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The article is devoted to the study of the current state of scientific, technical and innovative activities in Ukraine based on the analysis of international rankings and domestic information sources, identifies the main problems that influence the innovative development of Ukraine and human capital, the developed methodical approaches to forecasting of evolution of personnel potential of domestic science for the next decades are analyzed..

It’s been established that the problem of disappearing of open water body and the use of Earth remote sensing data for their monitoring is relevant and poorly covered in current Ukrainian and foreign scientific studies. The necessity of complex solution method has been also determined. The purpose of this paper is to study the dynamics of surface water area over a 45-year period (over a long period of time) across  the Iziaslav district of Khmelnytsky on the  basis  of  programming analysis of satellite imagery and the results from field surveys at key research sites.

The article deals with the main quantification methods of the system of checks and balances. Taking into account the main historical stages of the development of ideas concerning the functioning of the checks and balances system, on the basis of the comparative method, the main features of understanding the functioning of different aspects of checks and balances system by using mathematical methods are emphasized.