15 January 2003, Volume 19 Issue 1
    

  • Select all
    |
  • 论文
    Entropy Production and Admissibility of Shocks
    Tai Ping LIU, Tommaso Ruggeri
    Acta Mathematicae Applicatae Sinica(English Series). 2003, 19(1): 1-10.
    Abstract ( )    Download PDF ( )   Knowledge map   Save
    In shock wave theory there are two considerations in selecting the physically relevant shock waves. There is the admissibility criterion for the well-posedness of hyperbolic conservation laws. Another consideration concerns the entropy production across the shocks. The latter is natural from the physical point of view, but is not sufficient in its straightforward formulation, if the system is not genuinely nonlinear. In this paper we propose the principles of increasing entropy production and that of the superposition of shocks. These principles are shown to be equivalent to the admissibility criterion.
  • Original Articles
    Entropy Production and Admissibility of Shocks
    Tai Ping LIU, Tommaso Ruggeri
    Acta Mathematicae Applicatae Sinica(English Series). 2003, 19(1): 1-10.
    Abstract ( )    Download PDF ( )   Knowledge map   Save
    In shock wave theory there are two considerations in selecting the physically relevant shock waves. There is the admissibility criterion for the well-posedness of hyperbolic conservation laws. Another consideration concerns the entropy production across the shocks. The latter is natural from the physical point of view, but is not sufficient in its straightforward formulation, if the system is not genuinely nonlinear. In this paper we propose the principles of increasing entropy production and that of the superposition of shocks. These principles are shown to be equivalent to the admissibility criterion.
  • 论文
    Comparison of MINQUE and Simple Estimate of the Error Variance in the General Linear Models
    Song Gui WANG, Mi Xia WU, Wei Qing MA
    Acta Mathematicae Applicatae Sinica(English Series). 2003, 19(1): 13-18.
    Abstract ( )    Download PDF ( )   Knowledge map   Save
    Comparison is made between the MINQUE and simple estimate of the error variance in the normal linear model under the mean square errors criterion, where the model matrix need not have full rank and the dispersion matrix can be singular. Our results show that any one of both estimates cannot be always superior to the other. Some sufficient criteria for any one of them to be better than the other are established. Some interesting relations between these two estimates are also given.
  • Original Articles
    Comparison of MINQUE and Simple Estimate of the Error Variance in the General Linear Models
    Song Gui WANG, Mi Xia WU, Wei Qing MA
    Acta Mathematicae Applicatae Sinica(English Series). 2003, 19(1): 13-18.
    Abstract ( )    Download PDF ( )   Knowledge map   Save
    Comparison is made between the MINQUE and simple estimate of the error variance in the normal linear model under the mean square errors criterion, where the model matrix need not have full rank and the dispersion matrix can be singular. Our results show that any one of both estimates cannot be always superior to the other. Some sufficient criteria for any one of them to be better than the other are established. Some interesting relations between these two estimates are also given.
  • 论文
    Global Convergence of the Broyden's Class of Quasi-Newton Methods with Nonmonotone Linesearch
    Da Chuan XU
    Acta Mathematicae Applicatae Sinica(English Series). 2003, 19(1): 19-24.
    Abstract ( )    Download PDF ( )   Knowledge map   Save
    In this paper, the Broyden class of quasi-Newton methods for unconstrained optimization is investigated. Non-monotone linesearch procedure is introduced, which is combined with the Broyden's class. Under the convexity assumption on objective function, the global convergence of the Broyden's class is proved.
  • Original Articles
    Global Convergence of the Broyden's Class of Quasi-Newton Methods with Nonmonotone Linesearch
    Da Chuan XU
    Acta Mathematicae Applicatae Sinica(English Series). 2003, 19(1): 19-24.
    Abstract ( )    Download PDF ( )   Knowledge map   Save
    In this paper, the Broyden class of quasi-Newton methods for unconstrained optimization is investigated. Non-monotone linesearch procedure is introduced, which is combined with the Broyden's class. Under the convexity assumption on objective function, the global convergence of the Broyden's class is proved.
