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25 April 2006, Volume 26 Issue 2 Previous Issue    Next Issue

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Production of Julia Set Sun Daochun Acta mathematica scientia,Series A. 2006, 26 (2):  161-167.  Abstract ( 1476 )   RICH HTML PDF (281KB) ( 1025 )   Save The author studied Julia set on rational dynamic with Haushorff's limit,and proved the several new theorems of Julia set, and provided still more thorybasis for computer graphics in this paper. Related Articles | Metrics

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Strong Consistency of the Maximum Likelihood Estimator in Generalized Linear Models Ding Jieli;Chen Xiru Acta mathematica scientia,Series A. 2006, 26 (2):  168-173.  Abstract ( 1962 )   RICH HTML PDF (285KB) ( 1055 )   Save Assuming the generalized linear model as described in \S1, let $\underline{\lambda}_n$and $\overline{\lambda}_n$ denote the minimum and maximum eigentvalues of$\sum\limits_{i=1}^{n}Z_iZ_i^{\prime}$ resp., and$\hat{\beta}_n$ denote the maximum likelihood estimator of $\beta_0$. It is shown in [1] that, when \{$Z_i,i\ge1$\}is bounded, the sufficient conditions for strong consistency of $\hat{\beta}_n$ are as follows:$\underline{\lambda}_n\rightarrow\infty$, $(\overline{\lambda}_n)^{1/2+\delta}=O(\underline{\lambda}_n)$(for some $\delta>0$) with natural link function, and $\underline{\lambda}_n\rightarrow\infty$,$\overline{\lambda}_n=O(\underline{\lambda}_n)$ with nonnatural link function resp.. In this paper, the authors improvethe latter result by showing that even in the case of nonnatural link function, the condition$(\overline{\lambda}_n)^{1/2+\delta}=O(\underline{\lambda}_n)$ remains to be sufficient. Related Articles | Metrics

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Supperconvergence of Triangular Quadratic Finite Element Method with Interpolated Coefficients for Nonlinear Elliptic Problem Xiong Zhiguang;Chen Chuanmiao Acta mathematica scientia,Series A. 2006, 26 (2):  174-182.  Abstract ( 1903 )   RICH HTML PDF (409KB) ( 1246 )   Save To solve the semilinear elliptic problem, the triangular quadratic finite elements and interpolated coefficient finite elements are discussed. Superconvergence O( h4)at each vertex and side midpoint is proved, which is similar to that of classical finite elements. These facts are also shown by numerical examples. Related Articles | Metrics

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Mathematical Analysis of a Model of a Replication-competent Virus in Tumor Cells Tao Youshan Acta mathematica scientia,Series A. 2006, 26 (2):  183-199.  Abstract ( 2209 )   RICH HTML PDF (458KB) ( 1057 )   Save The author considers a procedure for cancer therapy which consists of injecting replication-competent viruses into the tumor. The viruses infect tumor cells, replicate insider them, and eventually cause their death. As infected cells die, the viruses inside them are released and then proceed to infect adjacent tumor cells. This process is modelled as a free boundary problem for a nonlinear system of hyperbolic differential equations, where the free boundary is the surface of the tumor. The unknowns are the densities of uninfected cells, infected cells, necrotic cells and the free virus particles, and the velocity of cells within the tumor as well as the free boundary r=R(t). The aim of this paper is to explore the conditions under which the tumor can be made to shrink to zero. Related Articles | Metrics

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Strictly B -Preinvex Functions Peng Jianwen;Zhu Daoli Acta mathematica scientia,Series A. 2006, 26 (2):  200-206.  Abstract ( 1652 )   RICH HTML PDF (249KB) ( 1117 )   Save Strictly B -preinvex function; Sufficient condition; Semistrictly B -preinvex function; Minimization problem Related Articles | Metrics

