East European Journal of Physics

4-15

Authors: Yu.V. Kulish

The solutions of generalized Klein-Gordon equations are considered. The generalizations of the Klein-Gordon equation allow one to derive convergent integrals for the Green functions of these equations. The generalized equations are presented as products of the operators for the Klein-Gordon equation with different masses. The solutions of derived homogeneous equations (total fields) are sums of fields corresponding to particles with the same values of the spin, the electric charge, the parities, but with different masses. Such particles are grouped into the kinds (families, dynasties) with members which are the generations. The chronological products of the scalar fields for kinds of particles are obtained at arbitrary quantity of the generations. These chronological products are the causal Green functions of generalized Klein-Gordon equations. The Lagrangians for the generalized Klein-Gordon equations of arbitrary order are derived. These Lagrangians are used to obtain the energy-momentum tensors for the particle kinds at arbitrary quantity of generations. It is shown that the generalized Hamiltonians (for total fields) have got positive eigenvalues for all the generations. These results are derived with the use of the indefinite metrics.

23-26

Authors: M. Bondarenko, V. Knigavko, O. Zaytseva

Significant progress in understanding the mechanisms of carcinogenesis is associated with the discovery of tumor suppressor genes (or antioncogenes). It is known that in the human population, the number of normally functioning suppressor genes varies in different individuals at birth. The aim of the study was to assess the probability of cancer development in an individual with a different initial number of undamaged normally functioning antioncogenes. On the basis of the probabilistic mathematical model of carcinogenesis, the most probable age of cancer development depending on the number of intact antioncogenes was assessed. As a result of the studies, the probability of cancer development depending on the age of the patient is estimated. The dependence of the probability of cancer development in an individual on the number of undamaged antioncogenes is also investigated. The analysis of the significance of the number of tumor suppressor genes, the damage of which may be the cause of initiation of cell malignancy, has been carried out.

35-48

Authors: K.K. Merkotan, T.M. Zelentsova, N.O. Chudak, D.A. Ptashynskiy, V.V. Urbanevich, O.S. Potiienko, V.V. Voitenko, O.D. Berezovskyi, I.V. Sharph, V.D. Rusov

Problems of the Standard Model, associated with the introduction of an electromagnetic field as a linear combination of fields on which various gauge groups representations are implemented, are analyzed. In this paper, we pay attention to the fact that in any model with gauge fields, the generators which are included in the covariant derivatives can be given only up to the transition to the equivalent representation. It is proposed that dynamic models with equivalent representations of generators should be physically equivalent. It means the requirement of the Lagrangian symmetry with respect to the transition from one equivalent generators representations to another. In particular, in the Lagrangian of the Standard Model, we have raising and lowering SU (2) group generators. The group multiplication law determines only the matrix elements modules of these generators while the arguments remain uncertain. In the paper, such uncertainty is considered as a local one. At different points of space-time, generators can be expressed in various equivalent representations. The compensation of the uncertain matrix elements arguments of the SU (2) group generators can be carried out with a local U (1) - transformation with the introduction of the corresponding gauge field, which can be considered as the electromagnetic field. The advantages of such electromagnetic field introduction in comparison with the method used in the Standard Model are analyzed.

54-61

Authors: A.I. Kalinichenko, E.N. Reshetnyak, V.E. Strel’nitskij

Influence of atomic sputtering on intrinsic stress and growth rate of the coating made by method of plasma - ion deposition with use of pulsed bias potential and at different incidence angles of ions is theoretically investigated. The formula for intrinsic stress calculation in deposited coating obtained in the model of the nonlocal thermoelastic peak of the ion, taking into account atomic sputtering processes, was used to calculate the stresses in TiN and CrN coatings deposited from Ti+ and Cr+ ion beams, respectively. The stress value for the coatings considered correlates with the modulus of elasticity of the coating material. The stress curve maximum decreases and shifts to the region of higher potentials with increasing angle of incidence. This behavior is due to the sputtering of quasi-table interstitial defects that determine the level of stress in the deposited coating. A formula is proposed for the coating deposition rate, which takes into account the sputtering of the coating atoms at arbitrary bias potential and the angle of incidence of the ions. It is shown that sputtering sharply reduces the coatings deposition rate and makes it impossible to deposit TiN and CrN coatings in the DC mode at potentials on the substrate exceeding 1.7 kV and 0.7 kV, respectively, and with normal ion incidence. Sputtering has the greatest influence on the intrinsic stress and the growth rate of the coating at ion deposition at inclined angles of incidence α = 45°...70° . The results of the calculations are compared with the available experimental data.

68-71

Authors: V.K. Galaydych

The slow surface electromagnetic waves that propagate along the planar waveguide structure that contains two identical isotropic left-handed material with the vacuum (or air) gap has been considered. The possibility of propagation of slow surface electromagnetic waves of TM and TE polarizations in the frequency range at which the dielectric permittivity and magnetic permeability are negative are shown. By selecting a frequency, one, two or three modes can be excited simultaneously. The group and phase velocities of the TE polarization waves are directed in opposite directions. The frequency range of the existence of the TE mode with an antisymmetric field distribution lies above the frequency range of the existence of the TE mode with a symmetric field distribution. The TM wave, depending on the wavelength, can be either forward or backward, or have zero group velocity. The wave of TM-polarization has a slightly varying group velocity in a sufficiently wide frequency range. A rich set of different properties of these waves make them promising in applications.

78-83

Authors: V.I. Maslov, I.P. Levchuk, S. Nikonova, I.N. Onishchenko

The possible dynamics of the electron beam, formed in the vicinity of Io, the natural satellite of Jupiter, and injected toward Jupiter, has been investigated analytically. When a beam penetrates the Jupiter plasma to a certain depth, the beam-plasma instability can be developed. In this case, the distribution function of electrons is expanded additionally by excited oscillations. These electrons, when their energy is of order of a required certain value, cause UV polar light. For closing of a current, the formation of a double electric layer is necessary. The necessary parameters and conditions for the formation of a double layer with a large jump of an electric potential at a certain height have been formulated, its properties, stability, behavior over time and beam reflection in its field for closing of a current have been described. Reflection of the beam can lead to its vortex dynamics.