СЕРИЯ ФИЗИКО-МАТЕМАТИЧЕСКИХ НАУК
Издатель: Институт математики НАН Беларуси, Минск, Республика Беларусь
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Известия Национальной академии наук Беларуси СЕРИЯ ФИЗИКО-МАТЕМАТИЧЕСКИХ НАУК Издатель: Институт математики НАН Беларуси, Минск, Республика Беларусь |
Summary: Generalizations of the classical theorem about global homeomorphism for Gateaux differentiable mapping between Banach spaces is considered.
Gorokhovik V.V., Kishtchenko M.G.
Affine selectors of affine multivalued mappings. pp. 11--18
Summary: We show that the existence of a convex compact family of single-valued affine selectors exhausting a multivalued mapping is a characteristic property that extracts affine multivalued mappings from the class of convex multivalued ones. Besides we prove a criterium of affinity of concave multivalued mappings. Then we introduce the notion of an exposed selector as well as the notion of an extreme selector and prove that each affine multivalued mapping can be presented as the closed convex hull of its exposed affine selectors and as the convex hull of its extreme affine selectors. These results extends the Straszewicz theorem and the Krein--Milman theorem from classical convex analysis to affine multivalued mappings.
Benyash-Krivets V.V.
Character variety of finitely generated groups. pp. 19--24
Summary: The explicit construction of the character variety of representations of a finitely generated group into GLn(K) is given.
Selkin V.M.
Formations of finite groups with an unique maximal t-closed w-local subformation. pp. 25--29
Summary: The t-closed w-local formations of finite groups with an unique maximal t-closed w-local subformation are studied.
Galmak A.M.
St-closed classes of polyadic groups. pp. 30--34
Summary: St-closed classes of n-axy groups which coincide with St-closed classes when n = 2 are given and studied.
Maksimov S.L.
About finite groups with Schmidt subgroups of the second rang. pp. 35--38
Summary: It is described a construction Hall subgroups of finite soluble group G with Schmidt subgroups with the second rang or without Schmidt's subgroups having the second rang.
Zherelo A.V.
On approximation of integrals with respect to measure based on solution of stochastic differential equation. pp. 39--43
Summary: Approximation formula for functional on solution of stochastic differential equation with respect to arbitrary martingale is given. The method of calculating of mathematical expectation of functional on solution is proposed.
Musafirov E.V.
On the differential systems with a reflective matrix representing by product of exponential matrix. pp. 44--50
Summary: For a linear differential system the necessary and sufficient conditions of a representation of the reflective matrix as a product of a finite number of exponential matrix are obtained. It has allowed to investigate a stability and existence of periodic solutions of some classes both linear, and nonlinear periodic differential systems.
Kopeikina T.B., Shashkov E.V.
On approximation of the controllability problem in delay systems. pp. 51--56
Summary: Approximation of the relative controllability problem for linear time-delay system x.(t) = Ax(t) + A1x(t - h) + Bu(t) through the problem of H-relative controllability for the system of ordinary differential equations is investigated. A criterion of H-relative controllability is obtained. The connection with some conditions of relative controllability of system (1) is established. One example is given.
Zalesky B.A.
Multiresolution algorithm of minimum network flow cut and its applications to image processing. pp. 57--62
Summary: A new multiresolution minimum network flow cut algorithm is presented. The description and the theoretical ground of the algorithm are done. It can be implemented as a hierarchical pyramid scheme (for instance, like dyadic or other pyramid algorithms). For the large class of networks the algorithm is significantly more efficient in comparison with traditional network flow algorithms.
Summary: 20-component theory of 1/2-spin particle with anomalous magnetic moment in presence of external electromagnetic and gravitational fields is investigated. The gravitation field is described as space-time curvature. It is shown that after exclusion of the additional vector-bispinor Yb(x) the wave equation for the principal Y-bispinor looks as generally covariant Dirac's equation with electromagnetic minimal and Pauli interactions and with an additional gravitational interaction through scalar curvature R(x)-tetm.
Fedorovykh A.M.
