15 April 2002, Volume 18 Issue 4
    

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  • 论文
    Convergence of a Stochastic Method for the Modeling of Polymeric Fluids
    Weinan E, Tie Jun LI, Ping wen zhang
    Acta Mathematicae Applicatae Sinica(English Series). 2002, 18(4): 529-536.
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    We present a convergence analysis of a stochastic method for numerical modeling of complex fluids using Brownian configuration fields (BCF) for shear flows. The analysis takes into account the special structure of the stochastic partial differential equations for shear flows. We establish the optimal rate of convergence. We also analyze the nature of the error by providing its leading order asymptotics.
  • Original Articles
    Convergence of a Stochastic Method for the Modeling of Polymeric Fluids
    Weinan E, Tie Jun LI, Ping wen zhang
    Acta Mathematicae Applicatae Sinica(English Series). 2002, 18(4): 529-536.
    Abstract ( )    Download PDF ( )   Knowledge map   Save
    We present a convergence analysis of a stochastic method for numerical modeling of complex fluids using Brownian configuration fields (BCF) for shear flows. The analysis takes into account the special structure of the stochastic partial differential equations for shear flows. We establish the optimal rate of convergence. We also analyze the nature of the error by providing its leading order asymptotics.
  • 论文
    Markov Skeleton Processes and Applications to Queueing Systems
    Zhen Ting HOU
    Acta Mathematicae Applicatae Sinica(English Series). 2002, 18(4): 537-552.
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    In this paper, we apply the backward equations of Markov skeleton processes to queueing systems. The transient distribution of the waiting time of a G1/G/1 queueing system, the transient distribution of the length of a G1/G/N queueing system and the transient distribution of the length of queueing networks are obtained.
  • Original Articles
    Markov Skeleton Processes and Applications to Queueing Systems
    Zhen Ting HOU
    Acta Mathematicae Applicatae Sinica(English Series). 2002, 18(4): 537-552.
    Abstract ( )    Download PDF ( )   Knowledge map   Save
    In this paper, we apply the backward equations of Markov skeleton processes to queueing systems. The transient distribution of the waiting time of a G1/G/1 queueing system, the transient distribution of the length of a G1/G/N queueing system and the transient distribution of the length of queueing networks are obtained.
  • 论文
    Linear Volterra Integral Equations
    M Federson, R Bianconi, L Barbanti
    Acta Mathematicae Applicatae Sinica(English Series). 2002, 18(4): 553-560.
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    The Kurzweil-Henstock integral formalism is applied to establish the existence of solutions to the linear integral equations of Volterra-type x(t)=~*∫_([a,t]) α(s)x(s)ds=f(t), t∈[a,b], where the functions are Banach-space valued. Special theorems on existence of solutions concerning the Lebesgue integral setting are obtained. These sharpen earlier results.
  • Original Articles
    Linear Volterra Integral Equations
    M Federson, R Bianconi, L Barbanti
    Acta Mathematicae Applicatae Sinica(English Series). 2002, 18(4): 553-560.
    Abstract ( )    Download PDF ( )   Knowledge map   Save
    The Kurzweil-Henstock integral formalism is applied to establish the existence of solutions to the linear integral equations of Volterra-type x(t)=~*∫_([a,t]) α(s)x(s)ds=f(t), t∈[a,b], where the functions are Banach-space valued. Special theorems on existence of solutions concerning the Lebesgue integral setting are obtained. These sharpen earlier results.
  • Original Articles
    Generalized Steiner Triple systems with Group Size g≡0, 3 (mod 6)
    Gen Nian GE
    Acta Mathematicae Applicatae Sinica(English Series). 2002, 18(4): 561-568.
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    Generalized Steiner triple systems, (GS(2,3,n,g), are equivalent to maximum constant weight codes over an alphabet of size g+1 with distance 3 and weight 3 in which each codeword has length n. The necessary conditions for the existence of a GS(2,3,n,g) are (nm1)gL0 (mod 2), n(nm1)g~2≡0 (mod 6), and n≥g+2. These necessary conditions are shown to be sufficient by several authors for 2≤g≤11. In this paper, three new results are obtained. First, it is shown that for any given g, gL0 (mod 6) and g≥12, if there exists a GS(2,3,n,g) for all n, g+2≤n≤7g+13, then the necessary conditions are also sufficient. Next, it is also shown that for any given g, gL3 (mod 6) and g≥15, if there exists a GS(2,3,n,g) for all n, nL1 (mod 2) and g+2≤n≤7g+6, then the necessary conditions are also sufficient. Finally, as an application, it is proved that the necessary conditions for the existence of a GS(2,3,n,g) are also sufficient for g=12,15.
