A problem of program maximin with constraints of asymptotic nature

We consider a linear game control problem for maximin with asymptotic constraints, which naturally arise in connection with the realization of "narrow" control pulses. In terms of content, this corresponds to pulsed control modes with full fuel consumption. The emerging game problem corresponds to the use of asymptotic control modes by both players, which is reflected in the expansion concept realized in the class of finitely additive measures. The original content control problem for each of the players is considered as a variant of abstract formulation related to attainability under asymptotic constraints, for which the corresponding generalized attainability problem is constructed and the representation of the attraction set playing the role of an asymptotic analogue of an attainability domain in the classical control theory is established. This concretization is realized for each of the players, on the basis of which a generalized maximin is obtained, for which a variant of the asymptotic realization in the class of ordinary controls is indicated. A "finite-dimensional" description of the attraction set is obtained, which makes it possible to find maximin using numerical methods. The solution of a model example of the problem of game interaction of two material points, including the stage of computer modeling, is considered. © 2018 Udmurt State University. All rights reserved

Role of Ecosystem of Reservoir Basin of the Dnieper River for Ensuring Life Standards and Population's Health in Ukraine.

In this article the reasons of the environment quality deterioration, inclu­ding its component - water are considered, as well as methods to resolve this problem are offered. High quality of life provides for high economic and social standards, including public health. The share of environmental quality impact on morbidity rate reaches 25%, while the role of water is extremely important. At present medicine does not yet have data on the interactions between different types of diseases and water chemical composition. We need to know the impact of each indicator of water quality on health and human lifespan. In Ukraine about 25 million of population, as well as industrial and agricultural enterprises meet their needs of the water at the expense of the Dnieper river basin. As a result of construction of six extra-large reservoirs they overregulated flow of the river, which led to serious contamination of the water and catastrophic consequences for the ecosystem. Proportion of shallow water constantly increases due to siltation of reservoirs. One of the major challenges is to provide population with qualitative natural water resources. Nature prompts effective solutions. For example, water passes through the natural barriers and is purified from biofouling. A widespread prohibition on discharging untreated water into reservoirs and total transition to water recycling technologies may significantly reduce chemical contamination