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25 August 2011, Volume 31 Issue 4 Previous Issue    Next Issue

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Data Assimilation: a Nonstandard Approach to a Heat Conduction Model YU Hang Acta mathematica scientia,Series A. 2011, 31 (4):  857-865.  Abstract ( 1230 )   RICH HTML PDF (331KB) ( 832 )   Save We consider an one dimensional heat conduction model ∂ty-Δy=0, in  (0, T)×Ω, which we would like to "predict" on a time interval (T0, T0) but for which the initial value of the state variable is unknown. However, "measures"of the solutions are known only at one point of Ω on a time interval (0, T0) where 0<T0<T. The classical approach in data assimilation is to look for the initial value at time 0 and this is known to be an ill-posed problem for heat equations. In this paper, by the property of null controllability of heat equations we give a result of approximate reconstruction of the value at T0. The approximation needs a sharp estimation of the cost of the null controllability of the heat equation. References | Related Articles | Metrics

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A Bundle Proximal Method for Solving General Mixed Variational Inequalities XIA Fu-Quan, HUANG Na-Jing Acta mathematica scientia,Series A. 2011, 31 (4):  866-879.  Abstract ( 1081 )   RICH HTML PDF (392KB) ( 791 )   Save In this paper, the authors consider a bundle proximal method for solving general mixed variational inequalities. The method is based on the auxiliary problem principle due to Cohen and the bundle Bregman proximal method for convex nonsmooth optimization due to Kiwiel. The strategy is to approximate, in the subproblems, the nonsmooth convex function f by a sequence of linear convex piecewise functions fk, which is constructed from accumulated subgradient linearizations of f. As in the bundle Bregman proximal method for nonsmooth optimization, the  method generates a sequence {xk} by taking xk to be an approximate minimizer of subproblems. This makes the subproblems more tractable. The authors first explain how to build a new iterative scheme and a stopping criterion to determine whether the current approximation is good enough. This criterion is different from that commonly used in the special case of nonsmooth optimization. The authors also prove that the convergence of the algorithm for the case that the mapping T satisfies  the pseudo-Dunn property. References | Related Articles | Metrics

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Comparison Theroems for the IMGS Iterative Method with Preconditioner LI Wei-Cheng, JIANG Yao-Lin Acta mathematica scientia,Series A. 2011, 31 (4):  880-886.  Abstract ( 1351 )   RICH HTML PDF (277KB) ( 870 )   Save In this paper, by comparing with the spectral radiuses of the iterative methods, the authors prove, for the first time, that the IMGS method[1-2] with the preconditioner I+Sα is faster than the basic AOR iterative method, and then prove that the preconditioned SOR method is  faster than the basic SOR method. Finally, the authors prove the monotony of the spectral radius with respect to the parameter and  improve some recent known results. References | Related Articles | Metrics

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Solving the Self-adjoint Operator Equation by Iterative Method of Complex Parameter HAN Chuan-Feng, ZHANG Chao Acta mathematica scientia,Series A. 2011, 31 (4):  887-891.  Abstract ( 1211 )   RICH HTML PDF (271KB) ( 769 )   Save Ill-posed problems are used widely. The authors take advantage of the special character of the self-adjoint compact operator equation, establishing its iterative method with complex parameter. Furthermore, they prove the regularization of this method and best orders of convergence. Finally, they examines the result by numerical experiments. References | Related Articles | Metrics

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Growth Estimates for a Class of Subharmonic Functions in the Half Plane PAN Guo-Shuang, DENG Guan-Tie Acta mathematica scientia,Series A. 2011, 31 (4):  892-901.  Abstract ( 1189 )   RICH HTML PDF (260KB) ( 779 )   Save A class of subharmonic  functions represented by the modified  kernels is  proved to have the  growth estimates u(z)= o(y1-αz|m+α), at infinity in the upper half plane C+, which generalizes the growth properties of analytic functions and harmonic functions. References | Related Articles | Metrics

