中国科学院数学与系统科学研究院期刊网

2002年, 第18卷, 第3期　刊出日期：2002-03-15
  

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    Original Articles
  • Asymptotic Properties of Solutions of Parabolic Equations Arising from Transient Diffusions
    A.M.Il'in , R. Z.Khasminskii , G.Yin
    应用数学学报(英文版). 2002, 18(3): 353-364.
    摘要 ( ) PDF全文 ( )   可视化   收藏
    This work is concerned with asymptotic properties of a class of parabolic systems arising from singularly perturbed diffusions. The underlying system has a fast varying component and a slowly changing component. One of the distinct features is that the fast varying diffusion is transient. Under such a setup, this paper presents an asymptotic analysis of the solutions of such parabolic equations. Asymptotic expansions of functional satisfying the parabolic system are obtained. Error bounds are derived.
    • 论文
  • Asymptotic Properties of Solutions of Parabolic Equations Arising from Transient Diffusions
    A.M.Il'in , R. Z.Khasminskii , G.Yin
    应用数学学报(英文版). 2002, 18(3): 353-364.
    摘要 ( ) PDF全文 ( )   可视化   收藏
    This work is concerned with asymptotic properties of a class of parabolic systems arising from singularly perturbed diffusions. The underlying system has a fast varying component and a slowly changing component. One of the distinct features is that the fast varying diffusion is transient. Under such a setup, this paper presents an asymptotic analysis of the solutions of such parabolic equations. Asymptotic expansions of functional satisfying the parabolic system are obtained. Error bounds are derived.
    • Original Articles
  • Some Oscillatory Singular Integrals on Herz-type Spaces (II)
    Gary Sampson, Jing Shi XU, Da Chun YANG
    应用数学学报(英文版). 2002, 18(3): 365-376.
    摘要 ( ) PDF全文 ( )   可视化   收藏
    In this paper, the authors prove that some oscillatory singular integral operators of non-convolution type with non-polynomial phases are bounded from the Herz-type Hardy spaces to the Herz spaces and from the Hardy spaces associated with the Beurling algebras to the Beurling algebras in higher dimensions, even though it is well-known that these operators are not bounded from the Hardy spaces H~1(R~n) into the Lebesgue space L~1 (R~n).
    • 论文
  • Some Oscillatory Singular Integrals on Herz-type Spaces (II)
    Gary Sampson, Jing Shi XU, Da Chun YANG
    应用数学学报(英文版). 2002, 18(3): 365-376.
    摘要 ( ) PDF全文 ( )   可视化   收藏
    In this paper, the authors prove that some oscillatory singular integral operators of non-convolution type with non-polynomial phases are bounded from the Herz-type Hardy spaces to the Herz spaces and from the Hardy spaces associated with the Beurling algebras to the Beurling algebras in higher dimensions, even though it is well-known that these operators are not bounded from the Hardy spaces H~1(R~n) into the Lebesgue space L~1 (R~n).
  • An Adaptive Neural Network Model for Nonlinear Programming Problems
    Xiang Sun ZHANG ;Xin Jian ZHUO;Zhu Jun JING
    应用数学学报(英文版). 2002, 18(3): 377-388.
    摘要 ( ) PDF全文 ( )   可视化   收藏
    In this paper a canonicalneural network with adaptively changing synaptic weights and activation function parameters is presented to solve general nonlinear programming problems. The basic part of the model is a sub-network used to find a solution of quadratic programming problems with simple upper and lower bounds. By sequentially activating the sub-network under the control of an external computer or a special analog or digital processor that adjusts the weights and parameters, one then solves general nonlinear programming problems. Convergence proof and numerical results are given.
    • Original Articles
  • An Adaptive Neural Network Model for Nonlinear Programming Problems
    Xiang Sun ZHANG ;Xin Jian ZHUO;Zhu Jun JING
    应用数学学报(英文版). 2002, 18(3): 377-388.
