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.
作者
赵江甫
刘海
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)
出处
《西南大学学报（自然科学版）》
CAS
CSCD
北大核心
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)。
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
covariogram
orientation-dependent chord length distribution function
kinematic measure
restricted chord function
generalized support function
