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25 April 2008, Volume 28 Issue 2 Previous Issue    Next Issue

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Causality Measure of Nonstationary Processes by Wavelet Tang Hongmin ; Xie Zhongjie Acta mathematica scientia,Series A. 2008, 28 (2):  201-213.  Abstract ( 1693 )   RICH HTML PDF (428KB) ( 1192 )   Save A new causality measure of nonstationary processes with stochastic trend is proposed in this paper, which is proved to be equivalent with Hosoya's one-sided causality measure. The new measure avoids complicated cointegration analysis in the literature and two tests are discussed in detail. One is the wavelet Wald test, the other is likelihood ratio test. They work well both in numerical simulation and empirical example. Related Articles | Metrics

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Discontinuous Solutions of the Navier-Stokes Equations for Compressible Flow with Density-Dependent Viscosity Zhang Ting Acta mathematica scientia,Series A. 2008, 28 (2):  214-221.  Abstract ( 1781 )   RICH HTML PDF (314KB) ( 1150 )   Save Department of Mathematics, Zhejiang University, Hangzhou 310027 Related Articles | Metrics

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Boundedness of the Commutator of Marcinkiewicz Integral on Hardy Space and Herz-type Hardy Space Cheng Meifang;Shu Lisheng Acta mathematica scientia,Series A. 2008, 28 (2):  222-231.  Abstract ( 2113 )   RICH HTML PDF (279KB) ( 1270 )   Save Let $\mu_{\Omega,b}$ be the commutator of the function $b\in$ Lip$_{\beta}(R^{n})$ and the Marcinkiewicz integral operator $\mu_{\Omega}$. In this paper, the authors study the boundedness properties of $\mu_{\Omega,b}$ on the classical Hardy spaces and the Herz-type Hardy spaces. Related Articles | Metrics

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On the Construction of {\boldmath $p$}-harmonic Morphisms LibingHuang ; Mo Xiaohuan Acta mathematica scientia,Series A. 2008, 28 (2):  232-239.  Abstract ( 1807 )   RICH HTML PDF (300KB) ( 1242 )   Save In this note the authors construct new $p$-harmonic morphisms by studying the $p$-tension field under changes of metrics for horizontally conformal submersions. In particular, the authors explicitly construct new $\frac{10}{3}$-harmonic morphism $\phi:R^4\setminus \{0\}\rightarrow R^3$ with respect to standard Euclidean metrics. Finally the authors characterize $p$-harmonic morphisms with one dimensional fibres (globally) in terms of principal bundles. Related Articles | Metrics

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The Hausdorff Dimension for a Class of Generalized Random Fractals Zhuang Yan;Dai Chaoshou Acta mathematica scientia,Series A. 2008, 28 (2):  240-250.  Abstract ( 2025 )   RICH HTML PDF (357KB) ( 1313 )   Save In this paper, a class of generalized random recursive construction with finite memory in Euclidean $d$-space is researched. For each $\beta\geq 0$, a function $\Psi(\beta)$ assiociated with the construction is introduced and a random measure $\mu_{\omega}$ is constructed. That the Hausdorff dimension of the random limit set $K(\omega)$ generated by the above construction is equal to $\alpha:=\inf\{\beta:\Psi(\beta)\leq1\}$ is proved. Related Articles | Metrics

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The Crossing Number of K2,4× Pn Wang Jing;Huang Yuanqiu Acta mathematica scientia,Series A. 2008, 28 (2):  251-255.  Abstract ( 1609 )   RICH HTML PDF (261KB) ( 1247 )   Save This paper determines the crossing number of the Cartesian products of $K_{2,4}$ with $P_n.$ Related Articles | Metrics

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The Existence of a Nontrivial Solution for Biharmonic Equation Tang Chunxia; Zhang Zhengjie Acta mathematica scientia,Series A. 2008, 28 (2):  256-265.  Abstract ( 1877 )   RICH HTML PDF (331KB) ( 1473 )   Save The paper mainly studies biharmonic equation in $R^N(N>4)$ as $$ \left\{ \begin{array}{ll} \Delta^2 u+\lambda u=\overline{f}(x,u);\\ \lim\limits_{|x|\rightarrow\infty}u(x)=0;\\ u\in{H^2}(R^N),\hspace{0.1cm}x\in{R^N }. \end{array} \right. $$ For studying it, the authors change it to the biharmonic equation with a perturbation in $R^N(N>4)$ as $$ \left\{ \begin{array}{ll} \Delta^2 u+\lambda u=f(u)+\varepsilon g(x,u);\\ \lim\limits_{|x|\rightarrow\infty}u(x)=0;\\ u\in{H^2}(R^N),\hspace{0.1cm}x\in{R^N } \end{array} \right. $$ and use the perturbation method to study it (where $f(u)=\lim\limits_{|x|\longrightarrow \infty}\overline{f}(x,u),\varepsilon g(x,u)=\overline{f}(x,u)-f(u),\varepsilon$ is a small constant). The authors can prove the existence of nontrivial solutions of the above question under some conditions. Related Articles | Metrics

