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences**. 2013;17(3):129-135

129-135

### Peculiarities of penetration of high velocity macroscopic particles in metallic target

#### Abstract

The experimental results of the macroscopic spherical particles penetration in the halfinﬁnite aluminium and steel targets have been analyzed. It is shown, that for particles, having sizes about 50–100 µm and velocities in the range 1000–3000 m/s, the hydrodynamical penetration model is not applicable. Under such conditions the penetration procedure is determined by the processes, taking place immediately in front of the particles surface. It fundamentally differs from models, suiting for describing the damage of target metal under the inﬂuence of large mechanical bodies. The speciﬁc penetration model for macroscopic particles, having small size have been formulated. The special properties of this mechanism which distinguish it from the common approach are shown.

**Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences**. 2013;17(3):136-146

136-146

### 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 of the real (not virtual) static Schwarzschild observer is solved.

**Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences**. 2013;17(3):147-184

147-184

### On a boundary value problem for mixed type equation with nonlocal initial conditions in the rectangle

#### Abstract

The boundary value problem for mixed type equation with nonlocal initial conditions in integral form is considered. The main result states that the nonlocal problem is equivalent to the classical boundary value problem for a loaded equation. This fact helps to prove the uniqueness and, under extra restrictions, the existence of a generalized solution of the problem.

**Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences**. 2013;17(3):185-189

185-189

### Mathematical modeling of the conservation of populations

#### Abstract

The system of diﬀerence equations describing the process of industrial ﬁsh catching while their abundance is maintained is proposed. Population size changing and, consequently, the volume of catch are predicted on the basis of this model study. The impact on the model of the parameters responsible for catch rate and factors that characterize the population growth rate is analyzed taking into account the terms of the equation describing the increase in the population size at the expense of ﬁsh farms. The proposed model and the results, in particular, can be used to solve problems of the size reducing of population of the rare breed ﬁsh and disappearance of valuable species of ﬁsh such as sturgeon.

**Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences**. 2013;17(3):190-194

190-194