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25 June 2008, Volume 28 Issue 3 Previous Issue    Next Issue

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On the {\boldmath $\widehat{psl(2|2)^{(2)}}_{k}$} Current Superalgebra and Conformal Field Theory Ding Xiangmao;Wang Guidong;Wang Shikun Acta mathematica scientia,Series A. 2008, 28 (3):  393-402.  Abstract ( 1898 )   RICH HTML PDF (371KB) ( 1229 )   Save The twisted Kac-Moody Lie superalgebra $\widehat{psl(2|2)^{(2)}}_k$ is investigated by means of the vector coherent state method and obtained the differential operators realization. The authors get the free field representation of $\widehat{psl(2|2)^{(2)}}_k$, which is the subalgebra of $\widehat{gl(2|2)^{(2)}}_k$ modulo the ${\Bbb Z}_4$-outer automorphism, the CFT has central charge $-2.$\noindent{\bf Key words:}Kac-Moody superalgebra; Differential operator realization; Free field realization; Conformal field theory. Related Articles | Metrics

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Maximum Genus of Graphs Embedded in the Klein Bottle Huang Yuanqiu ;Tang Ling ;Liu Yanpei Acta mathematica scientia,Series A. 2008, 28 (3):  403-411.  Abstract ( 1936 )   RICH HTML PDF (371KB) ( 1241 )   Save Let $\phi: G\rightarrow S$ be a 2-cell embedding of a graph $G$ into a surface $S$. If all faces of $G$ are consecutively adjacent, equivalently the dual graph of the embedded graph $G$ contains a Hamilton circuit, then the embedding $\phi$ is said to be a consecutively adjacent face embedding. In this paper the authors study the maximum genus of a graph that admits a consecutively adjacent face embedding in the Klein Bottle. Related Articles | Metrics

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Quadratic Finite Volume Element Method Along Characteristics for the Semiconductor Device of Heat Conduction: H1Error Estimates Chen Chuanjun; Yuan Yirang Acta mathematica scientia,Series A. 2008, 28 (3):  412-423.  Abstract ( 2046 )   RICH HTML PDF (412KB) ( 1195 )   Save A fully discrete quadratic finite volume element method along characteristics for the semiconductor device of heat conduction is given, which is used by piecewise lagrange quadratic trial function and piecewise constant test function. Under general conditions, an optimal H1 error estimate is obtained. Related Articles | Metrics

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Global Structure of Positive Solutions of Singular Nonlinear Sturm-Liouville Problems Sun Jingxian ;Li Hongyu Acta mathematica scientia,Series A. 2008, 28 (3):  424-433.  Abstract ( 2146 )   RICH HTML PDF (328KB) ( 1316 )   Save In this paper, the following nonlinear Sturm-Liouville problem $$\left\{ \begin{array}{lcl} -u''=\lambda f(x, u),\\ \alpha_0 u(0)+\beta_0 u'(0)=0,\ \ \alpha_1 u(1)+\beta_1 u'(1)=0; \end{array} \right.$$ is discussed by topological methods. In the case that the nonlinear term is non-singular or singular, global structure of the positive solution set of the above problem is obtained, and the existence of positive solutions of the above problem is proved under the condition that the nonlinear term $f(x,u)$ does not satisfy f(x,u)≥0(u≥0). Related Articles | Metrics

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A Phragmen-Lindelof Theorem for Plurisubharmonic Functions Wang Guang ; Wu Mijing Acta mathematica scientia,Series A. 2008, 28 (3):  434-437.  Abstract ( 1774 )   RICH HTML PDF (243KB) ( 1221 )   Save In this paper, a Phragmen-Lindelof theorem for plurisubharmonic functions is given, through which a result of [8] is extended. Related Articles | Metrics