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Near-trangular Embeddings for Triangulations of the Sphere and the Torus (I) Ren Han; Deng Mo; Lu Junjie Acta mathematica scientia,Series A. 2006, 26 (2):  207-211.  Abstract ( 1733 )   RICH HTML PDF (356KB) ( 1078 )   Save A near-triangular embedding is a graph embedded into some surface whose facial walks but one are 3-gons. In this paper the authors show that if a graph G is a triangulation of the sphere S0 (or the torus S1), then Ghas a near-triangular embedding into Sk for k = h,h+1,\cdots ,\lfloor\frac{\beta(G)}{2}\rfloor$, where h = 0(or 1) and $\beta(G)$ is the Betti number of G. Related Articles | Metrics

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(h,φ)-Lipschitz Function, Its Generalized Directional Derivative and Generalized Gradient Xu Yihong;Liu Sanyang Acta mathematica scientia,Series A. 2006, 26 (2):  212-222.  Abstract ( 1731 )   RICH HTML PDF (291KB) ( 1034 )   Save With the help of Ben-Tal's generalized algebraic operations, a new kind of functions, termed (h,φ)-Lipschitz functions, is introduced. The relationship between it and Lipschitz function is discussed.Generalized directional derivative and generalized gradient are developed and their properties are obtained. As an application, the relationship between generalized directional derivative and contingent cone is presented. Related Articles | Metrics

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An Active-set Trust Region Method for Nonlinear System Wang Changyu;Yu Zhensheng Acta mathematica scientia,Series A. 2006, 26 (2):  223-232.  Abstract ( 2052 )   RICH HTML PDF (375KB) ( 1339 )   Save In this paper, the authors present a trust region method for nonlinear system. The main idea of this paper is that by introducting slack variables, the authors transformate the problem into a nonlinear optimization with nonnegative constraints. By using active set strategy, the authors need only to solve a reduced trust region subproblem which is solved inexactly by the truncated conjugate gradient method. Under weak conditions, the authors obtain a general convergence result. Related Articles | Metrics

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Nontrivial Solutions of Systems of Nonlinear Hammerstein Integral Equations and Applications Yang Zhilin Acta mathematica scientia,Series A. 2006, 26 (2):  233-240.  Abstract ( 1971 )   RICH HTML PDF (260KB) ( 1182 )   Save In this paper, by using topological methods and cone theory, the authorstudies the system of nonlinear Hammesrstein integral equations u(x)=∫G kx,y)f(y,u(y),v(y)) dy, v(x)=∫G k(x,y)g(y,u(y),v(y))dy, The author proves the existence of nontrivial solutions of the above system under appropriate conditions. And the main results are applied to study the existence of nontrivial solutions of boundary value problems for systems of nonlinear second order ordinary differential equations. Related Articles | Metrics

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Holder Laws and Multiple Points for Self-intersection Local Time Increments of Generalized α-stable Process Chen Zhenlong; Li Huiqiong Acta mathematica scientia,Series A. 2006, 26 (2):  241-250.  Abstract ( 1419 )   RICH HTML PDF (349KB) ( 1144 )   Save In this paper the authors discuss the Holder laws for self-intersection local time increments of N-parameter d-dimension generalized α-stable process, prove the existence of multiple points, and obtan the lower bounds about Hausdorff dimension and Hausdorff measure of multiple time. The obtained results contain and extend the existing results of generalized Brownian sheet and Stable sheet. Related Articles | Metrics

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Minimum Integrity of Graphs Ma Runnian;Liu Naigong Acta mathematica scientia,Series A. 2006, 26 (2):  251-257.  Abstract ( 1826 )   RICH HTML PDF (344KB) ( 1118 )   Save The integrity of a graph is mainly studied and some results on the integrity are given. Given the number of vertices and the number of edges in a class of graphs, the problem of how to determine a graph that has the minimum integrity among the class is studied. Also, if the number of vertices and the integrity in a class of graphs are fixed, the problem of how to determine a graph that has the maximum number of edges among them is investigated. For the optimal designs of the minimal integrity, the theoretics and methods are provided. Related Articles | Metrics