  • 论文
    Generalized Steiner Triple systems with Group Size g≡0, 3 (mod 6)
    Gen Nian GE
    Acta Mathematicae Applicatae Sinica(English Series). 2002, 18(4): 561-568.
    Abstract ( )    Download PDF ( )   Knowledge map   Save
    Generalized Steiner triple systems, (GS(2,3,n,g), are equivalent to maximum constant weight codes over an alphabet of size g+1 with distance 3 and weight 3 in which each codeword has length n. The necessary conditions for the existence of a GS(2,3,n,g) are (nm1)gL0 (mod 2), n(nm1)g~2≡0 (mod 6), and n≥g+2. These necessary conditions are shown to be sufficient by several authors for 2≤g≤11. In this paper, three new results are obtained. First, it is shown that for any given g, gL0 (mod 6) and g≥12, if there exists a GS(2,3,n,g) for all n, g+2≤n≤7g+13, then the necessary conditions are also sufficient. Next, it is also shown that for any given g, gL3 (mod 6) and g≥15, if there exists a GS(2,3,n,g) for all n, nL1 (mod 2) and g+2≤n≤7g+6, then the necessary conditions are also sufficient. Finally, as an application, it is proved that the necessary conditions for the existence of a GS(2,3,n,g) are also sufficient for g=12,15.
  • 论文
    On Eigenvalue Intervals and Eigenfunctions of Nonresonance Singular Dirichlet Boundary Value Problems
    Zhao Cai HAO
    Acta Mathematicae Applicatae Sinica(English Series). 2002, 18(4): 569-578.
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    In this paper we shall consider the nonresonance Dirichlet boundary value problem {-x'' + ρp(t)x = λf(t,x), t∈(0, 1), x(0)=x(1)=0, where λ>0 is a parameter, ρ>0 is a constant. Intervals of 5 are determined to ensure the existence of a nonnegative solution of the boundary value problem. For λ=1, we shall also offer criteria for the existence of eigenfunctions. The main results include and improve on those of [2,4,6,8].
  • Original Articles
    On Eigenvalue Intervals and Eigenfunctions of Nonresonance Singular Dirichlet Boundary Value Problems
    Zhao Cai HAO
    Acta Mathematicae Applicatae Sinica(English Series). 2002, 18(4): 569-578.
    Abstract ( )    Download PDF ( )   Knowledge map   Save
    In this paper we shall consider the nonresonance Dirichlet boundary value problem {-x'' + ρp(t)x = λf(t,x), t∈(0, 1), x(0)=x(1)=0, where λ>0 is a parameter, ρ>0 is a constant. Intervals of 5 are determined to ensure the existence of a nonnegative solution of the boundary value problem. For λ=1, we shall also offer criteria for the existence of eigenfunctions. The main results include and improve on those of [2,4,6,8].
  • Original Articles
    Well-posedness and Global Attractors for the Burgers-Ginzburg-Landau Equations
    Bo Ling GUO, Hai Yang HUANG
    Acta Mathematicae Applicatae Sinica(English Series). 2002, 18(4): 579-588.
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    In this paper we consider the Burger-Ginzburg-Landau equations, and prove the existence of the global attractor in H_0~n*H~n, A_n≥0, with finite Hausdorff and fractal dimensions
  • 论文
    Well-posedness and Global Attractors for the Burgers-Ginzburg-Landau Equations
    Bo Ling GUO, Hai Yang HUANG
    Acta Mathematicae Applicatae Sinica(English Series). 2002, 18(4): 579-588.
    Abstract ( )    Download PDF ( )   Knowledge map   Save
    In this paper we consider the Burger-Ginzburg-Landau equations, and prove the existence of the global attractor in H_0~n*H~n, A_n≥0, with finite Hausdorff and fractal dimensions
  • 论文
    On Boundary Stability of Wave Equations with Variable Coefficients
    Yu Xia GUO, Peng Fei YAO
    Acta Mathematicae Applicatae Sinica(English Series). 2002, 18(4): 589-598.
