15 February 2002, Volume 18 Issue 2
    

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  • Original Articles
    Nonlinear Time Series Analysis Since 1990: Some Personal Reflections
    Howel Tong
    Acta Mathematicae Applicatae Sinica(English Series). 2002, 18(2): 177-184.
    Abstract ( )    Download PDF ( )   Knowledge map   Save
    I reflect upon the development of nonlinear time series analysis since 1990 by focusing on five major areas of development. These areas include the interface between nonlinear time series analysis and chaos, the nonparametric/semiparametric approach, nonlinear state space modelling, financial time series and nonlinear modelling of panels of time series.
  • 论文
    Nonlinear Time Series Analysis Since 1990: Some Personal Reflections
    Howel Tong
    Acta Mathematicae Applicatae Sinica(English Series). 2002, 18(2): 177-184.
    Abstract ( )    Download PDF ( )   Knowledge map   Save
    I reflect upon the development of nonlinear time series analysis since 1990 by focusing on five major areas of development. These areas include the interface between nonlinear time series analysis and chaos, the nonparametric/semiparametric approach, nonlinear state space modelling, financial time series and nonlinear modelling of panels of time series.
  • Original Articles
    Local and Parallel Finite Element Algorithms for Eigenvalue Problems
    Jin Chao XU, Ai Hui ZHOU
    Acta Mathematicae Applicatae Sinica(English Series). 2002, 18(2): 185-200.
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    Some new local and parallel finite element algorithms are proposed and analyzed in this paper for eigenvalue problems. With these algorithms, the solution of an eigenvalue problem on a fine grid is reduced to the solution of an eigenvalue problem on a relatively coarse grid together with solutions of some linear algebraic systems on fine grid by using some local and parallel procedure. A theoretical tool for analyzing these algorithms is some local error estimate that is also obtained in this paper for finite element approximations of eigenvectors on general shape-regular grids.
  • 论文
    Local and Parallel Finite Element Algorithms for Eigenvalue Problems
    Jin Chao XU, Ai Hui ZHOU
    Acta Mathematicae Applicatae Sinica(English Series). 2002, 18(2): 185-200.
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    Some new local and parallel finite element algorithms are proposed and analyzed in this paper for eigenvalue problems. With these algorithms, the solution of an eigenvalue problem on a fine grid is reduced to the solution of an eigenvalue problem on a relatively coarse grid together with solutions of some linear algebraic systems on fine grid by using some local and parallel procedure. A theoretical tool for analyzing these algorithms is some local error estimate that is also obtained in this paper for finite element approximations of eigenvectors on general shape-regular grids.
  • 论文
    Attractors and Dimensions for Discretizations of a Dissipative Zakharov Equations
    Qian Shun CHANG, Bo Ling GUO
    Acta Mathematicae Applicatae Sinica(English Series). 2002, 18(2): 201-214.
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    In this paper, a dissipative Zakharov equations are discretized by difference method. We make prior estimates for the algebric system of equations. It is proved that for each mesh size, there exist attractors for the discretized system. The bounds of the Hausdorff dimensions of the discrete attractors are obtained, and the various bounds are dependent of the mesh size.
  • Original Articles
    Attractors and Dimensions for Discretizations of a Dissipative Zakharov Equations
    Qian Shun CHANG, Bo Ling GUO
    Acta Mathematicae Applicatae Sinica(English Series). 2002, 18(2): 201-214.
    Abstract ( )    Download PDF ( )   Knowledge map   Save
    In this paper, a dissipative Zakharov equations are discretized by difference method. We make prior estimates for the algebric system of equations. It is proved that for each mesh size, there exist attractors for the discretized system. The bounds of the Hausdorff dimensions of the discrete attractors are obtained, and the various bounds are dependent of the mesh size.
  • Original Articles
    Enumeration of Maximum Acyclic Hypergraphs
    Jian Fang WANG , Hai Chu LI
    Acta Mathematicae Applicatae Sinica(English Series). 2002, 18(2): 215-218.
