Object. Structural and functional characteristics of the system. Subject of the Study. Laws and properties of the system. Type of symmetry and topology of the system space, the periodic system of chemical elements being an example. The modification conversion system for describing the properties and laws of the elements. Purpose. Making an integrated system of elements for explicating its properties and laws. Theoretical Description of the Article. The article gives proof of the model of the system, resulting in the logical-philosophical, topical and systemic analyzes through its interpretation in materials of science. The periodic system of chemical elements has been chosen as an interpretive basis as it is the most complete and reliable model system known to modern science. The paper shows how the symmetry of these cells formed an integral system. On the one hand, it is a reliable confirmation of the original topos model, on the other hand, the application of this model allows to convert the modern periodic table into a system overcoming a number of problems that still have not been resolved. The table of the elements is the best approximation to what we call the system, but it has certain imperfections: it is a problem of the falling of a third of elements out of the classification principle. The Symmetry Principle As Applied to the Elements. Model and formula system symmetry. Bitoroidal hexagonal symmetry. The topology of the system: two mirrored torus inscribed in a sphere. The hexagonal cell symmetry in the topological transformation on the surface of the torus. The Final Conclusion: a system has been built on the basis of a topos (cell of symmetry) with a new type of hexagonal symmetry (with two toruses inscribed in a circle containing 120 items). Moreover, the system converges to 120 items and may not exceed this limit due to the properties of closed symmetry.
topics, topos, semantic lattice, a symmetry cell, a symmetry type, system topology, systems analysis, systems modelling, the periodic law, lanthanoids, actinoids, the table of elements, a toroid, a torus
1. Исходные позиции системного моделирования
Системному анализу должен предшествовать выбор (построение) модели, которая отвечает требованиям топологии системного пространства и принципу симметрии с учетом класса и типа сингонии [Ivanenko, Galiulin, 1995, р. 180]. В современной математике и физике учение о симметрии — достаточно развитая совокупность теорий. Одной из них является кристаллофизика [Галиулин, 2002, 10]. Рост кристалла обусловлен регулярными, соответствующими типу его симметрии, переходами от отношений ближнего порядка к дальнему, и наоборот (рис. 1) [Галиулин, 1991, 11].
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