Известия Академии наук Беларуси. Сер. физ.-матем. наук, 1996, No.4
/ Издания академии / Научные журналы
Известия Академии наук Беларуси. Сер. физ.-матем. наук, 1996, No.4
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Известия Академии наук Беларуси
СЕРИЯ ФИЗИКО-МАТЕМАТИЧЕСКИХ НАУКИздатель: Беларуская навука, Минск, Республика Беларусь |
Номер 4, 1996
СОДЕРЖАНИЕ
МАТЕМАТИКА
Kovalevskaya E.I.
Effective estimates of the measure of some sets in R2 with given approximation properties. pp. 5--9
Summary: Let F be a surface in R4, F = (x, y, f1(x), f2(y)), where f1(x), f2(y) are three times continuously differentiable functions on some rectangle P and f1(x) > b1 > 0, f2(y) > b2 > 0 when (x, y) Î P. We obtain an upper estimate for the Lebesgue measure of those (x, y) Î P, for which F is l-extremal, l > 4.
Beresnevich V.V.
Effective estimates of the measure of real numbers with given order of approximation by quadratic irrationalities. pp. 10--15
Summary: We obtain an effective estimate of measure of the set B1(Q, e) lying in some interval I and satisfying the following property: a point x belongs to the set if and only if there exists a non-zero polynomial P(x) of the second degree with integer coefficients, H(P) £ Q, such that |P(x)| < e; e is a sufficiently small positive number.
Tishchenko K.I.
Systems of linearly independent polynomials with height gaps and Wirsing's problem. pp. 16--22
Summary: An improvement of E.Wirsing's result is obtained (in the case of algebraic numbers of degree n £ 10).
Milman V.A.
Extension of functions that preserves the modulus of continuity. pp. 23--28
Summary: An extension of a real-valued function f from a subspace of a metric space to the whole space is considered. The extension proposed preserves the modulus of continuity of f.
Zhuk V.A.
On an approach to solving the third boundary problem on a segment with moving boundary. pp. 29--33
Summary: An approach to numerical solution of the 3-rd boundary problem for parabolic equation on a segment with moving boundary is proposed. Difference boundary conditions with the second order of approximation are obtained. Convergence of the difference scheme for linear equations is investigated.
Malyutin V.B.
Evaluation of continual integrals of cylindrical functions on the space of functions taking values in L1. pp. 34--38
Summary: The representation of continual integral on the space of functions taking values in L1in the form of integral of finite multiplicity on commuting and anticommuting variables is obtained.
Prusov I.A.
Some problems of dynamics of viscous incompressible fluid. pp. 39--43
Summary: General formulae for a flat motion of the viscous incompressible fluid for an arbitrary domain and their transformations for domains bounded by a straight line or a circumference are given.
Korzan L.A.
Homogeneous mixed problem of elasticity theory for a strip with cuts that lie on the real axis. pp. 44--49
Summary: This paper gives a solution of the uniform mixed problem of the theory of elasticity for a strip with sections that lie on the real axis. Idea of this solution is that the mixed problem is reduced to boundary Riemann's problem on a hyperelliptical Riemann surface.
Matalytski M.A.
Investigation of queueing networks with many servers systems and different classes of customers. pp. 50--53
Summary: Networks of queues with many service for service of different classes of customers are investigated. Kelly's results are generalized.
Trush N.N., Mirskaya E.I.
On moments convergence rate for spectral density estimates. pp. 54--59
Summary: The moments convergence rate of the second order spectral estimates of stationary time series is investigated. These estimates are based on time averaging modified periodograms.
ФИЗИКА
Bogush A.A.
On the matrices and vector parameters of the quantum Lorentz group. pp. 60--65
Summary: The q-deformed finite Lorentz transformation 4 ´ 4-matrices Lq Î SOq(3.1) ~ SLq(2.C) Ä SL'q(2.C) and the corresponding representation operators acting in the quantum bispinor space are constructed in explicit vector parametrical form. New quantum deformation parameters a(q) = a and a(q-1) = - a are used for the original and the inverse quantum matrices.
Otchik V.S.