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    Acyclic hypergraphs are analogues of forests in graphs. They are very useful in the design of databases. In this article, the maximum size of an acyclic hypergraph is determined and the number of maximum r-uniform acyclic hypergraphs of order n is shown to be
  • 论文
    Enumeration of Maximum Acyclic Hypergraphs
    Jian Fang WANG , Hai Chu LI
    Acta Mathematicae Applicatae Sinica(English Series). 2002, 18(2): 215-218.
    Abstract ( )    Download PDF ( )   Knowledge map   Save
    Acyclic hypergraphs are analogues of forests in graphs. They are very useful in the design of databases. In this article, the maximum size of an acyclic hypergraph is determined and the number of maximum r-uniform acyclic hypergraphs of order n is shown to be
  • Original Articles
    Linearization Ill-Posedness for 2.5-D Wave Equation Inversion Model
    Ji Jun LIU
    Acta Mathematicae Applicatae Sinica(English Series). 2002, 18(2): 219-230.
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    For the weakly inhomogeneous acoustic medium in Q={(x, y, z:z>0}, we consider the inverse problem of determining the density function p(x, y). The inversion input for our inverse problem is the wave field given on a line. We get an integral equation for the 2-D density perturbation from the linearization. By virtue of the integral transform, we prove the uniqueness and the instability of the solution to the integral equation. The degree of ill-posedness for this problem is also given.
  • 论文
    Linearization Ill-Posedness for 2.5-D Wave Equation Inversion Model
    Ji Jun LIU
    Acta Mathematicae Applicatae Sinica(English Series). 2002, 18(2): 219-230.
    Abstract ( )    Download PDF ( )   Knowledge map   Save
    For the weakly inhomogeneous acoustic medium in Q={(x, y, z:z>0}, we consider the inverse problem of determining the density function p(x, y). The inversion input for our inverse problem is the wave field given on a line. We get an integral equation for the 2-D density perturbation from the linearization. By virtue of the integral transform, we prove the uniqueness and the instability of the solution to the integral equation. The degree of ill-posedness for this problem is also given.
  • 论文
    Portfolio Optimization Model with Transaction Costs
    Shu Ping CHEN , Chong LI, Sheng Hong LI;Xiong Wei WU(4)
    Acta Mathematicae Applicatae Sinica(English Series). 2002, 18(2): 231-248.
    Abstract ( )    Download PDF ( )   Knowledge map   Save
    The purpose of the article is to formulate, under the lX risk measure, a model of portfolio selection with transaction costs and then investigate the optimal strategy within the proposed. The characterization of a optimal strategy and the efficient algorithm for finding the optimal strategy are given.
  • Original Articles
    Portfolio Optimization Model with Transaction Costs
    Shu Ping CHEN , Chong LI, Sheng Hong LI;Xiong Wei WU(4)
    Acta Mathematicae Applicatae Sinica(English Series). 2002, 18(2): 231-248.
    Abstract ( )    Download PDF ( )   Knowledge map   Save
    The purpose of the article is to formulate, under the lX risk measure, a model of portfolio selection with transaction costs and then investigate the optimal strategy within the proposed. The characterization of a optimal strategy and the efficient algorithm for finding the optimal strategy are given.
  • 论文
    Boundary Value Problems for Singular Second-Order Functional Differential Equations
    Hui Zhao LIU, Da Qing JIANG , Yan WANG
    Acta Mathematicae Applicatae Sinica(English Series). 2002, 18(2): 249-254.
    Abstract ( )    Download PDF ( )   Knowledge map   Save
    Positive solutions to the boundary value problem, are obtained by applying the Schauder fixed point theorem, where w(x) is a continuous function defined on [0, 1] and f(x, y) is a function defined on (0, 1)2(0, X), which satisfies certain restrictions and may have singularity at y=0. The result corrects and improves an existence theorem due to Erbe and Kong [1].