    摘要 ( ) PDF全文 ( )   可视化   收藏
    In this paper a canonicalneural network with adaptively changing synaptic weights and activation function parameters is presented to solve general nonlinear programming problems. The basic part of the model is a sub-network used to find a solution of quadratic programming problems with simple upper and lower bounds. By sequentially activating the sub-network under the control of an external computer or a special analog or digital processor that adjusts the weights and parameters, one then solves general nonlinear programming problems. Convergence proof and numerical results are given.
  • The Alternating-Direction Schemes and Numerical Analysis for the Three-dimensional Seawater Intrusion Simulation
    Zhi Yue ZHANG
    应用数学学报(英文版). 2002, 18(3): 389-404.
    摘要 ( ) PDF全文 ( )   可视化   收藏
    Both numerical simulation and theoretical analysis of seawater intrusion in coastal regions are of great theoretical importance in environmental sciences. The mathematical model can be described as a coupled system of three dimensional nonlinear partial differential equations with initial-boundary value problems. In this paper, according to the actual conditions of molecular and three-dimensional characteristics of the problem, we construct the characteristic finite element alternating-direction schemes which can be divided into three continuous one-dimensional problems. By making use of tensor product algorithm, and priori estimation theory and techniques, the optimal order estimates in H~1 norm are derived for the error in the approximate solution.
    • 论文
  • The Alternating-Direction Schemes and Numerical Analysis for the Three-dimensional Seawater Intrusion Simulation
    Zhi Yue ZHANG
    应用数学学报(英文版). 2002, 18(3): 389-404.
    摘要 ( ) PDF全文 ( )   可视化   收藏
    Both numerical simulation and theoretical analysis of seawater intrusion in coastal regions are of great theoretical importance in environmental sciences. The mathematical model can be described as a coupled system of three dimensional nonlinear partial differential equations with initial-boundary value problems. In this paper, according to the actual conditions of molecular and three-dimensional characteristics of the problem, we construct the characteristic finite element alternating-direction schemes which can be divided into three continuous one-dimensional problems. By making use of tensor product algorithm, and priori estimation theory and techniques, the optimal order estimates in H~1 norm are derived for the error in the approximate solution.
  • Some New Reductions From a Lax Integrable System
    En Gui FAN
    应用数学学报(英文版). 2002, 18(3): 405-410.
    摘要 ( ) PDF全文 ( )   可视化   收藏
    An isospectral problem with four potential is discussed. The corresponding hierarchy of Lax integrable evolution equations is derived. For the hierarchy, it is shown that there exist other new reductions except those presented by Tu, Meng and Ma. For each reduction case the relevant Hamiltonian structure is established by means of trace identity.
    • Original Articles
  • Some New Reductions From a Lax Integrable System
    En Gui FAN
    应用数学学报(英文版). 2002, 18(3): 405-410.
    摘要 ( ) PDF全文 ( )   可视化   收藏
    An isospectral problem with four potential is discussed. The corresponding hierarchy of Lax integrable evolution equations is derived. For the hierarchy, it is shown that there exist other new reductions except those presented by Tu, Meng and Ma. For each reduction case the relevant Hamiltonian structure is established by means of trace identity.
    • 论文
  • Permanence in Nonautonomous Predator-prey Lotka-Voterra Systems
    Wu Jun SUN ;Zhi Dong TENG ;Yuan Hong YU
    应用数学学报(英文版). 2002, 18(3): 411-422.
    摘要 ( ) PDF全文 ( )   可视化   收藏
    In this paper some easily verifiable sufficient conditions on the permanence of solutions for general nonautonomous two-species predator-prey model are established. These new criteria improve and extend the results given by Ma, Wang, Teng and Ten, Yu
    • Original Articles
  • Permanence in Nonautonomous Predator-prey Lotka-Voterra Systems
    Wu Jun SUN ;Zhi Dong TENG ;Yuan Hong YU
    应用数学学报(英文版). 2002, 18(3): 411-422.
    摘要 ( ) PDF全文 ( )   可视化   收藏
    In this paper some easily verifiable sufficient conditions on the permanence of solutions for general nonautonomous two-species predator-prey model are established. These new criteria improve and extend the results given by Ma, Wang, Teng and Ten, Yu
    • 论文
  • Optimal Harvesting and Stability for a Predator-prey System with Stage Structure
    Xin Yu SONG, Lan Sun CHEN
    应用数学学报(英文版). 2002, 18(3): 423-430.
