【作者】 李涛；

【导师】 任德麟；

【作者基本信息】 武汉科技大学 ， 应用数学， 2010， 硕士

【摘要】 凸域中的平均弦长问题,主要是凸性与积分几何结合而出现的问题分支,弦幂积分的应用,使得凸体几何问题变得丰富多样.例如凸域内两点间的平均距离,运动测度,包含测度,平均弦长等.而中间的关键部分是弦幂积分问题,这个部分是本文主要研究的重点,通过具体的实例进行演绎推理.鉴于这些问题的解决,有助于反映凸域的几何特性,我们将通过一些基本理论基础,综合有关定义性质,来探究几何问题处理的一般方法.当然,要运用这个方法去解决好实际问题还有一定难度,由于理论化的知识处理对象是简单的凸域,如果换做复杂的凸域,可能问题就会复杂化,那么就要细致研究,根据要解决的问题着手进行多方面的考虑.在下面的文章中,将从理论基础的相关知识,具体探讨了弦幂积分问题.实际应用中,我们通过弦幂积分这个纽带,把问题升华到一般方法,以及新问题的巧妙方法应用.具体运用时,我们要灵活多样.本文研究加深凸理论在简单凸域应用中的直观化,从而有助于我们能更深入研究复杂凸域问题.考虑平均弦长的实际意义,我们要知道重点是弦幂积分的计算,本文结合具体的实例,整理出一般研究方法并总结出重要的结论.更多还原

【Abstract】 The average chord length problems of convex domain, mainly is convex combination with integral geometry problems that occur and branch, with the chord-power integrals, making the application of geometric convex body becomes rich and varied problem. For example, in convex domain, we see the average distance between two points, kinematic measure, including measure, average chord length etc. But among the key part is chord-power integrals problem, this section is the focus of research, the paper mainly by specific examples for deductive reasoning.In view of the solution of these problems, conducing to reflect the geometric convex domain properties, we’ll pass through some basic theoretical foundation, comprehensive related definitions, explore geometry problems processing methods. Of course, we want to use this method to solve practical problems have certain difficulty, because theorization knowledge object is simple convex domain, if changed the complex convex domain may problem is complicated, so be about meticulous research, according to the problems to solve embark on various consideration.Below the article, from the theoretical basis, step by step, specific discusses chord-power integrals problem. Practical applications, we through chord-power integrals this link to question sublimate arrives general method, and the new question the ingenious methods applications. Specific application, we should be flexible and diversified. This paper studies deepen convex theory in simple convex field application of direct, thus we can further our study into complex convex domain problem.Considering the average string long practical significance, we want to know what key is chord-power integrals calculation, combined with some examples, sort out research methods and summarizes the feasible conclusion.更多还原