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The Henig Efficient Subdifferential of Set-valued Mapping and Stability Yu Guolin;Liu Sanyang Acta mathematica scientia,Series A. 2008, 28 (3):  438-446.  Abstract ( 2033 )   RICH HTML PDF (340KB) ( 1376 )   Save In normed linear spaces, the concepts of cone-Henig efficient subgradient and cone-Henig efficient subdifferential for a set-valued mapping are introduced. By using the convex set separation theorem, the existence theorem for cone-Henig efficient subdifferential is proposed, and the sufficient and necessary condition for a linear functional being a cone-Henig efficient subgradient is established. Finally, the stability problem for a kind of perturbed set-valued opimization problem is considered in sense of Henig efficiency. Related Articles | Metrics

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Convergence for Pairwise NQD Random Variables chenpingyan Acta mathematica scientia,Series A. 2008, 28 (3):  447-453.  Abstract ( 1537 )   RICH HTML PDF (231KB) ( 1282 )   Save In this paper, the author discusses the $L^r$ convergence for pairwise NQD random variables under $r$-th Ces\`aro uniform integrability, which is the same as that in the independent case. Related Articles | Metrics

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Stability and Traveling Fronts in Lotka-Volterra Cooperation Model with Stage Structure Wu Shiliang ;Li Wantong Acta mathematica scientia,Series A. 2008, 28 (3):  454-464.  Abstract ( 2628 )   RICH HTML PDF (385KB) ( 1445 )   Save In this paper, the authors derive and study a delayed diffusion system, which models the interaction between the two species, the adult members of which are in cooperation. By using the method of sub- and super-solutions due to Redlinger, we show that the diffusive delay model generates simple global dynamics, i.e., the zero steady state and the boundary equilibria are linear unstable and the unique positive steady state is globally asymptotically stable. We also establish the existence of traveling wave fronts connecting the zero solution of this equation with the unique positive steady state. The approach used in this paper is the upper-lower solutions technique and the monotone iteration recently developed by Wang, Li and Ruan for reaction-diffusion systems with spatio-temporal delays. Related Articles | Metrics

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A Compensatory Phenomenon to the Classical Sphere Theorem Wang Peihe;Shen Chunli Acta mathematica scientia,Series A. 2008, 28 (3):  465-471.  Abstract ( 1539 )   RICH HTML PDF (328KB) ( 1306 )   Save This paper discusses the topology of manifolds with a small well of positive $k$-th Ricci curvature and generalizes the classical sphere theorem. Also, the authors will describe an interesting compensatory phenomenon of the manifold with respect to the classical sphere theorem. Related Articles | Metrics

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The Properties of cut* Topological Spaces Peng Liangxue;Huang Guifang Acta mathematica scientia,Series A. 2008, 28 (3):  472-479.  Abstract ( 1950 )   RICH HTML PDF (322KB) ( 1155 )   Save In this note, the class of cut*spaces are introduced. A connected topological space X is called a cut* space, if $X\setminus \{x\}$ is connected for any $x\in X$, and $X\setminus \{x,y\}$ is not connected for any distinct points $x,y\in X$. The properties of cut* spaces are discussed. The authors show that if X is a cut* spaces, then $\{x\}$ is open or closed for any $x\in X$, and $X$ has infinite closed points. The authors also discuss the properties of some special cut* spaces, which satisfy that $X\setminus \{x\}$ is COTS for any $x\in X$. The authors show that there doesn't exisxt a cut* space $X$, satisfying that $X\setminus \{x\}$ is a irreducible cut space for any $x\in X$. In the last part of the note, the authors show that $X$ is compact or Lindel\"of, if $X$ is a cut* space and $X\setminus \{x\}$ is LOTS for any $x\in X$. Related Articles | Metrics

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Full Regularity of {\boldmath $p$}-Harmonic Type Systems Below the Critical Growth Zheng Shenzhou;Zhao Shule Acta mathematica scientia,Series A. 2008, 28 (3):  480-488.  Abstract ( 1710 )   RICH HTML PDF (320KB) ( 1237 )   Save For $p\geq 2$, the authors establish that each weak solution of a class of degenerate elliptic systems below the critical growth belongs to Morrey spaces. Furthermore, the authors obtain that the first derivative of each weak solution is locally H\"older continuous under additional conditions. Related Articles | Metrics