    摘要 ( ) PDF全文 ( )   可视化   收藏
    The dynamics of a predator-prey system, where prey population has two stages, an immature stage and a mature stage with harvesting, the growth of predator population is of Lotka-Volterra nature, are modelled by a system of retarded functional differential equations. We obtain conditions for global asymptotic stability of three nonnegative equilibria and a threshold of harvesting for the mature prey population. The effect of delay on the population at positive equilibrium and the optimal harvesting of the mature prey population are also considered.
    • Original Articles
  • Optimal Harvesting and Stability for a Predator-prey System with Stage Structure
    Xin Yu SONG, Lan Sun CHEN
    应用数学学报(英文版). 2002, 18(3): 423-430.
    摘要 ( ) PDF全文 ( )   可视化   收藏
    The dynamics of a predator-prey system, where prey population has two stages, an immature stage and a mature stage with harvesting, the growth of predator population is of Lotka-Volterra nature, are modelled by a system of retarded functional differential equations. We obtain conditions for global asymptotic stability of three nonnegative equilibria and a threshold of harvesting for the mature prey population. The effect of delay on the population at positive equilibrium and the optimal harvesting of the mature prey population are also considered.
    • 论文
  • Construction and Dimension Analysis for a Class of Fractal Functions
    Hong Yong WANG, Zong Ben XU
    应用数学学报(英文版). 2002, 18(3): 431-440.
    摘要 ( ) PDF全文 ( )   可视化   收藏
    In this paper, we construct a class of nowhere differentiable continuous functions by means of the Cantor series expression of real numbers. The constructed functions include some known nondifferentiable functions, such as Bush type functions. These functions are fractal functions since their graphs are in general fractal sets. Under certain conditions, we investigate the fractal dimensions of the graphs of these functions, compute the precise values of Box and Packing dimensions, and evaluate the Hausdorff dimension. Meanwhile, the H?lder continuity of such functions is also discussed.
    • Original Articles
  • Construction and Dimension Analysis for a Class of Fractal Functions
    Hong Yong WANG, Zong Ben XU
    应用数学学报(英文版). 2002, 18(3): 431-440.
    摘要 ( ) PDF全文 ( )   可视化   收藏
    In this paper, we construct a class of nowhere differentiable continuous functions by means of the Cantor series expression of real numbers. The constructed functions include some known nondifferentiable functions, such as Bush type functions. These functions are fractal functions since their graphs are in general fractal sets. Under certain conditions, we investigate the fractal dimensions of the graphs of these functions, compute the precise values of Box and Packing dimensions, and evaluate the Hausdorff dimension. Meanwhile, the H?lder continuity of such functions is also discussed.
    • 论文
  • Existence and Uniqueness of Endemic States for the Age-structured MSEIR Epidemic Model
    Xue Zhi LI, Geni Gupur, Guang Tian ZHU
    应用数学学报(英文版). 2002, 18(3): 441-454.
    摘要 ( ) PDF全文 ( )   可视化   收藏
    The existence and uniqueness of positive steady states for the age-structured MSEIR epidemic model with age-dependent transmission coefficient is considered. Threshold results for the existence of endemic states are established; under certain conditions, uniqueness is also shown
    • Original Articles
  • Existence and Uniqueness of Endemic States for the Age-structured MSEIR Epidemic Model
    Xue Zhi LI, Geni Gupur, Guang Tian ZHU
    应用数学学报(英文版). 2002, 18(3): 441-454.
    摘要 ( ) PDF全文 ( )   可视化   收藏
    The existence and uniqueness of positive steady states for the age-structured MSEIR epidemic model with age-dependent transmission coefficient is considered. Threshold results for the existence of endemic states are established; under certain conditions, uniqueness is also shown
  • On the Convergence Rate of a Space Decomposition Method
    Shu Ri ZHOU, Jin Ping ZENG, Gui Hua SHAN
    应用数学学报(英文版). 2002, 18(3): 455-460.