On energy levels of nonpolynomial oscillator. pp. 66--70
Summary: Solutions of the Schroedinger equation with the potential r2 + l r2 / (1 + gr2) are obtained in the form of series of hypergeometric and confluent hypergeometric functions. Approximate expressions valid for large g are found for energy levels.
Batishche S.A., Tarkovsky V.V.
Spectral and temporal features of lasing in Al2O3:Ti3+ lasers under flashlamp dye laser pumping. pp. 71--74
Summary: Our investigation shows a distinct spectral dependence of Al2O3 : Ti3+ -- laser efficiency under microsecond flashlamp dye laser pumping. The maximum of the dependence lies at 550 nm and does not coincide with the maximum of the laser crystal absorption spectrum. It is supposed that the phenomenon is connected with generation of Ti4+ ions under powerful laser pumping, which intensively absorb the pump radiation in the blue-green spectral region, decreasing the laser efficiency. Ti4 ions, probably, relax to Ti3 ions with t ~ 3 µs.
Trusova I.A., Polyakov M.E.
An alternative explanation of anomalous degradation of quantum well lasers. pp. 75--77
Summary: An alternative explanation of anomalous degradation of quantum well lasers is proposed. The growth of dark line defects is attributed to the action of residual stresses, as dominating ones, whose values increase with decreasing temperature.
Revinski A.F.
First-principle based calculating the spectral function of electron-phonon interaction. pp. 78--81
Summary: The spectral function of electron-phonon interaction is calculated with the adiabatic approximation, using the first-principle pseudopotential method. The temperature dependence of energy bands is presented.
Sirota N.N.
On thermodynamics of excited states. pp. 82--90
Summary: It is shown that the thermodynamic properties and the phase relations of energetically excited condensed phases of physical-chemical systems find the adequate description in quasistatistical thermodynamics. Influence of energy excitation on change of specific volume, diamagnetic susceptibility, bulk modulus, stability determinant, and diffusion coefficient of energetically excited phases is investigated. Thermodynamics of excited states determines the conditions, under which formation and stability of metastable phase occurs as result of external influence. From the thermodynamic relations of excited states, it follows directly that under conditions of excitation and the thermodynamic supersaturation realization of numerous of practically important processes, such as synthesis of diamonds at low temperatures and pressures is possible.
Yarunichev V.P., Korshunov F.P., Kurilovich N.F.
Influence of g-irradiation on electric properties of Pb4Ag2Nb10O30 and Pb4Rb2Nb10O30 in the structural phase transitions region. pp. 91--93
Summary: Influence of g-irradiation on dielectric properties of Pb4Ag2Nb10O30 compounds in the area of phase transition is investigated. It is shown that under influence of the irradiation the decrease of e, tgd, s and displacement of the Curie point due to forming radiation defects are observed in these compounds.
Shipilo V.B., Starchenko I.M., Anichenko N.G.
X-ray study of interaction in the system Si3N4--TiN after thermoprocessing under high pressure. pp. 94--98
Summary: The interaction in the Si3N4 system at high pressures and temperatures is investigated by the X-ray structure and X-ray spectral microanalysis. A significant influence of the TiN additions on sintering processes of Si3N4 ceramics at high pressure and sharp distinction of these processes from those of sintering at atmospheric pressure are brought out.
Gusakov V.E.
Singularities of distribution of charge states for atoms in high-temperature superconductors. pp. 99--103
Summary: Charge states of all atoms in the cell of RBa2Cu3Ox cuprates (R = Yb, Er, Ho,Y,Gd, Eu, Sm, Nd, Pr; x = 6, 7) have been determined. The analyses of charge states were performed on the base of calculation the electric field gradient (EFG) with the scope of quantum chemical MO LCAO method taking into account d-orbital. It was founded that for superconducting and non-superconducting cuprates the Cu(2) atom is in 3d9 configuration. The charge state of the Cu(1) atom is conformed to the partially filled shell of 3d10 for the superconducting cuprates and completely filled shell of 3d10 for the non-superconducting cuprates. The excess hole in the RBa2Cu3O7 resides on the apical O(4) oxygen atom. Removing oxygen atoms from the O(1) position in the cell of RBa2Cu3Ox (transition from superconducting to the non-superconducting cuprates) leads to the dramatic change in the character of the chemical bonds of the apical oxygen atom -- charge configuration of the O(4) atom from O-1 to O-2. The analysis of the filling character of the O(4) orbital and change state of the Ba atom leads to the conclusion that in RBa2Cu3Ox cuprates there is hybridization between the apical oxygen O(4) and Ba orbital.
