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25 February 2011, Volume 31 Issue 1 Previous Issue    Next Issue

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Existence of a Shock Wave in a One-dimensional Radiation Hydrodynamic System ZHU Yi-Feng, JIANG Peng Acta mathematica scientia,Series A. 2011, 31 (1):  1-17.  Abstract ( 1933 )   RICH HTML PDF (440KB) ( 1184 )   Save In this paper, the authors mainly study shock waves in a one-dimensional radiation hydrodynamic system. By using the Rankine-Hugoniot condition and entropy condition, this problem can be formulated as an initial boundary value problem with a free boundary for radiation hydrodynamic system. First, the  authors transform this free boundary to the fixed one by using change of variables involving unknowns. Then they investigate the existence and uniqueness of the solution to the initial boundary value problem for this nonlinear system. For this problem, the  authors first construct an approximate solution by using the compatibility conditions of the data. Then they use the Picard iteration and the Newton iteration for this nonlinear system respectively to construct a sequence of approximate solutions. By using a series of estimates and a compactness argument, the convergence of the sequence of approximate solutions is obtained. The limit of this sequence gives a shock wave of the original radiation hydrodynamic system. References | Related Articles | Metrics

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Study of Finite Elements for Hamilton Systems CHEN Chuan-Miao, TANG Qiong Acta mathematica scientia,Series A. 2011, 31 (1):  18-33.  Abstract ( 1812 )   RICH HTML PDF (765KB) ( 1360 )   Save Two nice properties of the continuous finite element method for Hamilton systems are proved as follows: in any case the m-degree finite elements always preserve the energy which is sympletic for linear systems and is approximately sympletic with high accuracy O(h2m+1) in each stepping for nonlinear systems. In long-time computation the deviation of trajectories and their periods in time-space plane will crease linearly with time. Numerical experiments show that their deviations are often  smaller than that of other schemes. References | Related Articles | Metrics

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The Nonexistence and Existence of Singular Three-point Boundary Value Problems |with Sign-changing Nonlinearities YAN Bao-Qiang Acta mathematica scientia,Series A. 2011, 31 (1):  34-52.  Abstract ( 1503 )   RICH HTML PDF (308KB) ( 1056 )   Save This paper discusses singular three-point boundary value problems y''(t)+a(t)f(t, y(t), y'(t))= 0, 0<t<1, y'(0)= 0, y(1)= αy(η) where 0<α<1, 0<η<1, f changes sign and may be singular at y= 0 and y'= 0 References | Related Articles | Metrics

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The Zero-Mach Limit of the Compressible Convection YUAN Hong-Jun, WANG Shu Acta mathematica scientia,Series A. 2011, 31 (1):  53-63.  Abstract ( 1533 )   RICH HTML PDF (274KB) ( 1104 )   Save The aim of this paper is to prove that the full compressible Navier-Stokes equations in two or three space dimensions converge to the full incompressible Navier-Stokes equations in the limit as the Mach number tends to zero. References | Related Articles | Metrics

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A General Iterative Method for Nonexpansive Mappings and Monotone Mappings YANG Chang-Sen, DU Yan-Xia, CHEN Li Acta mathematica scientia,Series A. 2011, 31 (1):  64-75.  Abstract ( 1281 )   RICH HTML PDF (293KB) ( 1024 )   Save The purpose of this paper is to study the strong convengence of a general iterative process to find a common element of the set of fixed points of  nonexpansive mapppings and the set of solutions of variations inequality for a strongly monotone mapping. References | Related Articles | Metrics

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Average Decay Estimates for Fourier Transforms of Measure Supported on Homogeneous Hypersurfaces CHENG Mei-Fang, ZHANG Zhen-Qiu Acta mathematica scientia,Series A. 2011, 31 (1):  76-81.  Abstract ( 1298 )   RICH HTML PDF (295KB) ( 1024 )   Save In this paper, the authors consider average decay estimates for the Fourier transform μ of densities supported on a homogeneous hypersurface. Based on these results, the authors also obain some mixed-norm inequalities for the convolution operator defined by Tf(x, θ)=f *μθ(x), where μθ(x) is the rotation measure. References | Related Articles | Metrics