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Generalized |Higher-order Cone-directed Derivatives and Applications to Set-valued Optimization WANG Qi-Lin, LI Shng-Jie Acta mathematica scientia,Series A. 2011, 31 (4):  902-909.  Abstract ( 1528 )   RICH HTML PDF (302KB) ( 955 )   Save In this paper, a generalized higher-order contingent (adjacent) set for a set and a generalized higher-order cone-directed contingent (adjacent) derivative for a  set-valued map are introduced.  By virtue of the derivatives, generalized higher-order necessary and sufficient conditions are obtained for a set-valued optimization problem, whose constraint condition is determined by a fixed set or a set-valued map, respectively. References | Related Articles | Metrics

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Nodal Solutions of a Nonlinear Eigenvalue Problem with Indefinite Weight Function MA Ru-Yun, Han-Xiao-Ling Acta mathematica scientia,Series A. 2011, 31 (4):  910-917.  Abstract ( 966 )   RICH HTML PDF (283KB) ( 781 )   Save The authors  are concerned with the existence of nodal solutions of the indefinite weight boundary value problem u''+rh(t)f(u)=0,   0<t<1,  u(0)=u(1)=0, where C[0,1] changes sign. The proof of the  main result is based upon bifurcation techniques. References | Related Articles | Metrics

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On the Estimate of Growth of Entire Solutions of Some Classes of Algebric Differential Equations GU Rong-Mei, DING Jian-Jun, YUAN Wen-Jun Acta mathematica scientia,Series A. 2011, 31 (4):  918-922.  Abstract ( 1245 )   RICH HTML PDF (270KB) ( 891 )   Save In this note, the authors give a general estimate of finite growth order of entire solutions  of some classes of algebraic differential equations by using the normal family theory, and also discuss a specific class of algebraic differential equations, in which the order of any transcendental entire solution is one. References | Related Articles | Metrics

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A Strong Vector Equilibrium Problem FU Jun-Yi Acta mathematica scientia,Series A. 2011, 31 (4):  923-929.  Abstract ( 1665 )   RICH HTML PDF (269KB) ( 820 )   Save In this paper, a strong vector equilibrium problem with moving cones is presented, and the existence of its solution and the closedness of  solution set are established. As applications, existence of solutions for strong vector F-implicit variational inequality problems and strong vector F-implicit complementarity problems is derived. References | Related Articles | Metrics

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Weighted Lipschitz Estimates for Vector-valued Multilinear Operators ZHOU Xiao-Sha, LIU Lan-Zhe Acta mathematica scientia,Series A. 2011, 31 (4):  930-945.  Abstract ( 1609 )   RICH HTML PDF (297KB) ( 781 )   Save In this paper, the weighted boundedness for the vector-valued multilinear operators generated by some integral operators and the weighted Lipschitz functions are obtained. The operators include Calder\'on-Zygmund singular integral operator, fractional integral operator, Littlewood-Paley operator, Marcinkiewicz operator and Bochner-Riesz operator. References | Related Articles | Metrics

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Approximation Order and Balance Order of Orthonormal Multiwavelets with Scale a JIANG Li, ZHU Shan-Hua, LV Yong Acta mathematica scientia,Series A. 2011, 31 (4):  946-957.  Abstract ( 1167 )   RICH HTML PDF (366KB) ( 1043 )   Save Generalizing the definition of m-order approximation of two-scale orthonormal multiwavelets to the case that the scale factor is equals to a(a ≥2), a sufficient and necessary condition is proposed for orthonormal multiwavelets with scale a to have m-order approximation, by studying the factorization of a-scale matrix symbol; Based on the m-balanced definition of orthonormal multiscaling functions with scale a, three sufficient and necessary conditions are investigated for such orthonormal multiwavelets to have m-order balance; Then, verify the theory by means of an example. References | Related Articles | Metrics

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Existence of Weak Solutions for the Minimizing Total Variation Flow with Dirichlet Boundary Conditions RUI Jie, YANG Xiao-Ping Acta mathematica scientia,Series A. 2011, 31 (4):  958-969.  Abstract ( 1268 )   RICH HTML PDF (321KB) ( 790 )   Save This paper concludes that the minimizing total variation flow with Dirichlet boundary conditions has a weak solution with initial data in L1(Ω) by using Crandall-Liggett's semigroup generation theorem and the quality of the completely accretive  operator. References | Related Articles | Metrics

