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Information × Registration Number 0223U001146, 0118U001547 , R & D reports Title Mathematical modeling of complex systems popup.stage_title Head Kostrobij Petro P., Доктор фізико-математичних наук Registration Date 25-01-2023 Organization Lviv Polytechnic National University popup.description2 The developed method for spatial modeling of the spread processes of COVID-19 using digital vector maps and a physical analogy with the concept of "center of gravity" made possible to build the movement trajectories of a gravity center both for new cases of the disease and for fatal cases for Ukraine and European countries, to find the amplitude of the movement of the gravity center in the directions of geographic latitude and longitude during the corresponding waves of the pandemic, to analyze the delays between the peaks of new cases and the peaks of mortality. A quantum-statistical model of a metal film was built, and it was found that a quantum-size effect is observed for the chemical potential of a metal film; the distance between adjacent maxima is approximately half the Fermi wavelength. In addition, taking into account the Coulomb interaction between electrons leads to a significant decrease in the chemical potential. It was found that taking into account the Coulomb interaction between electrons leads to the loss of the linear dependence of the period of alternating peaks. The methods of constructing the Chebyshev approximation and the Chebyshev approximation with interpolation by a generalized polynomial, rational and exponential expressions of continuous tabulated functions of many variables have been developed, which consists in the sequential determination of average power approximations using the least squares method with two variable weighting functions. One weight function ensures the construction of an average-level approximation, and the second — is a refinement of the expression parameters used to approximate, according to the linearization scheme. Convergence of the method is ensured thanks to the original method of successive refinement of the values of the weighting functions. The given algorithms are simple to implement, reliable, and effective. They provide the possibility of calculating approximation parameters with the required accuracy. Product Description popup.authors Antonova Tamara Bun Rostyslav A. Vozna Svitlana Mykolayivna Hladun Volodymyr R Manzij Oleksandra Stepanivna Markovych Bohdan M Medynskyy Ihor P. Pizyur Yaropolk V Pabyrivskyy Viktor Volodymyrovych Polovyi Vitalii Yevhenovych Ryzha Iryna A. Senyk Andrii Topylko Petro popup.nrat_date 2023-01-25 Close