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Generalization of Lyapunov Inequality for |Dirichlet BVPs with Impulses and its Applications WENG Ai-Zhi, SUN Ji-Tao Acta mathematica scientia,Series A. 2011, 31 (1):  82-91.  Abstract ( 1647 )   RICH HTML PDF (320KB) ( 965 )   Save In this paper,  first the authors obtain the nonexistence of nontrivial solutions for the linear Dirichlet boundary value problem with impulses $$\left\{     \begin{array}{ll}       x''(t)+a(t)x(t)=0, t\neq \tau_{k},  \\       \Delta x(\tau_{k})=c_{k}x(\tau_{k}),\\        \Delta x'(\tau_{k})=d_{k}x(\tau_{k}),  \\       x(0)=x(T)=0,     \end{array}   \right. (k=1,2\cdots,m)$$   where $a:[0,T]\rightarrow R$, $c_{k}$ and $d_{k}$ are constants, $k=1,2,\cdots,m$,  $\Delta x(\tau_{k})=x(\tau_{k}^{+})-x(\tau_{k}^{-})$, $\Delta x'(\tau_{k})=x'(\tau_{k}^{+})-x'(\tau_{k}^{-})$, $0<\tau_{1}<\tau_{2}<\cdots<\tau_{m}<T$. Secondly, by applying Leray-Schauder degree, the authors obtain the existence and uniqueness of solutions for the nonlinear Dirichlet boundary value problem with impulses $$\left\{     \begin{array}{ll}       x''(t)+f(t,x(t))=0, t\neq \tau_{k}, \\       \Delta x(\tau_{k})=I_{k}(x(\tau_{k})), \\       \Delta x'(\tau_{k})=M_{k}(x(\tau_{k})),  \\       x(0)=x(T)=0,     \end{array}   \right. (k=1,2\cdots,m)$$   where $f\in C([0,T]\times R, R)$, $I_{k},M_{k}\in C(R,R)$, $k=1,2,\cdots,m$.  As a corollary of the  results, the Lyapunov inequality is extended to impulsive systems. References | Related Articles | Metrics

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Triple Positive Solutions of 2m-point Boundary Value Problem of Sturm-Liouville Type with one Dimensional p-Laplacian ZHAO Jun-Fang, GE Wei-Gao Acta mathematica scientia,Series A. 2011, 31 (1):  92-102.  Abstract ( 1710 )   RICH HTML PDF (330KB) ( 952 )   Save In this paper, we are concerned with the following multi-point boundary value problem with one-dimensional p-Laplacian $$\left\{  \begin{array}{rl} &\disp (\phi_{p}(x'(t)))'+h(t)f(t,x(t),x'(t))=0,\hspace{3mm}0<t<1,\\ &\disp x'(0)-\sum_{i=1}^{m-1}\alpha_{i}x(\xi_{i})=0,\ \ \ x'(1)+\sum_{i=1}^{m-1}\beta_{i}x(\eta_{i})=0,  \end{array}  \right.$$ where $\phi_{p}(s)=|s|^{p-2}s,~p>1,~\alpha_{i}>0,~\beta_{i}>0,~0<\sum\limits_{i=1}^{m-1}\alpha_{i}\xi_{i}\leq1,~ 0<\sum\limits_{i=1}^{m-1}\beta_{i}(1-\eta_{i})\leq1,~0=\xi_{0} <\xi_{1}<\xi_{2}<\cdots<\xi_{m-1}<\eta_{1}<\eta_{2}<\cdots<\eta_{m-1}<\eta_{m}=1,~i=1,2,\cdots,m-1.$ By using a fixed point theorem in a cone, we obtain the existence of three positive solutions at least. The interesting point is that the boundary condition is a new kind of Sturm-Liouville type boundary condition, which has rarely been treated up to now. References | Related Articles | Metrics

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QP-free Method for Nonlinear Programming Problems JIANG Ai-Ping Acta mathematica scientia,Series A. 2011, 31 (1):  103-116.  Abstract ( 2092 )   RICH HTML PDF (392KB) ( 945 )   Save In this paper, A QP-free feasible method is proposed to obtain the local convergence under some weaker conditions for the minimization of a smooth function subject to smooth inequalities.  Based on the solutions of linear systems of equation reformulation of the KKT optimality conditions, this method uses the 3-1 NCP function[1]. The method is iterative, which means each iteration can be viewed as a perturbation of a Newton or Quasi Newton on both the primal and dual variables for the solution of the equalities in the KKT first order conditions of optimality, and the feasibility of all iterations is ensured in this method.  In particular, this method is implementable and globally convergent without assuming  the strict complementarity condition, the isolation of the accumulation point and the linear independence of the gradients of active constrained functions. The method has also superlinear convergence rate under some mild conditions which are the same as those in[2].  Some preliminary numerical results indicate that this new QP-free feasible method is quite promising. References | Related Articles | Metrics

