The approximate analytical method for solving the Schrodinger equation with the Gaussian potential is proposed. The essence of the method is to represent the wave function as a superposition of wave functions of exact solving problem Also, in order to control the accuracy, the problem was solved numerically in the momentum representation.

Keywords: Schrodinger equation, integral equation, wave function, Gaussian potential, harmonic oscillator.

Yu.A. Grishechkin – Faculty of Physics and Information Technology, F. Skorina Gomel State University

A.V. Paulenka – Faculty of Physics and Information Technology, F. Skorina Gomel State University

V.N. Kapshai – Faculty of Physics and Information Technology, F. Skorina Gomel State University

The influence of additives of cholesterol compounds on the optical properties of liquid lubricants based on mineral and synthetic oils was studied. It is shown that the introduction of cholesterol esters in vaseline oil and polyethylsiloxane liquid leads to a change in their optical properties, which is expressed in the direct dependence of the rotation angle of the plane of polarization of light on the content of cholesterol esters in liquid lubricants. The effect on this dependence of the length of the radical of fatty acid in the ether of cholesterol was established.

Keywords: cholesterol esters, optical properties of solutions, radical of fatty acid in cholesterol ester, liquid lubricating media.

S.F. Ermakov – Faculty of Physics and Information Technology, F. Skorina Gomel State University

E.B. Shershnev – Faculty of Physics and Information Technology, F. Skorina Gomel State University

Y.V. Nikitjuk – Faculty of Physics and Information Technology, F. Skorina Gomel State University

S.I. Sokolov – Faculty of Physics and Information Technology, F. Skorina Gomel State University

The activity of cavitation in water solutions of carbon dioxide was investigated. In a number of regimes erosion rate was estimated. It is shown that in oversaturated solution of carbon dioxide the activity of cavitation is close to zero. In process of degassing the activity of cavitation grows and tends to the activity level in the distilled water. It is drawn that at the first stage of degassing intensive shock waves are not generated by bubbles pulsation and cavitation in this mode cannot make the intensive destroying impact on firm surfaces and on biological fabric. At the second stage concentration of intensively collapsing bubbles significantly increases.

Keywords: cavitation, water solutions of carbon dioxide, cavitation activity, bubbles collapses.

A.V. Kotukhov – Belarusian State University of Informatics and Radioelectronics

N.A. Zharko – Belarusian State University of Informatics and Radioelectronics

V.S. Minchuk – Belarusian State University of Informatics and Radioelectronics

N.V. Dezhkunov – Belarusian State University of Informatics and Radioelectronics

A method for obtaining phospholipid concentrate from vegetable oils and a method for determining the size characteristics of the dis-persed phase from phospholipid structures are proposed. It was found with light scattering and atomic force microscopy that the dispersed phase of the phospholipid suspension was formed by structures with linear particle sizes not exceeding 100 nm. The method of obtaining phospholipids in the nanosuspension form can be the basis for new technologies of phospho-lipid concentrates as sources of emulsifiers for the food industry, technological substance, as well as processing of oilseeds.

Keywords: spectrophotometry, atomic force microscopy, phospholipids, nanostructures, technological substances.

J.S. Mikhalovsky – Belarus State Economic University, Minsk

M.P. Matveyko – Belarus State Economic University, Minsk

G.B. Melnikova – A.V. Luikov Heat and Mass Transfer Institute of NAS of Belarus, Minsk

E.N. Volnyanko – V.A. Belyi Metal-Polymer Research Institute of NAS of Belarus, Gomel

V.N. Babodey – Scientific and Practical Centre for Foodstuffs of NAS of Belarus, Minsk

A.V. Pchelnikova – Scientific and Practical Centre for Foodstuffs of NAS of Belarus, Minsk

In the framework of the thermodynamic approach to the study of macrosystems using the Cardano method, three two-parameter equations of state are considered. Basing on the given forms of the form of the Redlich–Kwong, Berthelot and Van der Waals equations of state, the explicit forms of their functional representations of the form are determined.

Keywords: semi-empirical equation of state, cubicity by volume, Cardano method, reduced variables, representation of the form .

A.S. Nevmerzhitskaya – Faculty of Physics and Information Technology, F. Skorina Gomel State University

G.Yu. Tyumenkov – Faculty of Physics and Information Technology, F. Skorina Gomel State University

In the homogeneous field approximation analytical solutions of the Maxwell – Bloch equations for the field emitted by a thin layer of a medium with a relatively high concentration of active centers are obtained. The solutions describe pulses of superradiance with phase modulation due to resonance nonlinearity. A model calculation was carried out for the parameters of media based on semiconductor quantum-dimensional structures. Taking into account the finiteness of the dipole particles phase relaxation time, dipole-dipole interaction, and absorption in quasi-resonance transitions, new modification of the law of Bloch vector conservation is formulated.