  • 论文
    A Finite Element Method for Singularly Perturbed Reaction-diffusion Problems
    Huo Yuan DUAN, Da Li ZHANG
    Acta Mathematicae Applicatae Sinica(English Series). 2003, 19(1): 25-30.
    Abstract ( )    Download PDF ( )   Knowledge map   Save
    A finite element method is proposed for the singularly perturbed reaction-diffusion problem. An optimal error bound is derived, independent of the perturbation parameter.
  • Original Articles
    A Finite Element Method for Singularly Perturbed Reaction-diffusion Problems
    Huo Yuan DUAN, Da Li ZHANG
    Acta Mathematicae Applicatae Sinica(English Series). 2003, 19(1): 25-30.
    Abstract ( )    Download PDF ( )   Knowledge map   Save
    A finite element method is proposed for the singularly perturbed reaction-diffusion problem. An optimal error bound is derived, independent of the perturbation parameter.
  • 论文
    A Restarted Conjugate Gradient Method for Ill-posed Problems
    Yan Fei WANG
    Acta Mathematicae Applicatae Sinica(English Series). 2003, 19(1): 31-40.
    Abstract ( )    Download PDF ( )   Knowledge map   Save
    This paper presents a restarted conjugate gradient iterative algorithm for solving ill-posed problems. The damped Morozov's discrepancy principle is used as a stopping rule. Numerical experiments are given to illustrate the efficiency of the method.
  • Original Articles
    A Restarted Conjugate Gradient Method for Ill-posed Problems
    Yan Fei WANG
    Acta Mathematicae Applicatae Sinica(English Series). 2003, 19(1): 31-40.
    Abstract ( )    Download PDF ( )   Knowledge map   Save
    This paper presents a restarted conjugate gradient iterative algorithm for solving ill-posed problems. The damped Morozov's discrepancy principle is used as a stopping rule. Numerical experiments are given to illustrate the efficiency of the method.
  • 论文
    A Combinatorial Theorem on Ordered Circular Sequences of n_1 u's and n_2 v' s with Application to Kernel-perfect Graphs
    Xiao Feng GUO, Huang YI
    Acta Mathematicae Applicatae Sinica(English Series). 2003, 19(1): 41-46.
    Abstract ( )    Download PDF ( )   Knowledge map   Save
    An ordered circular permutation S of u's and v' s is called an ordered circular sequence of u' s and v' s. A kernel of a digraph G=(V,A) is an independent subset of V, say K, such that for any vertex vi in V\K there is an arc from v_i to a vertex v_j in K. G is said to be kernel-perfect (KP) if every induced subgraph of G has a kernel. G is said to be kernel-perfect-critical (KPC) if G has no kernel but every proper induced subgraph of G has a kernel. The digraph G = (V,A) = C_n(j_1,j_x,…,j_k) is defined by: V(G) = {0,1,…,n-1}, A(G) = {uv | v-u≡j_i (mod n) for 1 ≤ i ≤ k}. In an earlier work, we investigated the digraph G = C_n (1,±δd,±2d,±3d,…,±sd), denoted by G(n,d,r,s), where δ = 1 for d > 1 or δ = 0 for d = 1, and n,d,r,s are positive integers with (n,d) = r and n = mr, and gave some necessary and sufficient conditions for G(n,d,r,s) with r ≥ 3 and s = 1 to be KP or KPC. In this paper, we prove a combinatorial theorem on ordered circular sequences of n_1 u's and n_2 v's. By using the theorem, we prove that, if (n,d) = r ≥ 2 and s ≥ 2, then G(n,d,r,s) is a KP graph.
  • Original Articles
    A Combinatorial Theorem on Ordered Circular Sequences of n_1 u's and n_2 v' s with Application to Kernel-perfect Graphs
    Xiao Feng GUO, Huang YI
    Acta Mathematicae Applicatae Sinica(English Series). 2003, 19(1): 41-46.
