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Документ On some numerical model to solving dynamical equations of nonrelativistic and relativistic backward-wave tube(Одеський національний університет імені І. І. Мечникова, 2022) Tkach, T. B.; Kvasikova, A. S.; Shpinareva, Iryna M.; Ткач, Т. Б.; Квасикова, А.С.; Шпінарева, Ірина МихайлівнаIt is developed an effective computational approach to solution the master corresponding system of differential equations, which describe the nonlinear stationary and nonstationary electromagnetic processes in the nonrelativistic and relativistic backward-wave tubes (carcinotrons) with maximal accounting for the different physical factors such as the relativistic effects, effects of dissipation, the presence of a space charge, wave reflections at the ends of the slowing system, stochastic factors by means including the special elements in a whole system etc as well as the detailed investigation of characteristics (dynamical and topological invariants) of dynamics of a carcinotron in automodulation and chaotic regimes with construction the corresponding bi-furcation diagrams. Below in order to further solve the master system of dynamical equations for carcinotron it is presented in brief the realizing numerical scheme, based on the use of the conservative finite-difference schemes of the "predictor-corrector" type and the sweep algorithm.Документ Optimized quantum defect method in relativistic theory of spectra of Li-like multicharged ions(Одеський національний університет імені І. І. Мечникова, 2022) Kvasikova, A. S.; Shpinareva, Iryna M.; Tkach, T. B.; Квасикова, А. С.; Ткач, Т. Б.; Шпінарева, Ірина МихайлівнаThe relativistic theory of radiative transitions using the general relativistic quantum defect approximation (GDA) was also used to study the wavelengths and oscillator strengths for the 1s22s (2S1/2) → 1s23p (2P1/2) transitions in Li-like multicharged ions with a nuclear charge Z= 14-70. and. The obtained results were compared with available theoretical and experimental (summarized) data. An important point is related to the accurate accounting of the complex contributions of the exchange-correlation (polarization) effect and the use of an efficient singlequasi- particle representation based on the general relativistic approximation of the quantum defect, which significantly ensures a physically reasonable agreement between the theory and the experiment.