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The author proposes algorithms for constructing a pre-basis and the basis of the set of solutions for systems of linear constraints of the type of equalities and inequalities in the domains of integers, which are based on combined coefficients of constraints. The article considers the algorithm for constructing the pre-basis and basis of systems of linear equations and algorithms for constructing the fundamental system of solutions for systems of linear homogeneous and linear inhomogeneous inequalities. [ABSTRACT FROM AUTHOR]

Theoretical foundations of asymmetric encryption based on the residue number system and its modified perfect form are developed. The selected moduli of the residue number system are considered to be secret keys. When recovering a number from its residues, multiplication by arbitrarily selected coefficients (public keys) takes place. It is established that cryptostability of the proposed algorithms is based on solving the problem of factorization or exhaustive search of sets of moduli. The developed approaches allow us to increase the block of plaintext almost indefinitely, eliminating the need to use different encryption modes. [ABSTRACT FROM AUTHOR]

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The object of research is the industrial risk of an industrial facility. One of the most problematic places is the uncertainty of the initial information regarding the object of study and the lack of a universal methodology that would allow an assessment of technological risks at all stages of the operation of an industrial object. A particularly acute problem concerns potentially hazardous industries. The analysis of existing methods and approaches to assessing the technological risks of industrial facilities at different stages of their functioning is carried out. It is established that one of the best methods is the Monte Carlo method, which allows to quantify the uncertainty of decisions. The use of the Monte Carlo method for quantitative hazard analysis in order to determine the probability of accidents and accidents, the magnitude of the risk, the magnitude of the possible consequences is justified. The elements of the theory of reliability for the quantitative assessment of risks are used. A quantitative hazard analysis in accordance with the theory of reliability makes it possible to determine the probability of accidents and accidents, the magnitude of the risk, the magnitude of the possible consequences. Probability methods and statistical analysis are integral parts of the quantitative analysis of hazards and technological risk. An algorithm is developed to determine the industrial risk of an industrial facility using the theory of reliability. A software package is developed based on the theory of reliability with a combination of Monte Carlo simulation of the system. The developed software package allows to analyze the level of technogenic risk when using various methods of connecting elements of the system, as well as evaluate changes in the reliability of the system when using other components. The program is presented on the example of a system, the components of which are the heaters PVT1- 7 (Ukraine) in the technological system of a thermal power plant. The system under study is at the border of an unacceptable and conditionally acceptable level of danger, which gives grounds for the need to take measures to increase the reliability of the system by increasing the number of backup system elements, or improving their quality. [ABSTRACT FROM AUTHOR]

Copyright of Economy & Forecasting / Ekonomìka ì Prognozuvannâ is the property of Ukrainian National Academy of Sciences, Institute for Economic Forecasting and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)