The problems of modeling processes and systems of the economy are considered, the optimal control problem is posed, the system of nonlinear differential equations representing the economy and the optimized target functional are determined; a variational method for solving the problem is chosen, the principle of invariance of nonlinear systems and the possibilities provided by them for modeling dynamic, including economic, systems are described. A critical analysis of the state in the field of economic modeling is given. The features and properties of the invariance principle of linear systems are considered in terms of the Laplace transform. Sensitivity functions of nonlinear systems and Gato and Frechet derivatives defining them are obtained. The application of sensitivity theory in problems of optimal control of nonlinear systems is shown by the example of a fairly simple problem.

Verbal analysis in this article is understood as an integral part of system analysis. It seems reasonable to use it when making complex decisions in poorly structured problem situations. Typical in this case is the situation that arises when we decide on the construction of a large-scale railway project of strategic importance for the state in the long term. Such projects often make errors in assessing the social effectiveness of their costs and results, and the costs are generally higher than estimated, but the results are lower. For this reason, at the stage of investment, the projects are stopped, in some cases for many years. Such conflicts arise both in Russia and abroad.

The article proposes a systematic approach to the evaluation of large-scale railway projects in the phase of their preinvestment feasibility studies, where the influence of the uncertainty factor and the risks caused by it is maximum. The system assessment structure of projects is a logical-heuristic model, whose information base is based on expert technologies and organizational procedures that form a system of complex investment decision-making. The software products patented in Russia have been developed and tested to support the relevant procedures. Primarily, the novelty of the approach consists, in the ways of transformation of verbal assessments of experts into numerical ones and, secondly, in the rules of accounting radical (non-stochastic) uncertainty while comparing project alternatives.

In the Russian Federation, there is a long process of out-migration from rural areas due to economic, social, engineering, and infrastructural disadvantages. The intensity of migration processes, the sex and age structure of the population are different between the individual settlements and rural areas, due to which the imbalance of social infrastructure capacity and the number of population is growing. The article aims to study the structure and trends of rural settlement on the example of the Republic of Buryatia, and to reveal the regularities of its structural and spatial transformation. The research methods used are statistical summary and grouping, extrapolation, classification, cartographic and graphical methods, calculation of settlement indicators. The information basis of the study was the data of the All-Russian Population Census of 2002, 2010, statistical data for 2020. The study has resulted in the following conclusions: the rural space of the Republic of Buryatia is characterized by extremely low engineering provision; there is an accelerated degradation of small settlements, while maintaining the framework of settlement, including administrative centers of municipal districts and large settlements.

The article reveals key management theories for modern conditions, which allow to investigate the development of the institution of non-profit organizations that can act as an additional source of resources for the established system of municipal management. The information base of the study is based on the works of the founders of the key management theories, which are the basis for the development of modern management approaches of social orientation With the help of a deep logical and structural analysis of the sources, the authors consistently provide arguments that justify the possibility of considering a non-profit organization as an element of the municipal management system from a theoretical point of view. The provisions of the theory of social market economy allowed to bring the concept of non-profit organization to a new theoretical level of comprehension as part of the municipal management system. The provisions of the theory of socio-economics substantiated the interrelation of economic and social components in municipal management, the mutual influence of which substantiates the inclusion of non-profit organizations in the municipal management system. Based on the synthesis of the theories of social market economy, socioeconomics, municipal governance and local self-governance, the authors offer their vision of the theoretical basis for the study of the institution of non-profit organizations as part of the municipal management system.

The article is devoted to the problem of self-education competence formation in the process of basic educational programs realization in the higher school and its further development in the process of professional activity realization in the sphere of public administration. Historical and modern interpretations of the concept “self-education” are considered. Particular attention is paid to the problems of internal and external motivation of students to self-education. The necessity of convergence of educational process and self-education, which requires a special scientific and methodological support, is substantiated. The accumulated global changes in all spheres of life, including professional activity, and the increasing dynamism of these changes require a fundamental modernization of the educational process, the use of mixed pedagogical technologies and the use of digital educational resources. Their focus on the formation of the ability to self-educate creates an opportunity for students to advance education and professional mobility in a changing world. This becomes an existential competence of a public civil servant and characterizes the level of his managerial maturity.

In the Russian Empire in the second half of the 19th century the development of territories (internal colonization) took place in the course of spontaneous relocations in search of free land. The reason was the scarcity of land in the central regions. The government tried to put this process under its control. One such attempt was the establishment of the Resettlement Office in August 1881. Nevertheless, the activities of the Resettlement Office demonstrated the urgency of one of the key issues of the empire's domestic policy and the need to resolve it.

The article analyzes the approaches to the understanding of the state apparatus from the point of view of the efficiency of its functioning. The methodological basis of modern studies is the sociological theory of Max Weber, who high-lighted the attributive characteristics of the bureaucratic system as the most effective form of government. The evolution of his proposed ideas in the process of development of society in general and the state apparatus in particular is considered. Important aspects in the approaches to efficiency evaluation, which should be taken into account in practical application, are noted.

The prediction of socio-demographic development of American transboundary regions as complex open mesoterritorial systems, historically and functionally based on the strengthening of diverse interaction between the United States and neighboring countries (Mexico and Canada), is relevant and practically significant in the design of changes in the settlement system of these territories. On the basis of unified system and meso-economic spatio-temporal modeling used in the present work, the author combined methods of multivariate analysis, linear programming, correlation calculations and others, adequate to the methodology and technique of socio-demographic forecasting. According to the results of an empirical study, hypotheses were confirmed about the possibility of a gradual escalation in the next decade of demographic and ethno-cultural turbulence in the settlement system of the trans-border territories of the southwestern United States bordering Mexico into the initial stage of regionalization caused by the projected increase in migration from Latin American countries; about an increase in imbalance and spatial inequality, reducing optimization in the ratio of the able-bodied population; in the conditions of a new technological order; on the increasing role of mutual influence of settlements of trans-regional regions of the USA, which form the material and territorial basis of the settlement system. The results of regression modeling of prospective changes in quantitative indicators of natural and mechanical population growth of a particular locality that has its rank in the settlement system of a cross-border region of the USA have shown that the qualitative nature and direction of dynamics of elements (objects, processes, environment, projects) of socio-demographic development depend on the size of the city center, neighboring settlements and suburbanized zones and the interactions between them.

Economic growth in the regions is substantially determined by the development of agriculture, which ensures the satisfaction of the population's needs for foodstuffs. Modeling of the development of animal husbandry and plant growing allows to reveal the factors influencing the functioning of agricultural branches, including the dependence of the territory on food export, to determine their quantitative influence on the increase in the number of cattle and gross harvest of crops, which determines the relevance of the chosen topic of the research. The preliminary classification of the districts of the Republic of Mari El has allowed to build models of development of animal husbandry and crop production for qualitatively homogeneous groups of territories by the level of economic development, reflecting the main factors, influencing on which it is possible to increase the productivity of agricultural development in certain groups of districts and, as a consequence, in the republic as a whole. The proposed study can be of practical importance in the activities of analytical services when drawing up programs of economic development of the Republic of Mari El.

The article deals with the influence of socio-economic factors on the formation of innovation potential of the Republic of Buryatia. The analysis is carried out in the context of the concept of sustainable development, formed on the principles of economic, social and environmental characteristics. According to the results of the assessment for 2010—2020, it was revealed that in the conditions of environmental restrictions associated with the preservation of the ecosystem of Lake Baikal, the economy of the region is growing, the volume of investments in fixed assets is increasing, the life expectancy of the population is growing. The region is developing along an eco-oriented path with the possibility of forming and implementing innovative potential.