En中的几何概率及其极值  

Geometric probability and its extremes in E

作　　者：赵江甫 ZHAO Jiang-fu(Department of Mathematics and Physics,Fujian Jiangxia University,Fuzhou 350108,Fujian,China)

机构地区：[1]福建江夏学院数理教研部,福建福州350108

出　　处：《山东大学学报（理学版）》2021年第4期76-85,共10页Journal of Shandong University(Natural Science)

基　　金：福建省教育厅中青年教师教育科研基金资助项目(JT180585);福建江夏学院科研培育人才基金资助项目(JXZ2019016)。

摘　　要：三维空间中,三个与凸体K相交的平面的公共点落入K内的概率已有结果。为了将此结论推广到更一般的n维欧式空间,设L、G、H为En中与凸体K相交的3个超平面,利用积分几何的方法,给出超平面束的交L∩G∩H与凸体K相交的几何概率,并利用等周不等式,得到此概率序列的极大值。利用Minkowski不等式和Cauchy公式,给出En中超平面偶的交L∩G与凸体K相交的几何概率的极大值。根据上述结论,得到两个关于超几何函数的不等式。The probability that three planes in 3-dimensional Euclidean space intersecting a convex body K have their common point inside K has been obtained.In order to extend the above conclusion to more general n-dimensional Euclidean space,let L,G,H be three randomly chosen hyperplanes,that intersect a convex body K in En.The probability that L∩G∩H intersecting the convex body K is given by method of integral geometry.And then the Extreme value of this probabilistic sequence is obtained through isoperimetric inequalities.The maximum of probability that L∩G intersecting the convex body K is found by using of Minkowski inequality and Cauchy’s formula.As their application,two inequalities about hypergeometric functions are given.

关 键 词：平均曲率积分 几何概率 蒲丰投针 极值问题 超平面束 

分 类 号：O186.5[理学—数学]