
PROBLEMS OF PHYSICS, MATHEMATICS AND TECHNICS N3 (32) 2017
PHYSICS
Avlasevich N.T., Lyalikov A.M. Visualization of the defects of a separate component of a composite diffractive optical element
The possibility of the visualization of the defects of a separate component of the thin composite diffractive optical element has been demonstrated. This element represents a thin substrate composition and a pair of combined elementary gratings. Possible variants of the defects visualization as the substrate and of the separate elementary gratings of the diffraction optical element have been considered. Interference methods well developed in holographic interferometry of phase objects have been used. Experimental results have been presented.
Keywords: diffractive optical element, diffraction grating, light wave, visualization of the defect, interference pattern.
N.T. Avlasevich – Y. Kupala Grodno State University
A.M. Lyalikov – Y. Kupala Grodno State University
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Girgel S.S. Power properties of vector vortex beams of Laplace – Gauss
The expressions for vectors of the field, density of energy and density of energy flows are received for vector vortex beams of Laplace – Gauss. Analytically spatial structure of longitudinal and track densities of energy flows is investigated. The executed graphic modeling of crossflows of energy supplements analytical conclusions.
Keywords: vector beams, Laplace – Gauss beams, vortex beams, power properties.
S.S. Girgel – Department of Physics, F. Skorina Gomel State University
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Kisel V.V., Ovsiyuk E.M., Voynova Y.A., Red’kov V.M. Quantum mechanics for a vector particle with quadrupole moment in the external uniform magnetic field
On the base of the matrix 10dimensional formalism, behavior of a vector particle with a quadrupole moment is studied in presence of external uniform magnetic field. Three series of the energy levels related to bound states of the particle are found. To assign them physical sense for all values of the main quantum number n = 0,1,2,... one must impose special restrictions on quadrupole moment – they are formulated explicitly. Also, the problem of a neutral vector particle with quadrupole moment in presence of magnetic field is studied. At this, solutions of three types are constructed in terms of Bessel functions, in each case the influence of the quadrupole moment consists in presence of a scale factor in the argument of the functions, which depends on the quadrupole moment parameter and magnitude of the uniform magnetic field.
Keywords: vector particle, quadrupole moment, magnetic field, Duffin – Kemmer formalism, separation of the variables, exact solutions.
V.V. Kisel – Belarusian State University of Informatics and Radioelectronics, Minsk
E.M. Ovsiyuk – I.P. Shamyakin Mosyr State Pedagogical University
Y.A. Voynova – Kochishchansky secondary school
V.M. Red’kov – B.I. Stepanov Institute of Physics National Academy of Sciences of Belarus, Minsk
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Semchenko A.V., Kovalenko D.L., Sidsky V.V., Tyulenkova O.I., Tyulenkova N.I., Solodukha V.A., Pyatlitski A.N., Kovalchuk N.S. ZnObased nanorods synthesised by solgel method
The liquidphase method for obtaining ZnO nanostructures is presented. To form nanorods of zinc oxide, substrates with the seed coat were used. The influence of synthesis conditions and modifying substances on the morphology of ZnO nanorods was studied.
Keywords: zinc oxide, solgel method, seed layer, hydrothermal synthesis, nanorods.
A.V. Semchenko – Faculty of Physics and Information Technology, F. Skorina Gomel State University
D.L. Kovalenko – 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
O.I. Tyulenkova – Faculty of Physics and Information Technology, F. Skorina Gomel State University
N.I. Tyulenkova – Faculty of Physics and Information Technology, F. Skorina Gomel State University
V.A. Solodukha – JSC “INTEGRAL”, Minsk
A.N. Pyatlitski – JSC “INTEGRAL”, Minsk
N.S. Kovalchuk – JSC “INTEGRAL”, Minsk
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Fedosenko N.N., Rogachev A.V., Agabekov V.E., Piliptsou D.G., Rudenkov A.S. Influence of molecular nitrogen on optical properties of coatings based on refractory oxides
Features of doping influence by nitrogen on optical properties of coatings TiO_{2}, ZrO_{2}, SiO_{2} are defined. Differences of spectral dependences of transmittances and reflection, a degree of polarization of the coatings received under various conditions are established.
Keywords: electron beam evaporation, coatings of oxides, morphology, reflectivity, index of refraction, degree of polarization, nitrogen doping.
N.N. Fedosenko – Faculty of Physics and Information Technology, F. Skorina Gomel State University
A.V. Rogachev – F. Skorina Gomel State University
V.E. Agabekov – Institute of Chemistry of New Materials of the NAS of Belarus
D.G. Piliptsou – Faculty of Physics and Information Technology, F. Skorina Gomel State University
A.S. Rudenkov – Faculty of Physics and Information Technology, F. Skorina Gomel State University
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MATHEMATICS
Belokon L.M. On the intersections of maximal subgroups of finite groups containing formation radicals
Vasil'ev A.F., Vasil'eva T.I., Parfiankou K.L. On finite groups with given triple factorization
Finite groups having three subgroups with pairwise relatively prime indices are studied. In particular, the structure of a group is established with such subgroups that are supersoluble, have a nilpotent commutator subgroup, and so on.
Keywords: finite group, supersoluble group, hereditary saturated formation, subnormal subgroup.