    Abstract ( )    Download PDF ( )   Knowledge map   Save
    An ordered circular permutation S of u's and v' s is called an ordered circular sequence of u' s and v' s. A kernel of a digraph G=(V,A) is an independent subset of V, say K, such that for any vertex vi in V\K there is an arc from v_i to a vertex v_j in K. G is said to be kernel-perfect (KP) if every induced subgraph of G has a kernel. G is said to be kernel-perfect-critical (KPC) if G has no kernel but every proper induced subgraph of G has a kernel. The digraph G = (V,A) = C_n(j_1,j_x,…,j_k) is defined by: V(G) = {0,1,…,n-1}, A(G) = {uv | v-u≡j_i (mod n) for 1 ≤ i ≤ k}. In an earlier work, we investigated the digraph G = C_n (1,±δd,±2d,±3d,…,±sd), denoted by G(n,d,r,s), where δ = 1 for d > 1 or δ = 0 for d = 1, and n,d,r,s are positive integers with (n,d) = r and n = mr, and gave some necessary and sufficient conditions for G(n,d,r,s) with r ≥ 3 and s = 1 to be KP or KPC. In this paper, we prove a combinatorial theorem on ordered circular sequences of n_1 u's and n_2 v's. By using the theorem, we prove that, if (n,d) = r ≥ 2 and s ≥ 2, then G(n,d,r,s) is a KP graph.
  • 论文
    The Asymptotic Behavior for Numerical Solution of a Volterra Equation
    Da XU
    Acta Mathematicae Applicatae Sinica(English Series). 2003, 19(1): 47-55.
    Abstract ( )    Download PDF ( )   Knowledge map   Save
    Long-time asymptotic stability and convergence properties for the numerical solution of a Volterra equation of parabolic type are studied. The methods are based on the first-second order backward difference methods. The memory term is approximated by the convolution quadrature and the interpolant quadrature. Discretization of the spatial partial differential operators by the finite element method is also considered
  • Original Articles
    The Asymptotic Behavior for Numerical Solution of a Volterra Equation
    Da XU
    Acta Mathematicae Applicatae Sinica(English Series). 2003, 19(1): 47-55.
    Abstract ( )    Download PDF ( )   Knowledge map   Save
    Long-time asymptotic stability and convergence properties for the numerical solution of a Volterra equation of parabolic type are studied. The methods are based on the first-second order backward difference methods. The memory term is approximated by the convolution quadrature and the interpolant quadrature. Discretization of the spatial partial differential operators by the finite element method is also considered
  • 论文
    Ruin Theory for the Risk Process Described by PDMPs
    Guo Jing WANG, Chun Sheng ZHANG, Rong WU
    Acta Mathematicae Applicatae Sinica(English Series). 2003, 19(1): 59-70.
    Abstract ( )    Download PDF ( )   Knowledge map   Save
    In this paper we consider the risk process that is described by a piecewise deterministic Markov processes (PDMP). We first present the construction of the risk process and then discuss some ruin problems for this new kind of risk model.
  • Original Articles
    Ruin Theory for the Risk Process Described by PDMPs
    Guo Jing WANG, Chun Sheng ZHANG, Rong WU
    Acta Mathematicae Applicatae Sinica(English Series). 2003, 19(1): 59-70.
    Abstract ( )    Download PDF ( )   Knowledge map   Save
    In this paper we consider the risk process that is described by a piecewise deterministic Markov processes (PDMP). We first present the construction of the risk process and then discuss some ruin problems for this new kind of risk model.
  • Original Articles
    Cauchy Problem for Quasilinear Hyperbolic Systems with Higher Order Dissipative Terms
    Wei Guo ZHANG
    Acta Mathematicae Applicatae Sinica(English Series). 2003, 19(1): 71-82.