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    In this paper, we consider the boundary stabilization of the wave equation with variable coefficients by Riemannian geometry method subject to a different geometric condition which is motivated by the geometric multiplier identities. Several (multiplier) identities (inequalities) which have been built for constant wave equation by Kormornik and Zuazua~([2]) are generalized to the variable coefficient case by some computational techniques in Riemannian geometry, so that the precise estimates on the exponential decay rate are derived from those inequalities. Also, the exponential decay for the solutions of semilinear wave equation with variable coefficients is obtained under natural growth and sign assumptions on the nonlinearity. Our method is rather general and can be adapted to other evolution systems with variable coefficients (e.g. elasticity plates) as well.
  • Original Articles
    On Boundary Stability of Wave Equations with Variable Coefficients
    Yu Xia GUO, Peng Fei YAO
    Acta Mathematicae Applicatae Sinica(English Series). 2002, 18(4): 589-598.
    Abstract ( )    Download PDF ( )   Knowledge map   Save
    In this paper, we consider the boundary stabilization of the wave equation with variable coefficients by Riemannian geometry method subject to a different geometric condition which is motivated by the geometric multiplier identities. Several (multiplier) identities (inequalities) which have been built for constant wave equation by Kormornik and Zuazua~([2]) are generalized to the variable coefficient case by some computational techniques in Riemannian geometry, so that the precise estimates on the exponential decay rate are derived from those inequalities. Also, the exponential decay for the solutions of semilinear wave equation with variable coefficients is obtained under natural growth and sign assumptions on the nonlinearity. Our method is rather general and can be adapted to other evolution systems with variable coefficients (e.g. elasticity plates) as well.
  • 论文
    On the Existence of Nontrivial Solutions of Quasi-asymptotically Linear Problem for the P-Laplacian
    Zhi Hui CHEN, Yao Tian SHEN
    Acta Mathematicae Applicatae Sinica(English Series). 2002, 18(4): 599-606.
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    In this paper, we study the existence of nontrivial solutions for the following Dirichlet problem for the p-Laplacian (p>1): {-Δ_pu≡-div |▽u|~(p-2)▽u)=f(x,u), x∈Ω, u=0, x∈partial deriv Ω, where Ω is a bounded domain in R~N (N≥1) and f(x, u) is quasi-asymptotically linear with respect to |u|~(p-2) u at infinity. Recently it was proved that the above problem has a positive solution under the condition that f (x,s)/s~(p-1) is nondecreasing with respect to s for all x∈Ω and some others. In this paper, by improving the methods in the literature, we prove that the functional corresponding to the above problem still satisfies a weakened version of (P.S.) condition even if f(x,s)/s~(p-1) isn't a nondecreasing function with respect to s, and then the above problem has a nontrivial weak solution by Mountain Pass Theorem.
  • Original Articles
    On the Existence of Nontrivial Solutions of Quasi-asymptotically Linear Problem for the P-Laplacian
    Zhi Hui CHEN, Yao Tian SHEN
    Acta Mathematicae Applicatae Sinica(English Series). 2002, 18(4): 599-606.
    Abstract ( )    Download PDF ( )   Knowledge map   Save
    In this paper, we study the existence of nontrivial solutions for the following Dirichlet problem for the p-Laplacian (p>1): {-Δ_pu≡-div |▽u|~(p-2)▽u)=f(x,u), x∈Ω, u=0, x∈partial deriv Ω, where Ω is a bounded domain in R~N (N≥1) and f(x, u) is quasi-asymptotically linear with respect to |u|~(p-2) u at infinity. Recently it was proved that the above problem has a positive solution under the condition that f (x,s)/s~(p-1) is nondecreasing with respect to s for all x∈Ω and some others. In this paper, by improving the methods in the literature, we prove that the functional corresponding to the above problem still satisfies a weakened version of (P.S.) condition even if f(x,s)/s~(p-1) isn't a nondecreasing function with respect to s, and then the above problem has a nontrivial weak solution by Mountain Pass Theorem.
  • 论文
    An SIS Epidemic Model with Stage Structure and a Delay
    Yan Ni XIAO, Lan Sun CHEN
    Acta Mathematicae Applicatae Sinica(English Series). 2002, 18(4): 607-618.
