共查询到11条相似文献,搜索用时 109 毫秒
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与匹多不等式有关的一个等式方明(四川平昌二中635400)约定a,b,c,△和a′,b′,c′,△′分别表示△ABC和△A′B′C′的边长和面积,H=a′2(b2+c2-a2)+b′2(c2+a2-b2)+c′2(a2+b2-c2).著名的匹多不等式... 相似文献
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高维欧氏空间中的广义度量方程及其应用 总被引:4,自引:0,他引:4
本文利用代数的方法,证明了:对于两个等数量有限基本元素构成的集合,杨路和张景中关于高维欧氏空间E^n中的度量方程仍然成立,得到了一个广义度量方程,其特殊情况就是著名的Cayley定理.作为初步应用,给出了两个单形外接超球球心距和棱切超球球心距的两个公式. 相似文献
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本文利用代数的方法建立了一个与距离几何中度量加单形的体积和外接超球半径有关的几何不等式,作为其应用,由此可以导出一系列重要的几何不等式.在文末还给出了“广义度量加”的概念,并提出若干猜想供进一步研究. 相似文献
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An Inequality for the Pedal Simplex 总被引:5,自引:0,他引:5
Sun Mingbao 《Geometriae Dedicata》2001,85(1-3):45-51
In this paper, we improve an inequality on the volume of the pedal simplex. 相似文献
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马统一 《数学的实践与认识》2007,37(13):173-179
利用距离几何理论和数学归纳法相结合的方法,证明和改进了著名的Veljan-Korchmaros不等式,得到了三个更强的结果.并应用它推广了n维Euler不等式. 相似文献
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Ding-hua YANG College of Mathematics Software Sciences Sichuan Normal University Chengdu China Chengdu Institute of Computer Applications Chinese Academy of Sciences Chengdu China 《中国科学A辑(英文版)》2007,50(3):423-438
In this paper, the concept of a finite mass-points system∑N(H(A))(N>n) being in a sphere in an n-dimensional hyperbolic space Hn and a finite mass-points system∑N(S(A))(N>n) being in a hyperplane in an n-dimensional spherical space Sn is introduced, then, the rank of the Cayley-Menger matrix AN(H)(or a AN(S)) of the finite mass-points system∑∑N(S(A))(or∑N(S(A))) in an n-dimensional hyperbolic space Hn (or spherical space Sn) is no more than n 2 when∑N(H(A))(N>n) (or∑N(S(A))(N>n)) are in a sphere (or hyperplane). On the one hand, the Yang-Zhang's inequalities, the Neuberg-Pedoe's inequalities and the inequality of the metric addition in an n-dimensional hyperbolic space Hn and in an n-dimensional spherical space Sn are established by the method of characteristic roots. These are basic inequalities in hyperbolic geometry and spherical geometry. On the other hand, some relative problems and conjectures are brought. 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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A lower bound of the form
is derived on the coding gain
of the densest n-dimensional (n-D) lattice(s). The bound is obtained based on constructing an n-D lattice which consists of parallel layers. Each layer isselected as a translated version of a densest ( n-1)-D lattice.0The relative positioning of the layers is adjusted to make the coding gainas large as possible. For large values of n, the bound isimproved through tightening Ryskov's inequality on covering radius andminimum distance of a lattice. 相似文献