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25 August 2007, Volume 27 Issue 4 Previous Issue    Next Issue

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On the Decomposition of Restricted Lie Superalgebras Chen Liangyun Zhang Yongzheng Acta mathematica scientia,Series A. 2007, 27 (4):  577-583.  Abstract ( 1949 )   RICH HTML PDF (285KB) ( 1033 )   Save can be decomposed into direct sum of indecomposable restricteideals and this decomposition is unique up to the order of the ideals. Moreover, they announce some results of restricted Lie superalgebras. Related Articles | Metrics

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Influence Analysis on Semiparametric Generalized Linear Mixed Model Zeng Linrui; Zhu Zhongyi Acta mathematica scientia,Series A. 2007, 27 (4):  584-593.  Abstract ( 1924 )   RICH HTML PDF (404KB) ( 1017 )   Save In this paper, the authors present a unified diagnostic method for semiparametric generalized linear mixed model.The equivalency of case deletion model and mean shift outlier model is investigated and the diagnostic statistics such as cook distance, score test statistic for outlier tests are derived. Secondly, the local influence for the models is investigated and the counting formulas of influence matrices for case weights perturbation model and mean shift perturbation model are obtained. Finally, numerical example illustrates that the method is effective. Related Articles | Metrics

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Asymptotic Analysis for MHD Equations on Thin Domains Yu Yongjiang; Li Kaitai Acta mathematica scientia,Series A. 2007, 27 (4):  594-610.  Abstract ( 1632 )   RICH HTML PDF (366KB) ( 1163 )   Save Based on the global existence of strong solution of MHD equations on three dimensional thin domain, asymptotic expansion for the strong solution (u,h) of MHD equations is obtained, and this expansion holds uniformly for all the time t≥0. When ε, the thickness of the domain, is small, the strong solution (u,h) of MHD equations can be formally expressed as u=\bar{u}(t)+u_p+U,\quad h=\bar{h}(t)+h_p+H,\quad \forall t≥0, or u=\bar{u}(t)+u_s+U^{\star},\quad h=\bar{h}(t)+h_s+H^{\star},\quad \forall t≥0, where (\bar{u},\bar{h}) is a solution of 2D-3C MHD equations, (u_{p},h_p) is a solution of P-S MHD equations, u_s,h_s are respectively solutions of two Stokes equations, (U,H),(U^\star,H^\star) are two function pairs depending only on the initial data. (U,H) and (U^\star,H^\star) are small with respect to \varepsilon. (u_{p},h_p) and u_{s},h_s are smaller. And the convergence of the expansion is proved. Related Articles | Metrics

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Normality Theorems of Algebroid Functions Gan Huilin; Sun Daochun Acta mathematica scientia,Series A. 2007, 27 (4):  611-615.  Abstract ( 1830 )   RICH HTML PDF (257KB) ( 1189 )   Save Let F be a family of algebroid functions defined in a subdomain D of the sphere V, if the number of branch points of all f from F is finite, and there exist three fix complex values 1,a2,a3 such that ∑3 k=1n(D,ak,f)≤1 holds for each f\in F, then F is normal in D. Normality Theorems of Algebroid Functions. Related Articles | Metrics

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Large Deviations and Finite Time Ruin Probability for Perturbed Risk Model with Variable Premium Rate Wei Xiao;Yu Jinyou; Hu Yijun Acta mathematica scientia,Series A. 2007, 27 (4):  616-623.  Abstract ( 2249 )   RICH HTML PDF (282KB) ( 1175 )   Save In this paper, the authors consider a perturbed risk model with variable premium rate and heavy-tailed claims. The precise large deviation for the claim surplus process of this risk model is obtained. The Cramer-Lundberg type limiting results for the finite time ruin probability are also given. Related Articles | Metrics