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    A disease transmission model of SIS type with stage structure and a delay is formulated. Stability of the disease free equilibrium, and existence, uniqueness, and stability of an endemic equilibrium, are investigated for the model. The stability results are stated in terms of a key threshold parameter. The effects of stage structure and time delay on dynamical behavior of the infectious disease are analyzed. It is shown that stage structure has no effect on the epidemic model and Hopf bifurcation can occur as the time delay increases.
  • Original Articles
    An SIS Epidemic Model with Stage Structure and a Delay
    Yan Ni XIAO, Lan Sun CHEN
    Acta Mathematicae Applicatae Sinica(English Series). 2002, 18(4): 607-618.
    Abstract ( )    Download PDF ( )   Knowledge map   Save
    A disease transmission model of SIS type with stage structure and a delay is formulated. Stability of the disease free equilibrium, and existence, uniqueness, and stability of an endemic equilibrium, are investigated for the model. The stability results are stated in terms of a key threshold parameter. The effects of stage structure and time delay on dynamical behavior of the infectious disease are analyzed. It is shown that stage structure has no effect on the epidemic model and Hopf bifurcation can occur as the time delay increases.
  • 论文
    Nonlinear Doob-Meyer Decomposition for General Filtration
    Qing Quan LIN
    Acta Mathematicae Applicatae Sinica(English Series). 2002, 18(4): 619-624.
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    The comparison theorem for generalized backward stochastic differential equations is discussed. Some topics related to equations of this type are also investigated.
  • Original Articles
    Nonlinear Doob-Meyer Decomposition for General Filtration
    Qing Quan LIN
    Acta Mathematicae Applicatae Sinica(English Series). 2002, 18(4): 619-624.
    Abstract ( )    Download PDF ( )   Knowledge map   Save
    The comparison theorem for generalized backward stochastic differential equations is discussed. Some topics related to equations of this type are also investigated.
  • 论文
    Periodic Solutions of a Model of Mitosis in Frog Eggs
    Bei Ye FANG, Zuo Huan ZHENG
    Acta Mathematicae Applicatae Sinica(English Series). 2002, 18(4): 625-628.
    Abstract ( )    Download PDF ( )   Knowledge map   Save
    In this paper, we discuss a simplified model of mitosis in frog eggs proposed by M. T. Borisuk and J. J. Tyson in [1]. By using rigorous qualitative analysis, we prove the existence of the periodic solutions on a large scale and present the space region of the periodic solutions and the parameter region coresponding to the periodic solution. We also present the space region and the parameter region where there are no periodic solutions. The results are in accordance with the numerical results in [1] up to the qualitative property
  • Original Articles
    Periodic Solutions of a Model of Mitosis in Frog Eggs
    Bei Ye FANG, Zuo Huan ZHENG
    Acta Mathematicae Applicatae Sinica(English Series). 2002, 18(4): 625-628.
    Abstract ( )    Download PDF ( )   Knowledge map   Save
    In this paper, we discuss a simplified model of mitosis in frog eggs proposed by M. T. Borisuk and J. J. Tyson in [1]. By using rigorous qualitative analysis, we prove the existence of the periodic solutions on a large scale and present the space region of the periodic solutions and the parameter region coresponding to the periodic solution. We also present the space region and the parameter region where there are no periodic solutions. The results are in accordance with the numerical results in [1] up to the qualitative property
  • Original Articles
    Error of One-leg Methods for Singular Perturbation Problems with Delays
    Si Qing GAN, Geng SUN
    Acta Mathematicae Applicatae Sinica(English Series). 2002, 18(4): 629-640.
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    This paper is concerned with the error behavior of one-leg methods applied to some classes of one-parameter multiple stiff singularity perturbed problems with delays. We derive the global error estimates of A-stable-one-leg methods with linear interpolation procedure.
  • 论文
    Error of One-leg Methods for Singular Perturbation Problems with Delays
    Si Qing GAN, Geng SUN
    Acta Mathematicae Applicatae Sinica(English Series). 2002, 18(4): 629-640.
    Abstract ( )    Download PDF ( )   Knowledge map   Save
    This paper is concerned with the error behavior of one-leg methods applied to some classes of one-parameter multiple stiff singularity perturbed problems with delays. We derive the global error estimates of A-stable-one-leg methods with linear interpolation procedure.
