(Vestsi Natsiyanalnai Akademii Navuk Belarusi)
SERIES OF PHYSICAL-MATHEMATICAL SCIENCES
Published by The Institute of Mathematics of NASB, Minsk, Republic of Belarus
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Proceedings of the National Academy of Sciences of Belarus (Vestsi Natsiyanalnai Akademii Navuk Belarusi) SERIES OF PHYSICAL-MATHEMATICAL SCIENCES Published by The Institute of Mathematics of NASB, Minsk, Republic of Belarus |
Summary: The complex Hele--Shaw problem for a doubly connected domain is reduced to the system of the abstract Cauchy--Kovalevskaya problem and the boundary value problem of Riemann--Hilbert--Poincare type. The first one is studied by using the Nirenberg--Nishida theorem. The Schwarz operator for a doubly connected circular domain and a modification of the Schwarz alternative method is applied at the investigation of both problems. Local existence and uniqueness of the classical solution to the system is proved.
Zyl A.N.
Difference schemes of high order accuracy for heat equation in arbitrary area. pp. 10--15
Summary: The difference scheme for solution of heat equation in a two-dimensional cylindrical arbitrary computational domain is developed. This scheme has the second order of local approximation by spatial variables. Such algorithm is constructed on the basis of approximation at a specially chosen noncalculated point. For the method suggested a priori estimate of stability is obtained.
Mukhin V.V.
Invariant measures on topological n-semigroups. pp. 16--21
Summary: The concept of invariant measures on topological n-semigroups is introduced. Several conditions of existence of such measures are established and their classification is given.
Podgornaya V.V.
Semi-normal semigroups and supersolvability of finite groups. pp. 22--25
Summary: It is proved that maximal subgroups with prime index are semi-normal and semi-normal Sylow group for greatest prime number p is normal in a finite group. Other properties of semi-normal subgroups of finite groups are established.
Tishchenko K.I.
On new methods in the approximation problem of real numbers by algebraic numbers having degree less than three. pp. 26--31
Summary: New result in the approximation problem of real numbers by algebraic numbers having degree less than three is obtained.
Yarotskaya L.D.
On the integral transform with the McDonald type kernel. pp. 32--37
Summary: Integral transform which is associated with the McDonald type functions as a kernel is considered. L2-properties, connection with the Hilbert and the Kontorovich--Lebedev transforms are proved. The Parseval equality and inversion theorem are established.
Danilovich L.A., Laptinsky V.N.
On the periodic solutions of linear matrix differential equations. pp. 38--41
Summary: The analytical representation of periodic solution of linear matrix differential equation is given.
Lugovskii S.A.
On the best weighted polynomial approximations of analytic functions. pp. 42--47
Summary: The exact asymptotic estimates of the best polynomial approximations by interpolation operators for classes of special functions have been founded.
Dmitruk N.M.
Optimization of von Neumann model of the expanding economy by optimal control methods. pp. 48--53
Summary: Optimization problem for a classical model of the expanding economy is considered. On the base of the optimal control methods the synthesis of the optimal technological processes on the plane is constructed.
Abu-Halava M.I., Gladyshev M.T.
Two layer open flow. pp. 54--58
Summary: The system which consists of four partial differential equations for the modeling of the piecewise constant stratification is investigated. Dynamics of two layer liquids in the gravity field taking into account a slope of the bottom, hydraulic drag on the bottom and borders of layers is considered. The rigidity of the system, divergent forms, reduction and the group generated by motion equations are studied.
Kravtsov M.K., Kravtsov V.M., Lukshin E.V.
On the number of non-integer vertices of a polytope of the three-axial assignment problem. pp. 59--65
Summary: Non-integer vertices of a polytope of three-axial assignment problem are investigated. In particular, sufficiently exact lower bounds are obtained. Formulae for determination of r-non-integer vertices of the mentioned polytope for some cases are obtained.
Summary: The effect of the vector nature of the electric field on the dynamics of lasers with fast relaxing polarization of the gain medium has been investigated. It is shown that the vector degree of freedom can lead to complex dynamics of non-autonomous lasers of class A and autonomous lasers of class B, including amplitude-polarization chaos. Scenarios leading to the chaotic dynamics are investigated. Stability domains of different regimes in such laser systems are determined.
Burakov V.S., Misakov P.Ya., Raikov S.N.
Intracavity laser spectrometry of simple molecules in gaseous media. pp. 78--83
Summary: By measuring small concentrations of NO2 the advantages of intracavity spectroscopy with pulsed dye lasers have been found out for the analysis of the component composition of a gaseous phase of plasmachemical reactor. The theoretical and experimental comparison of a sensitivity of the intracavity spectrometers with nanosecond and microsecond multimode lasers has been carried out.
Katsev I.L., Zege E.P., Prikhach A.S.
Summary image quality characteristics for observation of an object through a stochastic phase surface. pp. 84--89
Summary: Image quality characteristics while an object is observed through a time dependent random surface are considered. Modulation transfer functions and noise characteristics for a conventional vision system and for a correlative system with image formation using a product of signals reflected by the object and the surface are compared.
