https://elib.bsu.by:443/handle/123456789/188740 NPCS Vol.19, no.4 (2016), pp. 315-418 2026-04-20T12:01:57Z https://elib.bsu.by:443/handle/123456789/204212 Заглавие документа: Exact Foldy-Wouthuysen Transformation and a Verification of Foldy-Wouthuysen Transformation Methods Авторы: Silenko, A. J. Аннотация: The exact Foldy-Wouthuysen transformation is considered. It can be successfully used for a verification of FW transformation methods for a particle with any spin. When a verified method is relativistic, the relativistic exponential operator should be expanded in a semirelativistic power series. The exact FW transformation can be fulfilled with the exponential and nonexponential FW transformation operators. Two examples of an application of the exact Foldy-Wouthuysen transformation are presented. 2016-01-01T00:00:00Z https://elib.bsu.by:443/handle/123456789/204211 Заглавие документа: Block Encryption Algorithm Based on Dynamic Chaos Авторы: Sidorenko, A. V. Аннотация: An algorithm using dynamic chaos for encryption and decryption of the plain text has been developed. To prove the stability of the proposed encryption algorithm, the quantitative parameters have been determined: information entropy, numerical characteristics for the distribution of byte values in open and encrypted texts, correlation coefficient, percentage of the value-changing bits (avalanche effect), number of pixels change rate (NPCR), unified average changing intensity (UACI). 2016-01-01T00:00:00Z https://elib.bsu.by:443/handle/123456789/204210 Заглавие документа: Expansions of the Solutions of the General Heun Equation in Terms of the Incomplete Beta Functions Авторы: Shahverdyan, T. A.; Red’kov, V. M.; Ishkhanyan, A. M. Аннотация: Applying the approach based on the equation for the derivative, we construct several expansions of the solutions of the general Heun equation in terms of the incomplete Beta functions. Several expansions in terms of the Appell generalized hypergeometric functions of two variables of the first kind are also presented. The constructed expansions are applicable for arbitrary sets of the involved parameters. The coefficients of the expansions obey four-, five- or six-term recurrence relations. However, there exist several sets of the parameters for which the recurrence relations involve fewer terms, not necessarily successive. The conditions for deriving finite-sum solutions via termination of the series are discussed. 2016-01-01T00:00:00Z https://elib.bsu.by:443/handle/123456789/204209 Заглавие документа: Coexistence of Spiking and Mixed-mode Oscillations in CO2 Laser with Saturable Absorber Авторы: Grigorieva, E. V.; Kaschenko, S. A. Аннотация: We analyze the dynamics of CO2 laser with a saturable absorber on the base of a model for three- and two-level active and passive media, respectively. This differential model is asymptotically reduced to a discrete one-dimensional map. The fixed point of such a map corresponds to stable periodic spikes and determines their characteristics: period and the energy. In addition, we describe the set of initial conditions which lead to spiking. With initial conditions beyond this set, the system generates mixed-mode oscillations consisting of both small-amplitude oscillations and large-amplitude bursts. Switching between coexisting regimes is discussed. 2016-01-01T00:00:00Z