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On Set-valued Solutions of an Iterative Equation ZHONG Ji-Yu, LI Xiao-Pei Acta mathematica scientia,Series A. 2011, 31 (4):  970-977.  Abstract ( 1263 )   RICH HTML PDF (249KB) ( 786 )   Save A second order iterative functional equation is considered for multifunction in Banach space. A result on the existence and uniqueness of its solution is presented without monotonicity. Furthermore continuous dependence of the solution upon the given function is  obtained. References | Related Articles | Metrics

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Some Properties of Foldover of Regular (sr)×sn Fractional Factorial Designs LEI Tie-Ju, OU Zu-Jun, QIN Hong Acta mathematica scientia,Series A. 2011, 31 (4):  978-982.  Abstract ( 1306 )   RICH HTML PDF (310KB) ( 947 )   Save In this paper,  the authors  study the issue of foldover of regular (sr)×sn fractional factorial designs,  where r~(≥2) is an integer and s is a prime or prime power.  A general decomposition structure of the foldover plan for a regular (sr)×sn fractional factorial design is obtained.  The relationship between an initial design and its combined design are studied. This is done both for  with and without consideration of the blocking factor. So the authors generalize the results about foldover from sn regular fractional factorial designs to the case of (sr)×sn regular fractional. References | Related Articles | Metrics

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A Necessary Condition of some Linear Partial Differential Operator |that Admits a Continuous Linear Right Inverse WU Mi-Jing, WANG Guang Acta mathematica scientia,Series A. 2011, 31 (4):  983-990.  Abstract ( 1088 )   RICH HTML PDF (321KB) ( 723 )   Save In the paper, the linear partial differential operator S(D=P(D)-∂2/∂2n+1) is disscused by using Phragmén-Lindel\"{o}f condition and d-quasihomogeneous polynomials, and a necessary condition of it, for which the continuous linear right inverse exists, is given. References | Related Articles | Metrics

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The Regular Growth of Dirichlet Series on the Whole Plane GU Zhen-Dong, SUN Dao-Chun Acta mathematica scientia,Series A. 2011, 31 (4):  991-997.  Abstract ( 1330 )   RICH HTML PDF (251KB) ( 866 )   Save By the method of Knopp-Kojima, the authors define the order of Dirichlet series and the order of regular growth of Dirichlet series,  and study the regular growth of  Dirichlet series on the whole plane, and obtain an equivalent   condition of the order of regular growth of Dirichlet series. References | Related Articles | Metrics

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Viscosity Approximation Methods for Strict Pseudo-contractions in q-uniformly Smooth Banach Spaces LIU Ying Acta mathematica scientia,Series A. 2011, 31 (4):  998-1007.  Abstract ( 1316 )   RICH HTML PDF (293KB) ( 801 )   Save In this paper, we introduce an iterative scheme by the viscosity approximation method for finding a common fixed point of a finite family of strictly pseudo-contractive mappings,  which solves some variational inequality in a real q-uniformly smooth Banach space. Our results improve and extend the corresponding results announced by many others. References | Related Articles | Metrics

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Asymptotic Behavior of Solutions to the Kirchhoff Type Equation YANG Zhi-Jian, CHENG Jian-Ling Acta mathematica scientia,Series A. 2011, 31 (4):  1008-1021.  Abstract ( 1661 )   RICH HTML PDF (353KB) ( 945 )   Save The paper studies the longtime behavior of solutions to the initial boundary value problem (IBVP) of the Kirchhoff type equation with strong damping utt-M(\||\nabla u||{2})Δu-Δut+g(x, u)+h(ut)=f(x), with M(s)=1+sm/2, m≥1. With two different methords, it proves that the related continuous semigroup S(t) posseses in phase space X=(H2(Ω)∩H01(Ω))×H01(Ω) a global attractor. At the end of the paper, an example is shown, which  indicates  the existence of nonlinear functions g(x, u) and h(ut). References | Related Articles | Metrics

