
PROBLEMS OF PHYSICS, MATHEMATICS AND TECHNICS N4 (9) 2011
PHYSICS
Andreev V.V., Maksimenko N.V. Polarizability of elementary particles in the theoreticalfield approach
The effective Lagrangians and amplitudes of Compton scattering on pion and nucleon with the account of electric and magnetic polarizabilities are obtained on the basis of the theoreticalfield approach and solutions of electrodynamic equations by means of Green functions covariant method. Calculations of magnetic and electric quasistatic polarizabilities of spinor particle were evaluated on the basis of matrix elements calculation for Compton scattering amplitudes.
Keywords: polarizability, Lagrangian, Compton scattering, Green function.
V.V. Andreev – Department of Physics, F. Skorina Gomel State University, Gomel, Belarus
N.V. Maksimenko – Department of Physics, F. Skorina Gomel State University, Gomel, Belarus
Download PDF (358 KB)
Andrusevich P.P., Pletyukhov V.A., Strazhev V.I. Transformations of the PauliGursey type in SU(3)model
It is shown that the group SU(3,3) is the complete continuous group of internal symmetry of the Lagrangian formulation of the theory of the massless Dirac fermion with three internal degrees of freedom. The color symmetry group SU(3) can be considered as a compact subgroup of the latter.
Keywords: transformations, internal symmetry, Dirac field, generators, group, invariance.
P.P. Andrusevich – Belarusian State University, Minsk, Belarus
V.A. Pletyukhov – A.S. Pushkin Brest State University, Brest, Belarus
V.I. Strazhev – Belarusian State University, Minsk, Belarus
Download PDF (326 KB)
Viarbitskaya S., Dujardin E., Girard C. Selfassembled nanoplasmonics
Stateoftheart plasmonic structures can be splitted into two classes depending on whether they were obtained by topdown or bottomup processes. The former have been extensively studied but they remain to be large and simple in terms of feature size and architecture, respectively. The latter have only been made available recently and need much investigation of their nearfield optical properties, yet they push the integration limit further and provide a new approach to complex architectures. Selfassembling of nanoparticles in complex superstructures is one of the suggested bottomup approaches. We discuss the challenging problem of the light evanescent wave optical addressing in such structures and introduce a concept of multiscale plasmonic architectures.
Keywords: subwavelength optics, nanophotonics, nanostructures, metal colloid, nearfield optics, plasmonics, selfassembled nanostructures.
S. Viarbitskaya – NanoSciences Group, CEMES/CNRS UPR 8011, 29 rue Jeanne Marvig, 31055 Toulouse Cedex 4, France
E. Dujardin – NanoSciences Group, CEMES/CNRS UPR 8011, 29 rue Jeanne Marvig, 31055 Toulouse Cedex 4, France
C. Girard – NanoSciences Group, CEMES/CNRS UPR 8011, 29 rue Jeanne Marvig, 31055 Toulouse Cedex 4, France
Download PDF (712 KB)
Girgel S.S. Physical properties of scalar 2D beams of Kummer – Gauss
The unified formalism allowing to deduce common expressions for paraxial twodimensional Gaussianlike light Kummer  Gaussian beams and discover correlations between them is developed. Ñonditions of their physical realizability acal LCLS parameters such as the number of photons per pulse, the pulse duration, and the focal spot size on the photoelectron and Auger spectra is modeled in detail and the results of these simulations are used as an aid in the interpretation of the experimental spectra obtained. We review here the results from the twophoton experiments at LCLS.
Keywords: free electron laser, Xray laser, polyatomic molecule, double corehole state.