    Abstract ( )    Download PDF ( )   Knowledge map   Save
    In this paper, the author studies the global existence, singularities and life span of smooth solutions of the Cauchy problem for a class of quasilinear hyperbolic systems with higher order dissipative terms and gives their applications to nonlinear wave equations with higher order dissipative terms
  • 论文
    Cauchy Problem for Quasilinear Hyperbolic Systems with Higher Order Dissipative Terms
    Wei Guo ZHANG
    Acta Mathematicae Applicatae Sinica(English Series). 2003, 19(1): 71-82.
    Abstract ( )    Download PDF ( )   Knowledge map   Save
    In this paper, the author studies the global existence, singularities and life span of smooth solutions of the Cauchy problem for a class of quasilinear hyperbolic systems with higher order dissipative terms and gives their applications to nonlinear wave equations with higher order dissipative terms
  • Original Articles
    On the Stabilizer of the Automorphism Group of a 4-valent Vertex-transitive Graph with Odd-prime-power Order
    Yan Quan FENG, Jin Ho Kwak, Ming Yao XU
    Acta Mathematicae Applicatae Sinica(English Series). 2003, 19(1): 83-86.
    Abstract ( )    Download PDF ( )   Knowledge map   Save
    Let X be a 4-valent connected vertex-transitive graph with odd-prime-power order p~k (k ≥ 1), and let A be the full automorphism group of X. In this paper, we prove that the stabilizer Av of a vertex v in A is a 2-group if p ≠ 5, or a {2,3}-group if p = 5. Furthermore, if p = 5 |A_v| is not divisible by 3~2. As a result, we show that any 4-valent connected vertex-transitive graph with odd-prime-power order p~k (k ≥ 1) is at most 1-arc-transitive for p ≠ 5 and 2-arc-transitive for p = 5.
  • 论文
    On the Stabilizer of the Automorphism Group of a 4-valent Vertex-transitive Graph with Odd-prime-power Order
    Yan Quan FENG, Jin Ho Kwak, Ming Yao XU
    Acta Mathematicae Applicatae Sinica(English Series). 2003, 19(1): 83-86.
    Abstract ( )    Download PDF ( )   Knowledge map   Save
    Let X be a 4-valent connected vertex-transitive graph with odd-prime-power order p~k (k ≥ 1), and let A be the full automorphism group of X. In this paper, we prove that the stabilizer Av of a vertex v in A is a 2-group if p ≠ 5, or a {2,3}-group if p = 5. Furthermore, if p = 5 |A_v| is not divisible by 3~2. As a result, we show that any 4-valent connected vertex-transitive graph with odd-prime-power order p~k (k ≥ 1) is at most 1-arc-transitive for p ≠ 5 and 2-arc-transitive for p = 5.
  • 论文
    Gelation of a Reversible Markov Process of Polymerization
    Dong HAN, Yian Lin HAN
    Acta Mathematicae Applicatae Sinica(English Series). 2003, 19(1): 87-96.
    Abstract ( )    Download PDF ( )   Knowledge map   Save
    In this paper a reversible Markov process as a chemical polymers reaction of two types of monomers is defined. By analyzing the partition functions of the process we obtain three different distributions of the average molecular weight, depending on the value of strength of the fragmentation reaction, and prove that a gelation of the process will occur in the thermodynamic limit.
  • Original Articles
    Gelation of a Reversible Markov Process of Polymerization
    Dong HAN, Yian Lin HAN
    Acta Mathematicae Applicatae Sinica(English Series). 2003, 19(1): 87-96.
    Abstract ( )    Download PDF ( )   Knowledge map   Save
    In this paper a reversible Markov process as a chemical polymers reaction of two types of monomers is defined. By analyzing the partition functions of the process we obtain three different distributions of the average molecular weight, depending on the value of strength of the fragmentation reaction, and prove that a gelation of the process will occur in the thermodynamic limit.
  • 论文
    On k-ordered Graphs Involved Degree Sum
    Zhi Quan HU, Tian FENG
    Acta Mathematicae Applicatae Sinica(English Series). 2003, 19(1): 97-106.
