A Mathematical Analysis of Structural Effects

结构效应的概念是由布劳引入社会学家的。他试图解释社会集体的属性对个人取向和行为的影响。但他的讨论是用自然的、非数学的语言进行的，在本研究中，我们试图将布劳的基本思想表达为一个数学模型。我们的主要工具是吸收马尔可夫链的数学理论。提出了吸收前平均跃迁数的概念。社会集体中的相互作用过程称为结构效应，可以用吸收马尔可夫链来描述。我们可以预期，这一新的特征值来自基本矩阵是一个基石的数学分析的结构效应。

The concept of structural effect was introduced to the sociologists by P.M.Blau. He tried to explicate the effects of attributes of social collectivities on individual orientations and conducts. But his discussions were made in natural, non-mathematical languages.In this study, we make an attempt to express Blau's basic idea as a mathematical model. Our major tool is the mathematical theory of absorbing Markov chain. We suggest a concept of mean number of transition before absorption. The interaction processes in social collectivities called structural effects could be explicitly depicted by Absorbing Markov chain. We can expect that this new characteristic value derived from fundamental matrix is a cornerstone for a mathematical analysis of structural effects.