PROPERTIES OF CHARACTERISTIC FUNCTIONS AND EXISTENCE OF LIMIT CYCLES OF LI(?)NARD''''S EQUATION

In this paper, the author considers Lienard's equation, studies the properties of so-called characteristic functions and gives three theorems which ensure that the equation has at least one limit cycle. The theorems generlize Filippov's Theorem which is a repesentative result, Dragilev's Theorem, Theorem 1, 2 of[6], Theorem 9 of[8] and Theorems 1, 2 of[9] respectively.     

Erratum to: Every Banach space admits a homogenous measure of non-compactness not equivalent to the Hausdorff measure

正[1, Theorem 4.4] states that every infinite dimensional Banach space admits a homogenous measure of noncompactness not equivalent to the Hausdorff measure. Howevere, there is a gap in the proof. In fact,we found that [1, Lemma 4.3] is not true. In this erratum, we give a corrected proof of [1, Theorem 4.4].     

On Alternating Sequences Relative to a c-Matching of a Hypergraph

In[1], C.Berge has modified Theorem 1 of [2]to a theorem which is a charac-terization of maximum c-Matchings in a hypergraph (see[1], P.416, Theorem 2),and at the same time can be considered as a generalization of Berge's theorem on     

周期图的重对数律

§1周期图的重对数律设零均值宽平稳序列{X_n,-∞相似文献   

关于似然比序随机比较的一些结果

研究了两组随机变量列之间似然比序的随机比较，得到的结果推广了Shaked 和 Shanthikumar (1994) 中的 Theorem 1.C.19 和Theorem 1.C.20.      

THE VALUE DISTRIBUTION OF RANDOM ANALYTIC DIRICHLET SERIES OF NEUTRAL GROWTH(I)

1IntroductionandtheMainResultTheBorelpointsofrandomanajyticDirichletserieshavebeenstudied[1'2]oilthecon(litiollthatthecoefficientsoftherandomDirichletseriesareindependentrandomvariables,sucfl;lstheRademacliersequencettheSteinhausesequence!andtheN-sequence.[1]Thepresentpaperdealswiththesimilarproblem,andintendstoobtainmoreaccurate(inasence)resultthan[2,Theorem4]evenifthecoefficientsofrandomDirichletseriesareassumedtobeamartingaledifferencesequence.ConsidertherandomDirichletseriesfi(s)=Zn=I…     

B值随机元阵列加权和的完全收敛性

在随机元阵列随机有界的条件下,得到了行间独立B值随机元阵列加权和的完全收敛性成立的充分条件,延伸了文献[9]的主要结果和文献[6]的部分结果.     

STATIONARY DISTRIBUTIONS OF INFINITE PARTICLE SYSTEMS WITH NONCOMPACT STATE SPACE.

This paper deals with the preblem of existence and uniqueness of the stationary distributions (abbr., s. d.'s) for the processes constructed in [4] .The main results are stated in § 1. For the reader's convenience we first restate the existence theorems (Theorem 1 and 2) of the processes given in [4]. Then two existence theorems (Theorem 3 and 4) and a uniqueness theorem (Theorem 5) for the s. d.'s of the processes are presented. The last result (Theorem 6), as an application of the previous ones, is about the Schlgl model which comes from nonequilibrium statisticali physics. The details of the proofs of Theorem 3—6 are given in § 2—4.     

行为NA的随机变量阵列的完全收敛性

本文研究了行为NA的随机变量阵列的完全收敛性.利用陈平炎等[4]研究的结果,得到了行为NA的随机变量阵列完全收敛的系列充分条件,这些结果推广和改进了Kuczmaszewska[3]相应的结果.     

