Participants of the surface acoustic waves scattering excited by means of optical-acoustic method on the crack which has trapezium form is investigated. It is shown that the form and amplitude of the scattered impulse of the surface acoustical wave is depended on the crack width and its locality relative to the ultrasonic source and receiver. Experimental investigation of the influence of the impulse-laser radia-tor on the form and amplitude of the ultrasonic signal excited under traveling laser spot of the rectangular form over the fatigues crack of micron dimensions has show good quality accordance with conducted theoretical investigations.

Keywords: surface acoustic wave, ultrasonic scattering, ultrasonic impulse, surface crack.

A.R. Baev – Institute of Applied Physics of NAS Belarus, Minsk, Belarus

V.G. Gudelev – B.I. Stepanov Institute of Physics of NAS Belarus, Minsk, Belarus

G.V. Kulak – I.P. Shamyakin Mozyr State Pedagogical University, Mozyr, Belarus

A.I. Mitskovets – B.I. Stepanov Institute of Physics of NAS Belarus, Minsk, Belarus

A.G. Matveeva – I.P. Shamyakin Mozyr State Pedagogical University, Mozyr, Belarus

P.I. Ropot – B.I. Stepanov Institute of Physics of NAS Belarus, Minsk, Belarus

Исследовано влияние рентгеновского излучения на электролитическое осаждение композиционных покрытий на основе никеля с наночастицами SiO₂ (7–15 нм) на низкоуглеродистую сталь. Обнаружены зависимости скорости осаждения композиционных покрытий от режимов электролиза и концентрации наночастиц SiO₂ в электролите. На основании экспериментальных данных разработана статистическая модель электроосаждения композиционных покрытий в поле рентгеновского излучения. В соответствии с методом полного факторного эксперимента рассмотрено влияние вариаций плотности катодного тока осаждения, температуры, концентрации наночастиц SiO₂ в электролите и рентгеновского излучения на выход по току на двух уровнях.

Keywords: electrodeposition, X-rays irradiation, the current efficiency, regression equations, the criteria.

A.V. Belko – Y. Kupala Grodno State University, Grodno, Belarus

N.G. Valko – Y. Kupala Grodno State University, Grodno, Belarus

The dependence of the phase composition and mechanical properties of carbon layers deposited on titanium nano-interlayer on their thickness has been determined. It is found that the catalytic effect of the substrate is most pronounced in the carbon layer with a thickness of less than 90 nm. In thicker layers the character of size effect on the structure and phase composition is similar to that of the carbon coatings without interlayer. It is shown that the size dependence of optical properties manifested in improving the transparency and changing the band gap with increasing the thickness of carbon layer is associated with the occurrence of diffusion process at the interphase.

Keywords: diamond-like carbon, bilayer coating, structure, morphology, hardness, internal stress, optical properties.

Zhou Bing – Nanjing University of Science and Technology, Nanjing, China

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

D.G. Piliptsou – Department of Physics, F. Skorina Gomel State University, Gomel, Belarus

A.S. Rudenkov – Department of Physics, F. Skorina Gomel State University, Gomel, Belarus

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

Jiang Xiaohong – Nanjing University of Science and Technology, Nanjing, China

– Nanjing University of Science and Technology, Nanjing, China

In₂S₃ thin films of various thicknesses were deposited onto glass substrates by thermal evaporation technique. Thicknesses of In₂S₃ films were defined by controlling the deposition parameters and were 1200 nm, 470 nm and 50 nm. All prepared thin films were annealed at 400^oC for 60 min. The structural properties and morphology have been studied by X-ray diffraction, Raman spectroscopy and Atomic force microscopy. X-ray diffraction results of In₂S₃ thin films with thicknesses of 1200 nm and 470 nm demonstrated peaks revealed in tetragonal structure. Raman spectroscopy shows that the intensity of peaks is affected by the film thickness. The average roughness (Ra) and the root mean square roughness (R_RMS) increases with thickness. This is associated with the increase of grain size in the In₂S₃ films.

