This article considers the first mixed problem for the one-dimensional wave equation with the second-order Cauchy-type conditions. The authors of the article prove that the usage of necessary and sufficient homogeneous matching conditions guarantees the classical solution in the middle of the plane between two parallel straight lines. The article gives the classical solution to the one-dimensional wave equation in analytical form if there are Dirichlet conditions at the side boundaries and Cauchy-type conditions at the plane bottom. By the classical solution is understood the function that is determined at all points of closing the defined domain. This function must have all classical derivatives included in the equation. In case of inhomogeneous matching conditions, the correct problem is formulated with the addition of the conjugation conditions.

In the article, the Krylov type estimates are obtained for the functional of solutions to stochastic delay differential equations driven by standard and fractional Brownian motions. Main ideas to obtain these estimates are to use the Nualart type estimates for the pathwise integral with respect to fractional Brownian motions and to use Krylov’s methods for Ito’s equations. With the help of the obtained estimates and basing on the Skorokhod and Prokhorov theorems, we have found sufficient conditions of existence of weak solutions of stochastic delay differential equations driven by standard and fractional Brownian motions with discontinuous right-hand sides and with a degenerate diffusion operator.

We consider the linear periodic system with zero mean of periodic coefficient. The necessary and sufficient conditions, under which linear periodic differential system has strongly irregular periodic solutions, were obtained.

A stationary distribution of condition probabilities of a closed queueing network is investigated. Devices of network nodes can operate in several modes. There are two types of customers in network nodes: ordinary (active) customers and temporarily non-active customers. There are input flows of signals that allow customers to change their state: from the non-active state to the state when they can receive service and vice versa.

The problem of statistical assignment of realizations of the stationary time series to the fixed classes is considered. The decision rule in a space of covariance functions is proposed and its efficiency is investigated analytically. The case of two classes is studied.

The model of pivotal flow in the sections Ω_m, i. e., at the values of the time t equal to t_m = mт, m = 0,1,2,...,M, has been considered. The existence of a unique solution in the each section Ω _m has been proved.

The aim of the present article is to derive so-called weak second-order necessary optimality conditions for nonlinear programming problems. Necessary weak second-order optimality conditions are proved under some additional requirements to the constraints.

The paper presents a new criterion of semiabelian of an n-ary group on the basis of the fact of self-returning of an arbitrary point with respect to the elements of the succession, composed of the midpoints of the sides of an arbitrary k-angle with an odd k (k ≥ 3) and one of the vertices of the k-angle in term symmetrical point and vector n-ary groups.

The geometry of Lobachevsky space is considered as a basis for modeling an effective medium. In Lobachevsky space, Maxwell's equations in the 3D complex Majorana - Oppenheimer formalism are solved exactly. The problem effectively reduces to one second-order differential equation. In the context of quantum mechanics, such an equation describes the motion of a particle in a potential field gradually increasing to infinity; a particle is reflected from the barrier. The geometry of Lоbachevsky space simulates a perfect mirror distributed in the space. The penetration depth of the field into the “medium-mirror” is determined by the frequency of an electromagnetic wave and by the curvature radius of an effective modeling space. The influence of the geometry on spin 1/2 particles is the same: the “medium” acts on fermions as a perfect mirror, the penetration depth of particles increases with energy and decreases with increasing the space curvature.

Within the framework of perturbation theory the energy levels and wave functions are found for an electron in twodimensional semiconductor circular quantum rings in the presence of the Rashba and Dresselhaus spin-orbit interactions with a realistic axially symmetric confining square well potential of finite depth.

A CW and quasi-CW Nd:KGd(WO₄)₂/KTP laser with longitudinal diode-pumping at λ ~879 nm and intracavity frequency doubling in a three-mirror linear cavity has been created. At frequency doubling, superior results are achieved with a N_g-cut crystal by virtue of a simpler character of its thermal lens. At a CW pump power of 15.6 W, the power of the second harmonic generated at a wavelength of 533.6 nm amounts to ~0.9 W. At quasi-CW pumping, the laser generates with a duty cycle of 10 % and emits 10-20 ms long pulses, whose peak power reaches 2.25 W with an optical conversion efficiency of 9%. In the case of a Nр -cut Nd:KGd(WO₄)₂ crystal, the peak power of the second harmonic does not exceed 2.1 W.

We developed a method for tunable light bitrap shaping meant for a simultaneous manipulation of two particles. The method is based on the light bibeam with a tunable angle between propagation directions of its components. We proposed, assembled, and tested experimentally an optical scheme for realization of the method. The method is suitable for the transformation of powerful laser radiation because all optical elements in the scheme have high light beam strength. The method is very effective since light energy losses occur only during reflections on input and output sides of optical elements. These losses can be reduced to a fraction of a percent by an anti-reflecting coating for the used wavelength on the sides of optical elements. The possibility of an energy redistribution between trap peaks permits one to conduct effectively with a pair of microparticles having different refraction indices and sizes. Light intensity maxima of the shaped bipeak light field are microscopic in size, since it can be used not only for manipulation of micron and submicron particles, but for high-resolution microscopy, for nondestructive testing of a coating thickness, and for precision laser processing of materials, including metals.

The basic concepts and specificity of the programming technology of CUDA video cards are presented. The efficiency of the technology is demonstrated on image processing tasks. Results of a comparative performance analysis of program implementations on the GPU and CPU are adduced for urgent tasks of image processing. It is shown that CUDA allows accelerating computations of image processing tasks by several orders of magnitude. In particular, the use of the CUDA technology has made possible to implement correlation algorithms for tracking objects on video sequences in real time.

The disadvantages of the classical architectures of artificial neural networks (ANNs) in the problems of intelligent control of an autonomous robotic vehicle are described. Based on updated bi-directional associative ANNs an adaptive neurocontroller has been developed which enables one to find the cause-effect relationships in the “robot-environment” system. The neurocontroller is based on the rule-based system and contains two ANNs that perform two different functions. The first one is implemented as a motoneurons unit that contains the robot motion control algorithm, and the second one is designed to identify in the sensory data sequence new patterns that are added to the first ANN based on the supervised learning scheme.

The some properties of solitons in negative media are considered.