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1.
关于含有Stirling公式的双边不等式   总被引:3,自引:0,他引:3  
本文证明了有关n!的一个便于应用的双边不等式,它对一切自然数都成立,且当n变大时,上界不式能给出误差界为O(n^-3)的Stirling渐近公式,从一定意义上说,文中的上界不等式具有最优形式,因为其中的常数0.5已作了最佳选择,文末还给出了关于Catalan数的一个双边不等式。  相似文献   

2.
沈一兵 《中国科学A辑》1987,30(9):917-926
本文给出空间形式中极小子流形共形度量的曲率上界估计,并用来研究极小子流形的稳定性。这就部分地解答了下述问题:已给极小子流形 Mn?Mn+p,寻找一个仅与 Mn和Mn+p的度量有关的条件,使得若区域 ?Mn满足这个条件,则?是稳定的。  相似文献   

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该文给出了一些负相协随机变量的指数不等式.这些不等式改进了由Jabbari和Azarnoosh[4]及Oliveira[7] 所得到的相应的结果.利用这些不等式对协方差系数为几何下降情形, 获得了强大数律的收敛速度为n-1/2(log log n)1/2(log n)2.这个收敛速度接近独立随机变量的重对数律的收敛速度, 而Jabbari和Azarnoosh[4]在上述情形下得到的收敛速度仅仅为n-1/3(log n)5/3.  相似文献   

4.
韩永生 《中国科学A辑》1988,31(3):247-253
Carleson曾证明了下述重要不等式:其中μ是R+n+1上的Carleson测度,fφ*是f的非切向极大函数。本文证明了反向Carleson型不等式,从而给出了Hardy型空间Hφ1的一个等价刻划,同时我们还得到了一些在经典H1空间的应用。  相似文献   

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本文根据不同重数张量空间之间的关系,采用对张量空间分划的方法,得到了张量空间中张量达到最小长度的一个充分条件和一个必要条件.此外,本文还讨论了最小长度的上界Kmax,得到了如下估计:对n维向量空间上的m阶张量空间,n[m/2]≤Kmax≤nm-1。  相似文献   

6.
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   

7.
利用R^3中卵形结果的高斯曲率不等式以及著名的等周不等式,将R^3中卵形闭曲面的高斯曲率K应用到空间曲面的等周亏格的上界估计中,得到了R^3中卵形闭曲面的等周亏格的一个新的上界,并给出其简单证明.  相似文献   

8.
龙瑞麟 《中国科学A辑》1978,21(3):264-278
本文在一般的条件下,在局部紧Abel群上建立了加权大筛法不等式,并对古典调和分析的对象Rk,Tk与Zk上的加权大筛法不等式,进行了更为详细的讨论.我们对这些具体对象得到了几种类型的不等式,它概括了这方面迄今已有的,除Montgomery与Voughan的具有差不多最好常系数的不等式以外的结果.其中有一个的常系数优于已有结果,有一个是新结果,另外一个是上面提到过的Montgomery与Vaughan的结果的高维类似.  相似文献   

9.
本文建立了一类新的更为广泛的非线性离散不等式.所得结果改进并推广了文中的有关结果.并利用所得结果考虑了差分方程Δ2u(n)+f(n,u(n),Δu(n))=0解的渐进性质,其中(n,u,ν)∈N×R×R,N=1,2,….  相似文献   

10.
正定Hermite矩阵的若干行列式不等式   总被引:7,自引:1,他引:7       下载免费PDF全文
本文对满足条件A=A>0,1/2(B+B)≥0的矩阵A,B,建立了四个行列式不等式.某些著名的行列式不等式和一些已知结用,均可作为其推论.  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.
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   

14.
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   

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正Applied Mathematics-A Journal of Chinese Universities,Series B(Appl.Math.J.Chinese Univ.,Ser.B)is a comprehensive applied mathematics journal jointly sponsored by Zhejiang University,China Society for Industrial and Applied Mathematics,and Springer-Verlag.It is a quarterly journal with  相似文献   

17.
正Journal overview:Journal of Mathematical Research with Applications(JMRA),formerly Journal of Mathematical Research and Exposition(JMRE)created in 1981,one of the transactions of China Society for Industrial and Applied Mathematics,is a home for original research papers of the highest quality in all areas of mathematics with applications.The target audience comprises:pure and applied mathematicians,graduate students in broad fields of sciences and technology,scientists and engineers interested in mathematics.  相似文献   

18.
A cumulative-capacitated transportation problem is studied. The supply nodes and demand nodes are each chains. Shipments from a supply node to a demand node are possible only if the pair lies in a sublattice, or equivalently, in a staircase disjoint union of rectangles, of the product of the two chains. There are (lattice) superadditive upper bounds on the cumulative flows in all leading subrectangles of each rectangle. It is shown that there is a greatest cumulative flow formed by the natural generalization of the South-West Corner Rule that respects cumulative-flow capacities; it has maximum reward when the rewards are (lattice) superadditive; it is integer if the supplies, demands and capacities are integer; and it can be calculated myopically in linear time. The result is specialized to earlier work of Hoeffding (1940), Fréchet (1951), Lorentz (1953), Hoffman (1963) and Barnes and Hoffman (1985). Applications are given to extreme constrained bivariate distributions, optimal distribution with limited one-way product substitution and, generalizing results of Derman and Klein (1958), optimal sales with age-dependent rewards and capacities.To our friend, Philip Wolfe, with admiration and affection, on the occasion of his 65th birthday.Research was supported respectively by the IBM T.J. Watson and IBM Almaden Research Centers and is a minor revision of the IBM Research Report [6].  相似文献   

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