M. Larsson – Stockholm University, Physics Department, 106 91 Stockholm, Sweden
P. Salen – Stockholm University, Physics Department, 106 91 Stockholm, Sweden
P. van der Meulen – Stockholm University, Physics Department, 106 91 Stockholm, Sweden
R.D. Thomas – Stockholm University, Physics Department, 106 91 Stockholm, Sweden
H.T. Schmidt – Stockholm University, Physics Department, 106 91 Stockholm, Sweden
R. Feifel – Uppsala University, Department of Physics and Astronomy, 751 20 Uppsala, Sweden
M.N. Piancastelli – Uppsala University, Department of Physics and Astronomy, 751 20 Uppsala, Sweden
L. Fang – Western Michigan University, Physics Department, Kalamazoo, MI 49008, USA
T. Osipov – Western Michigan University, Physics Department, Kalamazoo, MI 49008, USA
B. Murphy – Western Michigan University, Physics Department, Kalamazoo, MI 49008, USA
P. Juranic – Western Michigan University, Physics Department, Kalamazoo, MI 49008, USA
N. Berrah – Western Michigan University, Physics Department, Kalamazoo, MI 49008, USA
E. Kukk – University of Turku, Department of Physics and Astronomy, 20014 Turku, Finland
K. Ueda – IMRAM, Tohoku University, Sendai 9808577, Japan
R. Richter – Sincrotrone Trieste, 34149 Basovizza, Trieste, Italy
K.C. Prince – Sincrotrone Trieste, 34149 Basovizza, Trieste, Italy
J.D. Bozek – SLAC, LCLS, Menlo Park, CA 94025, USA
C. Bostedt – SLAC, LCLS, Menlo Park, CA 94025, USA
S. Wada – SLAC, LCLS, Menlo Park, CA 94025, USA
M. Tashiro – Institute for Molecular Science, Okazaki 4448585, Japan
M. Ehara – Institute for Molecular Science, Okazaki 4448585, Japan
F. Tarantelli –Chemistry Department, University of Perugia and ISTMCNR, 06123 Perugia, Italy
Download PDF (589 KB)
Pilipovich V.A., Konojko A.I., Polikanin A.M. Methods and means of the electrooptical modulation of infrared spectrum radiathion
Means and methods of amplitudepolarization modulation of planepolarized light are considered. These methods can be realized by means of the splitting planepolarized light beam on two beams, their phase modulation and subsequent summation.
Keywords: electrooptical effect, amplitude modulation, phase modulation, polarization splitter, birefringence, isotropic angle.
V.A. Pilipovich – B.I. Stepanov Institute of Physics NAS of Belarus, Minsk, Belarus
A.I. Konojko – B.I. Stepanov Institute of Physics NAS of Belarus, Minsk, Belarus
A.M. Polikanin – B.I. Stepanov Institute of Physics NAS of Belarus, Minsk, Belarus
Download PDF (440 KB)
Savenko V.S. Electroplastic effect at twinning metals
Use of pulses of a current of high density, electric and magnetic fields, ionic implantation allowed intensifying plastic deformation of metals, thus, giving basic opportunity for management of plastic deformation twinning with the help of forces of the nonmechanical nature, influencing on conditions and character of hardening of a material by means of controllable twinning.
Keywords: twinning, twinning dispositions, metals, electroplastic effect, deformation, disclosing, indentor.
V.S. Savenko – I.P. Shamyakin Mozyr State Pedagogical University, Mozyr, Belarus
Download PDF (631 KB)
Semchenko I.V., Khakhomov S.A., Samofalov A.L., Tretyakov S.A. Advantages of artificial lowreflecting structures based on the optimal helices at the refraction and absorption of electromagnetic waves
The analytical study of refractive and absorbing properties of a sample of the artificial medium consisting of the optimal helices with equal permittivity and permeability has been carried out. Significant advantage of this medium in comparison with «pure» dielectric and magnetic materials was shown on the basis of the obtained results.
Keywords: composite materials, chirality, helical element, permittivity, permeability.
I.V. Semchenko – Prorector of F. Skorina Gomel State University, Gomel, Belarus
S.A. Khakhomov – Prorector of F. Skorina Gomel State University, Gomel, Belarus
A.L. Samofalov – Department of Physics, F. Skorina Gomel State University, Gomel, Belarus
S.A. Tretyakov – Aalto University School of Electrical Engineering, Finland
Download PDF (336 KB)
Khilo N.A., Kazak N.S., Ryzhevich A.A., Solonevich S.V. Laser radiation converters on the base of crystals
We designed and made a compact laser radiation converter on the basis of a biaxial crystal oriented along its binormal. The deviñe is designed for apodization and decreasing laser beam divergence, as well as for shaping hollow light beams with a wave front dislocation. Optical elements of the converter allow to transform both pulsed, and continuous powerful laser radiation. It is possible to transfer converted beams at large distance in transparent media. The device holds much promise for manipulation by particles on the principle of a laser tweezer, for laser processing of materials, for influence on organic cells and its components, and in interferometry and profilometry.
