共查询到20条相似文献,搜索用时 171 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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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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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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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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设∑为Euclid空间R4中的凸超曲面,其中曲率为H,我们得到了Willmore泛函∫∑H2dσ的一个几何下界估计.这个下界是一个涉及∑的面积、∑所界的凸体K的体积、以及K的.Minkowski均值积分的不变量.还得到了Euclid空间R4中一凸体包含另一凸体的充分条件. 相似文献
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Luis Montejano 《Geometriae Dedicata》1991,37(3):307-316
We prove that the Euclidean ball is the unique convex body with the property that all its sections through a fixed point are convex bodies of constant width. Furthermore, we characterize those convex bodies which are sections of convex bodies of constant width.Research supported by the Alexander von Humboldt-Foundation. 相似文献
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Study in a local geometry of non-smooth convex bodies via their supporting cones. The supporting cones are differential objects if the convex bodies are tangible. Examples of completely tangible and non-tangible convex bodies are presented. 相似文献
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Schneider 《Discrete and Computational Geometry》2008,29(4):575-593
Abstract. Goodey and Weil have recently introduced the notions of translation mixtures of convex bodies and of mixed convex bodies.
By a new approach, a simpler proof for the existence of the mixed polytopes is given, and explicit formulae for their vertices
and edges are obtained. Moreover, the theory of mixed bodies is extended to more than two convex bodies. The paper concludes
with the proof of an inclusion inequality for translation mixtures of convex bodies, where the extremal case characterizes
simplices. 相似文献
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Schneider 《Discrete and Computational Geometry》2003,29(4):575-593
Abstract. Goodey and Weil have recently introduced the notions of translation mixtures of convex bodies and of mixed convex bodies.
By a new approach, a simpler proof for the existence of the mixed polytopes is given, and explicit formulae for their vertices
and edges are obtained. Moreover, the theory of mixed bodies is extended to more than two convex bodies. The paper concludes
with the proof of an inclusion inequality for translation mixtures of convex bodies, where the extremal case characterizes
simplices. 相似文献
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本文研究了Rn中凸集上不变的赋值函数与凸体的投影问题.利用赋值函数的方法,我们获得了凸体在任意维平面上投影的Cauchy公式和Kubota公式,这些结果推广了经典的Cauchy公式和Kubota公式. 相似文献
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R. H. Aramyan 《Journal of Contemporary Mathematical Analysis (Armenian Academy of Sciences)》2018,53(6):363-368
The problem of the sine representation for the support function of centrally symmetric convex bodies is studied. We describe a subclass of centrally symmetric convex bodies which is dense in the class of centrally symmetric convex bodies. Also, we obtain an inversion formula for the sine-transform. 相似文献
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Lars Michael Hoffmann 《Acta Appl Math》2009,105(2):141-156
Translative integral formulas for curvature measures of convex bodies were obtained by Schneider and Weil by introducing mixed
measures of convex bodies. These results can be extended to arbitrary closed convex sets since mixed measures are locally
defined. Furthermore, iterated versions of these formulas due to Weil were used by Fallert to introduce quermass densities
for (non-stationary and non-isotropic) Poisson processes of convex bodies and respective Boolean models. In the present paper,
we first compute the special form of mixed measures of convex cylinders and prove a translative integral formula for them.
After adapting some results for mixed measures of convex bodies to this setting we then use this integral formula to obtain
quermass densities for (non-stationary and non-isotropic) Poisson processes of convex cylinders. Furthermore, quermass densities
of Boolean models of convex cylinders are expressed in terms of mixed densities of the underlying Poisson process generalizing
classical formulas by Davy and recent results by Spiess and Spodarev.
相似文献
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C. Miori C. Peri S. Segura Gomis 《Journal of Mathematical Analysis and Applications》2004,300(2):464-476
Fencing problems regard the bisection of a convex body in a way that some geometric measures are optimized. We introduce the notion of relative diameter and study bisections of centrally symmetric planar convex bodies, bisections by straight line cuts in general planar convex bodies and also bisections by hyperplane cuts for convex bodies in higher dimensions. In the planar case we obtain the best possible lower bound for the ratio between the relative diameter and the area. 相似文献
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Approximation of convex bodies by multiple objective optimization and an application in reachable sets 总被引:1,自引:0,他引:1
In this paper, we focus on approximating convex compact bodies. For a convex body described as the feasible set in objective space of a multiple objective programme, we show that finding it is equivalent to finding the non-dominated set of a multiple objective programme. This equivalence implies that convex bodies can be approximated using multiple objective optimization algorithms. Therefore, we propose a revised outer approximation algorithm for convex multiple objective programming problems to approximate convex bodies. Finally, we apply the algorithm to solve reachable sets of control systems and use numerical examples to show the effectiveness of the algorithm. 相似文献
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We prove a polynomial expansion for measure-valued functionals which are translation covariant on the set of convex bodies. The coefficients are measures on product spaces. We then apply this construction to the curvature measures of convex bodies and obtain mixed curvature measures for bodies in general relative position. These are used to generalize an integral geometric formula for nonintersecting convex bodies. Finally, we introduce support measures relative to a quite general structuring body B and describe connections between the different types of measures. 相似文献