Software creation for cyber-physical systems is based on complex algorithms. A feature of the modern organization of production and commerce is the consolidation of participants in these activities into complex network structures. In this case, a scientifically based analysis of network processes of a physical and economic nature is necessary. In the present paper, the formalization of the problem is carried out using graph theory. A mathematical model based on partial differential equations, defined on a graph with one cycle is developed. The analysis comes down to the important problem of expanding a given function into eigenfunctions of the Sturm-Liouville tasks with measure on the graph. The obtained results are fundamental for cyber-physical systems of a wide range of applications.
This paper is on the problem of effective business management related to the segment of long-term participants of various business activities, comprehensively interacting with the social and business environment. The study considers the periodicity of most economic processes, which has a complex characteristic. The optimization criterion was a functional, which included an assessment of the internalization of the impact of the results of such activity. As a result, a mathematical model was obtained, which serves as the basis for expert systems aimed at accounting of externalities of a wide range of nationwide, institutional, business and social activity.
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