2000 Fiscal Year Final Research Report Summary

A Mathematical Analysis of Structural Effects

Research Project

Project/Area Number	11610226
Research Category	Grant-in-Aid for Scientific Research (C)
Allocation Type	Single-year Grants
Section	一般
Research Field	社会学(含社会福祉関係)
Research Institution	Fukuoka University
Principal Investigator	KOBAYASHI Jun'ichi Faculty of Humanities, Fukuoka University, Professor, 人文学部, 教授 (20113243)
Project Period (FY)	1999 – 2000
Keywords	structural effect / absorbing Markov chain / characteristic quantity / mean number of steps before absorption / mean number of transition before absorption
Research Abstract	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.

(2 results)