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L_p-混合质心体和对偶L_p-混合质心体 总被引:1,自引:0,他引:1
本文引进了L_p-混合质心体Γ_(p,i)K、对偶L_p-混合质心体Γ_(-p,i)K和R~n中星体K和L的L_p-混合调和Blaschke加K+_pL的概念,成功地解决了L_p-混合质心体和对偶L_p-混合质心体的Shephard型问题.并且结合星体的L_p-混合调和Blaschke加的概念,分别建立了L_p-混合质心体的均质积分和对偶均质积分的Brunn-Minkowski型不等式.所获结论推广了已有文献的结果. 相似文献
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关于L_p-混合质心体的Busemann-Petty问题 总被引:1,自引:0,他引:1
对p≥1,Lutwak和Zhang引进了R~n中一个星体K的L_p-质心体Γ_pK的概念,Grinberg和Zhang研究了L_p-质心体算子Γ_p的Busemann-Petty问题;最近,马统一引进了星体K的L_p-混合质心体Γ_(p,i)K(i∈R)的概念,即L_p-质心体是它的特殊类.本文研究了Γ_(p,i)K(?)Γ_(p,i)L是否一定(?)的问题.其结果是Grinberg和Zhang关于L_p-质心体算子Γ_p的Busemann-Petty问题的推广形式. 相似文献
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《数学季刊》2015,(4)
For p 0, Lutwak, Yang and Zhang introduced the concept of L_p-polar projection body Γ_(-p)K of a convex body K in Rn. Let p ≥ 1 and K, L ? Rnbe two origin-symmetric convex bodies, we consider the question of whether Γ_(-p) K ? Γ_(-p) L implies ?_p(L) ≤ ?_p(K),where ?_p(K) denotes the L_p-affine surface area of K and K = Voln(K)~(-1/p) K. We prove a necessary and sufficient condition of an analog of the Shephard problem for the L_p-polar projection bodies. 相似文献
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《应用数学与计算数学学报》2018,(3)
广义质心体是关于概率测度的Orlicz质心体的多元情形.考虑广义质心体的非对称版本,即将关于概率测度的非对称Orlicz质心体推广到多元情形,并建立相应的质心不等式. 相似文献
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《应用数学与计算数学学报》2016,(3)
1988年,Lutwak首次明确地提出了经典相交体的概念.2005年,Haberl和Ludwig对经典相交体进行了推广,给出了L_p-相交体的概念.最近,汪卫等提出了广义相交体的概念.主要利用L_p-Brunn-Minkowski理论、Hlder积分不等式和Minkowski积分不等式,研究了广义相交体的单调性,并建立了关于径向线性组合和L_p-调和Blaschke组合的Brunn-Minkowski型不等式. 相似文献
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《数学季刊》2016,(4)
Zhu,Lü and Leng extended the concept of L_p-polar curvature image. We continuously study the L_p-polar curvature image and mainly expound the relations between the volumes of star bodies and their L_p-polar curvature images in this article. We first establish the L_p-affine isoperimetric inequality associated with L_p-polar curvature image. Secondly,we give a monotonic property for L_p-polar curvature image. Finally, we obtain an interesting equation related to L_p-projection body of L_p-polar curvature image and L_p-centroid body. 相似文献
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Haberl and Ludwig defined the notions of L_p intersection bodies. In this paper,we introduce the L_p mixed intersection bodies, and establish some geometric inequalities for L_p mixed intersection bodies. Furthermore, the Busemann-Petty type problem for L_p mixed intersection bodies are shown. 相似文献
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《数学季刊》2015,(4)
It is proved that if λ_1, λ_2, ···, λ_7are nonzero real numbers, not all of the same sign and not all in rational ratios, then for any given real numbers η and σ, 0 σ 1/16, the inequality |λ_1x~2_1+ λ_2x~2_2+∑7 i=3λ_ix~4_i+ η| ( max1≤i≤7|x_i|)~(-σ)has infinitely many solutions in positive integers x_1, x_2, ···, x_7. Similar result is proved for |λ_1x~2_1+ λ_2x~2_2+ λ_3x~2_3+ λ_4x~4_4+ λ_5x~4_5+ λ_6x~4_6+ η| ( max1≤i≤6|xi|)-σ.These results constitute an improvement upon those of Shi and Li. 相似文献
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马统一 《数学物理学报(A辑)》2009,29(6):1750-1764
引进了多个几何体(主要是凸体(Convex body)和星体(Star body)) 相似``偏差'的一个度量方法, 从而推广了已有的相似``偏差'度量方法.并在此度量下,利用Rn 中Hölder不等式的一个加强获得了文献[1]建立的混合投影体的极的Aleksandrov-Fenchel不等式和文献[2]建立的混合相交体的Aleksandrov-Fenchel不等式的稳定性版本. 相似文献
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Haberl and Ludwig introduced the L_p-intersection body I_pK for an originsymmetric star body K in R~n,where p < 1 and p ≠ 0.In this paper,we consider the Busemann-Petty’s problem for L_p-intersection bodies I_pK and I_pL.That is,whether I_pK ■ IpL implies Vol_n(K) ≤ Vol_n(L).We obtain that for two origin-symmetric star bodies K and L in R~n,such that(R~n,||·||K) embeds in L_p and I_pK ■ IpL,then vol_n(K) ≤ vol_n(L) for 0 < p < 1 and vol_n(K) ≥ vol_n(L) for p < 0. 相似文献
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设K是C~2类严格闭凸曲线γ围成的面积为A的平面凸体,r(θ)为γ的曲率半径.本文得到Ros亏格Δ(K)=∫O~πr(θ)r(θ+π)dθ-A的下界和上界.这些界涉及γ的渐屈线围成的代数面积、Wigner焦散线围成的面积以及视角. 相似文献
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《数学季刊》2017,(1)
Some new inequalities of Hermite-Hadamard's integration are established. As for as inequalities about the righthand side of the classical Hermite-Hadamard's integral inequality refined by S Qaisar in [3], a new upper bound is given. Under special conditions,the bound is smaller than that in [3]. 相似文献