    Abstract ( )    Download PDF ( )   Knowledge map   Save
    A graph g is k-ordered Hamiltonian, 2 ≤ k ≤ n, if for every ordered sequence S of k distinct vertices of G, there exists a Hamiltonian cycle that encounters S in the given order. In this article, we prove that if G is a graph on n vertices with degree sum of nonadjacent vertices at least n + 3k-9/2, then G is k-ordered Hamiltonian for k=3,4,…[n/19]. We also show that the degree sum bound can be reduced to n + 2 [k/2]-2 if k(G) ≥ 3k-1/2 or δ(G) ≥ 5k-4. Several known results are generalized.
  • Original Articles
    On k-ordered Graphs Involved Degree Sum
    Zhi Quan HU, Tian FENG
    Acta Mathematicae Applicatae Sinica(English Series). 2003, 19(1): 97-106.
    Abstract ( )    Download PDF ( )   Knowledge map   Save
    A graph g is k-ordered Hamiltonian, 2 ≤ k ≤ n, if for every ordered sequence S of k distinct vertices of G, there exists a Hamiltonian cycle that encounters S in the given order. In this article, we prove that if G is a graph on n vertices with degree sum of nonadjacent vertices at least n + 3k-9/2, then G is k-ordered Hamiltonian for k=3,4,…[n/19]. We also show that the degree sum bound can be reduced to n + 2 [k/2]-2 if k(G) ≥ 3k-1/2 or δ(G) ≥ 5k-4. Several known results are generalized.
  • Original Articles
    On the Upper Bound of Second Eigenvalues for Uniformly Elliptic Operators of any Orders
    Jia GAO, Xiao Ping YANG, Chun Lin QIAN
    Acta Mathematicae Applicatae Sinica(English Series). 2003, 19(1): 107-116.
    Abstract ( )    Download PDF ( )   Knowledge map   Save
    Let Ω is contained in R~m (m ≥ 1) be a bounded domain with piecewise smooth boundary partial derivΩ. Let t and r be positive integers with t > r + 1. We consider the eigenvalue problems (1.1) and (1.2), and obtain Theorem 1 and Theorem 2, which generalize the results in [1,2,5].
  • 论文
    On the Upper Bound of Second Eigenvalues for Uniformly Elliptic Operators of any Orders
    Jia GAO, Xiao Ping YANG, Chun Lin QIAN
    Acta Mathematicae Applicatae Sinica(English Series). 2003, 19(1): 107-116.
    Abstract ( )    Download PDF ( )   Knowledge map   Save
    Let Ω is contained in R~m (m ≥ 1) be a bounded domain with piecewise smooth boundary partial derivΩ. Let t and r be positive integers with t > r + 1. We consider the eigenvalue problems (1.1) and (1.2), and obtain Theorem 1 and Theorem 2, which generalize the results in [1,2,5].
  • 论文
    The Existence and Multiplicity of Positive Solutions for a Third-order Three-point Boundary Value Problem
    Qing Liu YAO
    Acta Mathematicae Applicatae Sinica(English Series). 2003, 19(1): 117-122.
    Abstract ( )    Download PDF ( )   Knowledge map   Save
    The existence of n positive solutions for a class of third-order three-point boundary value problems is investigated, where n is an arbitrary natural number. The main tool is Krasnosel'skii fixed point theorem on the cone.
  • Original Articles
    The Existence and Multiplicity of Positive Solutions for a Third-order Three-point Boundary Value Problem
    Qing Liu YAO
    Acta Mathematicae Applicatae Sinica(English Series). 2003, 19(1): 117-122.
    Abstract ( )    Download PDF ( )   Knowledge map   Save
    The existence of n positive solutions for a class of third-order three-point boundary value problems is investigated, where n is an arbitrary natural number. The main tool is Krasnosel'skii fixed point theorem on the cone.
