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The analysis of state management based on system and structural-functional approaches allowed to identify the current needs of its development, and demonstrate that it performs the tasks of control and regulation, including the transformation of inter-ethnic and rural communities in the regions of Siberia. It is revealed that the state ethnic and agrarian policy does not solve the problem of economic and socio-cultural transformations in the life of communities. It is shown that the optimal solution to this problem would be the regulatory impact assessment (RIA), as well as the construction of theoretical models for the practical implementation of state regulation of transformation processes. The structure of the theoretical model of socio-cultural regulation of transforming communities is proposed.

On the basis of T. Parsons’ classical concept of social institutions the authors consider the family as a social institution and its role in determining the transformation of interethnic communities. The model of the mechanism of determination is offered including the ethnic structure of the population, type of family, intergenerational relations in the family, social and interethnic attitudes of children (youth), acculturation strategies of youth, social communication of family with other social institutions. The model is verified with the materials of specific sociological studies in the republics of Sakha (Yakutia), Khakassia, Tuva. The positive role of ethnically mixed families in the integration of interethnic communities is revealed.

A study has been made of the problem on the process of formation of a zone of higher-than-average permeability with a moving boundary in an initially low-permeability porous medium (problem on hydraulic fracturing of a bed) in a three-dimensional formulation. A characteristic feature of the three-dimensional problem was the taking into account the existence of two zones (zone with a regular permeability and the destruction zone) in the porous medium, whose contact region was determined using the condition of mass balance on the moving boundary. Special features fundamental to the process of mass transfer in such filtration-inhomogeneous porous media have been revealed and analyzed.

The problem of the squeezing out of a solution from aggregates in a porous medium has been considered and investigated. A specific feature of the problem lies in taking account of the existence of two compaction zones in deforming aggregates of a porous medium. Features essential to mass transfer in a deformable aggregated porous medium have been determined and analyzed.