Proc. of the Natl. Academy of Sciences of Belarus, Ser. Phys.Math. Sci., 2001, No.4
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Proc. of the Natl. Academy of Sciences of Belarus, Ser. Phys.Math. Sci., 2001, No.4

Proceedings of the National Academy of Sciences of Belarus (Vestsi Natsiyanalnai Akademii Navuk Belarusi)
SERIES OF PHYSICALMATHEMATICAL SCIENCESPublished by The Institute of Mathematics of NASB, Minsk, Republic of Belarus 
CONTENTS
MATHEMATICS
Silaeva N. A.
On the analog of the theorem of Schmidt in the 3dimensional padic space. pp. 510
Summary: An extremality of general type curves in Q^{3}_{p} is proved.
Gribovskaya E. E.
Finite soluble groups with indices of maximal subgroups are p, p^{2} or 8. pp. 1114
Summary: Let G be a finite soluble group whose index of every maximal subgroup is either a prime or a prime's square or 8. It is proved that pchief rang r_{p}(G/F(G)) £ 2 for every p > 2 and r_{2}(G/F(G)) £ 3 and G Î N_{2'}N_{2} U. From this result follows that a nilpotent length of a finite soluble group G is not more 4 and its plength is not more 1 for every prime p > 2 and 2length is not more 2.
Pal'chik E. M., Shmidt A. M.
On the finite groups admitting a coprime automorfism. pp. 1518
Summary: The following main result is proved. Let X be a finite solvable group admitting automorhism y of prime order r, (x,r) = 1, B = C_{x}(y). If B a Hall subgroup of X then X = B • F(X).
Benediktovitch I.I.
A free resolution of the Veronese's curve. pp. 1924
Summary: Free resolution of a homogeneous ideal J (the ideal of the Veronese's curve) in a projective space P^{n} is calculated. The Grobner basis technique is used. Cohomologies of a bundle, associated with J, has been calculated.
Egorov A. D., Zherelo A. V.
About some questions of integration with respect to Gaussian mesuares on L_{2}(X, g) space. pp. 2530
Summary: A class of integrals with respect to Gaussian measures on L_{2}(X,g) (where X is a linear topological space, g is Gaussian measure on X) which associates with quasimesures µ on X with characteristic functional of the form c_{µ}(x) = exp {(1)^{p}/(2p)! K_{2p} (x, ...^{(2p)}.., x)} is considered. For special cases of spaces X and measures µ^{^} orthonormal systems in reproducing Hilbert space of measure µ^{^} and approximation formulas for functional integrals with respect to measure µ^{^} are constructed.
Simonov A. Yu.
On optimality conditions for singular solutions of the general vector optimization problem. pp. 3134
Summary: The problem of minimizing a mapping F: X® Y acting from a finitedimensional normed space X into an ordered finitedimensional vector space (Y, £) is considered. Under the assumption that the codimension of the positive cone of Y is equal to one high order necessary minimality conditions for singular (nonregular) points of F are proved.
Demenchuk A. K.
On almost periodic partially irregular solutions of ordinary differential systems. pp. 3538
Summary: Let x^{.} = A(t)x + X(t, x) be a almost periodic differential systems. Suppose that mod (A) Ç mod (X) = {0}. The existence problem for almost periodic irregular with respect to mod (A) solutions of such system is considered. This problem is reduced to the similar problem for a system of smaller dimension, and the sufficient conditions for existence of such solutions are obtained.
Zelenyak D. M.
The solving of dissipative inequalities for relaxation systems of second order. pp. 3944
Summary: The set of solutions of dissipation inequality for relaxation systems of second order with direct inputoutput action is described. The extremal elements in this set are pointed out,
Rybachenko I. V.
About the estimation of deviation of rational interpolating operator of Fejer's type in limited interval. pp. 4549
Summary: The estimation of deviation of special rational interpolating operator in uniform metrics for Lipschitz's functions of bounded variation was found. This estimation is less than best polynomial approximation in order sense.
