共查询到20条相似文献,搜索用时 156 毫秒
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Lutwak提出了凸体的Lp-曲率映象的概念,并证明了凸体与其Lp-曲率映象的体积之间的一个不等式.本文给出了Lutwak结果的一个一般形式,继而证明了凸体与其Lp-曲率映象的极的体积之间的一个不等式,并得到了凸体的Lp-投影体和Lp-曲率映象的体积之间的一个不等式. 相似文献
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Lutwak提出了凸体的Lp-曲率映象的概念,并证明了凸体与其Lp-曲率映象的体积之间的一个不等式.本文给出了Lutwak结果的一个一般形式,继而证明了凸体与其Lp-曲率映象的极的体积之间的一个不等式,并得到了凸体的Lp-投影体和Lp-曲率映象的体积之间的一个不等式. 相似文献
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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
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杜昌敏 《应用数学与计算数学学报》2012,(4):396-402
结合p-投影体和p-几何最小表面积的定义,首先,得到了一类凸体p-几何最小表面积的单调性.然后,给出了另外一类凸体p-几何最小表面积的积分表达式,并由此定义了这类凸体的p-混合几何最小表面积,从而得到了一些不等式. 相似文献
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汪雷雷 《应用数学与计算数学学报》2018,(2)
证明了凸体的极小L_p(p0)表面积的存在唯一性,刻画了凸体的L_p表面积达到极小值时凸体的特征,并建立了关于极小L_p表面积的一个仿射等周不等式. 相似文献
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将关于中心对称凸体的低维椭球截面的Dvoretzky的著名定理推广到了一般凸体上. 相似文献
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本文中以刚性微凸体与可变形微凸体的相互作用模拟金属压力加工过程中模具与工件之间的摩擦过程,并用上限法分析所提出的模型.将数学模型进行多变量最优化处理后发现,金属压力加工过程中,除了可能发生工件上的微凸体与模具上的微凸体相互粘结、撕裂和犁沟等现象外,工件上的微凸体可能沿工件表面波浪式前进,形成塑性波,也可能被辗平而消失.在形成塑性波的条件下,摩擦系数与微凸体几何形状有关.但微凸体的连结强度对摩擦系数影响不大.微凸体的几何形状对工件表面下的塑性变形层的深度有显著的影响.实验结果证实了本文所提出的模型的前提的正确性以及部分理论分析结果. 相似文献
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《Computational Geometry》2005,30(2):129-144
A convex geometry is a combinatorial abstract model introduced by Edelman and Jamison which captures a combinatorial essence of “convexity” shared by some objects including finite point sets, partially ordered sets, trees, rooted graphs. In this paper, we introduce a generalized convex shelling, and show that every convex geometry can be represented as a generalized convex shelling. This is “the representation theorem for convex geometries” analogous to “the representation theorem for oriented matroids” by Folkman and Lawrence. An important feature is that our representation theorem is affine-geometric while that for oriented matroids is topological. Thus our representation theorem indicates the intrinsic simplicity of convex geometries, and opens a new research direction in the theory of convex geometries. 相似文献
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通过Banach 空间与局部凸空间的对比,将Banach 空间上的Diestel-Faires 定理在局部凸空间上进行推广。进一步给出了局部凸空间上的Orlicz-Pettis定理与推论。 相似文献
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Mohsen Alimohammady Yeol Je Cho Vahid Dadashi Mehdi Roohi 《Applied Mathematics Letters》2011,24(8):1289-1294
This paper deals with some basic notions of convex analysis and convex optimization via convex semi-closed functions. A decoupling-type result and also a sandwich theorem are proved. As a consequence of the sandwich theorem, we get a convex sub-differential sum rule and two separation results. Finally, the derived convex sub-differential sum rule is applied to solving the convex programming problem. 相似文献
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B. Klartag 《Journal of Functional Analysis》2007,245(1):284-310
We investigate the rate of convergence in the central limit theorem for convex sets established in [B. Klartag, A central limit theorem for convex sets, Invent. Math., in press. [8]]. We obtain bounds with a power-law dependence on the dimension. These bounds are asymptotically better than the logarithmic estimates which follow from the original proof of the central limit theorem for convex sets. 相似文献
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基于各种Ekeland变分原理的等价形式, 主要研究局部凸空间中给定有界凸子集乘以距离函数为扰动的单调半连续映射的向量Ekeand变分原理的等价性问题. 首先利用局部凸空间中的向量Ekeland变分原理证明了向量Caristi-Kirk不动点定理,向量 Takahashi非凸极小化定理和向量Oettli-Th\'{e}ra定理. 进一步研究了向量Ekeland变分原理与向量Caristi-Kirk不动点定理,向量Takahashi非凸极小化定理和向量Oettli-Th\'{e}ra定理的等价性. 相似文献
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A STRONG OPTIMIZATION THEOREM IN LOCALLY CONVEX SPACES 总被引:1,自引:0,他引:1
This paper presents a geometric characterization of convex sets in locally convex spaces on which a strong optimization theorem of the Stegall-type holds, and gives Collier's theorem of w Asplund spaces a localized setting. 相似文献
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Li-wen Zhou Yi-bin Xiao Nan-jing Huang 《Journal of Optimization Theory and Applications》2017,172(3):824-844
In this paper, some new results, concerned with the geodesic convex hull and geodesic convex combination, are given on Hadamard manifolds. An S-KKM theorem on a Hadamard manifold is also given in order to generalize the KKM theorem. As applications, a Fan–Browder-type fixed point theorem and a fixed point theorem for the a new mapping class are proved on Hadamard manifolds. 相似文献
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In this article, we deal with some computational aspects of geodesic convex sets. Motzkin-type theorem, Radon-type theorem, and Helly-type theorem for geodesic convex sets are shown. In particular, given a finite collection of geodesic convex sets in a simple polygon and an “oracle,” which accepts as input three sets of the collection and which gives as its output an intersection point or reports its nonexistence; we present an algorithm for finding an intersection point of this collection. 相似文献
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V. Klee extended a well-known theorem of Minkowski to non-compact convex sets. We generalize Minkowski’s theorem to convex sets which are not necessarily closed. 相似文献