Keywords: In₂S₃ thin films, thermal evaporation, structural and morphological properties, grain size.

H. Izadneshan – Islamic Azad University of Marvdasht, Marvdasht, Iran; Scientific-Practical Mate-rials Research Centre of the National Academy of Sciences of Belarus, Minsk, Belarus

Valery F. Gremenok – Head of Laboratory of Solid State Physics State Scientific and Production Association «Scientific-Practical Materials Research Centre of the National Academy of Sciences of Belarus», Minsk, Belarus

In this paper, crystalline microstructure, chemical composition and morphology of Pb_1-xSn_xTe thin films with the composition range of prepared by the “hot wall” method on glass substrates were investigated. The X-ray diffraction studies showed a poly-crystalline single phase cubic crystalline structure with the dependence of the lattice constant on composition x with a linear behavior described by the Vegard’s law. The energy dispersive analysis showed that the obtained films are homogeneous and the compositions of the films are reproducible. Scanning electron microscopy revealed the thin films microstructure consisted of densely packed crystals with dimensions of 0,3–4,0 mm and crystallite growth direction is perpendicular to substrate plane.

Keywords: lead tin telluride, “hot wall” method, polycrystalline films, crystalline structure, lattice parameter, chemical composition.

Seidi Hassan – Islamic Azad University of Takestan, Takestan, Iran; Scientific-Practical Materials Research Centre of the National Academy of Sciences of Belarus, Minsk, Belarus

Valery F. Gremenok – Head of Laboratory of Solid State Physics State Scientific and Production Association «Scientific-Practical Materials Research Centre of the National Academy of Sciences of Belarus», Minsk, Belarus

V.A. Ivanov – Scientific-Practical Materials Research Centre of the National Academy of Sciences of Belarus, Minsk, Belarus

In the paper Cauchy problems for a homogeneous and nonhomogeneous linear differential equations with generalized coefficients in algebra mnemofunctions are investigated. Associated Cauchy functions and associated Wronskians are introduced and studied. Expressions for the Cauchy functions and for the fundamental matrices are found by the fundamental system of solutions. Representations as-sociated solutions of the Cauchy problem are given by means of Cauchy functions.

Keywords: linear differential equation of the second order, algebra mnemofunctions, associated solutions, associated fundamental matrices, fundamental systems of solutions, associated Cauchy functions, associated Wronskians.

T.S. Autushka – Belarusian State University, Minsk, Belarus

In the paper we consider the system where are the continued functions; a and b are the constants. For this system we established conditions under which this system has a linear Mironenko reflecting function and therefore a linear mapping in period The obtained conditions allow us point out the initial data of the solutions of the two-point boundary task and therefore, the initial data of the -periodic solutions of the system in the case when its coefficients are periodic continued functions.

Keywords: reflective function Mironenko, in-period transformation, boundary problem, periodic solutions.

E.V. Varenikova – I.G. Petrovski Briansk State University, Novozybkov, Russia

The known and new results on identities of n-ary group are staded in this paper.

Keywords: n-ary group, identity, idempotent.

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

The L.A. Shemetkov’s theorem on the complementability of -residual of finite soluble group is developed for a local formation .

Keywords: finite group, formation, residual, complement, local formation.

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

In this paper, we characterize the nilpotency and supersolvability of a finite group G by assuming some subgroups of prime power order are either semi cover-avoiding or S-quasinormally embeded in G. Some known results are generalized.

Keywords: semi cover-avoiding subgroup; S-quasinormally embeded subgroup; p-nilpotent group; supersolvable group.

Abid Mahboob – University of Science and Technology of China, Hefei, China

Lijun Huo – University of Science and Technology of China, Hefei, China

Jinghua Lu – Southwest University of Science and Technology, Mianyang, China

The object of study is a nonlinear fifth-order differential equation with a rational right-hand side. The goal of the study is to find the conditions for the existence of the first integrals of the equation and study the analytical properties of the obtained first integrals. In main part of the nonlinear differential fifth-order equation obtained the equations for residues and the resonance equation. Depending on the roots of the resonance equation, the necessary conditions of existence of the first integrals of nonlinear differential equation of the fifth order with a rational right-hand side is found. For these differential equation corresponding first integrals considered in this paper special cases are given. The obtained results can be used in the analytical theory of the ordinary differential equations.

