共查询到19条相似文献,搜索用时 140 毫秒
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本文用新方法讨论解决了n维椭圆空间Sn中若干几何问题。给出了关于n维球面单形的余弦定理、高的公式、内切及外接球半径r,R以及内心I与外心Q间的距离公式。同时将著名的欧拉不等式推广到Sn中。 相似文献
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关于n维单形体积不等式的一个定理 总被引:1,自引:0,他引:1
刘根洪 《数学的实践与认识》1986,(4)
<正> 本文将给出关于两个n维单形体积间的一个不等式定理的证明,以及它们体积相等时的充要条件. 定理.设G是n维单形∑(A)=(a_0,a_1,…,a_n)的重心,a_iG交单形∑(A)的 相似文献
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杨世国 《数学的实践与认识》2006,36(9):383-385
近期将欧氏平面E2上的正弦定理和余弦定理推广到三维欧氏空间E3中,建立了E3中四面体空间角正弦定理、二面角正弦定理和四面体余弦定理,利用向量给出了三维余弦定理和三维正弦定理的简单证明. 相似文献
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关于单形的一类三角不等式及应用 总被引:1,自引:0,他引:1
孙明保 《数学的实践与认识》2002,32(3):466-469
本文给出了联系 n维单形顶点角与二面角的一类三角不等式 .作为其应用 ,改进了关于垂足单形体积的一个不等式 相似文献
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本文研究了双曲空间Hn(K)中n维高维单形的几何不等式问题.利用距离几何的理论与方法,获得了涉及n维双曲单形体积,侧面积与棱长的几个几何不等式,这些几何不等式是双曲单形几何不等式的基础. 相似文献
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We consider a separable complete metric space equipped with a convex combination operation. For such spaces, we identify the corresponding convexification operator and show that the invariant elements for this operator appear naturally as limits in the strong law of large numbers. It is shown how to uplift the suggested construction to work with subsets of the basic space in order to develop a systematic way of proving laws of large numbers for such operations with random sets. 相似文献
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We report some results on the theory of quasiperiodic sphere packings controlled by a finite group G in the n-dimensional Euclidean space, constructed by means of an higher dimensional Euclidean space which contains G-invariant lattices. A generalization of the Hermite constant is used to find upper bounds of the density. 相似文献
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本文研究了n维欧氏空间En中n维单形的体积有关问题.利用距离几何的理论与解析方法,建立了n维情形的Routh定理,作为其特例建立了n维情形的Ceva定理. 相似文献
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In this paper, by using the theory and method of distance geometry, we study the geometric inequality of a n-dimensional simplex in the spherical space and establish two geometric inequalities involving the edge-length and volume of one simplex and the volume,height and(n-1)-dimensional volume of the side of another simplex in the n-dimensional spherical space. They are the extensions of the results [10] in the n-dimensional Euclidean geometry to the n-dimensional spherical space. 相似文献
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应用度量几何理论与解析方法,研究了n维欧氏空间En中n维单形的性质,将三角形内心与中线两个性质推广到n维单形,获得n维单形内心与中位面的两个性质. 相似文献
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证明了关于独立同分布随机变量序列的加权U-统计量的一个重对数律,类似于献「3」证明了一个加权U-统计量的解耦不等式。 相似文献
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The paper deals with the existence and characterization of minimum or extremum paths connecting two given points in a vector space, which is divided by a barrier (a curve C if the space is 2-dimensional) into two parts with different norms. The global problem of existence of polygonal paths of shortest length is dealt with in Section 2. An example shows that, for a curve with a point of inflection, such paths may not exist. However, the existence of such paths is proved for a more restricted class of curves (Theorem 2.3). The notion of permissible polygonal paths is introduced, and it is shown that, for a very general class of curves, such paths of shortest length do exist (Theorem 2.2).Sections 3 and 4 deal with the local conditions at the intersection of the extremal path with the curve C. Theorem 4.1 establishes a geometric characterization of the point of intersection, and Eqs. (13) and (15) are formulas for the angles that the segments of the extremal path make with a fixed axis or with the normal to C at the point of intersection. The case where the unit circles of the tax norms are Euclidean circles with different radii leads to the traditional Snell law. Section 6 deals with the law of reflection at the curve C, which in the case of the Euclidean norm asserts the equality of the angles of incidence and reflection. The n-dimensional case, where the curve C is replaced by a hypersurface, is considered briefly in Section 7. 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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