Studies the limitation of the equilibrium approximations to the kinetics of complex reactions.

The purpose of this paper is to show how to apply the singular perturbation method to the rate equations in reaction kinetics that involve different time scales. The Lindemann scheme has been chosen for illustration, and the steady-state and equilibrium approximations used in the Lindemann scheme are discussed.

The existing drainage systems in Polesia have exhausted their resource and need reconstruction and modernization to improve the overall technological, economic and environmental efficiency of their operation.To study the influence of the main factors of variation of the distance between the drains methods of statistical modeling and the probability theory are used, which developed a mathematical model for determining standard deviation determining factor of the investigated function. According to the results of the studies, it was found that the drainage flow module characterizing the intensity of soil and territory drainage is formed mainly due to the values of the drainage speed, filtration coefficient and the time of excess water drainage and has a significant impact on the distance between the drains, which is 86-98 %. Based on the simulation for the conditions of Ukrainian Polesia dynamics and the average weighted modules in drainage outflow under different weather and climatic conditions for growing different crops on different soils, the considerable variability of their values in time and space are obtained, the normalized curves constructed security module drainage outflow for the main arable crops on mineral and peat soils. The obtained results convincingly show that both current and average values of the drainage flow modulus in the studied conditions have a pronounced variability in climatic conditions, the type of crops grown and the type of soil. With its value for the selected key factors the drainage system substantially differs primarily from the maximum current values and values during the vegetation period calculated from accepted values by more than a few times, what determines the need to take account of this designing reconstruction projects, construction and operation of such facilities.

Drainage on drained lands is the main regulator of water-air and general natural reclamation regime. Currently, the most promising economic and mathematical method is considered, which combines the advantages of hydro-mechanical and empirical methods and is based on the implementation of a set of forecast and optimization calculations. However, in the conditions of transition to market relations, this method, as it is implemented, does not allow to determine the optimal drainage parameters differentially with respect to different levels of crop yield in compliance with modern economic and environmental requirements in the changeable natural-agro-reclamation conditions of the real object, so it needs further improvement. In this regard, the principles of construction and implementation of a comprehensive model for optimizing agricultural drainage parameters are developed, taking into account the climatological strategy of object management, based on the implementation of interrelated structural and technological, forecast-simulation and optimization blocks of models. This makes it possible to determine economically feasible and environmentally acceptable design solutions based on the relevant criteria. As economic criteria and conditions of the optimization deal with the minimization of costs subject to climatic risk, and environmental component -condition in the form of a matching constraint values of the module of drainage flow within the system ecologically acceptable value. The scientific principles of construction and implementation of structural-technological, forecast-simulation and optimization blocks of models based on changeable natural-agro-meliorative conditions of a real object have been developed, which allow obtaining differentiated values of yield corresponding to the considered variants of drainage parameters, as well as evaluating the technological and environmental efficiency of its operation within the project period.

No abstract