Vol 26, No 2 (2018)

Precise dispersion equations for a plane symmetric dielectric anisotropic waveguide are obtained, in which the waveguide layer is isotropic, and the framing media are assumed to be anisotropic uniaxial media. The tensors of the dielectric permittivity of the framing media are not assumed to be diagonal, namely, in one of them this tensor is formed by rotating the diagonal tensor by some angle between the optical axis of the anisotropic medium and the direction of propagation of the electromagnetic wave. The tensor of dielectric permittivity of another anisotropic medium is rotated by the same angle, but in the opposite direction, with the optical axes of both framing media lying in a plane parallel to the boundaries of the waveguiding structure. Thus, in framing media, the existence of six-component electromagnetic waves is maintained. In the dispersion properties of such a waveguide, certain features are observed in comparison with the case when the framing media are assumed to be isotropic. It is found that the first symmetric mode of such a waveguide has a finite deceleration with zero thickness of the isotropic layer, which indicates the possibility of the appearance of surface electromagnetic waves (the so-called Dyakonov waves) at the boundaries of this isotropic layer. It is noted that the transition of the antisymmetric mode to the Dyakonov wave occurs with a finite thickness of the waveguiding layer. Dependencies of the deceleration of the elementary (symmetric) mode on the angle of rotation of the optical axis of anisotropic media relative to the direction of propagation of the guided wave of the waveguide structure are given.

We consider a plane problem of steady-state motion of an ideal incompressible fluid flow in a channel between two parallel planes under the action of a given pressure drop. The problem is considered in Cartesian coordinates. The formulation is analogous to the well-known Poiseuille problem with the difference that an ideal fluid is considered instead of a viscous one. The non-flow condition is set as the boundary ones on the channel walls. So, that the velocity vector is parallel to the bounding surfaces over the channel walls. The pressure drop is set as a given positive quantity. An approach proposed based on the use of the first integral of the Euler equations while preserving nonlinear terms. We represent the derivation of main relations for the case of 2D steady-state motion of an incompressible fluid. The solution of equations for hydrodynamic characteristics in the form of expansions in powers of the Cartesian coordinates was found out by analytical way. The standard programs of Maple package are used to determine the coefficients of decomposition for some values of defining parameters. As a result expressions for hydrodynamic characteristics are obtained and their features investigated. In particular, zones of recurrent motions and zones of intense vortex motion of fluid were revealed.

In this paper we consider the dynamics of large-scale queueing systems with an infinite number of servers. We assume that there is a Poisson input flow of requests with intensity . We suppose that each incoming request selects two any servers randomly and at the next step of an algorithm is sending this request to the server with the shorter queue instantly. A share () of the servers that have the queues lengths with not less than can be described using a system of ordinary differential equations of infinite order. We investigate this system of ordinary differential equations of infinite order with a small real parameter. A small real parameter allows us to describe the processes of rapid changes in large-scale queueing systems. We use the simulation methods for this large-scale queueing systems analysis. The numerical simulation show that the solution of the singularly perturbed systems of differential equations have an area of rapid change of the solutions, which is usually located in the initial point of the problem. This area of rapid function change is called the area of the mathematical boundary layer. The thickness of the boundary layer depends on the value of a small parameter, and when the small parameter decreases, the thickness of the boundary layer decreases. The paper presents the numerical examples of the existence of steady state conditions for evolutions () and quasi-periodic conditions with boundary layers for evolutions ().

For the evolution equation in a Banach space, the linear inverse source problem is studied. It is required to recover an unknown nonhomogeneous term by means of an additional nonlocal condition written in the form of a Riemann-Stieltjes integral. The main assumption is related to the superstability (quasinilpotency) of the evolution semigroup. More precisely, it is assumed that the evolutionary semigroup associated with the abstract differential equation has an infinite negative exponential type. Without other restrictions, a theorem on the solvability of the inverse problem is obtained. It is shown that the solution can be represented by a convergent Neumann series. Exact conditions under which an infinite series becomes a finite sum are found. Here, the algorithm for calculating the solution becomes finite. Model examples are considered, including an important example of the inverse problem with final overdetermination. The above results can be applicated in special parts of mathematical physics related to the theory of elasticity and the linear transport theory. As is customary, our research takes place in the general case with a choice of the complex scalar field, but the main facts are also true in the real case. The created theory allows transfer to nonlocal problems for evolution equations, when instead of the traditional initial condition special time averaging is used to find the solution.

Criminal activity of the corrupted employees of the Russian government institutions of various levels is one of the significant reasons of stay of the country in a condition of crisis. There is an association of considerable part of the operating bureaucracy in uniform antisocial system. A main goal of such a system is achievement of the highest level of the welfare and welfare of friends and relatives. On the other hand, the conglomerate of the interconnected participants of this criminal community, instead of fully performing fully their official duties, realizes plans of the destructive coordinated impact on the state social and economic basis, gaining and strengthening the power influence in political, economic and social spheres. The purpose of the authors of this work is a brief description of the idea of cognitive approach to the system analysis of corruption process. It is presented by simulation model of the avalanche type of special structure for demonstration of the dual mechanism of management of the social explosion caused by corruption. The idea of applying cognitive modeling of corruption process is based on the dialectic concept: control of an internal contradiction. It allows to reflect dynamics of a system condition and to show result of accumulation of a quantitative property with transition to the new quality. In the marked area development of corruption activity leads to explosion, breaking integrity of social and economic system. Cognitive research (in structural aspect) gives us the chance to reveal the mechanism of action of the factors influencing the course of “reproduction” of the corrupted elite. However, some factors promote braking, others, on the contrary, accelerate approach of national accident. Organizational and legal impacts on a source of degradation allow conducting fight against corruption. The Russian mentality, national, cultural features, and legislative basis do not allow adopting fully experience of fight against corruption of some countries, for example, of China, the USA, Singapore, etc. Therefore, it is necessary to develop the ways. In this study, the computer program of the avalanche process is used. Results of the computer experiments realizing the mechanism of double regulation of a condition of the studied phenomenon are given. The model is simple and evident, contains not many parameters and variables, and allows explaining inevitability of social and economic crisis in conditions of the current legislation and the weakened moral and ethical influence on the criminal antisocial union. Provisions and conclusions of this study prove inevitability of catastrophic consequences in social and economic space, but they can be delayed for considerable time due to disciplinary, legal, educational influence.