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New Perturbation Results on Frames in Hilbert Spaces Li Dengfeng ;Yang Lijun Acta mathematica scientia,Series A. 2008, 28 (3):  489-499.  Abstract ( 1926 )   RICH HTML PDF (321KB) ( 1356 )   Save In this paper, some new results of frame perturbation in Hilbert spaces are obtained.The authors also discuss perturbations of Riesz bases, near-Riesz bases and Riesz frames.Moreover, it is showed that many known results are corollaries of the results. Related Articles | Metrics

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A Spectral Characterization for Stability of C0-semigroups on ∑e1 Type Banach Spaces Su Weigang; Zhong Huaijie Acta mathematica scientia,Series A. 2008, 28 (3):  500-507.  Abstract ( 1907 )   RICH HTML PDF (347KB) ( 1231 )   Save This paper discusses the special properties of the spectrum of bounded linear operators in a class of indecomposable ∑e1 type Banach spaces;gives a spectral characterization for stability of uniformly bounded C0-semigroups on ∑e1 type Banach spaces, and gives an application to the stability theorem. Related Articles | Metrics

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On the Completeness and Closure of Random Systems { tλn (ω) } in a Weighted Banach Space Yang Xiangdong; Deng Guantie Acta mathematica scientia,Series A. 2008, 28 (3):  508-514.  Abstract ( 2003 )   RICH HTML PDF (255KB) ( 1244 )   Save In this paper, the authors investigate the completeness and closure of random systems{ tλn (ω) } in the weighted Banach space $C_{\alpha}$, where $C_{\alpha}$ denotes the Banach spaces consisting of functions of one complex variable continuous on the right half real axis and satisfying $|f(t)|{\rm e}^{-\alpha(t)}\rightarrow0~(t\rightarrow +\infty$). Related Articles | Metrics

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Three Nontrival Positive Solutions for Second Order Three Point Boundary Value Problems with Sign Changing Nonlinearities Li Cheng;Liu Lishan Acta mathematica scientia,Series A. 2008, 28 (3):  515-522.  Abstract ( 2247 )   RICH HTML PDF (279KB) ( 1306 )   Save In this paper, the existence of multiple nontrival positive solutions for a class of singular second order three point boundary value problems with sign changing nonlinearities is investigated. Growth conditions are imposed on $f$, which yield the existence of at least three nontrival positive solutions by using the Leggett-Williams fixed point theorem. Related Articles | Metrics

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Universal Admissibility of Linear Estimators in Growth Curve Model with Respect to Restricted Parameter Sets Zhang Shangli;Qin Hong Acta mathematica scientia,Series A. 2008, 28 (3):  523-529.  Abstract ( 1776 )   RICH HTML PDF (316KB) ( 1309 )   Save Related Articles | Metrics

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Some Integral Criteria for α -Normal Functions Liu Yongmin;Hu Zhangjian Acta mathematica scientia,Series A. 2008, 28 (3):  530-534.  Abstract ( 1922 )   RICH HTML PDF (245KB) ( 1148 )   Save For $0< \alpha< \infty$, $N^\alpha$ is the class of meromorphic functions $f$ defined in the unit disk $D$ satisfying $\sup\limits_{z\in D}(1-|z|^2)^\alpha f^\#(z)<\infty$, where $f^\#(z)=|f'(z)|/(1+|f(z)|^2)$. Some new characterizations of the $\alpha$-normal functions are given for $0< \alpha< 1$. Characterizations are given in terms of the Bergman-Carleson measure conditions and the compact Bergman-Carleson conditions. Related Articles | Metrics

