Table of Content

30 June 2013, Volume 28 Issue 2

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The M/M/1 Queue with Controlled Multiple Working Vacations

ZHANG Hong-bo, FENG Ping-hua

2013, 28(2):  159-165. 

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In this paper, we study an M/M/1 queue with multiple working vacations under following Bernoulli control policy: at the instants of the completion of a service in vacation, the server will interrupt the vacation and enter regular busy period with probability 1 p (if there are customers in the queue) or continue the vacation with probability p. For this model, we drive the analytic expression of the stationary queue length and demonstrate stochastic decomposition structures of the stationary queue length and waiting time, also we obtain the additional queue length and the additional delay of this model. The results we got agree with the corresponding results for working vacation model with or without vacation interruption if we set p = 0 or p = 1, respectively. 


2-harmonic Submanifolds in a Quasi Constant Holomorphic Sectional Curvature Space

ZHU Jing-yong, SONG Wei-dong

2013, 28(2):  166-171. 

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In the present paper, the authors study totally real 2-harmonic submanifolds in a quasi constant holomorphic sectional curvature space and obtain a Simons’ type integral inequality of compact submanifolds as well as some pinching theorems on the second fundamental form.



Oscillation of Second-order Nonlinear Dynamic Equation on Time Scales

YANG Jia-shan

2013, 28(2):  172-179. 

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The oscillation for a class of second order nonlinear variable delay dynamic equation on time scales with nonlinear neutral term and damping term was discussed in this article. By using the generalized Riccati technique, integral averaging technique and the time scales theory, some new sufficient conditions for oscillation of the equation are proposed. These results generalize and extend many known results for second order dynamic equations. Some examples are given to illustrate the main results of this article.

On Solving a System of Generalized Mixed Equilibrium-like Problems in Hilbert Spaces

LIU Bang-tao, LUO Min

2013, 28(2):  180-189. 

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A system of generalized mixed equilibrium-like problems is introduced and the existence of its solutions is shown by using the auxiliary principle technique in Hilbert spaces.



The Existence of Positive Solutions of p-Laplacian Non-homogeneous Multi-point Boundary Value Problems

TIAN Ya

2013, 28(2):  190-195. 

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We study the following nonlinear m-point p-Laplacian boundary value problem with non-homogenous condition: (Φp(u′)′)+f(t, u, u′)=0, 0<t<1, u′(0)=0, ...=λ, where Φp(s)=...<1. Under sufficient conditions, we show that there exists a positive number λ* such that the problem has at least one positive solution for 0 < λ < λ and no solution for λ > λ*. The proof is based on the Schauder fixed point theorem and upper-lower technics. 

Dual Characteristic Pairs in Generalized Complex Structures

YIN Yan-bin, LIU Ling, LIU Hua-qiao

2013, 28(2):  196-201. 

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This paper presents the relations between spinors and dual characteristic pairs, and gives a way to get the dual characteristic pairs of Dirac structure associated to a generalized complex structure.





A Note of the Hyperovaloid Characterization

WANG Bao-fu, SHENG Li

2013, 28(2):  202-205. 

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Let L_r be the r-th affine mean curvature of a hyperovaloid in A ⁿ⁺¹ , in this paper, we prove that if Lr=0 and for some fixed 1 ≤i₁< ···< i_r<n,...= C everywhere on M, then M must be an ellipsoid, where C is a constant.

On the Equality of Hausdorff Dimensions and Conformal Measures of Parabolic Maps

ZHUANG Wei

2013, 28(2):  206-213. 

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Let f, g be two parabolic maps of degree ≥ 2. HD(J) denotes the Hausdorff dimension of the Julia set J and m f and m g denote the t-conformal measure supported on the Julia set J(f) and J(g) respectively. In this paper we show that if J(f) and J(g) are locally connected and f and g topologically conjugate, then HD(J(f)) = HD(J(g)), m_g = m_foh^-1 .





Traveling Waves for 2-1 Dimension Lattice Difference Equations 

HE Yan-sheng, HOU Cheng-min

2013, 28(2):  214-223. 

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A definition is introduced about traveling waves of 2-1 dimension lattice difference equations. Discrete heat equation is introduced and a discussion is given for the existence of traveling waves. The theory of traveling waves is extended on 2-1 dimension lattice difference equations. As an application, an example is presented to illustrate the main results.

Some New Theorems of Lipschitz Type Mappings in Cone Metric Spaces

HAN Yan, XU Wang-bin, XU Shao-yuan

2013, 28(2):  224-233. 

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In this paper, some new existence and uniqueness of common fixed points for three mappings of Lipschitz type are obtained. The conditions are greatly weaker than the classic conditions in cone metric spaces. These results improve and generalize several wellknown comparable results in the literature. Moreover, our results are supported by some examples.



Bifurcation and Limit Cycle of a Ratio-dependent Predator-prey System with Refuge on Prey

LIU Yan-wei, LIU Xia

2013, 28(2):  234-240. 

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Influences of prey refuge on the dynamics of a predator-prey model with ratio-dependent functional response are investigated. The local and global stability of positive equilibrium of the system are considered. Theoretical analysis indicates that constant refuge leads to the system undergo supercritical Hopf bifurcation twice with the birth rate of prey species changing continuously.



The Optimality Conditions for Multiobjective Semi-infinite Programming Involving Generalized Unified (C, α, ρ, d)-convexity

ZHANG Qing-xiang, ZHANG Yong-zhan

2013, 28(2):  241-249. 