  • Original Articles
    Boundary Value Problems for Singular Second-Order Functional Differential Equations
    Hui Zhao LIU, Da Qing JIANG , Yan WANG
    Acta Mathematicae Applicatae Sinica(English Series). 2002, 18(2): 249-254.
    Abstract ( )    Download PDF ( )   Knowledge map   Save
    Positive solutions to the boundary value problem, are obtained by applying the Schauder fixed point theorem, where w(x) is a continuous function defined on [0, 1] and f(x, y) is a function defined on (0, 1)2(0, X), which satisfies certain restrictions and may have singularity at y=0. The result corrects and improves an existence theorem due to Erbe and Kong [1].
  • 论文
    Boundary Nevanlinna-pick Interpolation for Meromorphic Functions
    Gong Ning CHEN , Li Xin JIA
    Acta Mathematicae Applicatae Sinica(English Series). 2002, 18(2): 255-262.
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    Versions of the multiple Nevanlinna-Pick interpolation problem in the class N-circumfiex involving both interior and boundary data are investigated. This leads to solvability criteria for the indicated problems and description of their solutions.
  • Original Articles
    Boundary Nevanlinna-pick Interpolation for Meromorphic Functions
    Gong Ning CHEN , Li Xin JIA
    Acta Mathematicae Applicatae Sinica(English Series). 2002, 18(2): 255-262.
    Abstract ( )    Download PDF ( )   Knowledge map   Save
    Versions of the multiple Nevanlinna-Pick interpolation problem in the class N-circumfiex involving both interior and boundary data are investigated. This leads to solvability criteria for the indicated problems and description of their solutions.
  • 论文
    Regularity of the Attractor for the Dissipative Hamiltonian Amplitude Equation Governing Modulated Wave Instabilities
    Zheng De DAI
    Acta Mathematicae Applicatae Sinica(English Series). 2002, 18(2): 263-271.
    Abstract ( )    Download PDF ( )   Knowledge map   Save
    In the present paper, the existence of global attractor for dissipative Hamiltonian amplitude equation governing the modulated wave instabilities in E0 is considered. By a decomposition of solution operator, it is shown that the global attractor in E0 is actually equal to a global attractor in E_1.
  • Original Articles
    Regularity of the Attractor for the Dissipative Hamiltonian Amplitude Equation Governing Modulated Wave Instabilities
    Zheng De DAI
    Acta Mathematicae Applicatae Sinica(English Series). 2002, 18(2): 263-271.
    Abstract ( )    Download PDF ( )   Knowledge map   Save
    In the present paper, the existence of global attractor for dissipative Hamiltonian amplitude equation governing the modulated wave instabilities in E0 is considered. By a decomposition of solution operator, it is shown that the global attractor in E0 is actually equal to a global attractor in E_1.
  • Original Articles
    Attractors for a Nonclassical Diffusion Equation
    Yue Long XIAO
    Acta Mathematicae Applicatae Sinica(English Series). 2002, 18(2): 273-276.
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    For a nonclassical diffusion equation, the asymptotic behavior is investigated, and the existence of a global attractor is proved.
  • 论文
    Attractors for a Nonclassical Diffusion Equation
    Yue Long XIAO
    Acta Mathematicae Applicatae Sinica(English Series). 2002, 18(2): 273-276.
    Abstract ( )    Download PDF ( )   Knowledge map   Save
    For a nonclassical diffusion equation, the asymptotic behavior is investigated, and the existence of a global attractor is proved.
  • 论文
    Mean Convergence of Lagrnage Type Interpolation on an Arbitrary System of Nodes
    Ying Guang SHI
    Acta Mathematicae Applicatae Sinica(English Series). 2002, 18(2): 277-288.
    Abstract ( )    Download PDF ( )   Knowledge map   Save
    Sufficient conditions of convergence and rate of convergence for Lagrange type interpolation in the weighted Lp norm on an arbitrary system of nodes are given.