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Initial Boundary Value Problems for a Class of Nonlinear Wave Equation of Higher Order Han Xianjun; Chen Guowang Acta mathematica scientia,Series A. 2007, 27 (4):  624-640.  Abstract ( 2282 )   RICH HTML PDF (332KB) ( 1321 )   Save In this paper the initial boundary value problems for a class of nonlinear wave equation utt－a1Uxx+a_2ux4+a3ux4tt=φ(ux )x+f(u,ux,uxxuxxx,ux4) are considered. The existence and uniqueness of the classical global solution are proved. The sufficient conditions of blow-up of solutions are given. Related Articles | Metrics

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The Minkowski Content of Uniform Cantor Set Jiang Feng; Chen Shirong Acta mathematica scientia,Series A. 2007, 27 (4):  641-647.  Abstract ( 1533 )   RICH HTML PDF (281KB) ( 1072 )   Save In this paper, the authors study the Minkowskicontent of a uniform Cantor set and calculate its upper and lower Minkowski contents. Thus the authors see that its Minkowski content does not exist. Related Articles | Metrics

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Asymptotic Behavior of Solutions for a Free Boundary Problem Modelling Tumor Growth Wei Xuemei; Cui Shangbin Acta mathematica scientia,Series A. 2007, 27 (4):  648-659.  Abstract ( 2104 )   RICH HTML PDF (387KB) ( 1015 )   Save In this paper the authors study a mathematical model of the effect of inbitors on the growth of nonnecrotic tumors based on the idea of Byrne and Chaplain. This model is a free boundary problem of a system of nonlinear reaction diffusion equations. The authors apply the monotone method in the theory of reaction diffusion equations combined with the iteration technique of free boundary problems to obtain asymptotic behavior of the solution, and prove that under some general assumptions on the nutrient consumption rate function f, the inhibitor consumption rate function g and the tumor cell proliferation rate function S, the global solution of this problem tends to the trivial stationary solution (which corresponds to the vanishing state of the tumor) in certain situations, and converges to a nontrival stationary solution (which corresponds to the dormant state of the tumor) in certain other situations, as the time goes to infinity. Related Articles | Metrics

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Inequalities for Widths of Convex Bodies with Applications Yuan Shufeng; Ke Rui; Leng Gangsong Acta mathematica scientia,Series A. 2007, 27 (4):  660-664.  Abstract ( 1794 )   RICH HTML PDF (273KB) ( 1066 )   Save In this paper the authors establish the following inverse inequality of Yang-Zhang's inequality for the width of a simplex: Let $\Omega$ be an n-dimensional simplex with volume Voln(\Omega)$,width $w(\Omega)$, and facet areas $S_1,S_2,\cdots,S_{n+1}$ respectively, then $$ w(\Omega)\ge r_n\cdot\frac{{{\rm Vol}_n}(\Omega)}{\displaystyle\max_{1\le i\le n+1}(S_i)}, $$ where $$ \gamma_n=\left\{\begin{array}{cl} \disp \frac{2n}{n+1}, & \qquad {\rm for~ odd}~~ n;\\ 2, & \qquad {\rm for~ even}~~ n. \end{array} \right. $$ As applications, the authors show some inequalities for orthogonal projections and sections of convex bodies. Related Articles | Metrics

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Weighted Composition Operators between Bers-type Spaces Wang Maofa; Liu Yun Acta mathematica scientia,Series A. 2007, 27 (4):  665-671.  Abstract ( 2030 )   RICH HTML PDF (287KB) ( 1173 )   Save In this paper, the authors study weighted composition operators between Bers-type spaces. Some sufficient and necessary conditions for such operators to be bounded, compact and weakly compact are given, respectively. This may be regarded as a generalization of the corresponding multiplication operator and composition operator cases. As a corollary, the authors obtain that the weak compactness and the compactness of weighted composition operators between Bers-type spaces are equivalent. In addition, the authors also characterize composition operators which have Fredholm properties and closed range on Bers-type spaces, respectively. Related Articles | Metrics