  • Original Articles
    Spatial Nonparametric Regression Estimation: Non-isotropic Case
    Zu Di LU, Xing CHEN
    Acta Mathematicae Applicatae Sinica(English Series). 2002, 18(4): 641-656.
    Abstract ( )    Download PDF ( )   Knowledge map   Save
    Data collected on the surface of the earth often has spatial interaction. In this paper, a non-isotropic mixing spatial data process is introduced, and under such a spatial structure a nonparametric kernel method is suggested to estimate a spatial conditional regression. Under mild regularities, sufficient conditions are derived to ensure the weak consistency as well as the convergence rates for the kernel estimator. Of interest are the following: (1) All the conditions imposed on the mixing coefficient and the bandwidth are simple; (2) Differently from the time series setting, the bandwidth is found to be dependent on the dimension of the site in space as well; (3) For weak consistency, the mixing coefficient is allowed to be unsummable and the tendency of sample size to infinity may be in different manners along different direction in space; (4) However, to have an optimal convergence rate, faster decreasing rates of mixing coefficient and the tendency of sample size to infinity along each direction are required.
  • 论文
    Spatial Nonparametric Regression Estimation: Non-isotropic Case
    Zu Di LU, Xing CHEN
    Acta Mathematicae Applicatae Sinica(English Series). 2002, 18(4): 641-656.
    Abstract ( )    Download PDF ( )   Knowledge map   Save
    Data collected on the surface of the earth often has spatial interaction. In this paper, a non-isotropic mixing spatial data process is introduced, and under such a spatial structure a nonparametric kernel method is suggested to estimate a spatial conditional regression. Under mild regularities, sufficient conditions are derived to ensure the weak consistency as well as the convergence rates for the kernel estimator. Of interest are the following: (1) All the conditions imposed on the mixing coefficient and the bandwidth are simple; (2) Differently from the time series setting, the bandwidth is found to be dependent on the dimension of the site in space as well; (3) For weak consistency, the mixing coefficient is allowed to be unsummable and the tendency of sample size to infinity may be in different manners along different direction in space; (4) However, to have an optimal convergence rate, faster decreasing rates of mixing coefficient and the tendency of sample size to infinity along each direction are required.
  • 论文
    On Nonexistence of Algebraic Curve Solutions to Second-order Polynomial Autonomous Systems Over the Complex Field
    Zhao Sheng FENG
    Acta Mathematicae Applicatae Sinica(English Series). 2002, 18(4): 657-662.
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    In this paper, by using the method of algebraic analysis, the results in our previous work are generalized. These results are of importance in the qualitative theory of polynomial autonomous systems.
  • Original Articles
    On Nonexistence of Algebraic Curve Solutions to Second-order Polynomial Autonomous Systems Over the Complex Field
    Zhao Sheng FENG
    Acta Mathematicae Applicatae Sinica(English Series). 2002, 18(4): 657-662.
    Abstract ( )    Download PDF ( )   Knowledge map   Save
    In this paper, by using the method of algebraic analysis, the results in our previous work are generalized. These results are of importance in the qualitative theory of polynomial autonomous systems.
  • Original Articles
    The Average Widths and Non-linear Widths of the Classes of Multivariate Functions with Bounded Moduli of Smoothness
    Yong Ping LIU, Gui Qiao XU
    Acta Mathematicae Applicatae Sinica(English Series). 2002, 18(4): 663-674.
    Abstract ( )    Download PDF ( )   Knowledge map   Save
    The classes of the multivariate functions with bounded moduli on R~d and T~d are given and their average σ-widths and non-linear n-widths are discussed. The weak asymptotic behaviors are established for the corresponding quantities.
  • 论文
    The Average Widths and Non-linear Widths of the Classes of Multivariate Functions with Bounded Moduli of Smoothness
    Yong Ping LIU, Gui Qiao XU
    Acta Mathematicae Applicatae Sinica(English Series). 2002, 18(4): 663-674.
    Abstract ( )    Download PDF ( )   Knowledge map   Save
    The classes of the multivariate functions with bounded moduli on R~d and T~d are given and their average σ-widths and non-linear n-widths are discussed. The weak asymptotic behaviors are established for the corresponding quantities.