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Relations with All Kinds of Crossed Coproducts FANG Xiao-Li, LI Jin-Ji Acta mathematica scientia,Series A. 2011, 31 (1):  117-131.  Abstract ( 1169 )   RICH HTML PDF (326KB) ( 1051 )   Save The so-called  generalized diagonal crossed coproduct, generalized L-R smash coproduct, generalized two-sided crossed coproduct  and  two-sided smash coproduct  are introduced and their relations are investigated. In particular, the authors  give two different interpretations about relations between generalized diagonal crossed coproducts and generalized L-R smash coproducts. As an application, an easy conceptual proof of an important but very technical result concerning iterated generalized smash coproducts is obtained. References | Related Articles | Metrics

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Convergence Properties for Weighted Sums of ρ -mixing Random Variables QIU De-Hua Acta mathematica scientia,Series A. 2011, 31 (1):  132-141.  Abstract ( 1533 )   RICH HTML PDF (302KB) ( 1014 )   Save In this paper, the author studies strong law of large numbers and complete convergence for weighted sums of ρ-mixing random variables. The author obtains some new results. The results extend and improve the corresponding results of Bai et al[1] and Baum et al[18] from i.i.d. case to ρ-mixing setting. Meanwhile, the results extend and improve the corresponding results of Volodin et al[4] from real-valued independent random variables to ρ-mixing setting. Furthermore, a complete convergence theorem for weighted sums of arrays of arbitrary random variables is obtained. References | Related Articles | Metrics

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A Kind of Large-range Convergence Algorithm for Weakly Regular Singular Boundary Value Problems ZHOU Yong-Fang, CUI Ming-Gen Acta mathematica scientia,Series A. 2011, 31 (1):  142-153.  Abstract ( 1431 )   RICH HTML PDF (354KB) ( 1086 )   Save In this paper, the weakly regular singular boundary value problem (p(x)y')'=f(x, y), 0<≤1, with p(x)=xb0g(x), 0≤b0<1, and the boundary conditions y(0)=A, αy(1)+β y'(1)=γ, or y'(0)=0, αy(1)+βy'(1)=γ(R.K. Pandey and Arvind K. Singh presented the second order finite difference methods[1] is considered. The existence of the solution and a new iterative algorithm which is large-range convergent are established for the problems in reproducing kernel space. Illustrative examples are included to demonstrate the validity and applicability of the technique through comparing the  method with the method given by R.K.Pandey and Arvind K.Singh. References | Related Articles | Metrics

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Controllability of a Quasilinear System with One Control HE Hong-Ying, DONG Wang-Yuan Acta mathematica scientia,Series A. 2011, 31 (1):  154-172.  Abstract ( 1453 )   RICH HTML PDF (406KB) ( 1016 )   Save This work deals with a class of quasilinear systems and gives the global null controllability and approximate controllability. The key is to use an observability inequality for the linearized systems, which is established by a modified Carleman inequality obtained in this text and a fixed point theorem. References | Related Articles | Metrics

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The Strong Irreducibility of Toeplitz Operators up to Similarity LAN Wen-Hua Acta mathematica scientia,Series A. 2011, 31 (1):  173-178.  Abstract ( 1381 )   RICH HTML PDF (269KB) ( 857 )   Save In this paper, the author studies the strong irreducibility of analytic Toeplitz operators with two Blaschke factors up to similarity on Hardy space, then the relationship between  the winding number of the Blaschke factors and Toeplitz operators induced by Blaschke factors is discussed. References | Related Articles | Metrics

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Limiting Behavior of Moving Average Processes of Martingale Difference Sequences CHEN Ping-Yan, LI Yuan-Mei Acta mathematica scientia,Series A. 2011, 31 (1):  179-187.  Abstract ( 1788 )   RICH HTML PDF (259KB) ( 1012 )   Save In this paper, for the moving average processes of martingale differences, the complete convergence, Marcinkiewicz-Zygmund strong law of large number and complete moment convergence are obtained and the existence of the moments of supermum of normed partial sums is discussed, which extend and improve some well-known results. References | Related Articles | Metrics

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Weighted Cesàro Operators on Zygmund Type Spaces on the Unit Ball ZHANG Jin-Fang, XU Hui-Ming Acta mathematica scientia,Series A. 2011, 31 (1):  188-195.  Abstract ( 1388 )   RICH HTML PDF (274KB) ( 1152 )   Save In this paper, the authors discuss the boundedness and compactness of the weighted Cesàro operators Tg between the Zygmund type spaces in the unit ball of Cn.  It is obtained that: (1) the sufficient and necessary condition for Tg to be bounded or compact operator from Zp to Zq; (2) the sufficient and necessary condition for Tg to be bounded or compact operator from Zp0 to Zq0. References | Related Articles | Metrics