First-order equations for graviton in formalism of relativistic vector algebra. pp. 69--73
Summary: A set of binary operations, called relativistic vector algebra, over scalars, vectors and tensors, which are transformed by irreducible representations (0,0), (1/2,1/2), (3/2,1/2), (1/2,3/2), (1,1) and (3/2,3/2) of the Lorentz group is constructed and studied. An algebraic formulation of the 30-dimensional and 50-dimensional relativistic first-order wave equations for graviton (a massless particle with spin 2) is given in terms of the introduced operations. A relation between solutions of the 30-dimensional and 50-dimensional equations is obtained in algebraic way.
Tikhomirov V.V.
Dirac--Schwinger equation in the field of a classical frequency circularly polarized electromagnetic wave. pp. 74--78
Summary: A low frequency limit of the Dirac--Schwinger equation in the field of a circularly polarized electromagnetic wave is derived. This limit principally differs from the Dirac -- Pauli equation and makes it possible to describe a recently predicted phenomenon of frequency growth of the electron spin precession in the field of a circularly polarized electromagnetic wave,
Aleynikov D.V., Tolkachev E.A.
Topological non-trivial effects in the energy spectrum of diatomic molecule. pp. 79--82
Summary: Accurately solving model describing the rotationally oscillatory dynamic of diatomic molecule is proposed. This model allow for nontrivial topological phenomenon caused by adiabatic variation of interatomic space. It is a new example of accuratelly solving quantum-mechanical problem, namely Shrodinger equation with Kratzer scalar potential and Dirac vector one, the latter being embeded into SU(2) group. This problem is virtual to one of four-dimensional singular oscillator restricted by equivariant condition.
Hoang Quoc Khanh, Komarov L.I. †
About order of consecutive filling of the one-electron states in atoms. pp. 83--89
Summary: Dynamic substantiation of Madelung -- Klechkovski rule of consecutive filling of the one-electron states in atoms is given. It based on the analysis of a state properties of an electron joining to atom with nucleus charge simultaneously increased on unit.
Vardanian R.S.
Correlation characteristic of a radiation field in a stochastic media. pp. 90--94
Summary: In the "staircase" approximation the dispersion and the correlation coefficient for source function is obtained. It is assumed, that the quantum survival probability is a d-correlated Gaussian field.
Petrova E.S.
The influence of the natural and magnetic gyrotropy on the polarization and energy of the vector Bessel light beams. pp. 95--100
Summary: Vector Bessel light beams in natural and magnetic gyrotropic media are investigated. The component vector of electromagnetic field for common case of arbitrary order vectorial Bessel beams in natural gyrotropic media are obtained. The reflection and refraction of Bessel beams on the boundary of natural gyrotropic and nongyrotropic media are calculated. The features of natural gyrotropy influence on reflection and refraction coefficients and polarization of the reflected beams compared with influence of magnetic gyrotropy are also analyzed. Pointing vector for magnetic-gyrotropic media is calculated and two refracted Bessel beams interference due to magnetic gyrotropy are discovered. Pointing vector for natural-gyrotropic media is also calculated.
Kluchnikov V.A.
Mathematical modeling of wave field spatial structure. pp. 101--105
Summary: The mathematical model of wave front scattering on physical heterogeneities is considered. The model is based on spectral iterative algorithm. Calculation advantages of the mathematical model is justified.
Grinchik N.N., Bordusov S.V.
Modeling of propagation and dissipation of electromagnetic waves in view of relaxation. pp. 106--113
Summary: The telegraph equation for a vector of electric intensity and the equation of thermal conductivity in view of thermoelectric phenomena for the calculation of dielectric losses in continuous medium is offered. The case when the current of polarization is a component part of the current of conductance is considered. It is Considered the attempt to take into account retardation both of a polarization as well as an external electromagnetic fields, which is caused not only by electrical but also by magnetic phenomena of dipoles relaxation. The solution of the problem of a periodic boundary mode distribution is obtained in view of heritage medium performance, which qualitatively complies with the experimental data.
Summary: New technology of construction of modular number systems with arbitrary ranges based on general grounds of codification theory of algebraic systems is proposed. Its dominant elements are relations of equivalence generated by sets of coprime ideals and main theorem of modular arithmetics.
Zaika V.C., Lopareva N.V.
Optimization of processes of data preparation of full-scale experiment with usage of an operationally -- software Delphi. pp. 120--124
Summary: Peculiar features of the data conversion of full-scale experiment with using an algorithm of Johnson for optimization of processes of automatic converting and sorting of the multichannel information in visual Delphi are considered.