共查询到20条相似文献,搜索用时 31 毫秒
1.
关于实四元数矩阵的数值半径 总被引:2,自引:1,他引:1
本文在[1]的基础上研究了实四元数矩阵的数值半径。得到了关于数值半径幂的不等式。C-数值半径的不等式也给出了。因此我们推广了曹重光教授的结果。 相似文献
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Extreme properties of quermassintegrals of convex bodies 总被引:3,自引:0,他引:3
In this paper, we establish two theorems for the quermassintegrals of convex bodies, which are the generalizations of the
well-known Aleksandrov’ s projection theorem and Loomis-Whitney’ s inequality, respectively. Applying these two theorems,
we obtain a number of inequalities for the volumes of projections of convex bodies. Besides, we introduce the concept of the
perturbation element of a convex body, and prove an extreme property of it. 相似文献
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In this article, the authors establish two theorems for mixed body, which are the generalizations of the well-known Loomis-Whitney's inequality. 相似文献
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In this article,the authors establish two theorems for mixed body,which are the generalizations of the well-known Loomis-Whitney's inequality. 相似文献
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Marek Lassak 《Geometriae Dedicata》1998,72(1):63-68
We present an analog of the well-known theorem of F. John about the ellipsoid of maximal volume contained in a convex body. Let C be a convex body and let D be a centrally symmetric convex body in the Euclidean d-space. We prove that if D is an affine image of D of maximal possible volume contained in C, then C a subset of the homothetic copy of D with the ratio 2d-1 and the homothety center in the center of D. The ratio 2d-1 cannot be lessened as a simple example shows. 相似文献
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Inequalities for polars of mixed projection bodies 总被引:2,自引:0,他引:2
LENG Gangsong ZHAO Changjian HE Binwu & LI XiaoyanDepartment of Mathematics Shanghai University Shanghai China Department of Mathematics Binzhou Teachers College Binzhou China 《中国科学A辑(英文版)》2004,47(2):175-186
In 1993 Lutwak established some analogs of the Brunn-Minkowsi inequality and the Aleksandrov-Fenchel inequality for mixed projection bodies. In this paper, following Lutwak, we give their polars forms. Further, as applications of our methods, we give a generalization of Pythagorean inequality for mixed volumes. 相似文献
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主要研究几何体的Bonnesen型等周不等式.得到了两个关于四面体的Bonnesen型等周不等式;进一步地,给出了关于四面体的等周不等式的一个简单证明. 相似文献
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Stephen D. Cohen 《Designs, Codes and Cryptography》1997,10(1):5-16
It is proved that the covering radius of a primitive binary BCH code of length q-1 and designed distance 2t+1, where is exactly 2t-1 (the minimum value possible). The bound for q is significantly lower than the one obtained by O. Moreno and C. J. Moreno [9]. 相似文献
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In this paper, some properties of mixed intersection bodies are given, and inequalities from the dual Brunn-Minkowski theory (such as the dual Minkowski inequality, the dual Aleksandrov-Fenchel inequalities and the dual Brunn-Minkowski inequalities) are established for mixed intersection bodies. 相似文献
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本文运用Aleksandrov-Fenchel不等式,首先推广了Lutwak,Bonnesen和Fenchel等建立的三个有用的定理,这三个定理在解决某些唯一性问题中扮演着重要角色.然后,把这些结果从一般的混合体积和投影体推广到混合投影体的极和混合仿射表面积上,获得了一些较理想的结果. 相似文献
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本文证明,在Gromov-Hausdorff拓扑下,Ricci曲率平行,截面曲率和单一半径有下界,体积有上界的Riemann流形的集合是c∞紧的.作为应用,我们证明一个pinching结果,即在某些条件下,Rucci平坦的流形必定平坦. 相似文献
16.
Shin-Yao Jow 《Advances in Mathematics》2010,223(4):1356-1371
Given a big divisor D on a normal complex projective variety X, we show that the restricted volume of D along a very general complete-intersection curve C⊂X can be read off from the Okounkov body of D with respect to an admissible flag containing C. From this we deduce that if two big divisors D1 and D2 on X have the same Okounkov body with respect to every admissible flag, then D1 and D2 are numerically equivalent. 相似文献
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In this paper, we prove that if M is an open manifold with nonnegative Ricci curvature and large volume growth, positive critical radius, then sup Cp=∞.p∈M As an application, we give a theorem which supports strongly Petersen‘s conjecture. 相似文献
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图的无符号拉普拉斯矩阵是图的邻接矩阵和度对角矩阵的和,其特征值记为q1≥q2≥…≥qn.设C(n,m)是由n个顶点m条边的连通图构成的集合,这里1≤n-1≤m≤(n2).如果对于任意的G∈C(n,m)都有q1(G*)≥q1(G)成立,图G*∈C(n,m)叫做最大图.这篇文章证明了对任意给定的正整数a=m-n+1,如果n... 相似文献
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Let K be an isotropic convex body in and let Zq(K) be the Lq-centroid body of K. For every N>n consider the random polytope KN:=conv{x1,…,xN} where x1,…,xN are independent random points, uniformly distributed in K. We prove that a random KN is “asymptotically equivalent” to Z[ln(N/n)](K) in the following sense: there exist absolute constants ρ1,ρ2>0 such that, for all and all NN(n,β), one has:
- (i) KNc(β)Zq(K) for every qρ1ln(N/n), with probability greater than 1−c1exp(−c2N1−βnβ).
- (ii) For every qρ2ln(N/n), the expected mean width of KN is bounded by c3w(Zq(K)).
Keywords: Convex body; Isotropic body; Isotropic constant; Random polytope; Centroid bodies; Mean width; Volume radius 相似文献
20.
We prove an extension of the classical John's Theorem, that characterises the ellipsoid of maximal volume position inside a convex body by the existence of some kind of decomposition of the identity, obtaining some results for maximal volume position of a compact and connected set inside a convex set with nonempty interior. By using those results we give some estimates for the outer volume ratio of bodies not necessarily convex. 相似文献