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Holomorphic Vector Bundles and Ward Solitons ZHU Xiu-Juan Acta mathematica scientia,Series A. 2011, 31 (4):  1022-1035.  Abstract ( 967 )   RICH HTML PDF (400KB) ( 890 )   Save The holomorphic vector bundle on the rational ruled surface corresponding to the finite-action 1-uniton was explicitly described by Ward in terms of a meromorphic framing, which has a singularity structure corresponding to that of the 1-uniton extended solution. In this paper, the author generalizes Ward's method to give explicitly the holomorphic bundle corresponding to all Ward solitons whose extended solutions have only simple poles and some Ward solitons  whose extended solutions have a second-order pole. References | Related Articles | Metrics

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Section Theorems and Their Applications to Variational Inequalities on Generalized Convex Spaces PIAO Yong-Jie Acta mathematica scientia,Series A. 2011, 31 (4):  1036-1044.  Abstract ( 1324 )   RICH HTML PDF (304KB) ( 864 )   Save The KKM type theorem on generalized convex spaces is introduced, and from which, an analytic alternative type theorem of section problem is obtained. As applications of  the above results,  the existence problems of solution for variational inequalities on generalized convex spaces are discussed. The main results of this paper improve and generalize the corresponding results in recent literatures. References | Related Articles | Metrics

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Boundedness of Multilinear Commutators of Fractional Hardy Operators WU Jiang-Long Acta mathematica scientia,Series A. 2011, 31 (4):  1055-1062.  Abstract ( 1490 )   RICH HTML PDF (285KB) ( 912 )   Save In this paper, the  boundedness of the multilinear commutator He, b generated by an n-dimensional fractional Hardy operator and   BMO function is established on the Lebesgue space, the homogenous Herz space Kqα, p(Rn) and the homogenous Morrey-Herz space MKp, q, α, λ(Rn). References | Related Articles | Metrics

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Crank-Nicolson Difference Scheme for Convection-Diffusion Problem by Using |Moving Mesh Method YANG Yin, ZHOU Qin Acta mathematica scientia,Series A. 2011, 31 (4):  1063-1070.  Abstract ( 1711 )   RICH HTML PDF (437KB) ( 957 )   Save The authors construct Crank-Nicolson difference scheme on moving mesh for a class of non-constant singularly perturbed convection-diffusion problem with source term, and introduce the iterative method and algorithm of moving mesh. The authors compare the error on moving mesh and uniform mesh by numerical experiments, and prove that it can decrease numerical oscillation effectively when using Crank-Nicolson difference scheme on moving mesh. References | Related Articles | Metrics

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A Note on the Generalized Bott-Duffin Inverse of Linear Operators DU Hong-Ke, SHAO Chun-Fang, XU Jun-Lian, JI Shu-Feng Acta mathematica scientia,Series A. 2011, 31 (4):  1071-1076.  Abstract ( 1071 )   RICH HTML PDF (271KB) ( 919 )   Save In this note, two theorems involving generalized Bott-Duffin inverses of bounded linear operators on a Hilbert space are proved, which are generalizations of that obtained in a finite dimensional space by Deng and Chen[7]. It is worthwhile to point out that the idea and the method used in this note are different from those used by  Deng and Chen. References | Related Articles | Metrics

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A Ky Fan Matching Theorem for MLC Mappings with Applications to Minimax Inequalities and Saddle Points WEN Kai-Ting, LI He-Rui, ZENG Fan-Pei Acta mathematica scientia,Series A. 2011, 31 (4):  1077-1082.  Abstract ( 1370 )   RICH HTML PDF (257KB) ( 1025 )   Save In this paper, a Ky Fan matching theorem for MLC mappings with transfer compactly open values is established in noncompact complete L-convex metric spaces. As applications, a Fan-Browder type coincidence theorem, a maximal element theorem, a minimax inequality and a saddle point theorem are obtained. References | Related Articles | Metrics

