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2013年 第28卷 第2期    刊出日期：2013-06-30

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具有控制策略的Ｍ/Ｍ/1多重工作休假排队

张宏波, 封平华

2013, 28(2):  159-165. 

摘要 ( 28 )   PDF (328KB) ( 16 )  

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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. 


拟常全纯截面曲率空间中的2调和子流形

朱静勇, 宋卫东

2013, 28(2):  166-171. 

摘要 ( 21 )   PDF (280KB) ( 12 )  

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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.



时间测度链上二阶非线性动力方程的振动性

杨甲山

2013, 28(2):  172-179. 

摘要 ( 20 )   PDF (375KB) ( 20 )  

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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.

Hilbert空间中关于广义混合似平衡问题组的求解

刘帮涛, 罗敏

2013, 28(2):  180-189. 

摘要 ( 16 )   PDF (366KB) ( 10 )  

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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.



一类p-Laplacian非齐次多点边值问题正解的存在性

田亚

2013, 28(2):  190-195. 

摘要 ( 20 )   PDF (313KB) ( 12 )  

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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. 


广义复结构中的对偶特征对

尹彦彬, 刘玲, 刘华侨

2013, 28(2):  196-201. 

摘要 ( 20 )   PDF (281KB) ( 26 )  

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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.



关于卵形面特征的一个注记

王宝富, 盛利

2013, 28(2):  202-205. 

摘要 ( 22 )   PDF (242KB) ( 16 )  

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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 L_r=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.



关于抛物有理函数的Hausdorff维数与共形测度的相等性

庄伟

2013, 28(2):  206-213. 

摘要 ( 33 )   PDF (353KB) ( 15 )  

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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 .



2-1维格点差分方程的传播波 

何延生, 侯成敏

2013, 28(2):  214-223. 

摘要 ( 18 )   PDF (391KB) ( 24 )  

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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.



锥度量空间中Lipschitz型映射的新公共不动点定理

韩艳, 徐望斌, 许绍元

2013, 28(2):  224-233. 

摘要 ( 25 )   PDF (371KB) ( 20 )  

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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.



一类食饵带有避难的比率依赖型捕食系统的分支和极限环

刘艳伟, 刘霞

2013, 28(2):  234-240. 

摘要 ( 25 )   PDF (327KB) ( 14 )  

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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.



广义一致(C,α,ρ,d)凸多目标半无限规划的最优性条件

张庆祥, 张永战

2013, 28(2):  241-249. 

摘要 ( 26 )   PDF (378KB) ( 28 )  

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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.



零级和有限级Dirichlet级数和随机Dirichlet级数的增长性

杨祺, 曹月波, 田宏根

2013, 28(2):  250-256. 

摘要 ( 24 )   PDF (259KB) ( 25 )  

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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.



逆度和连通度

马小玲, 田应智

2013, 28(2):  257-260. 

摘要 ( 21 )   PDF (238KB) ( 21 )  

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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)) .



解析函数新子类的某些性质

汤获, 李书海, 邓冠铁, 马丽娜

2013, 28(2):  261-268. 

摘要 ( 23 )   PDF (331KB) ( 25 )  

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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.


一个关于P-混沌蕴涵分布混沌以及具有正拓扑熵的Devaney混沌的注记

尹建东, 邱玉芬

2013, 28(2):  269-273. 

摘要 ( 34 )   PDF (260KB) ( 28 )  

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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.



双极可压Euler-Maxwell方程组光滑解的整体存在性

徐前进, 李新, 冯跃红

2013, 28(2):  274-283. 

摘要 ( 18 )   PDF (396KB) ( 19 )  

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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.



一个推广的极大型非线性差分方程解的特性

石启宏, 苏兴, 袁国强, 肖倩

2013, 28(2):  284-289. 

摘要 ( 30 )   PDF (293KB) ( 21 )  

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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.



多复变中的Alexander型定理

刘爱超, 闫春燕, 段晓玲, 刘浩

2013, 28(2):  290-296. 

摘要 ( 29 )   PDF (319KB) ( 19 )  

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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.





随机环境中的超过程的对偶过程与比较定理

陈丽, 薛玲霞, 兰社云

2013, 28(2):  297-302. 

摘要 ( 23 )   PDF (287KB) ( 21 )  

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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.



由microRAN介导的具有时滞负反馈环的基因振荡表达

张丰盘, 路金瑞, 刘志广

2013, 28(2):  303-310. 

摘要 ( 25 )   PDF (614KB) ( 13 )  

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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. 


反对合矩阵的秩等式

王世恒

2013, 28(2):  311-316. 

摘要 ( 26 )   PDF (254KB) ( 33 )  

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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.