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A Chung Type Law of the Iterated Logarithm of MLE in Random Censoring Model with Incomplete Information Zhu Qiang; Gao Fuqing Acta mathematica scientia,Series A. 2007, 27 (4):  672-681.  Abstract ( 1761 )   RICH HTML PDF (322KB) ( 1175 )   Save In this paper, the authors prove that the MLE in random censoring model with incomplete information obeys the Chung type law of the iterated logarithm under some mild conditions. As a corollary, the Chung type laws of the iterated logarithm of the MLE of parameters of exponential lifetime distribution and Weibull distribution are obtained. Related Articles | Metrics

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The Convergence of a Multiscale Asymptotic Expansion for the Steady Heat Transfer Problem of Periodic Composite Materials Song Shicang; Cui Junzhi Acta mathematica scientia,Series A. 2007, 27 (4):  682-687.  Abstract ( 1801 )   RICH HTML PDF (403KB) ( 1127 )   Save A new asymptotic expansion is given for a class of steady heat transfer problems of periodic composite materials. Compared to the classical form, the stronger H1per(Q) periodic boundary condition of auxiliary equation is replaced with 0 boundary condition. The new asymptotic expansion is still convergent to the solution of the original problem. This method is convenient for numerical computation, because the conforming element space for H10(Q) is easier to be constructed than for H1per(Q) . On the other hand, the new asymptotic expansion solution satisfies boundary condition of the original problem, which cannot be preserved in classical method. Related Articles | Metrics

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Totally Real Pseudo-umbilical Submanifolds with Flat Normal Bundle of Complex Projective Space Zhang Liang; Song Weidong Acta mathematica scientia,Series A. 2007, 27 (4):  688-695.  Abstract ( 1719 )   RICH HTML PDF (300KB) ( 1092 )   Save In this paper, the authors prove that two types of totally real pseudo-umbilical submanifolds with flat normal bundle must be minimal and determine their shapes under the circumstances that the submanifolds are compact. Moreover, the authors also show that the normal bundle of a totally real and totally umbilical submanifold can't be flat. Related Articles | Metrics

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Product of two Orthogonal Projections in a Hilbert Space H Yao Xiyan; Du Hongke Acta mathematica scientia,Series A. 2007, 27 (4):  696-701.  Abstract ( 1818 )   RICH HTML PDF (243KB) ( 1190 )   Save In this paper, structure of regular pairs of orthogonal projections are established. Moreover, a necessary and sufficient condition for an operator A to be able represented as a product of two orthogonal projections is given. Related Articles | Metrics

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Solutions of Initial Value Problems for Second-order Nonlinear Impulsive Integro-differential Equations Wang Wenxia;Zhang Lingling Acta mathematica scientia,Series A. 2007, 27 (4):  702-710.  Abstract ( 2274 )   RICH HTML PDF (304KB) ( 972 )   Save In this paper, by using the monotone iterative technique, the existence of maximal and minimal solutions of initial value problems for second-order impulsive differential equations depending on x' in Banach Space is discussed. In order to illustrate the obtained results, an example of infinite system for a scalar second-order impulsive integro-differential equation is given. Related Articles | Metrics

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Nonlinear Boundary Value Problems for Differential Inclusions Hong Shihuang Acta mathematica scientia,Series A. 2007, 27 (4):  711-719.  Abstract ( 2317 )   RICH HTML PDF (300KB) ( 1168 )   Save This paper presents sufficientcon ditions for the existence of solutions to nonlinear boundary-value problems of multi-valued differential inclusions in Banach spaces. The results are obtained via a new fixed point theorem which is developed in the paper, and lead to new existence principles. Related Articles | Metrics

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Discontinuous Boundary Value Problem of Quasilinear Mixed Equations Ma Zhongtai; Xu Guangshan;Wen Guochun Acta mathematica scientia,Series A. 2007, 27 (4):  720-726.  Abstract ( 2168 )   RICH HTML PDF (305KB) ( 1084 )   Save The discontinuous boundary value problem of quasilinear mixed type equations of second order in a much more general domain is discussed by using the method of complex analysis with a deformation such that the boundary curves of the hyperbolic domain are transformed onto the segments, and then, the solvable results in the more general domains are obtained, which are generalizations of the recent results in articles. Related Articles | Metrics