    摘要 ( ) PDF全文 ( )   可视化   收藏
    Domain decomposition method and multigrid method can be unified in the framework of the space decomposition method. This paper has obtained a new result on the convergence rate of the space decomposition method, which can be applied to some nonuniformly elliptic problems.
    • 论文
  • On the Convergence Rate of a Space Decomposition Method
    Shu Ri ZHOU, Jin Ping ZENG, Gui Hua SHAN
    应用数学学报(英文版). 2002, 18(3): 455-460.
    摘要 ( ) PDF全文 ( )   可视化   收藏
    Domain decomposition method and multigrid method can be unified in the framework of the space decomposition method. This paper has obtained a new result on the convergence rate of the space decomposition method, which can be applied to some nonuniformly elliptic problems.
    • Original Articles
  • Stability of Solution of a Class of Quasilinear Elliptic Equations
    Qi Kang RAN, Ai Nong FANG
    应用数学学报(英文版). 2002, 18(3): 461-470.
    摘要 ( ) PDF全文 ( )   可视化   收藏
    In this paper, using capacity theory and extension theorem of Lipschitz functions we first discuss the uniqueness of weak solution of nonhomogeneous quasilinear elliptic equations mdiv Ap (x, u) + ap (x, u) = f (x) in space W (/, p)(Q), which is bigger than W(/, p)(Q). Next, using revise reverse H?lder inequality we prove that if Pc is uniformly p-think, then there exists a neighborhood U of p, such that for all t ] U, the weak solutions of equation corresponding t are bounded uniformly. Finally, we get the stability of weak solutions on exponent p.
    • 论文
  • Stability of Solution of a Class of Quasilinear Elliptic Equations
    Qi Kang RAN, Ai Nong FANG
    应用数学学报(英文版). 2002, 18(3): 461-470.
    摘要 ( ) PDF全文 ( )   可视化   收藏
    In this paper, using capacity theory and extension theorem of Lipschitz functions we first discuss the uniqueness of weak solution of nonhomogeneous quasilinear elliptic equations mdiv Ap (x, u) + ap (x, u) = f (x) in space W (/, p)(Q), which is bigger than W(/, p)(Q). Next, using revise reverse H?lder inequality we prove that if Pc is uniformly p-think, then there exists a neighborhood U of p, such that for all t ] U, the weak solutions of equation corresponding t are bounded uniformly. Finally, we get the stability of weak solutions on exponent p.
  • Digraphs and Inclusion Intervals of Brualdi-type for Singular Values
    Jiong Sheng LI, Kai YANG, Qing Xue WANG
    应用数学学报(英文版). 2002, 18(3): 471-476.
    摘要 ( ) PDF全文 ( )   可视化   收藏
    A complex matrix A is said to be a matrix realization of the digraph D if D is the associated digraph of A, and A is said to have the property B if every singular value of A is contained in the union of Brualdi-type intervals. A digraph D is said to be a forcible B-digraph if every matrix realization of D has the property B. In this paper, we give a sufficient condition for a matrix to have the property B and characterize the forcible B-digraphs.
    • Original Articles
  • Digraphs and Inclusion Intervals of Brualdi-type for Singular Values
    Jiong Sheng LI, Kai YANG, Qing Xue WANG
    应用数学学报(英文版). 2002, 18(3): 471-476.
    摘要 ( ) PDF全文 ( )   可视化   收藏
    A complex matrix A is said to be a matrix realization of the digraph D if D is the associated digraph of A, and A is said to have the property B if every singular value of A is contained in the union of Brualdi-type intervals. A digraph D is said to be a forcible B-digraph if every matrix realization of D has the property B. In this paper, we give a sufficient condition for a matrix to have the property B and characterize the forcible B-digraphs.
  • On the Monotonicity of (k;g,h)-graphs
    Bao Guang XU, Ping WANG, Jian Fang WANG
    应用数学学报(英文版). 2002, 18(3): 477-480.