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The Navier-Stokes Equations in Stream Layer or on Stream Surface and a Dimension Split Method Li Kaitai;Jia Huilian Acta mathematica scientia,Series A. 2008, 28 (2):  266-282.  Abstract ( 1863 )   RICH HTML PDF (576KB) ( 1421 )   Save \noindent{\bf Abstract:} In this paper, the authors propose the concept of stream surface and stream layer. By using classical tensor calculus, the authors derive 3D Navier-Stokes Equations(NSE) in the stream layer under semigeodesic coordinate system, Navier-Stokes equation on the stream surface and 2-D Navier-Stokes equations on a two dimensional manifold. After introducing stream function on the stream surface, a nonlinear initial-boundary value problem satisfied by stream function is obtained,existence and uniqueness of its solution are proved. Based on this theory the authors propose a new method called ``dimension split method" to solve 3D NSE. Related Articles | Metrics

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Strong Convergence Rate of Weighted Sums for NOD Sequences Gan Shixin;Chen Pingyan Acta mathematica scientia,Series A. 2008, 28 (2):  283-290.  Abstract ( 2045 )   RICH HTML PDF (260KB) ( 1443 )   Save In this paper the authors study the strong convergence rate of weighted sums for NOD sequences. The authors obtain some new complete convergence results of weighted sums for NOD sequences. The results extend the results of Chen Ruilin$^{[1]}$ in NA sequence case and partially extend the corresponding work of i.i.d. case due to Stout$^{[2]}$. Related Articles | Metrics

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Testing for Homogeneity of Between-individual Variances and Autocorrelation Coefficients in Longitudinal Nonlinear Models with Random Effects and AR(1) Errors Lin Jinguan; Wei Bocheng Acta mathematica scientia,Series A. 2008, 28 (2):  291-301.  Abstract ( 2395 )   RICH HTML PDF (423KB) ( 1382 )   Save Homogeneity of between-individual variances and/or autocorrelation coefficients is one of standard assumptions in longitudinal analysis. However, this assumption needs to be tested statistically. Zhang \& Weiss$^{[15]}$ discussed the tests for heterogeneity of between - and/or within-individual variances in linear models with random effects. Lin \& Wei$^{[10]}$ considered the tests for homogeneity of between-individual autocorrelation coefficients in nonlinear models with AR(1) errors but without random effects. However, for such models, the tests for homogeneity of autocorrelation coefficients between individuals as autocorrelation on all individuals exists, have not been considered. This paper is devoted to the tests for homogeneity of between-individual variances and/or autocorrelation coefficients in the framework of nonlinear regression models with random effects and AR(1) errors. Several diagnostic tests using score statistic are constructed. The properties of test statistics are nvestigated through Monte Carlo simulations. An real-data and simulated-dat examples are analyzed in Section 5 to illustrate the proposed methodology. Related Articles | Metrics

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A Recurrence Formula of Moments for the Meyer-Konig and Zeller Operators on a Simplex Zhang Chungou Acta mathematica scientia,Series A. 2008, 28 (2):  302-307.  Abstract ( 1581 )   RICH HTML PDF (222KB) ( 1067 )   Save In this paper, the author first gives an integral expression of moments for the Meyer-K\"onig and Zeller operators of one variable by a simpler method than that in [2], then using the method the author establishes a recurrence formula of moments for the Meyer-K\"onig and Zeller operators of two variables on a simlex, finally derive the integral expression of the second and third moments for the operators as an application of the recurrence formula. Related Articles | Metrics

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Stable Analysis for Dynamic Equations on Time Scales ou liuman;Zhu Siming Acta mathematica scientia,Series A. 2008, 28 (2):  308-319.  Abstract ( 1928 )   RICH HTML PDF (345KB) ( 1236 )   Save Recently, a new theory known as dynamic equations on time scale has been built vigorously. In this paper, each kind of stability concepts and the Lyapunov's stability criteria (stable, uniformly stable, asymptotically stable, exponential asymptotically stable, etc.) are obtained for dynamic equations on time scale. Related Articles | Metrics

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Existence of Weak Solutions to a Class of Elliptic Stochastic Partial Differential Equations Ran Qikang Acta mathematica scientia,Series A. 2008, 28 (2):  320-328.  Abstract ( 2240 )   RICH HTML PDF (309KB) ( 1098 )   Save In this paper the authors study of following problem: Let $D$ be a bounded open set of $R^N(N>1)$ and $(\Omega,F,P)$ is a probability space. The authors study the existence of weak solutions of the following stochastic boundary value problem: $$ \left\{ \begin{array}{ll} -{\rm div} A(x,\omega,u, \nabla u)=f(x,\omega, u),\,\, &(x,\omega)\in D\times \Omega,\\ u=0, &(x,\omega)\in \partial D\times \Omega, \end{array}\right. $$ where by div and $\nabla$ the authors denote differentiation with respect to $x$ only. First, the authors introduce the concept of the weak solution, then the authors transform the stochastic problem into a deterministic one in high-dimensions. Finally, the authors prove the existence of weak solutions. Related Articles | Metrics

