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Information × Registration Number 0220U100628, 0119U100334 , R & D reports Title Development of new analytic-geometric, asymptotic and qualitative methods for investigating invariant sets of divergent-objective equations. popup.stage_title Head Perestiuk Mykola O., Registration Date 22-01-2020 Organization Taras Shevchenko National University of Kyiv popup.description2 Object of study: systems of equations of different types, stochastic equations, boundary value problems, uncertainty, service networks, dynamic systems, random processes, boleans. Workplaces: development of new constructive methods of analysis and optimization of systems under uncertainty. Research methods: modern methods of decision theory in uncertainty, optimal control, new methods of system analysis and optimization of stochastic and deterministic systems, modern methods of combinatorial ontimization in groups. Representations of the minimum estimates for parabolic systems with rapidly oscillating coefficients were obtained and their closeness to the estimates of the corresponding systems with averaged parameters were investigated. Constructive methods for the construction of a priori and a posteriori estimates of unknown acoustic and electromagnetic fields are modeled using the Kelmholtz equation. An approximate solution to the linear regression analysis problem is proposed when all observation matrices are perturbed. Asymptotic varieties are classified and their free objects are described. Stochastic networks with controlled input streams of requirements and with service of various types, including indicator and phase type, are investigated. For the process of servicing the requirements in such networks, the characteristics were found in the stationary mode. An approximate Gaussian process is constructed for the congested network operation mode. The conditions for weak convergence of the impulse process with Markov switching under Poisson approximation conditions and control with the equilibrium point of the function of the quality criterion for which the stochastic approximation procedure is obtained are obtained. Statistical methods of fractional Brownian motion modeling based on spectral images in the form of stochastic integrals by Wiener processes are developed and the conditions and convergence speed of the developed models are probed.  Product Description popup.authors Asrorov Farkhod A. Vasylyk Olga I. Holovashchuk Nataliia S. Kapustian Oleksii V. Parasiuk Igor O. Perestiuk Mykola O. Petravchuk Anatoliy P. Romaniuk Iryna V. Stanzschizkiy Oleksiy M. popup.nrat_date 2020-04-02 Close