  • Original Articles
    Periodic Solutions of a Second Order Non-autonomous Differential System
    Zhou JIN, Sun SUN
    Acta Mathematicae Applicatae Sinica(English Series). 2003, 19(1): 123-128.
    Abstract ( )    Download PDF ( )   Knowledge map   Save
    This paper gives new sufficient conditions for the existence of periodic solutions of a second order non-autonomous differential system by using Mawhin's coincidence degree theory and Brousk's theorem. These results substantially extend and improve the corresponding results in the literatures [1,6,7].
  • 论文
    Periodic Solutions of a Second Order Non-autonomous Differential System
    Zhou JIN, Sun SUN
    Acta Mathematicae Applicatae Sinica(English Series). 2003, 19(1): 123-128.
    Abstract ( )    Download PDF ( )   Knowledge map   Save
    This paper gives new sufficient conditions for the existence of periodic solutions of a second order non-autonomous differential system by using Mawhin's coincidence degree theory and Brousk's theorem. These results substantially extend and improve the corresponding results in the literatures [1,6,7].
  • Original Articles
    Reduction of Volume-preserving Flows on an n-dimensional Manifold
    Yong Ai ZHANG, De Bin HUANG, Zeng Rong LIU
    Acta Mathematicae Applicatae Sinica(English Series). 2003, 19(1): 129-134.
    Abstract ( )    Download PDF ( )   Knowledge map   Save
    A geometric reduction procedure for volume-preserving flows with a volume-preserving symmetry on an n-dimensional manifold is obtained. Instead of the coordinate-dependent theory and the concrete coordinate transformation, we show that a volume-preserving flow with a one-parameter volume-preserving symmetry on an n-dimensional manifold can be reduced to a volume-preserving flow on the corresponding (n-1)-dimensional quotient space. More generally, if it admits an r-parameter volume-preserving commutable symmetry, then the reduced flow preserves the corresponding (n - r)-dimensional volume form.
  • 论文
    Reduction of Volume-preserving Flows on an n-dimensional Manifold
    Yong Ai ZHANG, De Bin HUANG, Zeng Rong LIU
    Acta Mathematicae Applicatae Sinica(English Series). 2003, 19(1): 129-134.
    Abstract ( )    Download PDF ( )   Knowledge map   Save
    A geometric reduction procedure for volume-preserving flows with a volume-preserving symmetry on an n-dimensional manifold is obtained. Instead of the coordinate-dependent theory and the concrete coordinate transformation, we show that a volume-preserving flow with a one-parameter volume-preserving symmetry on an n-dimensional manifold can be reduced to a volume-preserving flow on the corresponding (n-1)-dimensional quotient space. More generally, if it admits an r-parameter volume-preserving commutable symmetry, then the reduced flow preserves the corresponding (n - r)-dimensional volume form.
  • 论文
    Characterizations on Heavy-tailed Distributions by Means of Hazard Rate
    Chun SU, Qi He TANG
    Acta Mathematicae Applicatae Sinica(English Series). 2003, 19(1): 135-142.
    Abstract ( )    Download PDF ( )   Knowledge map   Save
    Let F(x) be a distribution function supported on [0,∞), with an equilibrium distribution function F_e(x). In this paper we shall study the function r_e(x) = (-ln F-bar e(x))' = F-bar(x)/∫_x~∞ F-bar (u) du, which is called the equilibrium hazard rate of F. By the limiting behavior of re(x) we give a criterion to identify F to be heavy-tailed or light-tailed. Two broad classes of heavy-tailed distributions are also introduced and studied.
  • Original Articles
    Characterizations on Heavy-tailed Distributions by Means of Hazard Rate
    Chun SU, Qi He TANG
    Acta Mathematicae Applicatae Sinica(English Series). 2003, 19(1): 135-142.
