The sol-gel method for the production of coatings based on titanium ethoxide is described. The optimal synthesis conditions and the parameters affect on the properties of the resulting materials are described. Investigations of structural and photocatalytic properties have been made. The effect of the concentration of cerium ions on the surface morphology of formed titanium coatings has been discussed.

Keywords: sol-gel process, film, structural properties, photo catalytic properties.

V.V. Vaskevich – Department of Physics, F. Skorina Gomel State University

D.L. Kovalenko – Department of Physics, F. Skorina Gomel State University

A.V. Semchenko – Department of Physics, F. Skorina Gomel State University

V.V. Sidsky – Department of Physics, F. Skorina Gomel State University

M.A. Kovalevich – Department of Physics, F. Skorina Gomel State University

The new solutions of the parabolic equation featuring the generalized Bessel – Gaussian beams of the continuous order are offered. They are characterized by three free continuous parameters and possess a spiral wave front. Restrictions on these parameters at which the explored fractional beams transfer terminating power are discovered. Graphic simulation of such beams is held.

Keywords: fractional beams, beams of Bessel – Gaussian, square integrability.

S.S. Girgel – Department of Physics, F. Skorina Gomel State University

Water suspensions of nanosized silica dioxide are obtained by dispersing in a liquid medium. The influence of sonication time on the size of the silica particles is investigated. It was shown that ultrasonic treatment with simultaneous mechanical mixing and the introduction of surfactants lead to the formation of larger number of particles with smaller size.

Keywords: ultrasonic dispergation, pyrogenic silica dioxide, nanosized particles, cavitation, hydrodynamic diameter.

Ya.À. Kosenok – Department of Physics, F. Skorina Gomel State University

V.E. Gaishun – Department of Physics, F. Skorina Gomel State University

O.I. Tyulenkova – Department of Physics, F. Skorina Gomel State University

T.A. Savitskaya – Belarusian State University, Minsk

I.M. Kimlenko – Belarusian State University, Minsk

K.A. Shakhno – Belarusian State University, Minsk

The phenomenon of occurrence of photodeflection signal in layer of carbon nanotubes of types zigzag and armchair by irradiation of Bessel light beams (BLB) was investigated. It was found that the rate of energy dissipation TE-mode BLB essentially depends on the radial coordinate , normalized coordinate . BLB taper angle as well as the frequency of the amplitude modulation BLB.

Keywords: photodeflection affect, carbon nanotube, Bessel light beam, energy dissipation rate, amplitude of the photodeflection signal, Bessel function, heat equation.

G.S. Mityurich – Department of Physics, F. Skorina Gomel State University

E.V. Chernenok – Department of Physics, F. Skorina Gomel State University

A.N. Serdyukov – Department of Physics, F. Skorina Gomel State University

The effectiveness of using an electron beam vacuum evaporation method is shown together with the optical thickness monitoring for formation of multilayer coatings based on twelve layers of SiO₂+ZrO₂ with high degree of polarization. The developed design of the polarization coating is based on refractory oxides for the wavelength nm. It can be used to form polarizers operating as reflective and transmissive optical elements as parts of laser systems.

Keywords: polarizer, electron beam evaporation, refractory oxides, multilayer optical coatings.

A.V. Rogachev – Rector of F. Skorina Gomel State University

N.N. Fedosenko – Department of Physics, F. Skorina Gomel State University

D.L. Gorbachev – Department of Physics, F. Skorina Gomel State University

For the first time, an analytical and numerical solution of the inverse problem for the spectrophotometric silicon dioxide layer on a silicon substrate is obtained. Analytical determination of the parameters of the layer and the substrate can be used as the first approximation in numerical calculations of the parameters of the three-layer model. Inhomogeneous structure of the surface and transition layers is in-terpreted by Maxwell-Garnett & Bruggeman model.

Keywords: interference spectrophotometry, transition layer, optical constants, thickness of the layer.

N.I. Staskov – À.A. Kuleshov Mogilev State University

The statistical weight of non-ideal gas is its most important characteristic of the underlying statistical theory of the macrosystem. In this paper the method of calculating the statistical weight of a non-ideal gas based on entropy of the critical state is proposed. Some non-ideal gases corresponding several well-known semiempirical two-parameter equation of state are considered.

Keywords: semi-empirical two-parameter equation of state, non-ideal gas, critical state, entropy, statistical weight.

G.Yu. Tyumenkov – Department of Physics, F. Skorina Gomel State University

Thin-film solar cells with the Cu_xIn_xZn_2-2xSe₂ (CIZS) absorber layer of on glass substrates are created. The given semiconductor material satisfies physical requirements for materials for photo-electric converters, and requirements for depreciation of solar cells production. Preliminary results of researches showed that glass/Mo/Cu_xIn_xZn_2-2xSe₂/CdS/ZnO/Al-Ni thin film solar cells can possess efficiency more than 10%.

Keywords: Cu_xIn_xZn_2-2xSe₂, thin films, solar cells, physical characteristics, efficiency.

