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The subject of the study is the processes of budget decentralization in the management of public finances, as well as mathematical methods and models for implementing the concept of hard budget restrictions in order to create conditions for the self-development of administrative-territorial units. The aim of the study is to develop adaptive economic and mathematical models for implementing the strategy of hard budget constraints implemented in the process of inter-budget regulation. The relevance of the study is due to the fact that currently the subject of acute discussion in the scientific community is the self-development of administrative-territorial entities and increasing their financial independence. In this regard, the focus of economic research is focused on the problems of budgetary decentralization as an engine of economic development, as well as the related topics of the use of mathematical tools for modeling decision support in this area. The created models are subject to the requirements of learnability, adaptability to changing conditions of environmental influences, and the ability to operate not only with quantitative, but also with qualitatively defined characteristics. The problem of mathematical modeling is solved by applying an interdisciplinary synthesis of the theories of stochastic automata operating in random environments and fuzzy logic. The proposed synthesis of theoretical and methodological devices is the novelty of the research. As a result , an economic and mathematical model of a fuzzy automaton is constructed for determining and quantifying the values of the norms for the distribution of tax revenues between budgets of different levels of the budget system. A fuzzy automaton interacts with a simulation model that reproduces budget flows and quantifies the decisions made by the automaton model. The practical significance of the research results lies in the program implementation of the developed models and their inclusion in the public finance management circuit. In the future , it is planned to create a mathematical model of the collective behavior of fuzzy automata models, the interaction of which solves the problem of coordinating the interests of budgets of different levels of the hierarchy in the distribution of tax revenues.

The article considers publication activity of academic and pedagogical workers of the university as an important criterion of the organization and its personnel work. Publication activity is an indirect presentation of results of employees' research work. The review of leading bases of academic citing of Russian authors, including international ones (Web of Scince, Scopus), as international publication activity shows the degree of science development in the Russian Federation in comparison with science in other countries. The article investigates the interrelation of subjective in-university assessment of the author's publication activity and objective positioning of the employee's works in academic community through local indicators of awarding and score rating fixed by the university, which in their turn can become a key administrative way of stimulating publication activity. The optimization task of creating a bonus plan for publications taking into account structural and budgetary constraints, as well as psychosocial aspects of the behavior of authors, was solved.