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Weak Type Estimate for a Class of Sublinear Operators in Weak Herz Spaces on Non-homogeneous Spaces Guo yan;Meng Yan Acta mathematica scientia,Series A. 2008, 28 (2):  329-340.  Abstract ( 2065 )   RICH HTML PDF (347KB) ( 1196 )   Save The authors introduce weak Herz spaces onnon-homogeneous spaces and establish some weak type estimates for a classof sublinear operators in these spaces. As an application, theauthors prove that the commutators generated by Calder\'on-Zygmundoperators with $\os$ functions for $r\ge1$ satisfy the same weak estimates, where $\os\subset\rb$ if $r>1$ and $\os=\rb$ if $r=1$. Related Articles | Metrics

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Two-Weight Integral Inequalities for Conjugate ${\cal A}$-Harmonic Tensors Gao Hongya; Hou Lanru Acta mathematica scientia,Series A. 2008, 28 (2):  341-348.  Abstract ( 1555 )   RICH HTML PDF (312KB) ( 1347 )   Save In this paper, the authors first introduce a new weight: $A^{\lambda_{3}}_{r}(\lambda_{1},\lambda_{2},\Omega)$-weight,and prove the local weighted integral inequalities for conjugate ${\cal A}$ -harmonic tensors. Then, as an application of the local result, the authors prove a global weighted integral inequality for conjugate ${\cal A}$-harmonic tensors in a bounded domain $\Omega$, which can be regarded as generalizations of the classical results. Finally, the authors give some applications of the above results to quasiregular mappings. Related Articles | Metrics

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Extended Cesàro Operators Between Different Weighted Bloch-type Spaces Ye Shanli ;Gao Jinshou Acta mathematica scientia,Series A. 2008, 28 (2):  349-358.  Abstract ( 1896 )   RICH HTML PDF (267KB) ( 1195 )   Save In this paper the extendedCes\'aro operator $\tg$ is characterized between the $\a$-Bloch spaces $\ba$ and the logarithmic weighted Bloch space $\bl$ on the unit disc. Some necessary and sufficient conditions are given for $\tg$ to be a bounded operator or a compact operator from $\bl(\ba)$ to $\ba(\bl)$. Related Articles | Metrics

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Ergodicity of Ek/G/1 Queueing System Li Xiaohua;Hou Zhenting Acta mathematica scientia,Series A. 2008, 28 (2):  359-366.  Abstract ( 1724 )   RICH HTML PDF (311KB) ( 1205 )   Save In this paper, the authors study $E_k/G/1$ queueing system via drift criterion and petite set. The sufficient and necessary conditions of Harris ergodicity, $l$-ergodicity and geometric ergodicity of queue length $L(t)$ are obtained, and the authors prove that it is not uniformly ergodicity. Related Articles | Metrics

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New Lower Bounds for the Number of Edges of Critical Graphs Gong Zaiwu;Wu Jianliang Acta mathematica scientia,Series A. 2008, 28 (2):  367-372.  Abstract ( 2082 )   RICH HTML PDF (219KB) ( 1167 )   Save A graph $G$ is critical if it is connected of class two, and $\chi' (G-e)<\chi' (G)$ for any $e$ of $G$. In this paper, it is proved that any $\Delta$-critical graph of order $n$ and size $m$ satisfies: $m\geq(3\Delta+6)n/10$, where $12\leq\Delta\leq18$. Related Articles | Metrics

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On Positive Solutions of Second-order Three-point Boundary Value Problem Wang shuli; Liu Jinsheng Acta mathematica scientia,Series A. 2008, 28 (2):  373-382.  Abstract ( 2254 )   RICH HTML PDF (313KB) ( 1234 )   Save In this paper, the existence of positive solutions of the second-order three-point boundary value problem $-u''(t)=b(t)f(u(t))$ for all $t\in[0,1]$ subject to $u'(0)=0$, $u(1)={\alpha}u({\eta})$ is studied, where $\alpha, \eta\in(0,1)$ are given, $f\in C\big([0,\infty),[0,\infty)\big)$, $b\in C\big([0,1],[0,\infty)\big)$ and there exists $t_0\in[0,1]$ such that $b(t_0)>0$. The problem is transformed into the Hammerstein's integral equation with its corresponding Green's funtion. By applying the fixed point index theory, authors obtain the optimal sufficient conditions for the existence of single and multiple positive solutions of the above mentioned problem concerning the first eigenvalue of the relevant linear problem. Related Articles | Metrics

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Existence of Global Solutions for Initial Value Problems of First Order Impulsive Integro-differential Equations in Banach Spaces Zhang Xinguang; Liu Lishan Acta mathematica scientia,Series A. 2008, 28 (2):  383-392.  Abstract ( 2147 )   RICH HTML PDF (330KB) ( 1372 )   Save By using generalized Darbo's fixed point theorem step by step, under weaker conditions, the authors present the existence of global solutions for initial value problems of first order impulsive integro-differential equations in Banach space. The results obtained improve and extend many known results. Related Articles | Metrics