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Existence and Uniqueness of Positive Solution for a Predator-prey Model with Diffusion GUO Gai-Hui, WU Jian-Hua Acta mathematica scientia,Series A. 2011, 31 (1):  196-205.  Abstract ( 1623 )   RICH HTML PDF (376KB) ( 1148 )   Save The predator-prey model with Beddington-DeAngelis functional response is considered. A necessary and sufficient condition for the existence of positive solutions is obtained. Moreover, a range of parameters for the uniqueness of positive solution is described in one dimension. The method used here is based on the global bifurcation theory, the implicit function theorem and the generalized maximum principle. References | Related Articles | Metrics

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Sharp Maximal Function Estimates for Calderón-Zygmund Type Operators and Commutators LIN Yan Acta mathematica scientia,Series A. 2011, 31 (1):  206-215.  Abstract ( 1391 )   RICH HTML PDF (299KB) ( 1041 )   Save In this paper, the author states sharp maximal function estimates for Calderón-Zygmund type operators and commutators. As their applications, the boundedness of these operators on Lebesgue spaces and Morrey type spaces is obtained. References | Related Articles | Metrics

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Inclusion Relations and Convolution Properties of a Certain Class of Analytic and Multivalent Functions Involving the Dziok-Srivastava Operator XU Nai Acta mathematica scientia,Series A. 2011, 31 (1):  216-228.  Abstract ( 1752 )   RICH HTML PDF (294KB) ( 1020 )   Save In the present paper, the author introduces and investigates a new subclass of multivalent analytic functions involving the Dziok-Srivastava linear operator. Some interesting properties such as inclusion relationships, convolution conditions for this function class are obtained. The results presented here would provide extensions of those given in earlier works. Several other new results are also obtained. References | Related Articles | Metrics

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A New Non-interior-point Continuation Method for Nonlinear Complementarity Problem with P0-function FANG Liang, HE Guo-Ping, WANG Yong-Li Acta mathematica scientia,Series A. 2011, 31 (1):  229-238.  Abstract ( 1399 )   RICH HTML PDF (395KB) ( 1259 )   Save In this paper, nonlinear complementarity problem with $P_0$-function is studied. Based on a new smoothing function,the problem is approximated by a family of parameterized smooth equations and a new non-interior-point continuation method is presented for solving it. At each iteration, the proposed algorithm only need to solve a system of linear equations and perform only one Armijo-type line search. The algorithm is proved to be globally as well as locally superlinearly convergent without strict complementarity. Moreover, the quadratic convergence rate can be achieved under mild conditions. Numerical experiments demonstrate the feasibility and efficiency of the new algorithm. References | Related Articles | Metrics

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Weighted Inequalities for Commutators of |Fractional Integrals LI Wen-Ming, ZHANG Ya-Jing, MO Hui-Xia Acta mathematica scientia,Series A. 2011, 31 (1):  239-249.  Abstract ( 1665 )   RICH HTML PDF (313KB) ( 1181 )   Save In this paper, the authors  give some strong-type and weak-type weighted inequalities for the higher order commutators of  the fractional integral operators with BMO functions. References | Related Articles | Metrics

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A Modified Nonlinear Uzawa Algorithm for Solving Saddle Point Problem LI Jian-Lei, HUANG Ting-Zhu, LI Liang Acta mathematica scientia,Series A. 2011, 31 (1):  250-262.  Abstract ( 1689 )   RICH HTML PDF (431KB) ( 1109 )   Save In this paper, the authors consider the solution of linear systems of large nonsymmetric saddle point problems by modifying the algorithm in [3]. The convergence of the modified algorithm is analyzed, and at the same time, numerical experiments are presented to illustrate the effectiveness of the modified algorithm. References | Related Articles | Metrics

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Positive Solutions of Singularly Perturbed (k, n-k) Conjugate Boundary Value Problems ZHONG Min-Ling, ZHANG Xin-Guang Acta mathematica scientia,Series A. 2011, 31 (1):  263-272.  Abstract ( 1777 )   RICH HTML PDF (315KB) ( 939 )   Save In this paper, by employing the so-called modified function, some new existence results of multiple positive solutions for a class of singularly perturbed (k, n-k) conjugate boundary value problems are established, where the perturbed term is only a Lebesgue integrable function. An example is worked out to indicate the application of the  main results. References | Related Articles | Metrics