  • Original Articles
    Mean Convergence of Lagrnage Type Interpolation on an Arbitrary System of Nodes
    Ying Guang SHI
    Acta Mathematicae Applicatae Sinica(English Series). 2002, 18(2): 277-288.
    Abstract ( )    Download PDF ( )   Knowledge map   Save
    Sufficient conditions of convergence and rate of convergence for Lagrange type interpolation in the weighted Lp norm on an arbitrary system of nodes are given.
  • Original Articles
    A Posteriori Parameter Choice Strategy for Nonlinear Monotone Operator Equations
    Hong Qi YANG , Zong Yi HOU
    Acta Mathematicae Applicatae Sinica(English Series). 2002, 18(2): 289-294.
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    In this paper we present an a posteriori parameter choice strategy for nonlinear ill-posed operator equations involving monotone operators. Under certain conditions, this a posteriori parameter choice strategy guarantees the optimal convergence rate O (δ~(1/2)) for Tikhonov-Browder regularization, where ' denotes the noise level of the data perturbation.
  • 论文
    A Posteriori Parameter Choice Strategy for Nonlinear Monotone Operator Equations
    Hong Qi YANG , Zong Yi HOU
    Acta Mathematicae Applicatae Sinica(English Series). 2002, 18(2): 289-294.
    Abstract ( )    Download PDF ( )   Knowledge map   Save
    In this paper we present an a posteriori parameter choice strategy for nonlinear ill-posed operator equations involving monotone operators. Under certain conditions, this a posteriori parameter choice strategy guarantees the optimal convergence rate O (δ~(1/2)) for Tikhonov-Browder regularization, where ' denotes the noise level of the data perturbation.
  • Original Articles
    A Kind of Discrete Non-Reflecting Boundary Conditions for Varieties of Wave Equations
    Xiu Min SHAO , Zhi Ling LAN
    Acta Mathematicae Applicatae Sinica(English Series). 2002, 18(2): 295-302.
    Abstract ( )    Download PDF ( )   Knowledge map   Save
    In this paper, a new kind of discrete non-reflecting boundary conditions is developed. It can be used for a variety of wave equations such as the acoustic wave equation, the isotropic and anisotropic elastic wave equations and the equations for wave propagation in multi-phase and so on. In this kind of boundary conditions, the composition of all artificial reflected waves, but not the individual reflected ones, is considered and eliminated. Thus, it has a uniform formula for different wave equations. The velocity CA of the composed reflected wave is determined in the way to make the reflection coefficients minimal, the value of which depends on equations. In this paper, the costruction of the boundary conditions is illustrated and CA is found, numerical results are presented to illustrate the effectiveness of the boundary conditions.
  • 论文
    A Kind of Discrete Non-Reflecting Boundary Conditions for Varieties of Wave Equations
    Xiu Min SHAO , Zhi Ling LAN
    Acta Mathematicae Applicatae Sinica(English Series). 2002, 18(2): 295-302.
    Abstract ( )    Download PDF ( )   Knowledge map   Save
    In this paper, a new kind of discrete non-reflecting boundary conditions is developed. It can be used for a variety of wave equations such as the acoustic wave equation, the isotropic and anisotropic elastic wave equations and the equations for wave propagation in multi-phase and so on. In this kind of boundary conditions, the composition of all artificial reflected waves, but not the individual reflected ones, is considered and eliminated. Thus, it has a uniform formula for different wave equations. The velocity CA of the composed reflected wave is determined in the way to make the reflection coefficients minimal, the value of which depends on equations. In this paper, the costruction of the boundary conditions is illustrated and CA is found, numerical results are presented to illustrate the effectiveness of the boundary conditions.
  • 论文
    Periodicity in a "Food-limited" Population Model with Toxicants and Time Delays
    Meng FAN, Ke WANG
    Acta Mathematicae Applicatae Sinica(English Series). 2002, 18(2): 309-314.
