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Purpose. Renewal of fixed assets is the most important factor in ensuring sustainable development and competitiveness of enterprises. The process of updating fixed assets is a fundamental aspect of investment activity, directly affecting production efficiency and long-term growth. The purpose of this study is to develop and analyze a mathematical model that describes the dynamics of equipment replacement, taking into account the growth rates of the cost of fixed assets, their return on investment and service life.

The article quantitatively analyzes the impact from number of factors, that influence the renewal  process through the use of the developed economic dynamics equation. The parameters of existing and new equipment are considered as primary data on fixed assets. In particular, the cost and performance per technic's unit. The results of the fixed assets renovation are indicators of product's growth rates, investment resources etc.

The article deals with the problem of legal socialization. Indicate the role and importance of legal socialization in the current development of legal science. It is shown that the more socialized man, the more it reveals its ability to be the main productive force of society, the more it is able to understand the natural environment, law, state and society as a whole system.

In the article the methodological aspects of the theory of law. Particular attention is paid
to problems of methodology in modern general theoretical law