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1.
董金柱 《数学学报》1959,9(2):156-169
<正> 方程组■的 Hilbert问题包括两部分,即问(E_2)在全平面上最多有几个极限环钱及它们的位置(它们如何分布).在一篇独具风格的论文中,(?)及(?)用创见的方法以惊人的气魄处理了方程组.(E_2),得到了(E_2)的极限环线在全平面土最多有三个的结果.本文是[2]的继续,目的是讨论方程组(E_2)的极限环线的位置,把它们的拓扑分布问题给以最后的解决.我们现在的问题是:设方程组(E_2)有三个极限环线,以 L_c~i(i=1,2,3)表之,以 I_i 表L_c~i 之补集 c(L_c~i)之有界分量,问位置  相似文献   

2.
§1 法国数学家杜拉克(H.Dulac)(1870—1955)在1923年发表的长篇论文“极限环论”是一篇知名文献。在这篇论文中,杜拉克推广了邦加赖(H.Poincaré)关于极限环个数有限的定理,去掉了邦加赖所加的限制,即在无通过鞍点的极限环存在的这一限制之下有限性定理才能成立,当时许多数学家,包括知名的班狄克生(I var Bendixon)在内,都曾为去掉这个限制而努力,但统归无效,杜拉克这篇论文,却终于成功地去掉邦加赖的限制而证明了这个定理,并因此而名噪一时。  相似文献   

3.
用定性分析和数值判定方法,对一类微分系统x=y,y=x(l-bx2) (α-cx2)y(其中l>0,b>0,c≠0)的极限环分布情况进行了研究,得出该系统有3个极限环,并且给出了该系统所有极限环的分布情况.  相似文献   

4.
的极限环集中分布问题,我在“二次系统Ⅱ类方程极限环的分布”(本刊,1983年第4期)一文中得到的结果实际上已经解决了这一问题,由于当时判断有误,没有发现这一点,认为“还不能把[4]中得到的两个区间连接起来”。 将文中(7)式的(i)应用于(8′),得  相似文献   

5.
李承治 《中国科学A辑》1982,25(12):1087-1096
本文的主要结果是:(ⅰ)将对特定类型二次系统所导出的三个重要的焦点量公式,推广到对一般形式的二次系统。(ⅱ)用文献[13]所提供的方法,给出一类至少存在四个极限环的二次系统,它包含了文献[11—13]中有关极限环(1,3)分布的结果。  相似文献   

6.
在1853年发表了一篇著名的论文“以称为平行四边形理论而著名的机械理论”,它是逼近论的开创性工作。关于这篇论文,目前已有过很多论评文章。但是无论从的这篇论文还是从这些评论来看,都没有说明如何将他所创造的方法应用到解决watt的平行四边形的最好结构上去。虽然在这篇文章中说以后要讲,但  相似文献   

7.
介绍广义二项式系数   总被引:4,自引:0,他引:4  
1 前言《应用数学进展》 (《Advances in AppliedMathematics》最近一期 ,即第 2 1卷第 2期 ( 1998年 8月 ) ,2 2 8页至 2 40页上刊登了 John Konvali-na的一篇论文 ,题目叫《广义二项式系数和子集-子空间问题》.在这篇论文中 ,Konvalina定义了两种广义二项式系数 ,从而组合地把二项式系数 ,Gauss系数 ,和 Stirling数的基本性质统一起来 .我很喜欢这篇论文 ,认为值得介绍给我国数学界 .这篇论文上印有“1998年 4月 8日 (编辑部 )收到 ,1998年 5月 5日被接受”,可见《应用数学进展》编辑部很喜欢也很重视这篇论文 .2 广义二项式系数设 …  相似文献   

8.
虽然需求量是随机变量,而不少企业决策者不用随机数学而简单用平均数来处之。一些库存管理教科书也不加检验直接假定随机需求量为正态分布,而实际分布往往是未知的。98年第4期“具有随机需求量的存货决策分析方法”一文巧妙的用切比雪夫不等式,这无疑比假定未知分布为正态分布严密而又有通用性,所以该论文确是一篇佳作。但是笔者感到“具”文提出的库存模型和实例中尚有不足之处可商椎。(一)正如“具”文所言“对于具有随机需求量的库存决策,不允许仓库出空是不现实的”所以“具”文的实例是:经济批量;不能立即补足存贮量;允许短缺;耗用量是…  相似文献   

9.
阿美如 《数学杂志》2000,20(2):156-160
这篇论文研究的是亚纯函数的唯一性。这篇论文的主要结论是:如果两个非常数亚纯函数f和g有三个CM公共值或四个IM公共值,并且f’和g’以零为IM公共值,则f和grMobius变换。其中一个结论是K.Tohge有一个结果的改进,而且我们采用了与K.Tohge不同的方法。『  相似文献   

10.
一、KdV方程的诞生和罗素早年发现的孤立波 1894年12月1日,德·佛累斯(G.de Vries)在他的导师柯脱维格(Korteweg)教授的指导下向著名的荷兰阿姆斯特丹大学提交了一篇申请博士学位的论文。在这篇用荷兰文写作的论文的第9页上,报导了他们研究单方向运动的浅水波方程  相似文献   