Shilin A. P.
On the one boundaryvalue problem for two pairs of functions on the real axis. pp. 5053
Summary: The boundaryvalue problem for two pairs of functions on the real axis in the case of rational coefficients is solved. The problem has the character of the Carleman boundaryvalue problem.
Zayats G. M.
On one problem about longitudinal impact on a composite elastic rod. pp. 5457
Summary: The problem on longitudinal oscillations of a finite composite elastic rod has been investigated in the case when one of its ends is subjected to impact by some load which after a while disjoins from the rod.
Kurbachev A. V.
The calculation of vibrations transfer through a thin plate in solid elastic medium. pp. 5861
Summary: The problem for the vibroisolating screen in the form of a thin plate placed in the elastic isotropic semispace and effected by longitudinal and transversal waves has been considered. Taking into account wave energy losses in the elastic medium wave fields have been defined and the conditions under which the plate is the effective vibroisolating construction have been obtained.
PHYSICS
Dorozhkin N. N., Ratkevich S. V.
Modified linear augmentedSlatertypeorbital method for electronic structure calculations of solids with arbitrary basis. pp. 6267
Summary: The modified linear augmented Slatertype orbital method (LASTO) for solving Schrodinger's equation in crystals with arbitrary atoms per unit cell is presented. This method will allow more efficiently calculating an electronic band structure and structural energy difference for vary transition metal compounds. The analytic expressions for the overlap matrix and Hamiltonian matrix elements were obtained.
Makhnach V. V.
Bounds for the anapole interaction of the charged fermions at energy ~ 66 GeV. pp. 6872
Summary: Analytical equations for the cross section and the forwardback asymmetry for reaction e^{} e^{+} ® l^{} l^{+} (l = µ, t) with respect to the anapole interaction are obtained. Bounds on numerical value of the anapole interaction parameter fore ee^{+} ® µ^{}µ^{+} reaction at (ÖS) ~ 66 GeV are given.
Tikhomirov V. V., Yuralevich S. E.
Nonrelativistic fermigas accretion onto a mini black hole. pp. 7378
Summary: Matter accretion onto a miniblack hole (MBH) formed at an early stage of the Universe expansion is considered. The equations of a spherically symmetric adiabatic accretion of a relativistic Pascal liquid are derived. A simple expression for a mass absorption rate of nonrelativistic Fermi gas by a MBH is obtained. A typical time of absorption of considerable amounts of the Earth's and neutron star's mass by a MBH is estimated. These estimates do not exclude the MBH presence in the Earth's depth and confirm the possibility of neutron star ignition by a captured MBH.
Petrova E. S.
Bessel light beams in magnetic gyrotropic media. pp. 7983
Summary: Bessel light beams in magnetic gyrotropic media are investigated, The solution of the Maxwell's wave equations are obtained and polarization states for common case of arbitrary order vectorial Bessel beams are founded. The influence of gyrotropy on polarization state is discussed. The reflection and refraction of bessel beams on the boundary of gyrotropic media is calculated. The features of gyrotropy influence on reflection and refraction coefficients and polarization of the reflected and transmitted beams is also analyzed.
Khilo P. A.
Sum frequency generation by Bessel light beams under conditions of quasisynchronism. pp. 8489
Summary: Peculiarities of sum frequency generation by Bessel light beams when quasisynchronous takes places in periodically polarized nonlinear crystals have been investigated.
Karpenko V. A., Romanenko A. A.
On possibility of determination of parameters of nanolayers by the modified Kretchman's sheme. pp. 9092
Summary: It is shown that the modification of Kretchman's sheme by deposition of dielectric thin film on the metal one allows to increase sensitivity of the device to adsorbed layers. An analytical solution of the inverse problem of adsorbed layer parameters determination is obtained.
Chernichenko Yu. D.
Mathematical model of heating plate process by means of impulse laser radiation. pp. 9395
Summary: In the plate the distribution of temperature is obtained by its the heating of impulse laser radiation with the spacetime density distribution of absorbed stream light.
