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1.
周永国 《数学杂志》2016,36(2):375-384
本文研究了涉及四个单形的一类不等式问题.利用距离几何的理论和方法获得了两个单形的棱长与另两个单形的内点、中线、高、外接超球半径、内切超球半径、旁切超球半径以及n-1维侧面的体积、外接超球半径、内切超球半径的一类新的几何不等式.推广了文献([5])中的全部结果.  相似文献   

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单形极集的两个几何不等式及其应用   总被引:5,自引:0,他引:5  
郭曙光 《数学杂志》1998,18(3):355-360
本文给出关于单形极集的两个几何不等式,作为其应用,获得单形的一个构造定理和关于单形中硕的一个几何不等式。  相似文献   

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关于Gerber不等式的一个猜想   总被引:4,自引:1,他引:3  
本文证明了陈计-单墫关于Gerber不等式的一个猜想,作为其应用,导出了单形内一点到顶点的距离与到面的距离的两个不等式.  相似文献   

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应用解析方法和几何不等式理论研究了n维欧氏空间En中涉及两个n维单形的几何不等式问题,建立了涉及两个单形的一类三角不等式.作为其应用,获得了涉及两个单形及其内点的几何不等式,特别,获得了n维单形与其垂足单形的体积的一类关系式,改进了关于垂足单形体积的几类几何不等式.  相似文献   

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涉及两个单形的几何不等式   总被引:1,自引:0,他引:1  
本文建立了涉及两个单形一个几何不等式,并应用它得到单形的一些几何不等式。  相似文献   

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本文首先对文[1]中的多个单形体积的Oppenheim不等式给出了一种简单证明,并同时将文[2]中的又一Oppenheim不等式推广到高维空间的多个单形上  相似文献   

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利用几何不等式理论与解析方法。研究n维欧氏空间E^n中n维单形的外接球半径与内切球半径之间的不等式关系。利用n维欧氏空间E^n中n维单形Ωn的高线,以及单形重心的性质,通过重心与单形Ωn各顶点的连线li(i=1,2,……,n+1)对Euler不等式进行分割.  相似文献   

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单形中面的性质及其应用   总被引:9,自引:1,他引:9  
郭曙光 《数学杂志》1997,17(3):413-416
本文首先给出单形中面的概念,得到了单形中面的一些性质,作为其应用,建立了涉及单形中面的两个不等式。  相似文献   

9.
Veljan-Korchmaros型不等式的稳定性   总被引:2,自引:0,他引:2  
关于Euclidean空间En(n≥2)中单形的几何不等式,由于支撑函数或径向函数的表达式很难找到,因此一般很难用Hausdorff度量或径向度量来度量两个单形的"偏差",使得涉及单形的几何不等式的稳定性的研究比较困难.利用单形棱长在确定单形时起决定性作用这一事实,引进了两个单形"偏正"度量的概念,从而较好地解决了单形偏正度量的问题,并建立了著名的Veljan-Korchmaros 不等式的稳定性版本.作为推论,还导出了一系列Veljan-Korchmaros型不等式的稳定性版本.  相似文献   

10.
本文利用距离几何理论和解析不等式的技巧,研究了度量加单形的宽度度量估计,建立了有关度量加单形宽度之间的几个几何不等式.  相似文献   

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We study a class of self-similar processes with stationary increments belonging to higher order Wiener chaoses which are similar to Hermite processes. We obtain an almost sure wavelet-like expansion of these processes. This allows us to compute the pointwise and local Hölder regularity of sample paths and to analyse their behaviour at infinity. We also provide some results on the Hausdorff dimension of the range and graphs of multidimensional anisotropic self-similar processes with stationary increments defined by multiple Wiener–Itô integrals.  相似文献   

13.
It is considered the class of Riemann surfaces with dimT1 = 0, where T1 is a subclass of exact harmonic forms which is one of the factors in the orthogonal decomposition of the spaceΩH of harmonic forms of the surface, namely The surfaces in the class OHD and the class of planar surfaces satisfy dimT1 = 0. A.Pfluger posed the question whether there might exist other surfaces outside those two classes. Here it is shown that in the case of finite genus g, we should look for a surface S with dimT1 = 0 among the surfaces of the form Sg\K , where Sg is a closed surface of genus g and K a compact set of positive harmonic measure with perfect components and very irregular boundary.  相似文献   

14.
Schr(o)dinger operator is a central subject in the mathematical study of quantum mechanics.Consider the Schrodinger operator H = -△ V on R, where △ = d2/dx2 and the potential function V is real valued. In Fourier analysis, it is well-known that a square integrable function admits an expansion with exponentials as eigenfunctions of -△. A natural conjecture is that an L2 function admits a similar expansion in terms of "eigenfunctions" of H, a perturbation of the Laplacian (see [7], Ch. Ⅺ and the notes), under certain condition on V.  相似文献   

15.
As early as in 1990, Professor Sun Yongsheng, suggested his students at Beijing Normal University to consider research problems on the unit sphere. Under his guidance and encouragement his students started the research on spherical harmonic analysis and approximation. In this paper, we incompletely introduce the main achievements in this area obtained by our group and relative researchers during recent 5 years (2001-2005). The main topics are: convergence of Cesaro summability, a.e. and strong summability of Fourier-Laplace series; smoothness and K-functionals; Kolmogorov and linear widths.  相似文献   

16.
张丽娜  吴建华 《数学进展》2008,37(1):115-117
One of the most fundamental problems in theoretical biology is to explain the mechanisms by which patterns and forms are created in the'living world. In his seminal paper "The Chemical Basis of Morphogenesis", Turing showed that a system of coupled reaction-diffusion equations can be used to describe patterns and forms in biological systems. However, the first experimental evidence to the Turing patterns was observed by De Kepper and her associates(1990) on the CIMA reaction in an open unstirred reactor, almost 40 years after Turing's prediction. Lengyel and Epstein characterized this famous experiment using a system of reaction-diffusion equations. The Lengyel-Epstein model is in the form as follows  相似文献   

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<正>Submission Authors must use LaTeX for typewriting,and visit our website www.actamath.com to submit your paper.Our address is Editorial Office of Acta Mathematica Sinica,Academy of Mathematics and Systems Science,Chinese Academy of Sciences,Beijing 100190,P.R.China.  相似文献   

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