Lutsevich A.B., Sheleg A.U., Yarunichev V.P.
Investigation of the electrical conductivity of lead-potassium niobate in the ferroelectric phase transition. pp. 90--94
Summary: Two anomalies on the temperature dependence curve of the electrical conductivity for lead-potassium niobate ceramic are found. The first anomaly is related to the ferroelectric phase transition (PT). The second anomaly is observed at near 280°C and it is also related to PT. The character of the anomaly in the neighborhood of the Curie point is different during heating and cooling. The anomaly of electrical conductivity has the form of an inflection during heating. The anomaly of electrical conductivity has the form of maximum, minimum or constant during cooling which depend on the initial degree of the sample perfection. The character of the s dependence in the range of ferroelectric PT similar to tg d. The anomaly tg d is observed below Tc. The anomaly s is observed above Tc.
Prytkova N.A., Tseluevskii M.S., Ladutko N.F., Ustinovich S.N., Tomilo J.M.
Influence of the silver and silver-added fusions on the superconductivity of BSCOO superconductors. pp. 95--98
Summary: Synthesis of samples are produced. Superconductive properties of BSCOO superconductors which contain silver and silver-added fusions based on Ag PSR-45 and PSR-29 in the quantity x = 0.0; 0.5; 1.0 and 2.0 %. It is shown that samples which contained components in the quantity x = 1.0 % have the best characterictics if compare with samples without these components.
Shepelevich V.G., Grechannikov E.E.
Electrical activity of the In, Ga and Ge in the alloy Bi--Sb. pp. 99--101
Summary: Rapidly solidifying foils of Bi - 15 at. % Sb which alloy by Ga, In and Ge having texture (1012) are subjects of the investigation. Differential thermo-e.m.f. of alloys are considered. It is found that Ga, In and Ge in the alloy Bi -15 at. % Sb behave as acceptor.
Gorlei P.N., Grigorishin A.N., Gatskevich E.I.
Field dependencies of super high frequency noise in tellurium. pp. 102--105
Summary: Analysis of analytical expressions for components of longitudinal electric current fluctuations caused by carriers distribution function fluctuations obtained earlier by authors was carried out for different boundary conditions: at presence and absence of external electric and magnetic fields. It was shown that specific tension of electric field leads to two breaks of current fluctuation density spectral curve and magnetic field leads to non-monotonous frequency dependence of these fluctuations.
Polyakov V.I., Yarmolitskii V.F.
Combined optical memory of keywords for associative memory devices. pp. 106--108
Summary: Design and operation of an optical memory of keywords based on special developed technology and made using electric, optic and holographic elements are discussed.
Sotskii A.B., Sotskaya L.I.
Variational of separation of variables in calculations of anisotropic strip optic waveguides. pp. 109--113
Summary: Calculations of modes guided by anisotropic strip optical waveguides reduced to solving of the self-consistent system of two ordinary differential equations are proposed. The effectiveness of the method is illustrated.
Gaiduk P.I.
Structure changes in arsenic-implanted alloys Si0.5Ge0.5 during ambient of rapid thermal annealing. pp. 114--119
Summary: The evolution of both GeAs precipitates and dislocation loops in arsenic-implanted (180 keV, 8 • 1015 cm -2) epitaxially grown, relaxed Si0.5Ge0.5 alloys have been studied as a function of the temperature-time and ambient of rapid thermal annealing. It is found that the annealing in oxygen-containing ambient considerably enhances the growth of both GeAs precipitates and dislocation loops. A possible influence of point defects on precipitate formation is discussed.
Summary: This article deals with physically justified hydrological model of a flood runoff of the river based on GIS-technologies of processing spatially distributed data for square of a drainage from 10 up to 1000 kì2. On the basis of developed model of creation of a runoff and generalized model of the river network the possibility of definition of dependence of not measured immediately parameters of model from the generalized characteristics of a drainage is shown. The developed model is used in a composition of the automated system of an operative estimation of flood conditions in basin of the Pripiat river.
Belov D.I., Sadychov R.H.
An algorithm for hidden-segment elimination on the plane and its computer graphics applications. pp. 125--130
Summary: New algorithm for hidden-segment elimination on the plane is developed. The algorithm exploits plane-sweep technique and new approach to determination of mutual overlapping of two segments. It is proved that the algorithm runs in O (N log N) time where N is a number of segments on the plane such that intersection of any two segments is possible only in vertex of one of the segments. On the bases of the algorithm a new efficient solutions of the hidden-surface elimination problem and simple polygon filling problem are suggested. Visualization applications of the algorithm for diagnostics is presented. The results of computer simulations are shown.
Summary: Finite groups are considered. A formation F is called superradical if the following two conditions hold. 1) F is a Sn-closed formation; 2) F contains every group G = AB where A and  are F-subnormal F-subgroups of G. New characterization of superradical solvable Sn-closed formations is proposed.
In the Belarusian Physical Society. pp. 136--138
To the memory of the Correspondent Member of the NAS of Belarus Viktor Pavlovich Gribkovski. p. 139
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