    摘要 ( ) PDF全文 ( )   可视化   收藏
    A (k;g)-graph is a k-regular graph with girth g. A (k;g)-cage is a (k;g)-graph with the least possible number of vertices. Let f (k;g) denote the number of vertices in a (k;g)-cage. The girth pair of a graph gives the length of a shortest odd and a shortest even cycle. A k-regular graph with girth pair (g,h) is called a (k;g,h)-graph. A (k;g,h)-cage is a (k;g,h)-graph with the least possible number of vertices. Let f(k;g,h) denote the number of vertices in a (k;g,h)-cage. In this paper, we prove the following strict inequality f (k;h-1,h)
    • 论文
  • On the Monotonicity of (k;g,h)-graphs
    Bao Guang XU, Ping WANG, Jian Fang WANG
    应用数学学报(英文版). 2002, 18(3): 477-480.
    摘要 ( ) PDF全文 ( )   可视化   收藏
    A (k;g)-graph is a k-regular graph with girth g. A (k;g)-cage is a (k;g)-graph with the least possible number of vertices. Let f (k;g) denote the number of vertices in a (k;g)-cage. The girth pair of a graph gives the length of a shortest odd and a shortest even cycle. A k-regular graph with girth pair (g,h) is called a (k;g,h)-graph. A (k;g,h)-cage is a (k;g,h)-graph with the least possible number of vertices. Let f(k;g,h) denote the number of vertices in a (k;g,h)-cage. In this paper, we prove the following strict inequality f (k;h-1,h)
  • A Class of Multiderivative Hybrid One-step Methods
    Feng Jian YANG;Xin Ming CHEN, Ai Guo ZHANG
    应用数学学报(英文版). 2002, 18(3): 481-488.
    摘要 ( ) PDF全文 ( )   可视化   收藏
    This paper presents a class of hybrid one-step methods that are obtained by using Cramer's rule and rational approximation to function exp(q). The algorithms fall into the catalogue of implicit formula, which involves sth order derivative and s+1 free parameters. The order of the algorithms satisfies s+1hph2s+2. The stability of the methods is also studied, necessary and sufficient conditions for A-stability and L-stability are given. In addition, some examples are also given to demonstrate the method presented.
    • Original Articles
  • A Class of Multiderivative Hybrid One-step Methods
    Feng Jian YANG;Xin Ming CHEN, Ai Guo ZHANG
    应用数学学报(英文版). 2002, 18(3): 481-488.
    摘要 ( ) PDF全文 ( )   可视化   收藏
    This paper presents a class of hybrid one-step methods that are obtained by using Cramer's rule and rational approximation to function exp(q). The algorithms fall into the catalogue of implicit formula, which involves sth order derivative and s+1 free parameters. The order of the algorithms satisfies s+1hph2s+2. The stability of the methods is also studied, necessary and sufficient conditions for A-stability and L-stability are given. In addition, some examples are also given to demonstrate the method presented.
    • 论文
  • Randomly Orthogonal (g,f)-factorizations in Graphs
    Gui Zheng LIU, He Ping LONG
    应用数学学报(英文版). 2002, 18(3): 489-494.
    摘要 ( ) PDF全文 ( )   可视化   收藏
    Let G be a graph with vertex set V(G) and edge set E(G) and let g and f be two integer-valued functions defined on V(G) such that 2k m 2 h f(x) for all x ] V(G). Let H be a subgraph of G with mk edges. In this paper it is proved that every (mg + m m 1,mf m m + 1)-graph G has (g,f)-factorizations randomly k-orthogonal to H and shown that the result is best possible.
    • Original Articles
  • Randomly Orthogonal (g,f)-factorizations in Graphs
    Gui Zheng LIU, He Ping LONG
    应用数学学报(英文版). 2002, 18(3): 489-494.
    摘要 ( ) PDF全文 ( )   可视化   收藏
    Let G be a graph with vertex set V(G) and edge set E(G) and let g and f be two integer-valued functions defined on V(G) such that 2k m 2 h f(x) for all x ] V(G). Let H be a subgraph of G with mk edges. In this paper it is proved that every (mg + m m 1,mf m m + 1)-graph G has (g,f)-factorizations randomly k-orthogonal to H and shown that the result is best possible.
  • The Approximation Theorem of Convolution Operator in Δ~p Set-valued Function Space
    Pei Xin YE
    应用数学学报(英文版). 2002, 18(3): 495-500.