    Abstract ( )    Download PDF ( )   Knowledge map   Save
    With the help of a continuation theorem based on Gaines and Mawhin's coincidence degree, we study the global existence of positive periodic solutions of a "food-limited population model with toxicants and time delays. Some new results are obtained.
  • Original Articles
    Periodicity in a "Food-limited" Population Model with Toxicants and Time Delays
    Meng FAN, Ke WANG
    Acta Mathematicae Applicatae Sinica(English Series). 2002, 18(2): 309-314.
    Abstract ( )    Download PDF ( )   Knowledge map   Save
    With the help of a continuation theorem based on Gaines and Mawhin's coincidence degree, we study the global existence of positive periodic solutions of a "food-limited population model with toxicants and time delays. Some new results are obtained.
  • 论文
    Isochronous Centers and Isochronous Functions
    Li Jun YANG
    Acta Mathematicae Applicatae Sinica(English Series). 2002, 18(2): 315-324.
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    We study isochronous centers of two classes of planar systems of ordinary differential equations. For the first class which is the Liénard systems of the form x=y-F(x), y=-g(x) with a center at the origin, we prove that if g is isochronous (see Definition 1.1), then the center is isochronous if and only if F=0. For the second class which is the Hamiltonian systems of the form x=-g(y), y=f(x) with a center at the origin, we prove that if f or g is isochronous, then the center is isochronous if and only if the other is also isochronous.
  • Original Articles
    Isochronous Centers and Isochronous Functions
    Li Jun YANG
    Acta Mathematicae Applicatae Sinica(English Series). 2002, 18(2): 315-324.
    Abstract ( )    Download PDF ( )   Knowledge map   Save
    We study isochronous centers of two classes of planar systems of ordinary differential equations. For the first class which is the Liénard systems of the form x=y-F(x), y=-g(x) with a center at the origin, we prove that if g is isochronous (see Definition 1.1), then the center is isochronous if and only if F=0. For the second class which is the Hamiltonian systems of the form x=-g(y), y=f(x) with a center at the origin, we prove that if f or g is isochronous, then the center is isochronous if and only if the other is also isochronous.
  • 论文
    Sufficient Conditions for the Oscillation of Non-autonomous Difference Equations
    Qiong MENG, Ju Rang YAN
    Acta Mathematicae Applicatae Sinica(English Series). 2002, 18(2): 325-332.
    Abstract ( )    Download PDF ( )   Knowledge map   Save
    In this paper, we obtain sufficient conditions for the oscillation of the non-autonomous difference equations x(n+1)-x(n)+∑ from (i=1) to m of pi(n)x(n-τ_i)(n)=0,which are the discrete analog of the delay differential equations considered in [1].
  • Original Articles
    Sufficient Conditions for the Oscillation of Non-autonomous Difference Equations
    Qiong MENG, Ju Rang YAN
    Acta Mathematicae Applicatae Sinica(English Series). 2002, 18(2): 325-332.
    Abstract ( )    Download PDF ( )   Knowledge map   Save
    In this paper, we obtain sufficient conditions for the oscillation of the non-autonomous difference equations x(n+1)-x(n)+∑ from (i=1) to m of pi(n)x(n-τ_i)(n)=0,which are the discrete analog of the delay differential equations considered in [1].
  • 论文
    The S~2NS Digraphs and the Cycle Linear System of a Digraph
    Jian Guo QIAN , Sheng Jjun MIAO
    Acta Mathematicae Applicatae Sinica(English Series). 2002, 18(2): 333-340.
