Table of Content

30 March 2012, Volume 27 Issue 1

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Existence of Solutions to the Higher Order Nonlinear Differential Equations

TANG Lin-shan, JIANG Cheng-shun

2012, 27(1):  1-10. 

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This paper is concerned with the following n-th ordinary differential equation: {u(n)(t) = ...=0, where a, c ∈ R, ≥, such that a²+b² >0 and c²+d²>0, n ≥ 2, f: [0,1] × R → R is a continuous function. Assume that f satisfies one-sided Nagumo condition, the existence theorems of solutions of the boundary value problem for the n-th-order nonlinear differential equations above are established by using Leray-Schauder degree theory, lower and upper solutions, a priori estimate technique. 

A New Seven-modes Truncation of the Plane Incompressible Navier-Stokes Equations 

WANG He-yuan, CUI Yan, HUANG Min

2012, 27(1):  11-17. 

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A new seven-modes truncation of Fourier series of Navier-Stokes equations for a two-dimensional incompressible fluid on a torus is obtained. And its stationary solutions, the existence of attractor and the global stability of the equations are firmly proved. At the same time, several issues such as some basic dynamical behaviors and routs to chaos are shown numerically by changing Reynolds number. The system exhibits a stochastic behavior approached through an involved sequence of bifurcations.



Stabilization of Slowly Varying Switched Linear Systems

ZHANG Bing, LIANG Tong

2012, 27(1):  18-23. 

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The stabilization problem of systems that switch among a finite set of slowly varying linear systems with arbitrary switching frequency is discussed. It is shown that if the entries of the pointwise stabilizing feedback gain matrix are continuously differentiable functions of the entries of the system coefficient matrices, then the closed-loop system is uniformly asymptotically stable if the rate of time variation of the system coefficient matrices is sufficiently small.



Existence of Multiple Positive Solutions for Second-order Three-point Boundary Value Problems on a Half-line

SUN Yan-mei

2012, 27(1):  24-28. 

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In this paper, we are concerned with the existence of multiple positive solutions to a second-order three-point boundary value problem on the half-line. The results are obtained by the Leggett-Williams fixed point theorem.



The Regularity Estimates for the Elliptic Equations in Orlicz Classes

TAO Xiang-xing, FANG Yi

2012, 27(1):  29-35. 

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The purpose of this paper is to give the element proof of the regularity estimates in Orlicz classes for the second order derivatives of the solutions to the general second order elliptic equations. The global regularities in Orlicz for the second order derivatives of the solutions of the Dirichlet problems are also given.



Signless Laplacian Characteristic Polynomials of Complete Multipartite Graphs

LU Shi-fang, ZHAO Hai-xing

2012, 27(1):  36-40. 

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For a simple graph G, let matrix Q(G)=D(G) + A(G) be it’s signless Laplacian matrix and Q_G(λ)=det(λI Q) it’s signless Laplacian characteristic polynomial, where D(G) denotes the diagonal matrix of vertex degrees of G, A(G) denotes its adjacency matrix of G. If all eigenvalues of Q_G(λ) are integral, then the graph G is called Q-integral. In this paper, we obtain that the signless Laplacian characteristic polynomials of the complete multi-partite graphs G=K_{n1,n2,···,nt}. We prove that the complete t-partite graphs K_{(n,n,···,n)}t are Q-integral and give a necessary and sufficient condition for the complete multipartite graphs K_{(m,···,m)s(n,···,n)}t to be Q-integral. We also obtain that the signless Laplacian characteristic polynomials of the complete multipartite graphs K_{(m,···,m,)s1(n,···,n,)s2(l,···,l)s3}. 

The Singular Upper Triangle Type Solutions with Spin 1/2 of Quantum Yang-Baxter Equation (II)

WANG Ke, WANG Xin, LI Xian

2012, 27(1):  41-53. 

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In these two papers (Ⅰ) and (Ⅱ), the singular upper triangle type solutions with spin 1/2 of quantum Yang-Baxter equation are given. In the Paper (Ⅱ), we give the general solutions of the Yang-Baxter equation in this case.