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The definition of generalized unified (C, α, ρ, d)-convex function is given. The concepts of generalized unified (C, α, ρ, d)-quasiconvexity, generalized unified (C, α, ρ, d)-pseudoconvexity and generalized unified (C, α, ρ, d)-strictly pseudoconvex functions are presented. The sufficient optimality conditions for multiobjective nonsmooth semi-infinite programming are obtained involving these generalized convexity lastly.



The Growth of Dirichlet Series and Random Dirichlet Series of Zero Order and Finite Order

YANG Qi, CAO Yue-bo, TIAN Hong-gen

2013, 28(2):  250-256. 

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In this paper, we study the relations between the coefficients and the growth of zero order and finite order Dirichlet series and random Dirichlet series in the whole plane. And when the random variable sequence {Xn {ω}} satisfies the certain condition, in the whole plane, the growth of the random entire function which is determined by the zero order and finite order random Dirichlet series is almost surely same with corresponding growth of random Dirichlet series on any horizontal straight line.





Inverse Degree and Connectivity

MA Xiao-ling, TIAN Ying-zhi

2013, 28(2):  257-260. 

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Let G be a connected graph with vertex set V(G), order n=|V(G)|, minimum degree δ(G) and connectivity κ(G). The graph G is called maximally connected if κ(G) = δ(G). Define the inverse degree of G with no isolated vertices as R(G) =Σ_v∈V(G)1/d(v) , where d(v) denotes the degree of the vertex v. We show that G is maximally connected if R(G) <1+2/δ + (n-2δ+1)/((n-1)(n-3)) .



Some Properties for New Subclass of Analytic Functions

TANG Huo, LI Shu-hai, DENG Guan-tie, MA Li-na

2013, 28(2):  261-268. 

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A new subclass A(β₁,β₂,···,β_k;λ) of analytic functions f(z) in the open unit disk U is introduced and studied. We provide coefficient inequalities, distortion theorems, extreme points and radius of close-to-convexity, starlikeness and convexity of this class.



A Note on P-chaos Implies Distributional Chaos and Chaos in the Sense of Devaney with Positive Topological Entropy

YIN Jian-dong, QIU Yu-fen

2013, 28(2):  269-273. 

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In 2007, T Arai and N Chinen proved that every P -chaotic map from a continuum into itself has positive topological entropy and is topologically mixing. In this work, we show that there exists a P -chaotic map defined on a general compact metric space but not on a continuum such that it has zero topological entropy and is not topologically mixing.





Global Existence of Smooth Solutions of Compressible Bipolar Euler-Maxwell Equations

XU Qian-jin, LI Xin, FENG Yue-hong

2013, 28(2):  274-283. 

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The bipolar compressible Euler-Maxwell equations as a fluid dynamic model arising from plasma physics to describe the dynamics of the compressible electrons and ions is investigated. This work is concerned with three-dimensional Euler-Maxwell equations with smooth periodic solutions. With the help of the symmetry operator techniques and energy method, the global smooth solution with small amplitude is constructed around a constant equilibrium solution with asymptotic stability property.



Characters of the Solutions to a Generalized Nonlinear Max-type Difference Equation

SHI Qi-hong, SU Xing, YUAN Guo-qiang, XIAO Qian

2013, 28(2):  284-289. 

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This paper is concerned with the boundedness and asymptotic behavior of positive solutions for a generalized difference equation arising from automatic control theory. The main results improve and extend the ones in the previous works to a large extent. One in particular is that Rouche’s theorem is available to prove the convergence of solutions.



The Alexander Type Theorem in Several Complex Variables

LIU Ai-chao, YAN Chun-yan, DUAN Xiao-ling, LIU Hao

2013, 28(2):  290-296. 

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In this paper, the Alexander type theorem in several complex variables is given by using the parametric representation of a kind of starlike mappings. As a corollary, a new method is set up to prove that the Roper-Suffridge extension operator keeps the property of starlike.





Dual Processes and Compapison Theorem of Superprocesses in Random Environents

CHEN Li, XUE Ling-xia, LAN She-yun

2013, 28(2):  297-302. 

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In this paper, we give the dual processes for superprocesses in random environments constructed by L Mytnik and the comparison theorem of these superprocesses with Dawson-Watanabe superprocesses.



Oscillatory Gene Expression by the microRAN Mediating Delayed Negative Feedback Loop

ZHANG Feng-pan, LU Jin-rui, LIU Zhi-guang

2013, 28(2):  303-310. 

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More and more experiments show that microRNAs can regulate gene expression by stimulating degradation of mRNA or repression of translation of mRNA. In this paper, we incorporate the microRNA into a previous mathematical model of gene expression through forming a microRNA-induced silencing complex(RISC). Our findings demonstrate the dynamical behavior of the constructed system. By Hopf theories, we derive the theoretical results of globally asymptotical stability and provide the sufficient conditions for the oscillation of the simple gene regulatory system, and by numerical simulation further demonstrate how the amplitudes against the change of delay in the gene regulatory network. 


Rank Equalities for Anti-involutory Matrices

WANG Shi-heng

2013, 28(2):  311-316. 

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Some rank equalities are established for anti-involutory matrices. In particular, we get the formulas for the rank of the difference, the sum and the commutator of anti-involutory matrices.