数学物理学报 ›› 2011, Vol. 31 ›› Issue (3): 702-708.

• 论文 • 上一篇    下一篇

一些新的运动公式及其应用

邹都1,2, 李德宜2, 谢凤繁2   

  1. 1.平顶山学院 数学与信息科学学院 河南平顶山 467000|2.武汉科技大学理学院 武汉 430081
  • 收稿日期:2008-04-03 修回日期:2009-10-18 出版日期:2011-06-25 发布日期:2011-06-25

Some New Kinematic Formulae and Their Applications

 ZU Du1,2, LI De-Yi2, XIE Feng-Fan2   

  1. 1.School of Mathematics and Information, Pingdingshan University, Henan Pingdingshan 467000|2.School of Science, Wuhan University of Science and Technology, Wuhan 430081
  • Received:2008-04-03 Revised:2009-10-18 Online:2011-06-25 Published:2011-06-25

摘要:

该文利用集合的Minkowski差研究了线段在有界集合中的包含测度,得到了相关的积分公式,并将结果应用于凸体, 讨论了Buffon型投针问题.

关键词: 积分几何, 运动公式, 包含测度

Abstract:

By Minkowski differences of sets, the containment measures of line segments inside bounded Lebesgue measurable sets are studied and some new integral formulae are obtained. An application to the Buffon's needle problem leads to a new conclusion.

Key words: Integral geometry, Kinematic formula, Containment measure

中图分类号: 

  • 53C65