    摘要 ( ) PDF全文 ( )   可视化   收藏
    The paper is a contribution to the problem of approximating random set with values in a separable Banach space. This class of set-valued function is widely used in many areas. We investigate the properties of p-bounded integrable random set. Based on this we endow it with Δ~p metric which can be viewed as a integral type hausdorff metric and present some approximation theorem of a class of convolution operators with respect to Δ~p metric. Moreover we also can establish analogous theorem for other integral type operator in Δ~p space.
    • 论文
  • The Approximation Theorem of Convolution Operator in Δ~p Set-valued Function Space
    Pei Xin YE
    应用数学学报(英文版). 2002, 18(3): 495-500.
    摘要 ( ) PDF全文 ( )   可视化   收藏
    The paper is a contribution to the problem of approximating random set with values in a separable Banach space. This class of set-valued function is widely used in many areas. We investigate the properties of p-bounded integrable random set. Based on this we endow it with Δ~p metric which can be viewed as a integral type hausdorff metric and present some approximation theorem of a class of convolution operators with respect to Δ~p metric. Moreover we also can establish analogous theorem for other integral type operator in Δ~p space.
    • Original Articles
  • Bifurcation and Chaos in a Weakly Nonlinear System Subjected to Combined Parametric and External Excitation
    Wei LI, Peng Cheng XU
    应用数学学报(英文版). 2002, 18(3): 501-512.
    摘要 ( ) PDF全文 ( )   可视化   收藏
    In this paper the dynamics of a weakly nonlinear system subjected to combined parametric and external excitation are discussed. The existence of transversal homoclinic orbits resulting in chaotic dynamics and bifurcation are established by using the averaging method and Melnikov method. Numerical simulations are also provided to demonstrate the theoretical analysis.
    • 论文
  • Bifurcation and Chaos in a Weakly Nonlinear System Subjected to Combined Parametric and External Excitation
    Wei LI, Peng Cheng XU
    应用数学学报(英文版). 2002, 18(3): 501-512.
    摘要 ( ) PDF全文 ( )   可视化   收藏
    In this paper the dynamics of a weakly nonlinear system subjected to combined parametric and external excitation are discussed. The existence of transversal homoclinic orbits resulting in chaotic dynamics and bifurcation are established by using the averaging method and Melnikov method. Numerical simulations are also provided to demonstrate the theoretical analysis.
  • Multiplicity of Periodic Solutions of Duffing Equations with Jumping Nonlinearities
    Zai Hong WANG
    应用数学学报(英文版). 2002, 18(3): 513-522.
    摘要 ( ) PDF全文 ( )   可视化   收藏
    We provide sufficient conditions for the existence and multiplicity of subharmonic solutions for Duffing's equations with jumping nonlinearities.
    • Original Articles
  • Multiplicity of Periodic Solutions of Duffing Equations with Jumping Nonlinearities
    Zai Hong WANG
    应用数学学报(英文版). 2002, 18(3): 513-522.
    摘要 ( ) PDF全文 ( )   可视化   收藏
    We provide sufficient conditions for the existence and multiplicity of subharmonic solutions for Duffing's equations with jumping nonlinearities.
    • 论文
  • Existence of Nonnegative Solutions to Singular Semi-positone Problems
    Hong Zhou WANG, Li Hu DENG, Wei Gao GE
    应用数学学报(英文版). 2002, 18(3): 523-528.
    摘要 ( ) PDF全文 ( )   可视化   收藏
    In this paper we study a class of semi-positone singular boundary value problem. With prior bounds estimate and topology degree method, some existence results of nonnegative solution will be shown.
    • Original Articles
  • Existence of Nonnegative Solutions to Singular Semi-positone Problems
    Hong Zhou WANG, Li Hu DENG, Wei Gao GE
    应用数学学报(英文版). 2002, 18(3): 523-528.
    摘要 ( ) PDF全文 ( )   可视化   收藏
    In this paper we study a class of semi-positone singular boundary value problem. With prior bounds estimate and topology degree method, some existence results of nonnegative solution will be shown.
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