Keywords: dense resonant medium, thin optical films, dipole-dipole interaction, quasi-resonance polarization.

Yu.V. Yurevich – Mogilev State University of Food Technologies

Let G be a finite group. Then G is called a Schmidt group if G is not nilpotent but every proper subgroup of G is nilpotent. A subgroup M of G is called modular in G if M is a modular element (in the sense of Kurosh) of the lattice L(G) of all subgroups of G, that is, (i) for all such that and (ii) for all such that In this paper, we prove that if every Schmidt subgroup A of G with is modular in G, then G is soluble, and if every Schmidt subgroup of G is modular in G, then the derived subgroup G' is nilpotent.

Keywords: finite group, modular subgroup, Schmidt group, derived subgroup, nilpotent group.

I.V. Bliznets – Faculty of Mathematics and Programming Technologies, F. Skorina Gomel State University

V.M. Selkin – Faculty of Mathematics and Programming Technologies, F. Skorina Gomel State University

In this paper the intersections of maximal subgroups close to -abnormal, whose indices are not divisible by some prime numbers are investigated.

Keywords: finite group, abnormal subgroup, -residual.

R.V. Borodich – Faculty of Mathematics and Programming Technologies, F. Skorina Gomel State University

Let be a nonempty formation groups. A subgroup H of a group G we call absolutely K--subnormal (absolutely -subnormal) in G if any subgroup containing H is K--subnormal (respectively -subnormal) subgroup of G. In this paper, the question of whether a finite group belongs to a saturated formation in which all Sylow subgroups are absolutely K--subnormal is investigated.

Keywords: finite group, Sylow subgroup, hereditary saturated formation, K--subnormal subgroup, absolutely K--subnormal subgroup.

A.F. Vasil'ev – Faculty of Mathematics and Programming Technologies, F. Skorina Gomel State University

A.G. Melchenko – Faculty of Mathematics and Programming Technologies, F. Skorina Gomel State University

The structure of a group G containing a maximal subgroup M such that all maximal subgroups of M are -subnormal in G in case is the formation of all nilpotent groups or a subgroup-closed saturated lattice formation is described.

Keywords: finite groups, subnormal subgroups, -subnormal subgroups, nilpotent groups, lattice formation.

M.N. Konovalova – Russian Presidential Academy of National Economy and Public Administration

I.L. Sokhor – A.S. Pushkin Brest State University

Extremal problems for the derivatives of Blaschke products in the Lebesgue space on a straight line are solved. The supremum and in-fimum of the seminorms from the derivatives of Blaschke products are obtained. Upper and lower ine-qualities for the higher derivatives of Blaschke products in the Lebesgue space were obtained by the author earlier.

Keywords: rational functions, Blaschke products, Bernstein type inequality.

Ò.S. Ìardvilko – Belarusian State University, Minsk

The flexural movement of a gear tooth made of fibrous material with anisotropic properties, which is under the action of a concentrated force at various characteristic points on the tooth surface, is investigated. An algorithm for calculating the coefficient of flexural deformation for three models of a gear tooth of composites has been developed.

Keywords: deformation, composite, evolvent, gear wheel.

V.V. Mozharovsky – Faculty of Mathematics and Programming Technologies, F. Skorina Gomel State University

M.V. Mîskaleva – Faculty of Mathematics and Programming Technologies, F. Skorina Gomel State University

D.S. Kuzmenkov – Faculty of Mathematics and Programming Technologies, F. Skorina Gomel State University

Throughout this paper, all groups are finite and G is a group. Let be some partition of the set of all primes Then G has a chief factor H/K such that The group G is said to be: -primary if G is -group for some i; -soluble if every chief factor of G is -primary. The symbol denotes the product of all normal -soluble subgroups of G. The chief factor H/K of G is said to be: -central (in G) if is -primary; a -factor if H/K is a -group. We say that G is: -nilpotent if every chief factor of G is -central; generalized -nilpotent if every chief -factor of G is -central. The symbol denotes the product of all normal generalized -nilpotent subgroups of G. We call any function f of the form {formations of groups}, where a generalized formation -function and we put for all If for some generalized formation -function f we have then we say that the class is Baer--local and f is a generalized -local definition of . In this paper, we describe basic properties, examples, and some applications of Baer--local formations.

Keywords: finite group, generalized formation -function, Baer--local formation, generalized -nilpotent group, Gaschutz product.