Chobot A.N., Mazovko A.V., Kurilovich N.F.
Influence of g-irradiation on magnetoelastic properties of Fe--Ni alloys by rare-earth elements. pp. 104--106
Summary: Temperature dependence of the Young modulus of Fe--Ni alloys with Gd additions is investigated. It is shown that g-radiation with doses up to 2 • 109 R does not influence behaviour of the elastic modulus of the alloys under investigation.
Makovetski G.I., Sokolovski T.D., Yanushkevich K.I.
Calculating energy of phonons and specific heat for crystals. pp. 107--109
Summary: Calculation of the binding energy of ions in NiS crystals are carried out. It enabled us to determine the longitudinal and transverse components of the force parameters of ionic pair interactions, to compute the specific heat of NiS, to evaluate the anharmonic contribution to the heat capacity. Contribution of the magnetic heat capacity to approximation of external zero field is determined.
Glushtsov A.I., Erofeenko V.T.
Numerical study of averaged boundary conditions for thin cylindrical electromagnetic hulls. pp. 110--114
Summary: This paper deals with the problem of shielding of electromagnetic fields by cylindrical thin shells. The exact and averaged boundary conditions are discussed.
ИНФОРМАТИКА
Zverovich I.E.
Classes of multi-intersections graphs. pp. 115--119
Summary: We propose a method for finding induced subgraph characterization of hereditary classes of intersection graphs with a given maximal multiplicity of subsets. As an illustration of the methods we give a corollary with a characterization of line graphs of multigraphs whose edge multiplicities are bounded by a fixed number (a result of V.Tashkinov, 1980).
АННОТАЦИИ ДЕПОНИРОВАННЫХ РАБОТ
Metelski N.N., Tarasevich A.E.
Algorithms for cutting problems based on isothetically convex approximations. p. 120
Barbashina E.E.
A concise formula for the third variation on a packet and necessary optimality conditions. p. 120
Ibragimov V.A., Makhnach V.I., Shved O.L.
Extension of a rigidly-ideally-plastic band with angular cuts in the state of lane stress. p. 121
Romanovskaya N.A.
Computing skew cyclic, cyclic and parametric contractions having the size divisible by 3. p. 121
Krushevsky A.E., Naumovich S.A.
Simulating rotation axis of a tooth in orthopaedic stomatology under action of arbitrary force. pp. 121--122
Minchenko L.I., Sokolchik P.P.
On sensitivity analysis of parametric extremum problems. p. 122
Vyarvilskaya O.N., Savchuk V.P., Savenkov V.A., Yunitski A.E.
A dynamic model of string transportation system. pp. 122--123
Monastyrny P.I., Shan'ko D.V.
On computational schemes of marching algorithm, their computer analysis and calibration. p. 123
Golubeva I.A., Zabello L.E., Svetlov S.V.
Stabilization of linear discrete systems under equality constraints on the control. pp. 123--124
Garasymiv Ya.M.
On optimal control theory for the Goursat--Darboux problem with random parameters. p. 124
Garasymiv Ya.M.
On optimal filtration theory for the Goursat--Darboux problem. p. 124
Datsik V.T., Semenchuk N.P.
A class of systems of nonlinear differential equations being of noninteger order. p. 125
Tunyak U.M.
Scalar-tensor gravitation theory in the Minkowski space. p. 125
Zverovich I.E.
On graphs with restricted threshold dimension. p. 126
In Belarusian Mathematical Society. pp. 127--135
A list of papers published in journal "Proceedings of the Academy of Sciences of Belarus, Physical-Mathematical Series", 1996. pp. 136--139.
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Разработана и поддерживается Николаем Н. Костюковичем. Последнее обновление: 7 ноября 2006 г.
Создана при участии Игнатия И. Корсака
Копирайт © 1996-2006 Национальная академии наук Беларуси
Копирайт © 1996 Издательство "Беларуская навука"
