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2010年 第25卷 第4期    刊出日期：2010-12-30

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关于任意随机序列的一个强大数定理

汪忠志

2010, 25(4):  475-480. 

摘要 ( 17 )   PDF (269KB) ( 18 )  

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This note is devoted to introduce a new concept of conditionally dominated random variables. Under suitable restrict conditions, a general strong law of large numbers for arbitrary continuous random variables is obtained.



集值变分包含的投影算法

苏珂, 孔祥庆, 何震

2010, 25(4):  481-494. 

摘要 ( 18 )   PDF (478KB) ( 16 )  

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A class of set-valued variational inclusions in Banach spaces and the convergence of the iterative algorithms are all studied in this paper. Moreover, the convergence and applications of projection algorithm to set-valued variational inclusions in Hilbert are also introduced. Many conclusions are generalized and improved.



关于具有局部可数sn-网的空间

康碧芳, 阎明刚, 李克典

2010, 25(4):  495-499. 

摘要 ( 19 )   PDF (267KB) ( 12 )  

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In this paper, spaces with a locally countable sn-network are discussed. It is shown that a space with a locally countable sn-network iff it is an snf-countable space with a locally countable k-network. As its application, almost-open and closed mappings(or finite-to-one and closed mapping) preserve locally countable sn-networks, and a perfect preimage theorem on spaces with a locally countable sn-network is established.



一类二阶非线性微分方程的区间振动准则

张伟鹏, 朱德明

2010, 25(4):  500-509. 

摘要 ( 23 )   PDF (385KB) ( 9 )  

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The main desire of this paper is to present several new interval oscillation criteria related to a generalized Riccati technique for certain second-order nonlinear differential equations. Our results extend some known equations. Finally, several examples illustrate the effectiveness of our results.



无6-圈平面图的不完全选色性

张海辉

2010, 25(4):  510-514. 

摘要 ( 17 )   PDF (194KB) ( 9 )  

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A graph G is called (k,d)*-choosable if for every list assignment L satisfying |L(v)|=k for all v ∈ V(G), there is an L-coloring of G such that each vertex of G has at most d neighbors colored with the same color as itself. In this paper, it is shown that every planar graph without 6-circuits and a triangle adjacent to itself or a quadrangle is (3,1)*-choosable.



补树的扩充侧廓

张振坤, 高风昕

2010, 25(4):  515-521. 

摘要 ( 13 )   PDF (319KB) ( 15 )  

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The extended profile problem is to find a proper interval supergraph with the smallest possible number of edges. The problem stems from the storage and elimination techniques of a sparse symmetric matrix A in 1950's. It has important applications in numerical algebra, VLSI designs and molecular biology. A tree T is a connected acyclic graph. The complement of a tree T is called a co-tree, denoted by Tˉ. In this paper the exact extended profile value of a cotree Tˉ is given.



扩散的Volterra-Lotka模型的正解存在性

王立周, 梅立泉

2010, 25(4):  522-529. 

摘要 ( 17 )   PDF (321KB) ( 14 )  

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In this paper, using the existence and comparison result for the quasi-monotone increasing system developed by C V Pao, the upper and lower solutions principle and an iterative method, we investigate the existence of the positive solutions of the Volterra-Lotka cooperating model.



亚纯函数分担两个公共集

张继龙

2010, 25(4):  530-534. 

摘要 ( 17 )   PDF (244KB) ( 11 )  

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In this paper, we deal with the problem of meromorphic functions sharing two sets, and we also give some supplements to several theorems due to H X Yi and L Z Yang, G D Song and N Li and other authors.



Bochner-Riesz极大算子及交换子在广义Morrey空间中有界性

朱诗红

2010, 25(4):  535-542. 

摘要 ( 18 )   PDF (363KB) ( 14 )  

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 Supported by the Natural Science Foundation of Tongling College(2007tlxykj006)； Supported by the Natural Science Foundation of Anhui Province(KJ2010B460)；



g-框架扰动的一些新结果

高文君

2010, 25(4):  543-549. 

摘要 ( 13 )   PDF (311KB) ( 25 )  

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Some new results for perturbation of g-frames are established, and it is shown that the existing partial results are the corollaries of our results.



树上奇偶马尔可夫链场上的若干强极限定理

马丽娜, 陈爽, 罗蕴玲, 李乃华

2010, 25(4):  550-558. 

摘要 ( 17 )   PDF (379KB) ( 7 )  

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First, a class of strong limit theorems are proved by constructing two nonnegative martingales. Then they are applied to the study of all kinds of even-odd Markov chain fields and Markov chain fields defined in the paper. Finally, some strong limit theorems for the even-odd Markov chain fields and Markov chain fields are obtained.



y-值半径与其稳定性

刘修生

2010, 25(4):  559-564. 

