共查询到17条相似文献,搜索用时 500 毫秒
1.
根据Lutwak引进的凸体i次宽度积分的概念,本文获得了凸体i次宽度积分的Blaschke-Santal幃不等式,并把Ky Fan不等式推广到了凸体i次宽度积分.最后,本文利用其与对偶均质积分之间的关系建立了两个中心对称凸体的极的Brunn-Minkowski型不等式. 相似文献
2.
3.
本文研究了Rn中平坦的外平行体的平均曲率积分.利用积分几何的方法和凸体理论的相关知识,得到了这些平均曲率积分的均值.作为推论,我们得到了这些平均曲率积分所对应的均质积分的均值. 相似文献
4.
5.
6.
7.
8.
9.
10.
11.
In this article, some kinematic formulas for dual quermassintegral of star bodies and for chord power integrals of convex bodies are established by using dual mixed volumes. These formulas are the extensions of the fundamental kinematic formula involving quermassintegral to the case of dual quermassintegral and chord power integrals. 相似文献
12.
Dual kinematic formulas 总被引:7,自引:0,他引:7
Gaoyong Zhang 《Transactions of the American Mathematical Society》1999,351(3):985-995
We establish kinematic formulas for dual quermassintegrals of star bodies and for chord power integrals of convex bodies by using dual mixed volumes. These formulas are extensions of the fundamental kinematic formula involving quermassintegrals to the cases of dual quermassintegrals and chord power integrals. Applications to geometric probability are considered.
13.
In this paper, we obtain a formula relating the chord power integrals of a convex body K and the dual quermassintegrals of its radial pth mean body RpK. With this, a relation among the chord power integrals of a convex body K under dilation transformations is found. As an interesting application, some geometric inequalities between the dual quermassintegrals of RpK and the volume of K, which are equivalent to the isoperimetric-type inequalities of chord power integrals, are also established. 相似文献
14.
Silvestru Sever Dragomir 《分析论及其应用》2023,39(1):1-15
In this paper, by making use of Divergence theorem for multiple integrals,
we establish some integral inequalities for Schur convex functions defined on bodies $B⊂\mathbb{R}^n$ that are symmetric, convex and have nonempty interiors. Examples for three
dimensional balls are also provided. 相似文献
15.
V. Marraffa 《Czechoslovak Mathematical Journal》2006,56(2):475-490
The McShane and Kurzweil-Henstock integrals for functions taking values in a locally convex space are defined and the relations
with other integrals are studied. A characterization of locally convex spaces in which Henstock Lemma holds is given. 相似文献
16.
在积分区域具有某种对称性时,给出重积分及曲面积分所具有的相应性质,并通过例题给出这些性质在重积分及曲线、曲面积分中的应用方法. 相似文献
17.
R. N. Miroshin 《Mathematical Notes》2007,82(3-4):357-365
Multiple integrals generalizing the iterated kernels of integral operators are expressed as single integrals in the case of a special representation of the kernel (this is our theorem). Besides integral equations, Markov processes involve these integrals as well. As a consequence of the theorem, we obtain transition probability densities of certain Markov processes. As an illustration, we consider nine examples. 相似文献