轴对称凸域的弦协差及其应用  

The Convariogram of Axisymmetric Convex Domains and Applications

作　　者：赵江甫 刘海[2] ZHAO Jiangfu;LIU Hai(Department of Mathematics and Physics,Fujian Jiangxia University,Fuzhou 350108,China;National Engineering Research Center for E-learning,Central China Normal University,Wuhan 430079,China)

机构地区：[1]福建江夏学院数理教研部,福州350108 [2]华中师范大学国家数字化学习工程技术研究中心,武汉430079

出　　处：《西南大学学报（自然科学版）》2022年第7期132-140,共9页Journal of Southwest University(Natural Science Edition)

基　　金：国家自然科学基金项目(61875068);福建省科技厅自然科学基金面上项目(2021J011229);福建省中青年教师教育科研项目(JAT210360);福建江夏学院科研培育人才基金项目(JXZ2019016)。

摘　　要：为了研究轴对称凸域的弦协差,以正五边形域为例,利用广义支持函数得到了正五边形域弦协差的具体解析式,给出了正五边形域的定向弦长分布函数的具体结果.通过建立凸体的弦协差与运动测度之间的关系式,得到了正五边形域中,当小针长度不超过其边长时,小针含于此正五边形域内的运动测度.在此基础上,分别给出无向小针、有向小针含于正五边形域内的几何概率.In order to analyze the convariograms of axisymmetric convex domains, taking the regular pentagon as an example, the explicit expression of the covariogram for a regular pentagon is obtained by using the generalized support function. The orientation-dependent chord length distribution function of the regular pentagon is given by using the covariogram. Further, through establishment of a relationship between the covariogram and the kinematic measure, a needle within a regular pentagon is given, when the length of needle does not exceed the side length of the regular pentagon. On this basis, the probabilities of a random segment, both undirected and directed, and entirely lying in a regular pentagon are given respectively.

关 键 词：弦协差 定向弦长分布函数 运动测度 限弦投影函数 广义支持函数 

分 类 号：O186.5[理学—数学]