*3.3. Mathematical Modelling*

The method of applied concretisation of the research results was illustrated by considering the energy cooperative movement in Ukraine and its relationship with the large-scale decentralisation process and the acquisition of a number of powers and rights by local communities to manage their own budgets. It has been proven that the convenience of cooperative organisational and legal forms is due to their flexibility and variability. Simultaneously, the basic resource base for the use of biofuels in agricultural regions of the country is indisputable. The development of energy cooperation is complex, as it has an impact on the revival of processing processes in agriculture and the organisation of the process of organic waste disposal, which is environmentally friendly and economically rational.

The authors' conceptual-analytical model of the complex support of mechanisms for the introduction of renewable energy is formalised by methods of mathematical logic. Thus, in order to achieve the goal of developing mechanisms for the implementation of renewable energy at the regional and local levels, a system of organisational and economic, fiscal, institutional and regulatory measures was applied.

This study also covered the issues of legal, social and infrastructural organisation of the process of transformation of coal enterprises in a city of constituent entities in old industrial regions.

Analysis of the legal, social and infrastructural organisation of the process of the transformation of coal enterprises was performed using cities as subjects in industrial regions. Thus, the fair transformation of coal regions should create a framework for public– private partnerships between central government, local communities and investors. As part of the renovation programmes of mono-regions, not only should support be provided to miners from liberated coal enterprises, but opportunities for education and retraining and new jobs for young people and the unemployed should also be created. Thus, the structural transformation of the economy of old industrial coal regions involves direct investment in new infrastructure in these regions, the development of new industries and the mitigation of unemployment.
