共查询到18条相似文献,搜索用时 234 毫秒
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本文我们利用一个可微函数给出了一对高阶对称规划问题 ,其中目标函数包含了Rn 中一紧凸集的支撑函数 .在引入高阶F 凸性 (F 伪凸性 ,F 拟凸性 )后 ,证明了高阶弱、高阶强及高阶逆对称对偶性质 . 相似文献
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对凸区域DRn上的二次可微函数,本文采用构造“混合函数”的方法,将多元函数微分中值定理推广到了高阶的情形,并给出了应用示例. 相似文献
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主要研究了两类近似凸集的关系和性质.首先,举例说明两类近似凸集没有相互包含关系.其次,在近似凸集(nearly convex)条件下,证明了在一定条件下函数上图是近似凸集与凸集的等价关系.同时,考虑了近似凸函数与函数上图是近似凸集的等价刻画、近似凸函数与函数水平集是近似凸集的必要性,并用例子说明近似凸函数与函数水平集是近似凸集的充分性不成立.最后,基于近似凸函数和拟凸函数的概念,给出了近似拟凸函数的概念并研究了近似拟凸函数与水平集是近似凸集的等价刻画. 相似文献
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引入实值函数关于有界闭凸值测度的集值积分,并讨论了集值积分的收敛定理,证明了当集值测度为有界闭凸集值的有界变差集值测度时,关于弱紧凸集值测度的积分性质对有界闭凸集值测度仍然保持.推广了实值函数关于弱紧凸值测度的积分. 相似文献
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用算子刻划的亚纯单叶函数类 总被引:6,自引:0,他引:6
本文用算子刻划了亚纯星象函数、亚纯凸象函数、亚纯近于凸函数和亚纯拟凸函数的新子类,建立了包含关系,讨论了这些类中函数积分算子的性质。 相似文献
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李万社 《纯粹数学与应用数学》1993,9(1):90-94
1980年,P.Duren和G.Schober引入了非零单叶函数族S_0,f∈S_0是指f(z)在单位园盘内单叶解析,恒不等于零并且用条件f(0)=1正规化。在后来的一系列文章中,他们研究了S_0的闭凸包HS_0中的线性极值问题。设ψ是S_0上的实值连续凸泛函,本文研究了凸极值问题maxψ(f)f∈S_0,得到极值函数值域及其不取弧的一些性质,这些结果包含了P.Duren和G.Schober的结果。 相似文献
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该文先介绍一些中国数学家在几何不等式方面的工作.作者用积分几何中著名的Poincarè公式及Blaschke公式估计一随机凸域包含另一域的包含测度, 得到了经典的等周不等式和Bonnesen -型不等式.还得到了一些诸如对称混合等周不等式、Minkowski -型和Bonnesen -型对称混合等似不等式在内的一些新的几何不等式.最后还研究了Gage -型等周不等式以及Ros -型等周不等式. 相似文献
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This paper shows some properties of symmetry function induced by a convex body in a normal linear space. Some relationships between symmetry function induced by a convex body and Minkowski functional of the convex body are presented. 相似文献
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E. Lutwak 《Discrete and Computational Geometry》1998,19(2):229-235
The following containment theorem is presented: If K and L are convex bodies such that every simplex that contains L also contains some translate of K , then in fact the body L must contain a translate of the body K . One immediate consequence of this theorem is a strengthened version of Weil's mixed-volume characterization of containment.
Received October 31, 1995, and in revised form February 28, 1996. 相似文献
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In Hudzik and Landes, the convexity coefficient of Musielak–Orlicz function spaces over a non-atomic measure space equipped with the Luxemburg norm is computed whenever the Musielak–Orlicz functions are strictly convex see [6]. In this paper, we extend this result to the case of Musielak–Orlicz spaces equipped with the Orlicz norm. Also, a characterization of uniformly convex Musielak–Orlicz function spaces as well as k-uniformly convex Musielak–Orlicz spaces equipped with the Orlicz norm is given. 相似文献
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Wolfgang Weil 《manuscripta mathematica》1973,8(4):335-362
It is shown that a convex body in n-dimensional Euclidean space can be approximated by a sequence of smooth convex bodies in such a way that the principal radii of curvature converge in a certain sense. This fact is used to characterize those first surface measures of convex bodies which belong to polytopes. Furthermore it is proved that the support function of a convex body whose first surface measure has bounded density must have continuous first partial derivatives. 相似文献
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In this paper we propose a method to construct probability measures on the space of convex bodies. For this purpose, first, we introduce the notion of thinness of a body. Then we show the existence of a measure with the property that its pushforward by the thinness function is a probability measure of truncated normal distribution. Finally, we improve this method to find a measure satisfying some important properties in geometric measure theory. 相似文献