矩阵遗传学，第4部分：遗传8维阴阳代数的周期变化和生理周期的代数模型
Matrix genetics, part 4: cyclic changes of the genetic 8-dimensional Yin-Yang-algebras and the algebraic models of physiological cycles
摘要：
本文继续分析了遗传的8维阴阳代数。该代数在遗传密码结构的矩阵研究过程中被揭示，并且在作者的文章arXiv：0803.3330和arXiv：0805.4692中被描述。本文给出了64个三联体的遗传（8 × 8）矩阵[CA; UG]（3）中遗传密码元素的多种循环排列的数据，其中C，A，U，G是遗传字母表中的字母。这些循环置换导致了初始遗传阴阳代数的矩阵表示形式的重组，从而产生的矩阵也作为新的阴阳代数的矩阵表示形式。它们在算法上与阿达玛矩阵相联系。遗传阴阳代数类型的周期变化的层次结构的发现的存在允许思考新的代数遗传模型的周期过程中遗传的生物系统，包括动物的周期变态模型。遗传8维代数及其8维数值系统的这些变化周期与现代和古代生理学、医学、这一观点认为毕达哥拉斯的著名思想（关于自然系统的组织与数字系统的和谐）应与阴阳循环变化的思想相结合，数字系统在考虑的情况下。这第二个想法让人想起了自然界周期性变化的古老观念。从这样的代数遗传的观点来看，生物时间的概念可以被认为是协调遗传多维代数类型的循环变化的这些层次系综的一个因素。
英文摘要：
The article continues an analysis of the genetic 8-dimensional Yin-Yang-algebra. This algebra was revealed in a course of matrix researches of structures of the genetic code and it was described in the author's articles arXiv:0803.3330 and arXiv:0805.4692. The article presents data about many kinds of cyclic permutations of elements of the genetic code in the genetic (8x8)-matrix [C A; U G](3) of 64 triplets, where C, A, U, G are letters of the genetic alphabet. These cyclic permutations lead to such reorganizations of the matrix form of presentation of the initial genetic Yin-Yang-algebra that arisen matrices serve as matrix forms of presentations of new Yin-Yang-algebras as well. They are connected algorithmically with Hadamard matrices. The discovered existence of a hierarchy of the cyclic changes of types of genetic Yin-Yang-algebras allows thinking about new algebraic-genetic models of cyclic processes in inherited biological systems including models of cyclic metamorphoses of animals. These cycles of changes of the genetic 8-dimensional algebras and of their 8-dimensional numeric systems have many analogies with famous facts and doctrines of modern and ancient physiology, medicine, etc. This viewpoint proposes that the famous idea by Pythagoras (about organization of natural systems in accordance with harmony of numerical systems) should be combined with the idea of cyclic changes of Yin-Yang-numeric systems in considered cases. This second idea reminds of the ancient idea of cyclic changes in nature. From such algebraic-genetic viewpoint, the notion of biological time can be considered as a factor of coordinating these hierarchical ensembles of cyclic changes of types of the genetic multi-dimensional algebras.
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