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Testing Heteroscedasticity by Wavelets in a Nonparametric Regression Model with Random Design Li Yuan;Yang Yidang Acta mathematica scientia,Series A. 2007, 27 (4):  727-740.  Abstract ( 1923 )   RICH HTML PDF (420KB) ( 1141 )   Save The authors consider a wavelet-based test for heteroscedasticity in a nonparametric regression model with random design. The empirical wavelet coefficients of the error variance in the model are given and shown to be asympototically i.i.d. normal. Then based on the approaches of Fan (1996), the test statistic for heteroscedasticity is constructed. Finally, the authors examine the performance of the test in a simulation study. The test is found to perform well, in terms of both sizes and powers. Related Articles | Metrics

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Java Implementation of Algorithm to Solve a Batch Scheduling Problem Chen Shi Acta mathematica scientia,Series A. 2007, 27 (4):  741-747.  Abstract ( 1524 )   RICH HTML PDF (420KB) ( 1090 )   Save In this article, the author discusses a new type of scheduling problem-resource dependent scheduling problem. The author introduces the concept of the problem, discusses the algorithm and gives the simulation for test by using Java Related Articles | Metrics

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The Distortion of Cross Ratio and Poincare Metric under Plane Quasiconformal Mappings Chu Yuming Acta mathematica scientia,Series A. 2007, 27 (4):  748-752.  Abstract ( 1901 )   RICH HTML PDF (233KB) ( 1153 )   Save In this paper, the author studies the distortion of cross ratio and poincar\'e metric under (1) If $f$ is a $k$-quasiconformal self mapping of $\overline R^2$, then $16^{\frac1k-1}\left(|(x_1,x_2,x_3,x_4)|+1\right)^{\frac1k}\leq | (f(x_1),f(x_2),f(x_3)$, $f(x_4) ) |+1 \leq16^{k-1}\left(|(x_1,x_2,x_3,x_4)|+1\right)^{k}$ for any four points $x_1,x_2,x_3$, $x_4\in\overline R^2$; (2) If $f$ is a $k$-quasiconformal self mapping of $R^2$ and $D$ is a proper subdomain of $R^2$, then $\frac1k\lambda_D(x_1,x_2)+4(\frac1k-1)\log2\leq\lambda_{f(D)}(f(x_1),f(x_2))\leq k\lambda_D(x_1,x_2)+4(k-1)\log2$ for any two points $x_1,x_2\in D$ plane quasiconformal mappings, obtaines the following two results. Related Articles | Metrics

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The Existence of Multiple Positive Solutions for a Class of Singular Boundary Value Problems of Impulsive Differential Equations in a Banach Space Zhang Xingqiu;Zhong Qiuyan Acta mathematica scientia,Series A. 2007, 27 (4):  753-760.  Abstract ( 1997 )   RICH HTML PDF (307KB) ( 1019 )   Save \noindent{\bf Abstract:} By using fixed point index theory, the existence of multiple positive solutions for a class of singular boundary value problems of impulsive differential equations in abstract space are obtained. An example is given to show the application of the result Related Articles | Metrics

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Concentration Behavior of the Ground State Solutions for Fourth Order Elliptic Equation Luo Lin; Xu Guojin Acta mathematica scientia,Series A. 2007, 27 (4):  761-768.  Abstract ( 1846 )   RICH HTML PDF (270KB) ( 1341 )   Save \noindent{\bf Abstract:} The main purpose of this paper is to analyze the concentration behavior of the ground state solutions for fourth order equation $\Delta ^2u=|x|^\alpha u^{p-1}$ in $\Omega $, $u=\Delta u=0$ on $\partial \Omega$~ ($\Omega \subset R^n$ is a ball centered at the origin). It is proved that for $p$ close to $2^*=\frac{2n}{n-4} (n>4)$, the ground state solution $u_p$ concentrates near the boundary of $\Omega$. Related Articles | Metrics