CASPIAN JOURNAL
MANAGEMENT AND HIGH TECHNOLOGIES
ALGORITHM TO IDENTIFY THE NUMBER OF COMPONENTS OF SOME KINDS OF KNOTS IN MATHEMATICAL MODELING OF VARIOUS PROCESSES
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Read | Syachina Evgeniya I. ALGORITHM TO IDENTIFY THE NUMBER OF COMPONENTS OF SOME KINDS OF KNOTS IN MATHEMATICAL MODELING OF VARIOUS PROCESSES // Caspian journal : management and high technologies. — 2018. — №1. — pp. 85-93. |
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Syachina Evgeniya I. - Assistant Professor, Astrakhan State University, 20a Tatishchev St., Astrakhan, 414056, Russian Federation, eanyushina@yandex.ru
Theory of knots serves to solve problems of various sciences, including non-mathematical ones, as knot can be a mathematical model of numerous objects and phenomena of the World around. In its turn, computer modeling can be carried out for models employing knots (including graph models) interrelated in one way or another. Nowadays some issues of the theory of knots require additional research (analysis). This work in detail shows the method worked out by the author that is aimed to identify the number of components for an optional rational linkage with the help of Reidemeister move for d-diagrams. The notion of free rational linkages has been introduced. Definitions of basic terms have been formulated. The statement that is a ground for the method in question has been proved. This method employed, there is need to make up neither a regular linkage diagram, nor a corresponding d-diagram. The only thing required is to know how to set a free rational linkage of the type . Some particular issues of realization of the algorithms suggested in computer modelinghave been considered.
Key words: узел, свойства узла, зацепление, математическая модель, компьютерное моделирование, диаграмма, четырехвалентный граф, хорда, рациональные узлы, рациональные зацепления, свободное рациональное зацепление, компоненты узлов, knot, knot properties, linkage, m