A.F. Vasil'ev – F. Skorina Gomel State University
T.I. Vasil'eva – Faculty of Mathematics and Programming Technologies, F. Skorina Gomel State University
K.L. Parfiankou – Faculty of Mathematics and Programming Technologies, F. Skorina Gomel State University
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Zubei E.V. On finite groups with Schmidt subgroups of rank 4
The structure of Hall subgroups of a finite group is considered. All Schmidt subgroups have rank 4.
Keywords: finite group, group of Schmidt, rank of the group, Hall subgroup.
E.V. Zubei – Faculty of Mathematics and Programming Technologies, F. Skorina Gomel State University
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Kniahina V.N. On the product of a Bgroup and a primary group
A finite nonnilpotent group G is called a Bgroup if every proper subgroup of the quotient group G/Ô(G) is nilpotent. The main properties of Bgroups are established and the group factorized by a primary and a Bgroup is studied. In particular, it is proved that if G=HK is the product of a Bsubgroup H with a primary subgroup K, and if the order of the nonnormal Sylow subgroup of H is not equal to 3 or 7, then G is solvable.
Keywords: finite group, Bgroup, primary group, product of subgroups.
V.N. Kniahina – Faculty of Mathematics and Programming Technologies, F. Skorina Gomel State University
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Monakhov V.S. The nilpotency criterion for the derived subgroup of a finite group
It is proved that the derived subgroup of a finite group is nilpotent if and only if for all primary commutators a and
b of coprime orders.
Keywords: finite group, commutator, derived subgroup, nilpotent subgroup.
V.S. Monakhov – Faculty of Mathematics and Programming Technologies, F. Skorina Gomel State University
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Selkin V.M., Skiba A.N. On permutable subgroups of finite groups
Khadanovich D.A. Finite groups with nÔsubgroups of prime orders
A subgroup H of a group G is called nÔsubgroup in G if there exists a normal subgroup K of G such that G=HK and It has been proved that any formation admits characterization by certain nÔsubgroups of prime orders.
Keywords: finite group, normal subgroup, Sylow subgroup, complement, coradical, nilpotent group, Abelian group.
D.A. Khadanovich – Faculty of Mathematics and Programming Technologies, F. Skorina Gomel State University
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Shamoyan R.F., Maksakov S.P. On some new estimates for a gradient of a function in product domains and related results
Some new estimates related to the gradient and derivative of an analytic or harmonic function in Bergman type spaces of analytic and harmonic functions in selfconnected domains are presented. Some new results related with L^{p}norm estimates of the nth order derivative or with the gradient of an analytic or harmonic function in Bergman type spaces of analytic and harmonic functions or such type multifunctional spaces in the case of simply connected domain in the complex plane are considered. New inequalities of a similar type are also presented, in which not only simple simplyconnected domains, but their Cartesian product, are involved. Proofs of inequalities of a more complex type are derived either directly from simpler inequalities of the same type, or are completely based on some interesting estimates obtained in the course of their proofs. Such inequalities attracted the attention of various authors in recent years. The theorems given in the article can have various interesting applications in the theory of function of both one and several complex variables.
Keywords: gradient, derivative of analytic function, simply connected domains, product of domains, multi functional spaces, Whitney decomposition.
R.F. Shamoyan – Bryansk State University
S.P. Maksakov – Bryansk State University
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INFORMATION SCIENCE
Korotkevich V.A., Korotkevich L.I., LukashovFursikov E.U., Nered I.V. Architecture and functionality of software package «Admission committee of F. Skorina Gomel State University»
The original architecture of the software package «Admission committee of F. Skorina Gomel State University» is considered, which is a set of desktop and web applications using a common database hosted on a group of SQLservers.
Keywords: software package, SQLserver, desktop application, web application, framework, admission committee.
V.A. Korotkevich – Faculty of Mathematics and Programming Technologies, F. Skorina Gomel State University
L.I. Korotkevich – Faculty of Mathematics and Programming Technologies, F. Skorina Gomel State University
E.U. LukashovFursikov – Faculty of Mathematics and Programming Technologies, F. Skorina Gomel State University
I.V. Nered – Faculty of Mathematics and Programming Technologies, F. Skorina Gomel State University
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Taranchuk V.B. Software suite for adaptation of geological models. The concept, solutions, implementation examples
Problems of development, tool filling, the organization of information streams, usages of the integrated program complex of the composer of digital geological and geoecological models are considered. Examples illustrate advantages of an offered process engineering of assemblage of components of the complex by synthesis of program units of computer algebra systems and geographic information systems, possibilities of interactive graphics visualization, comparison of results.
Keywords: digital geological model, scattered set of points, approximating digital field, Computer Algebra System Mathematica, Geographic Information System Surfer, interactive graphics visualization.
V.B. Taranchuk – Belarusian State University, Minsk
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Tsimokhin I.V., Osipenko N.B. Automation of people’s faces recognition by photograph
An algorithm for faces recognition is described. The algorithm has two stages. The aim of the first stage is to detect faces on source images; the aim of the second stage is to create attributes describing detected faces. Those attributes are used to compare faces and decide whether there is the same or different person on different images.
Keywords: face recognition, ViolaJones method, principal component analysis.
I.V. Tsimokhin – Faculty of Mathematics and Programming Technologies, F. Skorina Gomel State University
N.B. Osipenko – Faculty of Mathematics and Programming Technologies, F. Skorina Gomel State University
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