对称框架同构类的计数——处理复杂系统的新思维系列之八  

Symmetrical Frame Isomorphism Class Count-the New Thinking of Dealing With Complex Systems Series Eight

作　　者：罗纯[1,2] 张晓丽[2] 张应山[2] 

机构地区：[1]上海应用技术学院理学院,上海200235 [2]华东师范大学金融与统计学院,上海200241

出　　处：《上海应用技术学院学报（自然科学版）》2011年第3期253-257,共5页Journal of Shanghai Institute of Technology: Natural Science

基　　金：教育部高等学校博士学科点专项基金资助项目(44K55050)

摘　　要：本系列论文基于《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多指标问题、非均匀性问题、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。对称性或对称分析方法,是众多学科关注的问题之一,我们认为构造对称框架是研究对称性问题的基础。本文利用框架的特征来构造稳定子群,再利用稳定子群得到商集,从而得到对称框架;并提出对称框架同构类的个数的计算公式;这种方法对对称分析的研究具有重要意义。This series of articles based on 《multilateral matrix theory》, inspired by the Eastern holistic thinking by trying to provide and improve a whole system to handle complex multi-target problems, non-uniformity problems, nonlinear problems, a powerful mathematical tool from Global to Local issues and its rigorous theoretical analysis and proof. Symmetry or symmetry analysis method is one of the concerns in the study of symmetry of the problem, the structure for a symmetrical framework is the ba- sis of symmetry problem. As the eighth series of papers, we acquire the stability subgroup through characteristics of framework, and then we can get quotient set and symmetric framework. We also pro- pose a method to calculate the number of isomorphism framework which is of great significance to the research of symmetry analysis.

关 键 词：稳定子群 对称框架 商集 

分 类 号：O152[理学—数学] N941.4[理学—基础数学]