共查询到19条相似文献,搜索用时 62 毫秒
1.
Minkowski不等式的若干推广 总被引:1,自引:0,他引:1
詹仕林 《纯粹数学与应用数学》2004,20(3):232-236
建立了复矩阵的若干行列式不等式,关于Hermite矩阵的Minkoswki不等式被推广到复矩阵中,一些文献的结论获得改进与推广. 相似文献
2.
赵长健 《数学年刊A辑(中文版)》2024,(1):15-24
本文通过引进新的混合弦测度和Orlicz混合弦测度概念,并且利用新近建立的Orlicz弦Minkowski不等式,建立了Orlicz空间上的混合弦积分的φ-弦对数Minkowski不等式.我们的结果φ-弦对数Minkowski不等式,在两种特殊情况下分别产生了弦对数Minkowski不等式和Lp-弦对数Minkowski不等式. 相似文献
3.
通过引入可变单位向量的概念并利用Gram矩阵的正定性建立了一个新的不等式,得到了Hlder不等式的加强,给出了Minkowski不等式(包括离散型和积分型)的改进. 相似文献
4.
5.
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
6.
研究了关于Lp混合均值积分的log-Minkowski不等式,应用Jensen不等式给出Lp混合均值积分的log-Minkowski不等式的简化证明,同时应用加强的Jensen不等式给出一加强不等式. 相似文献
7.
8.
岳嵘 《数学的实践与认识》2008,38(3):135-141
针对"亚正定阵理论(Ⅱ)"一文的广义Minkowski不等式不成立问题,在已有的修正结果基础上,给出一种完整的修正结果;并更正了"亚正定阵的几个开问题及一些不等式"一文中有关的错误结论;用反例说明"广义正定矩阵的进一步研究"一文中的有关结论是错误的,给出完整的修正结果. 相似文献
9.
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
10.
11.
Reisner proved a reverse of the Blaschke-Santal5 inequality for zonoid bodies, Bourgain and Milman showed another reverse of the Blaschke-Santal5 inequality for centered convex bodies. In this paper, two reverses of the Blaschke-Santal5 inequality for convex bodies are given by the Petty projection inequality and above two reverses. Further, using above methods, we also obtain two analogues of the Petty's conjecture for projection bodies, respectively. 相似文献
12.
Qi Guo 《Discrete and Computational Geometry》2005,34(2):351-362
Given a convex body $C\subset R^n$ (i.e., a compact convex set with nonempty
interior), for $x\in$ {\it int}$(C)$, the interior, and a hyperplane $H$ with $x\in H$,
let $H_1,H_2$ be the two support hyperplanes of $C$ parallel to $H$. Let $r(H, x)$
be the ratio, not less than 1, in which $H$ divides the distance between
$H_1,H_2$. Then the quantity
$${\it As}(C):=\inf_{x\in {\it int}(C)}\,\sup_{H\ni x}\,r(H,x)$$
is called the Minkowski measure of asymmetry of $C$. {\it As}$(\cdot)$ can be viewed as a real-valued function defined on the family of
all convex bodies in $R^n$. It has been known for a long time that {\it As}$(\cdot)$
attains its minimum value 1 at all centrally symmetric convex bodies and maximum
value $n$ at all simplexes. In this paper we discuss the stability of the
Minkowski measure of asymmetry for convex bodies. We give an estimate for the
deviation of a convex body from a simplex if the corresponding Minkowski measure
of asymmetry is close to its maximum value. More precisely, the following result
is obtained: Let $C\subset R^n$ be a convex body. If {\it As}$(C)\ge n-\varepsilon$ for some $0\le
\varepsilon < 1/8(n+1),$ then there exists a simplex $S_0$ formed by $n+1$
support hyperplanes of $C$, such that
$$(1+8(n+1)\varepsilon)^{-1}S_0\subset C\subset S_0,$$
where the homethety center is the (unique) Minkowski critical point of $C$. So
$$d_{{\rm BM}}(C,S)\le 1+8(n+1)\varepsilon$$
holds for all simplexes $S$, where $d_{{\rm BM}}(\cdot,\cdot)$ denotes the Banach-Mazur distance. 相似文献
13.
14.
Jerzy Grzybowski Ryszard Urbanski 《Proceedings of the American Mathematical Society》1997,125(11):3397-3401
In this paper we introduce a quotient class of pairs of convex bodies in which every member have convex union.
15.
定义一个与Minkowski不等式相关的二元函数,由它的单调性和准线性,可得出Minkowski不等式的一些加细. 相似文献
16.
For the affine distance d(C, D) between two convex bodies C, D C R^n, which reduces to the Banach-Mazur distance for symmetric convex bodies, the bounds of d(C, D) have been studied for many years. Some well known estimates for the upper-bounds are as follows: F. John proved d(C, D) ≤ n^1/2 if one is an ellipsoid and another is symmetric, d(C, D) ≤ n if both are symmetric, and from F. John's result and d(C1, C2) ≤ d(C1, C3)d(C2, C3) one has d(C, D) ≤ n^2 for general convex bodies; M. Lassak proved d(C, D) ≤ (2n - 1) if one of them is symmetric. In this paper we get an estimate which includes all the results above as special cases and refines some of them in terms of measures of asvmmetrv for convex bodies. 相似文献
17.
A subset S of a d-dimensional convex body K is extensive if S
∂K and for any p, q ∈ S the distance between p and q is at least one-half of the maximum length of chords of K parallel to the segment pq. In this paper we establish the general upper bound |S| ≤ 3
d
— 1. We also find an upper bound for a certain class of 3-polytopes, which leads to the determination of the maximum cardinalities
of extensive subsets and their extremal configurations for tetrahedra, octahedra and some other 3-polytopes.
This revised version was published online in June 2006 with corrections to the Cover Date. 相似文献
18.
ForanytwoconvexbodiesCandDlntheEuc1ideanspaceR"denotebyd(C,D)theminimalnumberAsuchthatthereexistsanaffineoperatorAwhichsatisfiesA(C)=D=AA(C),whereAA(C)denotesahomotheticcopyofA(C)withhom0thetycentrelnsomepointofA(C).d(C,D)iscalledtheMinkowskid1stancebetweenCandD.JohnL'jprovedthatifCisanellipsoid,thend(C,D)相似文献
19.
Emanuel Milman 《Journal of Theoretical Probability》2009,22(1):256-278
Recently, Bo’az Klartag showed that arbitrary convex bodies have Gaussian marginals in most directions. We show that Klartag’s
quantitative estimates may be improved for many uniformly convex bodies. These include uniformly convex bodies with power
type 2, and power type p>2 with some additional type condition. In particular, our results apply to all unit-balls of subspaces of quotients of L
p
for 1<p<∞. The same is true when L
p
is replaced by S
p
m
, the l
p
-Schatten class space. We also extend our results to arbitrary uniformly convex bodies with power type p, for 2≤p<4. These results are obtained by putting the bodies in (surprisingly) non-isotropic positions and by a new concentration
of volume observation for uniformly convex bodies.
Supported in part by BSF and ISF. 相似文献