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Total number
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0215U000013,
0111U000552
,
Investigation of violations of statistical stability of physical quantities and processes and the development of adequate mathematical models of hyper
Klimenko Vitalii, Gorban Igor,
14-01-2015
The Institute of Mathematical Machines and System Problems of NAS Ukraine
The results of the research found that the frequency of real events and selective medium physical processes do not show a trend towards convergence. This means that the statistical phenomenon sustainability is limited and there is the concept of probability mathematical abstraction that has no physical interpretation. Developed physical and mathematical theory of hyper phenomena, which provides a description of real physical events, variables, processes and fields based on their inherent limited statistical stability. Generalized law of large numbers and the central limit theorem in case of lack of convergence of the sample mean. Laid the foundations of mathematical analysis and divergent valued functions. An expanded concept of border and convergence of sequences and functions. Famous for unique features notion of convergence, continuity, differentiation, primary, indefinite integrals and definite integrals are generalized to the case of multi-valued functions. The class of "difficult task" computer algebra efficient solution which is possible only by means of automatic programs with a fairly high level of "artificial" intelligence. Established that already at the present level of computing automatic programs are more efficient than automated. Built-theoretic model of multiple tasks on which developed new quality of the structure of the data set and general principles of automatic process solutions to complex scientific and engineering problems. For long-term physical (technical) facilities developed approach to correctly describe the tasks as algebraic equations, providing a mathematical description of the static equilibrium position rod systems and internal forces in its elements and physical objects described by elliptic equations.
Є.О. Бондаренко
І.І. Горбань
А.К. Бєляєв
В.Б. Корбут
В.П. Волобоєв
В.П. Клименко
Н.Г. Аронова
О.В. Ґедзь
О.Д. Бех
П.С. Сапатий
С.Д. Лутов
Т.М. Швалюк
Ю.Г. Коровицький
2020-04-02
Updated: 2026-01-07
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