Keywords: differential equation of the fifth order, first integral, resonances, equation for residues, characteristic equation.

G.T. Mozhdzher – Y. Kupala Grodno State University, Grodno, Belarus

In the main part we consider a system describing the motion of four bodies under the action of gravity. Using the set of elementary algebraic transformations, a simplified system consisting of nonlinear differential equations, each of which has the second order was developed. 21 autonomous nonlinear differential equation of the first order with respect to one of the components of the system, whose general solution has the Painleve property were obtained. Necessary and sufficient conditions for Painleve properties in the studied system were established.

Keywords: movement of four bodies, constant interaction Painleve property, meromorphic solution.

A.T. Sazonava – Y. Kupala Grodno State University, Grodno, Belarus

The paper deals with asymptotic properties of diagonal quadratic Hermite – Pad’e approximants of type I for exponential system with arbitrary real The proved theorems complement the known results of P. Borwein, F. Wielonsky.

Keywords: Hermite – Pad’e approximants of type I, quadratic and Hermite – Pad’e approximants, asymptotic equality, saddle-point method.

A.P. Starovoitov – Department of Mathematics, F. Skorina Gomel State University, Gomel, Belarus

In this paper Mironenko method to study the periodic solutions of the rational differential equations is used. The obtained results to de-rive the sufficient conditions for a critical point of some polynomial differential systems to be a center are applied.

Keywords: reflecting function; center conditions; periodic solution.

Zhengxin Zhou – Yangzhou University, Yangzhou, China

Open queueing network with different types of customers and multiregime service strategies is investigated. Every node can operate in several regimes answering different degrees of their working capacity. The condition of the node is described abstractly and can not coincide with number of the customers in it. The conditions of multiplicativity and an analytical view of stationary distribution of the network states probabilities are found.

Keywords: queueing network, different types of customers, multiregime service, abstract description, stationary distribution.

O.V. Yakubovich – Department of Mathematics, F. Skorina Gomel State University, Gomel, Belarus

Y.E. Dudovskaya – Department of Mathematics, F. Skorina Gomel State University, Gomel, Belarus

Luminescence of polyester fibers colored by different luminophores using craising mechanism was investigated. Arrangement for interrupted modification of fibers by luminescent colorants was designed. Optimal thickness of fiber bundle (90-100 fibers) subjected to modification was estimated. Effective fiber coloration takes place when the drawing out degree is between 2 and 3. It was shown that fibers modified by Oksasin and Rodamin are characterized by the highest intensity of luminescence in UV radiation.

Keywords: polyester fibers, craising, modification, luminescent colorants, luminescence spectrum.

V.A. Goldade – F. Skorina Gomel State University, Gomel, Belarus; V.A. Belyi Metal-Polymer Institute of National Academy of Sciences of Belarus, Gomel, Belarus

N.V. Kuzmenkova – Belarusian Trade and Economics University of Consumer Cooperatives, Gomel, Belarus

V.V. Kravchenko – F. Skorina Gomel State University, Gomel, Belarus

V.E. Sytsko – Belarusian Trade and Economics University of Consumer Cooperatives, Gomel, Belarus

The article deals with the cellular automata rules classification in the context of generating pseudo-random sequence of the maximum possible length. The analysis of the possible sets of rules was successful and wittingly failed configurations were identified. The tech-nique for selecting a specific set of rules for different situations has been proposed.

Keywords: maximum length pseudorandom sequence, pseudorandom test sequence, cellular automata, cyclic boundary conditions.

I.A. Murashko – P.O. Sukhoi Gomel State Technical University, Gomel, Belarus

D.E. Hrabrov – P.O. Sukhoi Gomel State Technical University, Gomel, Belarus