V.G. Safonov – Belarusian State University, Minsk

I.N. Safonova – Belarusian State University, Minsk

A.N. Skiba – Faculty of Mathematics and Programming Technologies, F. Skorina Gomel State University

Let and be the set of all positive integers and all primes, respectively. A subgroup H of G is called -subnormal in G (H -sn G) if there is a chain such that for every i=1,…,n, where We obtained finite simple non-abelian groups G with 1 -sn G.

Keywords: finite group, simple non-abelian group, -subnormal subgroup.

V.N. Tyutyanov – International University MITSO, Gomel

A.A. Trofimuk – Faculty of Mathematics and Programming Technologies, F. Skorina Gomel State University

Various modes of information hiding are proposed. Their influence on the main characteristics of the steganographic communication channel using the network steganography method based on HTTP as an example is analyzed. The method of spatial distribution of data among container elements makes it possible to increase the security of a secret message by means of steganography.

Keywords: steganography, computer networks.

Y.A. Drybin – Belarusian State University, Minsk

V.S. Sadov – Belarusian State University, Minsk

O.M. Demidenko – Faculty of Mathematics and Programming Technologies, F. Skorina Gomel State University

A new approach to assessing the probabilistic characteristics of the reliability (safety) of the production process, including elements of potential danger, based on the use of probabilistic-algebraic simulating is considered.

Keywords: probabilistic-algebraic simulation, reliability, technological processes of production, stochastic algebras, graphs.

Y.V. Zherdetsky – Faculty of Mathematics and Programming Technologies, F. Skorina Gomel State University

A scheme of the evolutionary design of a model of a system of a regression type is presented. It consistently reflects the bifurcation points in the following ways: setting goal, a selective description of the conceptual representation of factors, forming factor signs, representation of a selective descriptions, formation of class-prototypes, combining class-prototypes into chain, construction of final classification of their coverage, and developing a balancing of the process of building a regression model.

Keywords: evolutionary modeling, classification, regression analysis, active system.

N.B. Osipenko – Faculty of Mathematics and Programming Technologies, F. Skorina Gomel State University

A.N. Osipenko – Faculty of Mathematics and Programming Technologies, F. Skorina Gomel State University

A study of the spatial movement of the musculoskeletal system of the athlete using a model of a biomechanical system with 25 links is presented. It is shown that in the analysis of sports exercises the problem is divided into a number of stages: full-scale experiment, automated processing of video results, the development of mathematical models using the algebra of quaternions and computational experiment on a computer. To obtain the initial data of the computational experiment, it is proposed to use the technology of “computer vision” based on the software complex iPi Soft. Thus the mathematical models are divided into two groups: those describing the movement of the pole of the biomechanical system, and the model based on quaternions for the description of the mechanics of the turns of the links in the joints of the musculoskeletal system of the athlete.

Keywords: motion analysis, motion capture, quaternions, computer vision, spatial motion, pole.

M.A. Kirkor – Mogilev State University of Food Technologies

A.E. Pokatilov – Mogilev State University of Food Technologies

A.M. Gal'mak – Mogilev State University of Food Technologies

Methods of landscape fire detection are examined and among them, special attention is devoted to monitoring with the help of rotary video camera placed on towers. A system of video-monitoring is suggested which secures free 360 degrees rotation of the IP-camera in horizontal plane and allows controlling the state of the forestland without “dead space”. The system allows detecting ignition with high efficiency, exercising radiation monitoring, and fixing the changes of radiation background parameters in case of forest fire beginnings.

Keywords: forest fire, radiation background, rotating video-camera, monitoring.

A.V. Kiselyov – F. Sñorina Gomel State University; “Perfect systems” Ltd. Co., Gomel

V.A. Goldade – F. Sñorina Gomel State University; V.A. Belyi Metal-Polymer Research Institute of NAS of Belarus

A method for producing foam glass materials based on alkali metal silicates and secondary mineral raw materials: glass wastes of domestic and industrial origin is presented. The optimal compositions and modes of heat treatment of foam glass are determined. The structural and thermophysical characteristics of the obtained materials are investigated.

Keywords: foam glass, cullet, foaming agent, density, water absorption, heat conductivity.

M.I. Moskvichyov – Faculty of Physics and Information Technology, F. Skorina Gomel State University

V.E. Gaishun – Faculty of Physics and Information Technology, F. Skorina Gomel State University

V.V. Sidsky – Faculty of Physics and Information Technology, F. Skorina Gomel State University

Ya.A. Kosenok – Faculty of Physics and Information Technology, F. Skorina Gomel State University

V.V. Vaskevich – Faculty of Physics and Information Technology, F. Skorina Gomel State University

A.S. Rusykin – Faculty of Physics and Information Technology, F. Skorina Gomel State University

P.S. Yanochkin – Faculty of Physics and Information Technology, F. Skorina Gomel State University