The new classes of differential games pursuit-evasion with the phase constraints, the terminal set and functionality, the fixed time of the game end on the Cartesian product of the set of closed subsets of the Euclidean space and set of continuous functions are solved. With the help of new differential-operator constructions, a general approach to the construction of optimal strategies of each of the players is invented.

A number of systems and single indicators for environmental sustainability assessment of different level objects is proposed. An assessment of sustainable development environmental dimension of world countries and regions of Ukraine with inverse interpretation in the context of quality and security of human life is carried out. The profiles of regions of Ukraine are generated with marking out of indicators of the greatest interest from regional development processes management point of view considering social-environmental-economical sustainability.

The mathematical model of informative environment is developed for the exposure of thermal anomalies in a current situation. The original image fusion methods were developed for two channel optoelectronic systems of supervision (OESS) at the sensors level and on the base of information map, which provides higher detect probability of thermal anomalies after their relevant features. The criterion of information fusion efficiency is developed for multispectral OESS on the base of the targeting task performance.

Reasonable hypothesis of formation of nitric-calcium-humic sulfur-containing hard compos with even distribution of calcspar and humic matters on all volume of granules during realization of isothermal mass crystallization of the saturated aquatic solutions of sulfate to the ammonium.

The processes of illumination of low mineralized and salt waters are studied with the use of additional reagents. Possibility of the use and efficiency are set in the processes of illumination of different types of coagulants and flokulants, selected most suitable from them for illumination of low mineralized, the optimal doses of reagents, condition of their use are certain, limiting factors that determine efficiency of discolouration with the help of chemical reagents are set. The processes of the reagent softening of waters of this type are studied.

It was suggested to apply the gas turbine plant «Aquarius» for regular gas-turbines engines heat utilization which transports natural gas in Ukrainian gas pipelines system. It is helped to create the modified energy saving technology for power engineering, industry, housing and communal services.

A new thermal diagram was offered and investigated. In this scheme was united in utilization complex a few regular gas turbines which helped to increase heat utilization of all compressor station.

For the first time in Ukraine team of students and teachers has developed experimental flight model of nanosatellite and structural - technological methods for ensuring of thermal conditions of all nanosatellite subsystems. Namely, onboard the data processing subsystem with the help of onboard computer and software applications, three axes attitude determination and control subsystem with sun sensors, radio frequency link telecommunication subsystem, telemetry tracking and control subsystem, electric power supply subsystem.

Application of cables with nano-hardened cross-linked polyethylene (XLPE) insulation is a strategic way to improve the reliability and ecological compatibility of systems of power supplies in all countries. However, there is no normative base for the diagnosis of these cables in Ukraine. Besides there is no necessary diagnostic equipment, despite the fact that the plant "Pivdenkabel" (Kharkiv, Ukraine), the first in the CIS mastered their industrial production for voltages up to 330 kV.

Signal processing devices based on crystal-like structures are the newest element base of information and telecommunication systems. To improve the efficiency of microwave microstrip signal processing devices proposed and developed two-phase crystal-like structures for increasing of signals in the passband and stopband suppression to 60 dB and reducing the size of devices in

An algorithm for computer simulation of molecular dynamics. Recommended method for studying nanosystems based on the results of molecular analysis - dynamic analysis of the basic properties of nanomaterials. Recommended method for determining the spatial distribution of polarization in dielectrics active nanolayers. The technique of describing the processes of nucleation and growth of artificial nanodomenov. To analyze the size effects built microscopic model intracluster atomic dynamics of the sensitive layer of the sensor.