广义对称表的定义和哲学意义  

Definition of Generalized Symmetric Array and Philosophical Significance

作　　者：张应山 赵建立[2] ZHANG Ying-shan;ZHAO Jian-li(School of Statistics,Faculty of Economics and Management,East China Normal University,Shanghai,200241,China;School of Mathematical Sciences,Liaocheng University,Liaocheng,252059,China)

机构地区：[1]华东师范大学经济与管理学部统计学院,上海200241 [2]聊城大学数学科学学院,山东聊城252059

出　　处：《聊城大学学报（自然科学版）》2018年第4期58-64,共7页Journal of Liaocheng University:Natural Science Edition

基　　金：国家自然科学基金项目(11301247);教育部高等学校博士学科点专项基金资助项目(200802691021)资助

摘　　要：基于《多边矩阵理论》,由东方整体性思维所启迪,试图提供并完善一套从整体到局部处理复杂系统对称多指标问题、对称非均匀性问题、对称非线性问题的强有力的数学工具,并对其进行严格的理论推导和证明.广义对称性或广义对称分析方法,是许多学科关注的问题之一,在研究广义对称性问题时,构造一个广义对称表成为研究广义对称性问题的基础.作为系列论文的第一篇,本文利用自由函数模型,根据正交幂等系统,采取对称置换不变性作为平衡指标,定义广义对称表,并从哲学层面讨论它的哲学意义.This series of articles based on “multilateral matrix theory”, inspired by the Eastern holistic thinking by trying to provide and improve a whole complex system to handle symmetrical multi-target problems, symmetrical non-uniformity problems, symmetrical nonlinear problems, a powerful mathematical tool from Global to Local issues and its rigorous theoretical analysis and proof. Generalized symmetry or generalized symmetry analysis method is one of the concerns in the study of generalized symmetry of the problem, the structure for a symmetrical array is the basis of generalized symmetry problem. As the first series of papers, in this paper, using the free function model, according to the orthogonal idempotent system, adopting the symmetrical permutation invariability as a balance index,both the definition and the philosophical meaning of generalized symmetrical arrays are discussed from philosophical level.

关 键 词：广义对称表 正交幂等系统 自由函数模型 对称置换不变性 对称矩阵象 

分 类 号：O212.6[理学—概率论与数理统计]