    Abstract ( )    Download PDF ( )   Knowledge map   Save
    Let F(x) be a distribution function supported on [0,∞), with an equilibrium distribution function F_e(x). In this paper we shall study the function r_e(x) = (-ln F-bar e(x))' = F-bar(x)/∫_x~∞ F-bar (u) du, which is called the equilibrium hazard rate of F. By the limiting behavior of re(x) we give a criterion to identify F to be heavy-tailed or light-tailed. Two broad classes of heavy-tailed distributions are also introduced and studied.
  • Original Articles
    Some Notes on Reaction Diffusion Systems with Nonlinear Boundary Conditions
    Wen Jun SUN
    Acta Mathematicae Applicatae Sinica(English Series). 2003, 19(1): 143-156.
    Abstract ( )    Download PDF ( )   Knowledge map   Save
    This paper deals with the existence and nonexistence of global positive solution to a semilinear reaction-diffusion system with nonlinear boundary conditions. For the heat diffusion case, the necessary and sufficient conditions on the global existence of all positive solutions are obtained. For the general fast diffusion case, we get some conditions on the global existence and nonexistence of positive solutions. The results of this paper fill the same gaps which were left in this field.
  • 论文
    Some Notes on Reaction Diffusion Systems with Nonlinear Boundary Conditions
    Wen Jun SUN
    Acta Mathematicae Applicatae Sinica(English Series). 2003, 19(1): 143-156.
    Abstract ( )    Download PDF ( )   Knowledge map   Save
    This paper deals with the existence and nonexistence of global positive solution to a semilinear reaction-diffusion system with nonlinear boundary conditions. For the heat diffusion case, the necessary and sufficient conditions on the global existence of all positive solutions are obtained. For the general fast diffusion case, we get some conditions on the global existence and nonexistence of positive solutions. The results of this paper fill the same gaps which were left in this field.
  • Original Articles
    A Liminf Result on Two-parameter Gaussian Process
    Li Xin ZHANG, Chuan Rong LU
    Acta Mathematicae Applicatae Sinica(English Series). 2003, 19(1): 157-166.
    Abstract ( )    Download PDF ( )   Knowledge map   Save
    In this paper, a liminf behavior is studied of a two-parameter Gaussian process which is a generalization of a two-parameter Wiener process. The results improve on the liminfs in [7].
  • 论文
    A Liminf Result on Two-parameter Gaussian Process
    Li Xin ZHANG, Chuan Rong LU
    Acta Mathematicae Applicatae Sinica(English Series). 2003, 19(1): 157-166.
    Abstract ( )    Download PDF ( )   Knowledge map   Save
    In this paper, a liminf behavior is studied of a two-parameter Gaussian process which is a generalization of a two-parameter Wiener process. The results improve on the liminfs in [7].
  • Original Articles
    Persistence and Periodic Solution on a Nonautonomous SIS Model with Delays
    San Ling YUAN, Zhi En MA, Jin ZHEN
    Acta Mathematicae Applicatae Sinica(English Series). 2003, 19(1): 167-176.
    Abstract ( )    Download PDF ( )   Knowledge map   Save
    An SIS model with periodic maximum infectious force, recruitment rate and the removal rate of the infectives has been investigated in this article. Sufficient conditions for the permanence and extinction of the disease are obtained. Furthermore, the existence and global stability of positive periodic solution are established. Finally, we present a procedure by which one can control the parameters of the model to keep the infectives stay eventually in a desired set.
  • 论文
    Persistence and Periodic Solution on a Nonautonomous SIS Model with Delays
    San Ling YUAN, Zhi En MA, Jin ZHEN
    Acta Mathematicae Applicatae Sinica(English Series). 2003, 19(1): 167-176.
    Abstract ( )    Download PDF ( )   Knowledge map   Save
    An SIS model with periodic maximum infectious force, recruitment rate and the removal rate of the infectives has been investigated in this article. Sufficient conditions for the permanence and extinction of the disease are obtained. Furthermore, the existence and global stability of positive periodic solution are established. Finally, we present a procedure by which one can control the parameters of the model to keep the infectives stay eventually in a desired set.
Journal Online
News More