Empirical Bayes Test for Two-parameter Exponential Distribution under Type-II Censored Samples

WANG Liang, SHI Yi-min, CHANG Ping

2012, 27(1):  54-58. 

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The empirical Bayes test problem is considered for scale parameter of two-parameter exponential distribution under type-II censored data. By using wavelets estimation method, the EB test function is constructed, of which the asymptotic optimality and convergence rates are obtained. Finally, an example concerning the main result is given.





Estimation of the Hausdorff Measure of a Kind of Sierpinski Carpet

ZHANG Yun-xiu, GU Hui

2012, 27(1):  59-62. 

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Suppose F₀ is an arbitrary triangle and F is a kind of Sierpinski carpet generated by F₀. We construct a projection mapping to obtain the lower bound of the Hausdorff measure of F; meanwhile the upper bound of the Hausdorff measure of F is calculated by the general covering.

A New GLKKM Theorem and Its Application to Abstract Economies

WEN Kai-ting

2012, 27(1):  63-67. 

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In this paper, a new GLKKM theorem in L-convex spaces is established. As applications, a new fixed point theorem and a maximal element theorem are obtained in Lconvex spaces. Finally, equilibrium existence theorems for economies and qualitative games in L-convex spaces are yielded.





CBMO Estimates for Commutators of Fractional Integral Operators with Variable Kernels

WANG Li-wei, SHU Li-sheng, QU Meng

2012, 27(1):  68-73. 

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Solving Fixed Point Problems in More General Nonconvex Sets Via an Interior Point Homotopy Method

SU Meng-long, LIU Mai-xue

2012, 27(1):  74-78. 

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In this paper, we are mainly devoted to solving fixed point problems in more general nonconvex sets via an interior point homotopy method. Under suitable conditions, a constructive proof is given to prove the existence of fixed points, which can lead to an implementable globally convergent algorithm.



Grand Zero Density Estimates of L-functions Associated with Cusp Forms

LI Ying-jie

2012, 27(1):  79-86. 

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In this paper a zero-density estimate of the large sieve type is given for the automorphic L-function L_f(s,χ), where f is a holomorphic cusp form and χ a Dirichlet character of mod q.





The Colored Jones Function

HAN You-fa, YAN Xin-ming, LV Li-li

2012, 27(1):  87-91. 

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In this paper, we discuss the properties of the colored Jones function of knots. Particularly,we calculate the colored Jones function of some knots(3₁,4₁,5₁,5₂₎. Furthermore,one can compute the Kashaev’s invariants and study some properties of the Kashaev’s conjecture.



Vertex-distinguishing VE-total Colorings of Cycles and Complete Graphs

XIN Xiao-qing, CHEN Xiang-en, WANG Zhi-wen

2012, 27(1):  92-97. 

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Let G be a simple graph of order at least 2. A VE-total-coloring using k colors of a graph G is a mapping f from V (G) E(G) into {1,2,···,k} such that no edge receives the same color as one of its endpoints. Let C(u)={f(u)} {f(uv) | uv ∈ E(G)} be the color-set of u. If C(u)=C(v) for any two vertices u and v of V (G), then f is called a k-vertex-distinguishing VE-total coloring of G or a k-VDVET coloring of G for short. The minimum number of colors required for a VDVET coloring of G is denoted by χ^ve_vt(G) and it is called the VDVET chromatic number of G. In this paper we get cycle C_n, path P_n and complete graph K_n of their VDVET chromatic numbers and propose a related conjecture. 

The Automorphism Group of U(4,Z) 

WANG Yu-lei, SUN Da-wei, WANG Zhi-jun

2012, 27(1):  98-103. 

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In this paper, the automorphism group of G is determined, where G is a 4 × 4 upper unitriangular matrix group over Z. Let K be the subgroup of AutG consisting of all elements of AutG which act trivially on G/G, G /ζG and ζG, then (i) InnG K AutG; (ii) AutG/K≌=G₁×D₈×Z₂, where G₁=(a,b,c|a⁴=b²=c²=1, a^b=a^-1, [a,c]= [b,c]=1; (iii) K/InnG≌=Z×Z×Z.