V.V. Khoroshko – Belarusian State University of Informatics and Radioelectronics, Minsk

I.N. Tsyrelchuk – Belarusian State University of Informatics and Radioelectronics, Minsk

V.F. Gremenok – Scientific and Practical Materials Research Centre of NAS Belarus, Minsk

A.N. Pyatlitski – JSC «INTEGRAL», Minsk

This paper presents the results of a study of the laser polishing quartz glass obtained by using finite element modeling. In addition, the results of experiments on the laser polishing quartz glass by using CO₂-laser.

Keywords: laser, quartz glass, polishing, simulation.

E.B. Shershnev – Department of Physics, F. Skorina Gomel State University

Yu.V. Nikitjuk – Department of Physics, F. Skorina Gomel State University

A.E. Shershnev – Department of Physics, F. Skorina Gomel State University

S.I. Sokolov – Department of Physics, F. Skorina Gomel State University

Conditions under which for a finite group G, a non-empty radical (radical local) formation and a subgroup m-functor – a set of primes, are investigated. The results include, as a consequence, statements on the intersections of the corresponding maximal subgroups without restrictions on their indexes.

Keywords: radical formations of finite groups, -radicals, intersections of maximal -subgroups, subgroup -abnormally -full m-functor.

L.M. Belokon – Mogilev State University of Food Technologies

A subgroup H of a group G is called F(G)-subnormal if it is subnormal in HF(G). In the paper all closed under taking Schmidt subgroups saturated formations of finite soluble groups such that contains every soluble group G which is the product of its F(G)-subnormal -subgroups were described. It was shown that a group G which contains three supersoluble F(G)-subnormal subgroups of pairwise coprime indexes in G is supersoluble.

Keywords: Fitting subgroup, F(G)-subnormal subgroup, supersoluble group, saturated formation, F(G)-radical formation.

A.F. Vasil’ev – Department of Mathematics, F. Skorina Gomel State University

V.I. Murashka – Department of Mathematics, F. Skorina Gomel State University

The open piecewise continuous queueing network with multimode service and polytypic demands is considered. The quantity of work, which is necessary for switching from one strategy to another, is random variable with arbitrary distribution function. The dispatching rule is DPS. It was proved that stationary distribution is invariant in relation to functional form of distribution of work’s quantities, which are necessary for switching of strategies of devices in units, on condition that first moments of these distributions are fixed.

Keywords: invariance, multimode service, DPS, piecewise continuous queueing network.

A.R. Eryomina – Y. Kupala Grodno State University

For a formation and for a set of primes, the solubly saturation of the formation of all finite groups whose all -subgroups belong to is investigated.

Keywords: finite group, -subgroup, formation, solubly saturated formation, s-critical group.

S.F. Kamornikov – Gomel Branch of International University «MITSO»

Compact and connected Abelian group G with totally ordered dual is considered. It is shown that nontrivial finite rank Hankel operator exists on G if and only if the dual group contains the first positive element. In this case the classical theorems by Kroneker, Hartman, and Peller are generalized to the case of Hankel operators on G.

Keywords: compact Abelian group, Hankel operator, finite rank operator, nuclear operator.

A.R. Mirotin – Department of Mathematics, F. Skorina Gomel State University

R.V. Dyba – Department of Mathematics, F. Skorina Gomel State University

Let be some totally (n-multiply) -saturated formation of finite groups and be totally (n-multiply) -saturated subformations of . Then denotes the semigroup of all totally (n-multiply) -saturated subformations of with multiplication where . It is proved that a soluble totally (n-multiply) -saturated formation generates a commutative semigroup of totally (n-multiply) -saturated subformations if and only if, when it is nilpotent. In particular, the problem 6.26 from [1] is solved for the class of soluble groups.

Keywords: formation of finite groups, totally -saturated formation, n-multiply -saturated formation, semigroup of formations, commutative semigroup of formation.

V.G. Safonov – Belarusian State University, Minsk

I.N. Safonova – Belarusian State University, Minsk

We provide complete characterizations of traces of some new analytic spaces of Herz-type in polydisk, unit ball and tubular domains over symmetric cones and bounded pseudoconvex domains with smooth boundary under additional natural condition on kernel. Our results extend previously known assertions.

Keywords: analytic functions, Herz-type spaces, polydisk, tubular domains, pseudoconvex domains.

R.F. Shamoyan – Bryansk State University, Bryansk

O.A. Zaytseva – Bryansk State University

The effect of different sources of noises in the range of 2.4–5 GHz on the quality of transmission signal by the Wi-Fi access point in the local area network is considered in the article.

Keywords: wireless network Wi-Fi, sources of noises, access point, band, microwave.

V.N. Kulinchenko – Department of Physics, F. Skorina Gomel State University

O.M. Demidenko – Prorector of F. Skorina Gomel State University

A mathematical model of the impact impulse load on the hollow-core slabs, which is an integral part of the design of the frame of the building, is considered. As a result, data on the occurrence of the natural oscillations in the studied construction with the passage of time are obtained.

Keywords: natural oscillation, hollow-core slabs, finite element method.

K.S. Kurochka – P.O. Sukhoi Gomel State Technical University

D.N. Trubenok – P.O. Sukhoi Gomel State Technical University

I.L. Stefanovsky – P.O. Sukhoi Gomel State Technical University