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Locally Dual Flat Randers Metrics ZHOU Yu-Sheng Acta mathematica scientia,Series A. 2011, 31 (4):  1083-1090.  Abstract ( 912 )   RICH HTML PDF (264KB) ( 889 )   Save In this paper, we find equations that charactrize locally dual flat Finsler metrics in the form F=α+β, where α=√aijyiyj is a Riemannian metric and β=biyi is a 1-form. Then we completely determine the local structure of those when α is of constant curvature or β is closed. References | Related Articles | Metrics

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New Approch of the Error Estimate for Nonconforming Plate Element ZHAO Zhong-Jian, CHEN Shao-Chun Acta mathematica scientia,Series A. 2011, 31 (4):  1091-1096.  Abstract ( 1393 )   RICH HTML PDF (290KB) ( 912 )   Save In this paper, some new methods of error estimates for nonconforming plate element is given according to the properties of divergence space. The error estimate of energy norm and L2(Ω) norm is proved. Compared with the former methods, it is more direct and convenient,  and it also obtains the order required. References | Related Articles | Metrics

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Solvability of Nonlinear Impulsive Volterra Type Integral Equations in Banach Space LI Ye, LIU Li-Shan Acta mathematica scientia,Series A. 2011, 31 (4):  1097-1104.  Abstract ( 1341 )   RICH HTML PDF (294KB) ( 941 )   Save In this paper, under weak conditions, by useing the MÖnch fixed point theorem and the method of estimate step by step, some existence theorems of solutions for the nonlinear impulsive Volterra type integral equations in Banach space are proved. The results  obtained improve and extend the known results. Then the authors give some applications to initial value problems for nonlinear impulsive first-order differential equations of mixed type in Banach space. References | Related Articles | Metrics

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The Boundedness of the Commutators for Marcinkiewicz Integral with Nondoubling Measures on Morrey Spaces CHEN Dong-Xiang, Wu Li-Li Acta mathematica scientia,Series A. 2011, 31 (4):  1105-1114.  Abstract ( 1235 )   RICH HTML PDF (278KB) ( 830 )   Save In this paper, the authors prove that the commutators of Marcinkiewicz integral μb not only has the (Mqp(ν), Mts(ν)) boundedness. On the other hand, the (Mqp(ν), Lip(β-n/p))-boundedness and the (Mqp(ν), RBMO(ν))-boundedness of μb are also obtained. References | Related Articles | Metrics

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Weak Estimates for Marcinkiewicz Commutators with Lipschitz Functions on Herz Space CHEN Jin-Yang, LI Liang, MA Bai-Lin Acta mathematica scientia,Series A. 2011, 31 (4):  1115-1121.  Abstract ( 930 )   RICH HTML PDF (286KB) ( 857 )   Save The paper proves that  a class of commutors generated by Lipschitz functions and Marcinkiewicz integrals with rough kernels is bounded from weak Herz space to Herz-type Hardy space. References | Related Articles | Metrics

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On the Existence of Weak Solutions for Nonlinear Schr\"{o}dinger-Klein-Gordon Equations SHI Qi-Hong, WANG Shu, WANG Chang-Wei Acta mathematica scientia,Series A. 2011, 31 (4):  1122-1132.  Abstract ( 1436 )   RICH HTML PDF (355KB) ( 792 )   Save In this paper, the Cauchy problem to the nonlinear Schr\"{o}dinger-Klein-Gordon equations in 3+1 time-space is studied. Under certain assumptions on nonlinear terms and the initial data, the existence of global weak solutions is obtained by the viscous method and the energy method combined with the compactness arguments. References | Related Articles | Metrics

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Uniqueness of Algebroidal Functions ZHANG Xiao-Mei, SUN Dao-Chun Acta mathematica scientia,Series A. 2011, 31 (4):  1133-1139.  Abstract ( 1068 )   RICH HTML PDF (291KB) ( 823 )   Save The uniqueness problem of two algebroidal functions with shared values in an angular domain is studied. Some results are obtained. References | Related Articles | Metrics