Non-commutative Kolmogorov Inequality and Zygmund Inequality

WU Tian-feng, ZHOU Jia, WANG Yun-xia

2012, 27(1):  104-109. 

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In this paper, we discuss some properties of distribution functions of τ-measurable operators and obtain non-commutative analogue of Kolmogorov inequality and Zygmund inequality.


Unicity Theorems of Mesomorphic Functions with Three Weighted Sharing Values 

WANG Xin-li, CAO Zhang-long

2012, 27(1):  110-116. 

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In this paper, with the idea of weighted sharing values, we deal with the problem of uniqueness of mesomorphic functions sharing three weighted values. We obtain some theorems which improve the results of H X Yi and W R Lu.

Sliding Mode Control for Fractional Differential Systems with State-delay 

SI Jia-fang, JIANG Wei

2012, 27(1):  117-122. 

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The problem of sliding mode control for fractional differential systems with statedelay is considered. A novel sliding surface is proposed and a controller is designed correspondingly, such that the state starting from any initial value will move toward the switching surface and reach the sliding surface in finite time and the state variables on the sliding surface will converge to equilibrium point. And the stability of the proposed control design is discussed.



Homomorphic Properties of Fuzzy Rough Groups 

QIN Ke-yun, ZHANG Xiao-hua

2012, 27(1):  123-127. 

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This paper is devoted to the discussion of homomorphic properties of fuzzy rough groups. The fuzzy approximation space was generated by fuzzy normal subgroups and the fuzzy rough approximation operators were discussed in the frame of fuzzy rough set model. The basic properties of fuzzy rough approximation operators were obtained.



The Excellent Extensions of Rings and Copure Dimensions 

LU Bo

2012, 27(1):  128-132. 

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Let R be a noetherian ring and S an excellent extension of R. cid(M) denotes the copure injective dimension of M and cfd(M) denotes the copure flat dimension of M. We prove that if M S is a right S-module then cid(M S)=cid(M R) and if S M is a left S-module then cfd(S M)=cfd(R M). Moreover, cid-D(S)=cid-D(R) and cfd-D(S)=cfdD(R).



The Duality on Vector Optimization Problems  

HUANG Long-guang

2012, 27(1):  133-138. 

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Duality framework on vector optimization problems in a locally convex topological vector space are established by using scalarization with a cone-strongly increasing function. The dualities for the scalar convex composed optimization problems and for general vector optimization problems are studied. A general approach for studying duality in vector optimization problems is presented.



The Lawson Partial Order on Wrpp Semigroups

LIU Hai-jun, GUO Xiao-jiang

2012, 27(1):  139-144. 

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In this paper,we introduce Lawson partial order ≤w on wrpp semigroups. After obtaining some properties of ≤w, we determine when ≤w is (left; right) compatible with the multiplication. These results extend and enrich the related results of Lawson and GuoLuo on abundant semigroups, of Guo-Shum on rpp semigroups and of Liu-Guo on wrpp semigroups.



Further Oscillation Results for a Class of Hyperbolic Equations with Continuous Distributed Deviating Arguments

ZHANG Meng, SONG Guo-hua

2012, 27(1):  145-151. 

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A class of hyperbolic equations with continuous distributed deviating arguments is considered and its oscillation theorems are discussed. These theorems are of higher degree of generality and deal with the cases which are not covered by the known criteria. Particularly, these criteria extend and unify a number of existing results.



A Smoothing Newton Method for the Box Constrained Variational Inequality Problems

XIE Ya-jun, MA Chang-feng

2012, 27(1):  152-158. 

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The box constrained variational inequality problem can be reformulated as a nonsmooth equation by using median operator. In this paper, we present a smoothing Newton method for solving the box constrained variational inequality problem based on a new smoothing approximation function. The proposed algorithm is proved to be well defined and convergent globally under weaker conditions.