    Abstract ( )    Download PDF ( )   Knowledge map   Save
    It is known that the study of the qualitative properties of a matrix A (which depend only on the sign pattern of A) can be turned into the study of the graph theoretical properties of the signed digraph S(A). The underlying digraph of the signed digraph of a strong sign nonsingular matrix (abbreviated S~2NS matrix) with a negative main diagonal is called an S~2NS digraph. In the study of S~2NS digraphs, the minimal forbidden configuration (or MFC for short) plays an important role. Three (classes of) MFS's were constructed by Thomassen, Brualdi and Shader, and Shao. In this paper, we show that a digraph D is an S2NS digraph if and only if its "cycle linear system" is solvable. This simplifies a parallel result obtained by Shao and Hu. As an application of the result, a graph theoretical characterization for a digraph to be an S~2NS digraph is given. At the end of the paper, we construct infinitely many new MFCs to show that for each even number k(k>0), there are basic MFCs with k terminal components (here, with no loss of generality, we assume that the number of the initial components of a digraph is no less than that of its terminal components throughout the following).
  • Original Articles
    The S~2NS Digraphs and the Cycle Linear System of a Digraph
    Jian Guo QIAN , Sheng Jjun MIAO
    Acta Mathematicae Applicatae Sinica(English Series). 2002, 18(2): 333-340.
    Abstract ( )    Download PDF ( )   Knowledge map   Save
    It is known that the study of the qualitative properties of a matrix A (which depend only on the sign pattern of A) can be turned into the study of the graph theoretical properties of the signed digraph S(A). The underlying digraph of the signed digraph of a strong sign nonsingular matrix (abbreviated S~2NS matrix) with a negative main diagonal is called an S~2NS digraph. In the study of S~2NS digraphs, the minimal forbidden configuration (or MFC for short) plays an important role. Three (classes of) MFS's were constructed by Thomassen, Brualdi and Shader, and Shao. In this paper, we show that a digraph D is an S2NS digraph if and only if its "cycle linear system" is solvable. This simplifies a parallel result obtained by Shao and Hu. As an application of the result, a graph theoretical characterization for a digraph to be an S~2NS digraph is given. At the end of the paper, we construct infinitely many new MFCs to show that for each even number k(k>0), there are basic MFCs with k terminal components (here, with no loss of generality, we assume that the number of the initial components of a digraph is no less than that of its terminal components throughout the following).
  • 论文
    The Existence of Solutions to Sturm-Liouville Boundary Value Problems with Laplacian-like Operator
    Wei Ping SUN , Wei Gao GE
    Acta Mathematicae Applicatae Sinica(English Series). 2002, 18(2): 341-348.
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    The existence of infinitely many solutions to Sturm-Liouville boundary value problem with a Laplacian-like operator is studied by applying generalized polar coordinates.
  • Original Articles
    The Existence of Solutions to Sturm-Liouville Boundary Value Problems with Laplacian-like Operator
    Wei Ping SUN , Wei Gao GE
    Acta Mathematicae Applicatae Sinica(English Series). 2002, 18(2): 341-348.
    Abstract ( )    Download PDF ( )   Knowledge map   Save
    The existence of infinitely many solutions to Sturm-Liouville boundary value problem with a Laplacian-like operator is studied by applying generalized polar coordinates.
  • 论文
    Minimal Martingale Measures for Discrete-time Incomplete Financial Markets
    Ping LI, Jian Ming XIA
    Acta Mathematicae Applicatae Sinica(English Series). 2002, 18(2): 349-352.
    Abstract ( )    Download PDF ( )   Knowledge map   Save
    In this note, we give a characterization of the minimal martingale measure for a general discrete-time incomplete financial market. Then we concretely work out the minimal martingale measure for a specific discrete-time market model in which the assets' returns in different times are independent.
  • Original Articles
    Minimal Martingale Measures for Discrete-time Incomplete Financial Markets
    Ping LI, Jian Ming XIA
    Acta Mathematicae Applicatae Sinica(English Series). 2002, 18(2): 349-352.
    Abstract ( )    Download PDF ( )   Knowledge map   Save
    In this note, we give a characterization of the minimal martingale measure for a general discrete-time incomplete financial market. Then we concretely work out the minimal martingale measure for a specific discrete-time market model in which the assets' returns in different times are independent.
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