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Time-periodic Solution to a Generalized Ginzburg-Landau Model Equation in Population Problems Wang Yanping;Chen Guowang Acta mathematica scientia,Series A. 2006, 26 (2):  258-266.  Abstract ( 1970 )   RICH HTML PDF (309KB) ( 1253 )   Save In this paper, the existence and uniqueness of the time-periodic generalized solution and the time-periodic classical solution to the generalized Ginzburg-Landau model equation in population problems are proved by the Galerkin method. Related Articles | Metrics

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Stationary Oscillation of Periodic Interval System Wu Xiaofei Acta mathematica scientia,Series A. 2006, 26 (2):  267-272.  Abstract ( 1674 )   RICH HTML PDF (255KB) ( 1004 )   Save In this paper, the methods of decomposition of large-scale system and Liapunov function are used in studying the existence of stationary oscillation of periodic interval system and some new results are obtained. Related Articles | Metrics

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An Inexact Alternating Direction Method for Solving a Class of Monotone Variational Inequalities Tong Xiaojiao;He Bingsheng Acta mathematica scientia,Series A. 2006, 26 (2):  273-282.  Abstract ( 1926 )   RICH HTML PDF (331KB) ( 1026 )   Save Alternating direction methods are suitable ones for solving large-scale problems. This paper presents a new alternating direction method for a class of variational inequalities. At each iteration, the proposed subproblem consists of a strongly monotonic linear variational inequality and a well-conditioned system of nonlinear equations, which is easily to be solved. The convergence theorem of the proposed method is proved based on the exact solution of the subproblem. Furthermore, the authors develop the proposed alternating direction method as an inexact method, which only needs to solve the subproblem inexactly. Under some inexact conditions, the convergence of inexact alternating direction method is proved too. Related Articles | Metrics

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(i,p)-homotopy Inverse and Group Homotopy Inverse Qian Youhua;quad Chen Shengmin Acta mathematica scientia,Series A. 2006, 26 (2):  283-286.  Abstract ( 1480 )   RICH HTML PDF (227KB) ( 1117 )   Save (i,p)-homotopy inverse and group homotopy inverse are defined in this paper on categories of topological space with base point. Their existence and properties are also presented. Related Articles | Metrics

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Impulsive Asymptoticity for Impulsive Functional Differential Equation Chen Fulai ;Wen Xianzhang Acta mathematica scientia,Series A. 2006, 26 (2):  287-296.  Abstract ( 1786 )   RICH HTML PDF (312KB) ( 1120 )   Save In this paper, sufficient conditions are given for impulsive functional differential asymptotic stability of impulsive functional differential equation of the form $$\left\{\begin{array}{ll} x,(t)=f(t,xt), t≥ t0, △x=I_k(t,x(t-)), t=tk,k∈ Z+, and these conditions extend or improve the corresponding ones in [7-9]. Related Articles | Metrics

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Existence of Periodic Solutions for n-th Order Neutral Differential Equations with Multiple Variable Lags Wang Genqiang;Yan Jurang Acta mathematica scientia,Series A. 2006, 26 (2):  306-313.  Abstract ( 1912 )   RICH HTML PDF (321KB) ( 1032 )   Save In this paper, the authors give four sufficient conditions for the existence ofperiodic solutions of n-th order nonlinear neutral differential equations with multiple variable lags. Related Articles | Metrics

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Accuracy Estimation of Precise Symplectic Integration Method Xu Mingyi;Zhang Yongchuan Acta mathematica scientia,Series A. 2006, 26 (2):  314-320.  Abstract ( 1713 )   RICH HTML PDF (328KB) ( 1272 )   Save In this paper the calculation accuracy of precise symplectic integration method is discussed. At first, the two and four degree accuracy algorithms are analyzed and the relation of the error to the value of the precise integration number is obtained.Then, the accuracy of any degree precise symplectic algorithm is also discussed and the obtained result is the same and simple. The total error of the method can be approximately written in the calculation error of one time step multiplied by the integration number. Finally, the appropriate integration number is estimated at the control accuracy. It can be found that by this method the accuracy of precise symplectic integration will no longer be controlled by the value of the time step. Related Articles | Metrics