Keywords: laser beam, laser radiation converter, crystal, apodization, multiring light beam.
N.A. Khilo – B.I. Stepanov Institute of Physics NAS of Belarus, Minsk, Belarus
N.S. Kazak – B.I. Stepanov Institute of Physics NAS of Belarus, Minsk, Belarus
A.A. Ryzhevich – B.I. Stepanov Institute of Physics NAS of Belarus, Minsk, Belarus
S.V. Solonevich – B.I. Stepanov Institute of Physics NAS of Belarus, Minsk, Belarus
Download PDF (705 KB)
MATHEMATICS
Belokursky M.S. The cubic nonautonomous differential systems, equivalent in sense of coincidence of reflecting functions to embedable systems
Necessary and sufficient conditions for nonautonomous differential system with cubic righthand side to be equivalent to embedable system in sense of Mironenko were obtained.
Keywords: reflecting function, embedable system, differential system, twopoint boundaryvalue problem.
M.S. Belokursky – Department of Mathematics, F. Skorina Gomel State University, Gomel, Belarus
Download PDF (313 KB)
Belsky V.A., Mironenko V.I. Reflecting function preserving polinomial perturbations of Abel equation
In this paper the method of constructing of Abel differential equations possessing the same Mironenko reflecting function is studied. For another equation with the same reflecting function to be constructed, the necessary and sufficient conditions for given Abel equation
are achieved.
Keywords: Abel equation, reflecting function, equivalence of differential equations, polynomial perturbations.
V.A. Belsky – Gomel Engineering Institute of the Ministry for Emergency Situations of the Republic of Belarus, Gomel, Belarus
V.I. Mironenko – Department of Mathematics, F. Skorina Gomel State University, Gomel, Belarus
Download PDF (373 KB)
Vasilyev A.F., Vasilyeva T.I. On finite groups with generally subnormal Sylow subgroups
Let
be a nonempty formation. A subgroup H of group
G is called subnormal in G if either H=G or there is a chain of subgroups
such that for every
i = 1, … , n. In the work the class of groups and every Sylow subgroup of G is subnormal in G) are studied. Properties of the class are obtained. In particular, for hereditary saturated formation
it is proved that the class is a hereditary saturated formation. Necessary and sufficient conditions are found, at which
Keywords: finite group, Sylow subgroup, subnormal subgroup, hereditary formation, saturated formation.
A.F. Vasilyev – Department of Mathematics, F. Skorina Gomel State University, Gomel, Belarus
T.I. Vasilyeva – Belarusion State University of Transport, Gomel, Belarus
Download PDF (381 KB)
Gal'mak A.M. În compatible vectormatrices
The properties of compatible vectormatrices are studied in this paper.
Keywords: matrice, vectormatrice, semigroup, group, ring, nary group.
Gal’mak A.M. – Department of Economic, Mogilev State University of Food Technologies, Mogilev, Belarus
Download PDF (408 KB)
Dashkova O.Yu. On modules over group rings of locally finite groups
Hodanovich D.A. On the derivative length of a finite solvable group
The upper estimations of the derivative length of the Frattini quotient group depending on the indices of the maximal subgroups which do not contain a Fitting subgroup in the solvable group have been obtained.
Keywords: finite group, solvable group, maximal subgroup, Fitting subgroup, Frattini subgroup, derivative length.
D.A. Hodanovich – Department of Mathematics, F. Skorina Gomel State University, Gomel, Belarus
Download PDF (345 KB)
INFORMATION SCIENCE
Sukach E.I., Ratobylskaya D.V. Opportunity program of probabilityalgebraic simulation of complex systems
The description of the computer system PALS performing the method of the probabilityalgebraic simulation of complex systems is presented. It allows estimating in dynamics the probability characteristics of the investigated property of complex systems with many states. The assessment of probability properties of structurallysimple and structurallycomplex systems is shown in the examples.
Keywords: probabilityalgebraic simulation, reliability of complex system, structurallysimple system, structurallycomplex system.
E.I. Sukach – Department of Mathematics, F. Skorina Gomel State University, Gomel, Belarus
D.V. Ratobylskaya – Department of Mathematics, F. Skorina Gomel State University, Gomel, Belarus
Download PDF (688 KB)