  • Original Articles
    Extension of Some Classical Results on Ruin Probability to Delayed Renewal Model
    Chun SU, Tao JIANG, Qi He TANG
    Acta Mathematicae Applicatae Sinica(English Series). 2002, 18(4): 675-680.
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    Embrechts and Veraverbeke~[2] investigated the renewal risk model and gave a tail equivalence relationship of the ruin probabilities ψ(x) under the assumption that the claim size is heavy-tailed, which is regarded as a classical result in the context of extremal value theory. In this note we extend this result to the delayed renewal risk model.
  • 论文
    Extension of Some Classical Results on Ruin Probability to Delayed Renewal Model
    Chun SU, Tao JIANG, Qi He TANG
    Acta Mathematicae Applicatae Sinica(English Series). 2002, 18(4): 675-680.
    Abstract ( )    Download PDF ( )   Knowledge map   Save
    Embrechts and Veraverbeke~[2] investigated the renewal risk model and gave a tail equivalence relationship of the ruin probabilities ψ(x) under the assumption that the claim size is heavy-tailed, which is regarded as a classical result in the context of extremal value theory. In this note we extend this result to the delayed renewal risk model.
  • 论文
    Cycles Containing a Given Arc in Regular Multipartite Tournaments
    Guo Fei ZHOU, Ke Min ZHANG
    Acta Mathematicae Applicatae Sinica(English Series). 2002, 18(4): 681-684.
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    In this paper we prove that if T is a regular n-partite tournament with n≥6, then each arc of T lies on a k-cycle for k=4,5,...,n. Our result generalizes theorems due to Alspach[1] and Guo~[3] respectively.
  • Original Articles
    Cycles Containing a Given Arc in Regular Multipartite Tournaments
    Guo Fei ZHOU, Ke Min ZHANG
    Acta Mathematicae Applicatae Sinica(English Series). 2002, 18(4): 681-684.
    Abstract ( )    Download PDF ( )   Knowledge map   Save
    In this paper we prove that if T is a regular n-partite tournament with n≥6, then each arc of T lies on a k-cycle for k=4,5,...,n. Our result generalizes theorems due to Alspach[1] and Guo~[3] respectively.
  • 论文
    Some Results for Classical Risk Process with Stochastic Return on Investments
    Guo Jing WANG, Rong WU
    Acta Mathematicae Applicatae Sinica(English Series). 2002, 18(4): 685-692.
    Abstract ( )    Download PDF ( )   Knowledge map   Save
    In this paper, we discuss the classical risk process with stochastic return on investment. We prove some properties of the ruin probability, the supremum distribution before ruin and the surplus distribution at the time of ruin and derive the integro-differential equations satisfied by these distributions respectively.
  • Original Articles
    Some Results for Classical Risk Process with Stochastic Return on Investments
    Guo Jing WANG, Rong WU
    Acta Mathematicae Applicatae Sinica(English Series). 2002, 18(4): 685-692.
    Abstract ( )    Download PDF ( )   Knowledge map   Save
    In this paper, we discuss the classical risk process with stochastic return on investment. We prove some properties of the ruin probability, the supremum distribution before ruin and the surplus distribution at the time of ruin and derive the integro-differential equations satisfied by these distributions respectively.
  • 论文
    Variational Description for the Generating Function Method of First Kind
    Ya Juan SUN, Meng Zhao QIN
    Acta Mathematicae Applicatae Sinica(English Series). 2002, 18(4): 693-702.
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    We propose the variational description of generating function approach of first kind for Hamiltonian ODEs, and extend the approach to the semi-linear wave equations. In this way, we can construct any finite order accuracy scheme, and show that the resulting numerical scheme is multisymplectic. At last, we present some numerical experiments by using derived new scheme.
  • Original Articles
    Variational Description for the Generating Function Method of First Kind
    Ya Juan SUN, Meng Zhao QIN
    Acta Mathematicae Applicatae Sinica(English Series). 2002, 18(4): 693-702.
    Abstract ( )    Download PDF ( )   Knowledge map   Save
    We propose the variational description of generating function approach of first kind for Hamiltonian ODEs, and extend the approach to the semi-linear wave equations. In this way, we can construct any finite order accuracy scheme, and show that the resulting numerical scheme is multisymplectic. At last, we present some numerical experiments by using derived new scheme.
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