TYPE K MONOTONE SYSTEMS WITH AN ORDER-INCREASING INVARIANT FUNCTION

51.IntroductionBeginingwiththepath-breakingworkofM.W.HirschI1-4]forcooperativesystemsandmonotonesemiflows,thereisnowanextensiveliteratureoncooperativesystemsandmoncatonedynamicalsystems.Assumingthatthesystemiscooperativeandirreducible,HirschshowedthataImosteveryforwardorbitwithcompactclosure,inthesenseofLebesguemeasure,tendstoequilibriaast- oc(see2,Theorem4.l]).Asimilarresultholdsforastronglymonotonesemifiowonastronglyorderspace(see[4,Theoremo.1]).Manypeoplehavegivensomeadditionalconditio…     

A Berry-Esséen bound for student's statistic in the non-I.I.D. case

We establish a Berry-Esséen bound for Student's statistic for independent (nonidentically) distributed random variables. In particular, the bound implies a sharp estimate similar to the classical Berry-Esséen bound. In the i.i.d. case it yields sufficient conditions for the Central Limit Theorem for studentized sums. For non-i.i.d. random variables the bound shows that the Lindeberg condition is sufficient for the Central Limit Theorem for studentized sums.Research supported by the SFB 343 in Bielefeld.     

Some estimates for sums of dependent random variables which hold almost surely

Some estimates are proved for sums of dependent random variables. Theorem 1 contains no assumptions regarding the existence of moments of the random variables. In Theorem 2 estimates are given for the growth of sums of random variables in a stationary sequence.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova Akad. Nauk SSSR, Vol. 55, pp. 113–116, 1976.     

The convergence of moments in the martingale central limit theorem

Summary An early extension of the Lindeberg-Feller Theorem was Bernstein's discovery of necessary and sufficient conditions for the convergence of moments in the central limit theorem for sums of independent random variables. In this paper we show that Bernstein's work has a generalisation to martingales. We extend his work in both the independence and the martingale cases by showing that there exists a duality between the behaviour of the moments of the martingale and the behaviour of the sums of squares of the martingale differences. Our proofs are quite unrelated to Bernstein's and are based on Burkholder's inequalities.     

不同分布NA序列加权和的完全收敛性

本文讨论了不同分布NA随机变量序列加权和的完全收敛性，获得了较[7]中的定理1及定理A更为一般的安全收敛性，并得到了完全收敛速度与矩条件之间的等价关系。     

随机变数配重和的两个收敛定理

本文给出随机变数配重和几乎必然收敛的两个定理,同时讨论了可分赋范线性空间中随机元的相应推广。 定理1 设随机变数序列{x_n}的律一致地以一个随机变数X的律为界,即对所有n和     

I.I.D.随机变量两两乘积之和的Hsu-Robbins型定理(II)

在本部分中,采用由Levy函数(4.1)所确定的值b     

Complete Convergence for Weighted Sums of Negatively Sup eradditive Dep endent Random Variables

In the paper, the complete convergence for the maximum of weighted sums of negatively superadditive dependent(NSD, in short) random variables is investigated by using the Rosenthal type inequality. Some su?cient conditions are presented to prove the complete convergence. The result obtained in the paper generalizes some corresponding ones for independent random variables and negatively associated random variables.     

NSD变量加权和的完全收敛性（英文）

In the paper, the complete convergence for the maximum of weighted sums of negatively superadditive dependent(NSD, in short) random variables is investigated by using the Rosenthal type inequality. Some sufficient conditions are presented to prove the complete convergence. The result obtained in the paper generalizes some corresponding ones for independent random variables and negatively associated random variables.     

Weak convergence of random sums and maximum random sums under nonrandom norming

Necessary and sufficient conditions are obtained for the weak convergence of random sums and maximum random sums of independent identically distributed random variables. Limit distributions for these sums are described. The indices are not assumed to be independent of the summands. Supported in part by Grants NFW000 and NFW300 from the International Science Foundation and the Russian Government and by Grant No. 93-011-1446 from the Russian Foundation for Fundamental Research. Proceedings of the XVII Seminar on Stability Problems for Stochastic Models, Kazan, Russia, 1995, Part I.     

I.I.D.随机变量两两乘积之和的Hsu-Robbins型定理(Ⅱ)

在本部分中,采用由 Ｌｅｖｙ函数（４．ｌ）所确定的值ｂｎ取代（Ｉ）［１］中的１／ｎ“位点”ａｎ,使得（Ｉ）中定理１中的附加条件（Ａ）得以解除,从而获得了可以称之为Ｈｓｕ－Ｒｏｂｂｉｎｓ型的充分必要条件．作为推论,还给出了两个互为复制的ｉｉｄ随机变量三角阵对应行之和乘积的Ｋｏｌｍｏｇｏｒｏｖ强大数律．