摘要 ( 16 )   PDF (296KB) ( 16 )  

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Let A be an n×n complex matrix, and let y =(α1,...,αn) be an n-dimensional complex vector. The y-numerical radius of A, denoted by r_y(A), is defined follows: r_y(A) = max {..., x_i = 1,x_i ∈ Cⁿ}, where Cn is an n-dimensional vector space over complex field C. In this paper we study norm properties and stability of y-numerical radius.



关于图的一致平衡性

温一慧

2010, 25(4):  565-571. 

摘要 ( 18 )   PDF (305KB) ( 18 )  

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In this paper, the definition of absolutely balanced and uniformly balanced for graphs are introduced, the difference between balance graphs are pointed out. Using (p,p+1)-graph as an example, we explained the existence of this difference and obtained some new results.



关于相依连续型随机序列的若干强偏差定理

范爱华

2010, 25(4):  572-577. 

摘要 ( 14 )   PDF (290KB) ( 12 )  

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Let {X_n, n ≥ 1} be a sequence of arbitrary continuous random variables, we introduce the notion of limit asymptotic logarithm likelihood ratio r(ω), as a measure of dissimilarity between probability measure P and reference measure Q. We get some strong deviation theorems for the partial sums of arbitrary continuous random variables under Chung-Teicher’s type conditions [6-7].



一类非线性双曲型方程解的爆破

王艳萍

2010, 25(4):  578-581. 

摘要 ( 16 )   PDF (230KB) ( 11 )  

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This paper gives the sufficient conditions of blow-up of the solution of a nonlinear hyperbolic equation with the initial boundary value conditions in finite time and proves the existence and uniqueness of the local solution of the problem.


一类奇异非线性分数微分方程正解的存在性

王金华, 向红军

2010, 25(4):  582-588. 

摘要 ( 19 )   PDF (326KB) ( 29 )  

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In this paper, we discuss a singular system of nonlinear fractional differential equation, in which the inhomogeneous term depends on the fractional derivative of lower order. By using the Krasnoselskii’s fixed point theorem and the Leray-Schauder nonlinear alternative method, some sufficient conditions for the existence of positive solution of the singular system are obtained.



一类非齐次拟线性双曲方程组整体经典解的存在性

金翠连

2010, 25(4):  589-600. 

摘要 ( 15 )   PDF (434KB) ( 10 )  

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In this paper, we consider a kind of quasilinear hyperbolic systems with inhomogeneous terms satisfying dissipative condition or matching condition. For the Cauchy problem of this kind of systems, we prove that, if the initial data is small and satisfies some decay condition, and the system is weakly linearly degenerate, then the Cauchy problem admits a unique global classical solution on t ≥ 0.



ARCH平方序列部分和的完全收敛性

张志强, 张日权, 冯井艳

2010, 25(4):  601-606. 

摘要 ( 19 )   PDF (270KB) ( 8 )  

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In this paper, we discuss the sufficient condition for complete convergence of partial sums of squares of the ARCH sequence, at the same time a moment inequality of maximum partial sums for squares of the ARCH sequence is proved.



F-知识与它的F-还原定理

周厚勇, 赵文菊, 史开泉

2010, 25(4):  607-614. 

摘要 ( 12 )   PDF (349KB) ( 26 )  

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By using the dual of one direction singular rough sets, the concepts of F-knowledge and its F-reduction were given; F-reduction theorem of F-knowledge and attribute supplement redundant principle of F-reduction are presented; the dual of one direction singular rough sets is one of the basic forms of singular rough sets; knowledge reduction is a new research direction on rough sets and rough system theory.





关于树的拉普拉斯谱半径

谭尚旺

2010, 25(4):  615-625. 

摘要 ( 16 )   PDF (407KB) ( 15 )  

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Some sharp upper bounds of Laplacian spectral radius of trees in terms of order, diameter, pendant vertex number, covering number, edge covering number or total independence number are given. And the ninth to thirteenth largest values of Laplacian spectral radius over the class of trees on a given order are also given.



一类多线性算子在广义Morrey空间L^p,ω上的有界性

刘明菊

2010, 25(4):  626-632. 

摘要 ( 20 )   PDF (332KB) ( 8 )  

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In this paper, the author study the boundedness of some multilinear operators on generalized Morrey spaces L^p,ω. They are the generalization of the corresponding results about commutators in [6]. Even then, from these results, we can concluded the cases of high order commutators.