Table of Content

30 December 2010, Volume 25 Issue 4

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On Strong Law of Large Numbers for Random Sequence 

WANG Zhong-zhi

2010, 25(4):  475-480. 

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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.


The Projective Algorithms of Set-valued Variational Inclusions 

SU Ke, KONG Xiang-qing, HE Zhen

2010, 25(4):  481-494. 

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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.


On Spaces with a Locally Countable sn-network 

KANG Bi-fang, YAN Ming-gang, LI Ke-dian

2010, 25(4):  495-499. 

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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.


Interval Criteria for Oscillation of Certain Second-order Nonlinear Differential Equations

ZHANG Wei-peng, ZHU De-ming

2010, 25(4):  500-509. 

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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.


Improper Choosability of Planar Graphs without 6-circuits

ZHANG Hai-hui

2010, 25(4):  510-514. 

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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.


The Extended Profiles of the Co-trees

ZHANG Zhen-kun, GAO Feng-xin

2010, 25(4):  515-521. 

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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.


The Existence of Positive Solutions for Volterra-Lotka Cooperating Model with Diffusion

WANG Li-zhou, MEI Li-quan

2010, 25(4):  522-529. 

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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.


Meromorphic Functions That Share Two Sets

ZHANG Ji-long

2010, 25(4):  530-534. 

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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.


Boundedness for Maximal Bochner-Riesz Operator and Commutator on Generalized Morrey Space 

ZHU Shi-hong

2010, 25(4):  535-542. 

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


Some New Results for Perturbation of g-frames 

GAO Wen-jun

2010, 25(4):  543-549. 

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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.


Some Strong Limit Theorems for Even-odd Markov Chain Fields Indexed by Trees 

MA Li-na, CHEN Shuang, LUO Yun-ling, LI Nai-hua

2010, 25(4):  550-558. 

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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.


On y-numerical Radius and Its Stability 

LIU Xiu-sheng

2010, 25(4):  559-564. 

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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.


On the Uniformly Balancedness of Graphs

WEN Yi-hui

2010, 25(4):  565-571. 

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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.


Some Strong Deviation Theorems for Dependent Continuous Random Sequence

FAN Ai-hua

2010, 25(4):  572-577. 

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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].


Blow-up of Solution for a Nonlinear Hyperbolic Equation 

WANG Yan-ping

2010, 25(4):  578-581. 

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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.



Existence of Positive Solution to a Singular System of Nonlinear Fractional Differential Equation 

2010, 25(4):  582-588. 

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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.


Global Classical Solutions of Inhomogeneous Quasilinear Hyperbolic Systems

JIN Cui-lian

2010, 25(4):  589-600. 

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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.


Complete Convergence for Partial Sums of the Squares of ARCH Sequence 

ZHANG Zhi-qiang, ZHANG Ri-quan, FENG Jing-yan

2010, 25(4):  601-606. 

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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-knowledge and Its F-reduction Theorems

F-knowledge and Its F-reduction Theorems

2010, 25(4):  607-614. 

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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.





On the Laplacian Spectral Radius of Trees

TAN Shang-wang

2010, 25(4):  615-625. 

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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.


Boundedness of Some Multilinear Operators on Generalized Morrey Spaces L^p,ω

LIU Ming-ju

2010, 25(4):  626-632. 

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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.