The paper examines geometric and algebraic properties of locally symmetric differential affine-connected manifolds of constant positive curvature by the example of spheres. The identities in a geodesic loop of spherical spaces are discussed, homotheties, geodesic symmetries and parallel translations are described in the local coordinate system which is common with a locally flat space with affine connection.

Hardy spaces play an important role in the complex analysis and its numerous applications. However, unlike a one-dimensional case, the Hardy-type spaces in a polydisc are investigated a little. In this paper, the integral representations of the classes of n-harmonic in a polydisc Un functions are received, in particular the characterization of n-harmonic functions in a polydisc which can be represented as a multiple Poisson integral from functions, measurable on a skeleton of a polydisc, from a class where 1 < pi < + ∞, is given. At the proof of the main result the general methods of the complex and functional analysis, theory of Hardy classes is used.

In recent decades the field of application of UV light sources has been rapidly increasing. They can be used for many purposes in everyday life, medicine, industry, especially for disinfection of air, water, and surfaces. The most efficient for this purpose is the UV radiation within the so-called germicidal range. The mercury-vapor low and medium pressure lamps are most widely used. However, nowadays a tendency has been promoted to withdraw mercury appliances not only from household usage, but from industry. This leads to a necessity of the development of mercury-free UV light sources such as excimer lamps and UV light-emitting diodes (UV-LEDs). Recently a new kind of lamps, so called cathodoluminescent UV light sources (especially with field emission cathodes), has been developed.

Using the methods of quasi-classical kinetic theory we analyze in detail nonlinear properties of the spectrum of the complex dielectric permittivity (CDP) in hydrogen bonded crystals (HBCs) in a wide range of temperatures (1-1500 K) and polarizing field intensities (100 kV/m-1000 MV/m). We have constructed the transcendent equation for the numerical calculation of the critical temperature, determined the zones (areas) of diffusion and Maxwell relaxation during the polarization in dielectrics. Limiting expressions for the efficiency spectra far from the critical temperature are investigated. The quantum nature of low-temperature (70-100 К) maxima and the classical nature of high-temperature (100-450 К) maxima of dielectric losses in HBCs are justified.

The paper deals with the problem of light propagation near the gravitating spherically symmetric bodies on the basis of the optical-mechanical analogy and the linear connection between the momentum and the energy of quantum within the metric approach to optical phenomena. This approach implies an effective description of the gravitational field by means of some optically inhomogeneous isotropic medium. From the solutions of eikonal equation and the geodesic lines equations, that lead to the same result in the case of the Schwarzschild metric, the relationship between the characteristics of massive astrophysical objects and the energy of quant in their gravitational field is defined.

The dynamics and features of behavior of liquid crystals in variable magnetic fields of different types (pulsating, oscillating, rotating, conical) are investigated. The efficiency of conical fields for the experimental study of liquid crystals is shown.

A technique is developed and the optical properties of cells of twist-LC composites, which are relevant for the element base of means for receiving, displaying and processing information, are modeled. A calculation method is proposed and a theoretical and computer model of the dependence of the transmission intensity on the orientation parameters of the twist-LC composite cell is performed.

Analytical properties of the high-speed overshoot effect in a shock-compressed binary gas mixture are investigated. The sufficient conditions for realization of this effect by variable approximate parameters in bimodal distributions for gas mixtures are obtained.

Circular dichroism (CD) is an important parameter, characterizing optically active medium. The devices for CD measurements presented on today market measures CD in wide spectral range. The high-precision standard optics, electronics and optomechanics are used in these devices, and data processing requires the application of a complex mathematical apparatus. These devices are quite expensive, have large dimensions, require specially trained staff, and measurement duration is tens of minutes. In this work we present a device for CD measurement on only one wavelength, the key element of which is polarization diffractive waveplate, the optical element of new generation. Device has a number of advantages: easy to use, compact, working in real time, and low cost. These advantages make it ideal for educational programs.

We present the results of dielectric measurements for toluene solutions of cooper (II) carboxylates (valerate, isovalerate, undecylate, myristate, stearate, benegate). We have measured for the first time the electric capacity Cp at various concentrations of these carboxylates in toluene in the solution temperature range.

The structure of granular silver films at the interface of liquid crystal (LC) cells and their influence on LC molecule orientation and ionic contamination are examined. Granular silver films were deposited on a glass substrate covered with an ITO electrode and a-C:H thin films. The morphology structure of the silver films was changed after their annealing at 200 °C. The silver granules became spheroidal with an average diameter of -30 nm and the channel area between them increased. The change in the structure of the Ag films led to an increase in the phase retardation and a decrease in the pretilt angle of the LC director from 51° to 7°. The density of ionic impurities in the LC cell with the annealed silver film was three times more than in the LC cell with the unannealed film. The impact of the alignment of the LC molecules at the surface of the granular silver films on the intensity of the plasmonic peak and its red shift in the absorption spectra is shown.

We consider the experience of teaching probability cycle, including the courses “Probability Theory”, “Mathematical Statistics” and “Theory of Stochastic Processes”, to students of technical universities with the use of interactive computer systems [or mathematical packages (MPs)]. The goals and objectives of courses within engineering education are described. Methodical problems of teaching probabilistic disciplines, the basic ideas of their resolution, methods and techniques of teaching are considered, as well as the role of using information technologies, methodological aspects of their use in the solution of specific applied tasks.

The paper summarizes the experience of teaching the discipline “Physical Electronics” to students in the field of training “Pedagogical Education”, the profile of “Physics and Informatics”. The place of discipline within pedagogical education is shown. The importance in the formation of students’ abilities to use natural-science and mathematical knowledge for orientation in the modern information space is indicated. Methods of organization of classroom and independent work of students, as well as criteria for evaluating results within the rating-rating system are presented.