11.
Asymptotic distributions of test statistics under alternatives are important from the point of view of their power properties. When the limiting distributions of test statistics are specified under the hypothesis in a certain sense, LeCam's third lemma ([4], Chapter 6) enables one to obtain their limiting distributions under close alternatives. In this paper we generalize LeCam's third lemma by using the rate of convergence in the case of asymptotically efficient test statistics. A general lemma is proved which is specified to linear combinations of order statistics (L-statistics) and linear rank statistics (R-statistics). Edgeworth-type asymptotic expansions for these statistics under alternatives are considered in [3]. Supported by the Russian Foundation for Fundamental Research (grant No. 93-01-01446). Proceedings of the XVI Seminar on Stability Problems for Stochastic Models, Part I, Eger, Hungary, 1994.  相似文献   

12.
万海平 《应用数学》2002,15(1):87-91
为检验两个分布的相等,我们给出基于投影寻踪、Bootstrap方法和数论方法的统计量,并讨论它的极限分布和Bootstrap逼近。最后我们给出一些模拟。  相似文献   

13.
寻求统计量的精确分布,在数理统计的理论中是一个重要的问题。然而,在多元统计分析中,往往很不容易得到统计量的精确分布,有些统计量的分布,例如非中心的Wishanrt分布,持续了几十年,还没有获得完满的结果。我国的许宝騄先生早在1939年,就得到了正态总体样本协差阵的特征根的联合分布(参看[1])。据徐钟济先生的回忆,当时R.A.  相似文献   

14.
In the first part of this review article some recent developments of maximal correlation coefficient, introduced by Gebelein (1941) [7], and its applications in various areas of statistics are discussed. The second part is devoted to find the distributions providing the maximal correlation coefficient between generalized order statistics (gos) and dual generalized order statistics (dgos), which are introduced by Kamps (1995) [8] and Burkschat et al. (2003) [4], respectively. Finally, in the third part, general theorems are presented, which give simple non-parametric criterion for the asymptotic independence between the different elements of gos, as well as dgos.  相似文献   

15.
While spherical distributions have been used in many statistical models for high-dimensional data analysis, there are few easily implemented statistics for testing spherical symmetry for the underlying distribution of high-dimensional data. Many existing statistics for this purpose were constructed by the theory of empirical processes and turn out to converge slowly to their limiting distributions. Some existing statistics for the same purpose were given in the form of high-dimensional integrals that are not easily evaluated in numerical computation. In this paper, we develop some necessary tests for spherical symmetry based on both univariate and multivariate uniform statistics. These statistics are easily evaluated numerically and have simple limiting distributions. A Monte Carlo study is carried out to demonstrate the performance of the statistics on controlling type I error rates and power.  相似文献   

16.
两个和K个分布函数相等的自助法检验(英文)   总被引:2,自引:2,他引:0  
两个和K 个分布函数相等的检验在统计领域中,长期以来一直受到关注.为了克服高维空间中数据点的稀疏性,并且对一般情况进行处理,我们提出了几个投影追踪类型的统计量,并得到了这些统计量的极限分布的一些结果.对一些自助法逼近的性质进行了研究.更进一步地,由于计算的原因,对统计量的逼近,我们采用了数论方法,并进行了一些模拟试验  相似文献   

17.
The main objective of this work is to calculate and compare different measures of multivariate skewness for the skew-normal family of distributions. For this purpose, we consider the Mardia (1970) [10], Malkovich and Afifi (1973) [9], Isogai (1982) [17], Srivastava (1984) [15], Song (2001) [14], Móri et al. (1993) [11], Balakrishnan et al. (2007) [3] and Kollo (2008) [7] measures of skewness. The exact expressions of all measures of skewness, except for Song’s, are derived for the family of skew-normal distributions, while Song’s measure of shape is approximated by the use of delta method. The behavior of these measures, their similarities and differences, possible interpretations, and their practical use in testing for multivariate normal are studied by evaluating their power in the case of some specific members of the multivariate skew-normal family of distributions.  相似文献   

18.
Summary In their paper [1], Ansari and Bradley discussed a two-sample rank test for dispersions and suggested the desirability of extending their results to the problem of several samples. In this paper, besides generalizing their results, we provide a few additional non-parametric tests, which include, among others, the multi-sample analogues of the two-sample normal scores test of dispersion and the tests considered by Mood [6], Klotz [4], and Siegel and Tukey [10]. The asymptotic distributions of the proposed test statistics are derived by an application of the author’s theorem [7]. The asymptotic efficiencies of these tests relative to one another and theF test ([9], pp. 83–87) are computed in the standard fashion along the lines of the author’s paper [7]. The work represents results obtained at the Courant Institute of Mathematical Sciences, New York University, under Sloan Foundation Grant for statistics and under U.S. Navy Contract Nonr-285 (38).  相似文献   

19.
Testing equality of two and k distributions has long been an interesting issue in statistical inference. To overcome the sparseness of data points in high-dimensional space and deal with the general cases, we suggest several projection pursuit type statistics. Some results on the limiting distributions of the statistics are obtained. Some properties of Bootstrap approximation are investigated. Furthermore, for computational reasons an approximation for the statistics the based on Number theoretic method is applied. Several simulation experiments are performed.  相似文献   

20.
In this paper, some test statistics Of Kolmogorov type and Cramervon Mises type based on projection pursuit technique are proposed for testing the sphericity problem of a high-dimensional distribution. The limiting distributions of the test statistics are derived under the null hypothesis. The asymptotic properties of Bootstrap approximation are investigated and the tail behaviors of the statistics are studied.  相似文献   

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