Smolik Ch. K. †, Makovetskii G. I., Severin G. M.
Determination of gold phonon density states function from the temperature dependence of specific heat. pp. 9698
Summary: Using of the extrapolation method for solution of illposed problem described by the first kind Fredholm integer equation is considered. The method is used for calculating the phonon spectrum of gold from the temperature dependence of the specific heat. The minimal errors of the solution is achieved for operator norm A = 1.
Sukhvalo S. V., Vlasov V. V.
Temperature dependencies of the magnetic characteristics and factors of an anisotropy of films of alloys FeNiCo doped Ti and Si. pp. 99102
Summary: The features of temperature changes of the magnetic characteristics of films of an alloy 14%Fe56%Ni30%Co doped Ti and Si in a range of temperatures 290650 K are considered. The spinreorientation transformations close 400 K and 550 K, accompanying by abnormal behaviour of coercive force and field of an anisotropy are revealed.
Karolik A. S.
Calculation of the dislocation electrical characteristics for onevalent metals. pp. 103107
Summary: Within the framework of the partialwave method the residual resistivity and thermoelectric characteristics of dislocations in noble (Cu, Ag, Au) and alkaline (K, Rb) metals are calculated. The quite satisfactory agreement with experiment is obtained. It is shown, that the thermoelectric power reveals by an order of magnitude higher sensitivity to the resonance level location relative to the Fermi energy in comparison with the residual resistivity.
Gaiduk P. I., Larsen A. N.
Rapid thermal annealing of arsenicimplanted Si_{1x}Ge_{x} alloy layers: dose dependence. pp. 108112
Summary: The structural defect evolution and dopant redistribution in arsenicimplanted relaxed Si_{1x}Ge_{x} alloy layers have been studied by TEM and differential Hall measurements. The appearance of the particularities in the dopant profiles in the area of EORdefect band is registered in Si_{1x}Ge_{x} alloy layers implanted with arsenic at an average dose. This is found to correlate well with enhanced shrinkage of interstitial dislocation loops. The above features are connected to the formation of mobile dopantvacancy complexes followed by complexdislocation interaction.
INFORMATICS
Klimovich C. G, Tikhonenko O. M.
Generalized characteristics of busy period distribution for a single server queueing system. pp. 113117
Summary: The sum of tags random vector characteristics for demands served during busy period for queue are determined, taking into consideration the dependence between tags values and service time of the demand.
Malinkovsky Yu. V., Kravchenko S. V.
Queuing networks with "negative" requests, with the bypassing of request nodes and bounded queuing time. pp. 118122
Summary: Open queuing networks with negative and positive requests, with the bypassing of request nodes and bounded queuing time is analyzed. It is ascertained that the stationary distribution of process states has a product form.
Astakhov A. M., Matalytskii M. A.
About finding of steady distribution for Markov queueing networks with many servers systems and different classes of customers. pp. 123128
Summary: Queueing networks with many servers systems and different classes of customers have been considered. It is shown that transient probabilities depend on network states.
SHORT NOTES
Tishchenko K. I.
On a problem of approximation of padic numbers by algebraic numbers. pp. 129130
ABSTRACTS OF DEPOSITED PAPERS
Bakhtin V. I.
Foliated functions and an operator of the averaged weighted shift for perturbations of hyperbolic maps. pp. 131
Bakhtin V. I.
Cramer's asymptotics in the averaging principle for systems with fast hyperbolic motions. pp. 131132
Severenchuk N. B.
SemiBrowder essential spectra of linear operators in Banach space. pp. 132
Monastyrny P. I., Kuzhel'naya A. I.
On some selection procedures of control parameters and optimization of the marching algorithm and the reduction method. pp. 133
Akinfina M. A.
A consistent estimation of spectral density of a stationary stable casual process. pp. 133134
In the Belarusian Physical Society. pp. 135137
SCIENTISTS OF BELARUS
Faina Mikhailovna Kirillova (On the occasion of the 70th birthday). pp. 138139
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