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Strong Converse Inequalities for Weighted Simultaneous Approximation by Gamma Operators in Lp (1≤p ≤∞) Spaces Qi Qiulan; Guo Shunsheng;Huang Suxia Acta mathematica scientia,Series A. 2008, 28 (3):  537-545.  Abstract ( 2105 )   RICH HTML PDF (296KB) ( 1304 )   Save In this paper, the authors consider the weighted simultaneous approximation by the Gamma operator and establish the strong converse inequality of type $B$ for the operator with the weighted $K$-functional $K^2_{\varphi}(f, t^2)_{w,p}$ in the space $L_p\;(1\le p\le \infty)$. Related Articles | Metrics

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On a Class of Singularly Perturbed Problems with Boundary Perturbation Tang Rongrong Acta mathematica scientia,Series A. 2008, 28 (3):  546-552.  Abstract ( 1788 )   RICH HTML PDF (271KB) ( 1244 )   Save By using the asymptotic theory, a class of singularly perturbed problems with boundary perturbation is considered. Under the appropriate conditions, the asymptotic solution and the existence conditions of the solution are obtained, and from the result a propagation problem in mural wave is applied. Related Articles | Metrics

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MLE of Generalized Linear Model Randomly Censored with Incomplete Information Xiao Zhihong;Liu Luqin Acta mathematica scientia,Series A. 2008, 28 (3):  553-564.  Abstract ( 1949 )   RICH HTML PDF (368KB) ( 1254 )   Save In this paper, one defines the generalized linear models(GLM) based on the observed data with incomplete information and random censorship under the case that regressors are given and regressors are stochastic, respectively. Under the given conditions, one discusses the existence and uniqueness of the solution on the likelihood equations with respect to the parameter vector of the two models, obtains and proves the consistency and asymptotical normality of the maximum likelihood estimators(MLE) on the two models, respectively. Related Articles | Metrics

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The Holder Continuity of Quasiconformal Mappings in Bounded Convex Domains Zheng Ningguo; Chu Yuming Acta mathematica scientia,Series A. 2008, 28 (3):  565-569.  Abstract ( 2190 )   RICH HTML PDF (279KB) ( 1308 )   Save By using the modulus of family of curves, the global Holder continuity of the K-quasiconformal mapping f which maps bounded convex domain D onto Bn is obtained, and the Holder exponent α=K1/(1-n) is optimal. Related Articles | Metrics

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Generalized Augmented Lagrangian Duality Theory and Applications in Vector Optimization Problems Chen Zhe Acta mathematica scientia,Series A. 2008, 28 (3):  570-577.  Abstract ( 1948 )   RICH HTML PDF (291KB) ( 1224 )   Save In this paper, the author introduces a generalized augmented Lagrangian for minimizing an extended vector-valued function. Based on the generalized augmented Lagrangian, the author constructs set-valued dual functions and dual optimization problems, obtain weak and strong duality results without any convexity required, apply the results for solving a constrained vector optimization problem. The results improve and generalize some known results. Related Articles | Metrics

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Stability and Hopf Bifurcation of an SIS Model with Species Logistic Growth and Saturating Infect Rate Xu Weijian; Acta mathematica scientia,Series A. 2008, 28 (3):  578-584.  Abstract ( 1956 )   RICH HTML PDF (357KB) ( 1161 )   Save In this paper, an SIS infective model with species Logistic growth and saturating infective rate is studied. The author discusses the existence and the globally asymptotical stability of the equilibrium, and obtains the threshold value at which disease is eliminated, which is just the basic rebirth number $R_{0}=1$. The author proves that when$R_{0}<1$, the non-disease equilibrium is globally asymptotically stable; when $R_{0}>1$ and $\alpha K\leq 1$, the positive equilibrium is globally asymptotically stable; when $R_{0}>1$ and $\Delta =0$, a Hopf bifurcation occurs near the positive equilibrium; when $R_{0}>1$ and $\Delta <0$, the system has a unique limit cycle which is stable near the outside of the positive equilibrium. Related Articles | Metrics