中国科学院数学与系统科学研究院期刊网

2004年, 第20卷, 第3期　刊出日期：2006-03-21
  

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    论文
  • Talagrand's $T_2$-transportation Inequality w.r.t. a Uniform Metric for Diffusions
    Li-ming Wu, Zheng-liang Zhang
    应用数学学报(英文版). 2004, 20(3): 357-364.
    摘要 ( ) PDF全文 ( )   可视化   收藏
    Using the method of Girsanov transformation, we establish the Talagrand's $T_2$-inequality for diffusion on the path space $C([0,N], \rr^d)$ with respect to a uniform metric, with the constant independent of $N$. This improves the known results for the $L^2$-metric.
    • Original Articles
  • Talagrand's $T_2$-transportation Inequality w.r.t. a Uniform Metric for Diffusions
    Li-ming Wu, Zheng-liang Zhang
    应用数学学报(英文版). 2004, 20(3): 357-364.
    摘要 ( ) PDF全文 ( )   可视化   收藏
    Using the method of Girsanov transformation, we establish the Talagrand's $T_2$-inequality for diffusion on the path space $C([0,N], \rr^d)$ with respect to a uniform metric, with the constant independent of $N$. This improves the known results for the $L^2$-metric.
    • 论文
  • Multiple Solutions of the Singular Impulsive Boundary Value Problems on the Half-line
    Bao-qiang Yan, Yan-sheng Liu
    应用数学学报(英文版). 2004, 20(3): 365-380.
    摘要 ( ) PDF全文 ( )   可视化   收藏
    This paper presents some results on the existence of double solutions for singular impulsive boundary value problems on the half line.
    • Original Articles
  • Multiple Solutions of the Singular Impulsive Boundary Value Problems on the Half-line
    Bao-qiang Yan, Yan-sheng Liu
    应用数学学报(英文版). 2004, 20(3): 365-380.
    摘要 ( ) PDF全文 ( )   可视化   收藏
    This paper presents some results on the existence of double solutions for singular impulsive boundary value problems on the half line.
    • 论文
  • The Modified Upwind Finite Difference Fractional Steps Method for Compressible Two-phase Displacement Problem
    Yi-rang Yuan
    应用数学学报(英文版). 2004, 20(3): 381-396.
    摘要 ( ) PDF全文 ( )   可视化   收藏
    For compressible two-phase displacement problem, the modified upwind finite difference fractional steps schemes are put forward. Some techniques, such as calculus of variations, commutative law of multiplication of difference operators, decomposition of high order difference operators, the theory of prior estimates and techniques are used. Optimal order estimates in $L^{{2}}$ norm are derived for the error in the approximate solution. This method has already been applied to the numerical simulation of seawater intrusion and migration-accumulation of oil resources.
    • Original Articles
  • The Modified Upwind Finite Difference Fractional Steps Method for Compressible Two-phase Displacement Problem
    Yi-rang Yuan
    应用数学学报(英文版). 2004, 20(3): 381-396.
    摘要 ( ) PDF全文 ( )   可视化   收藏
    For compressible two-phase displacement problem, the modified upwind finite difference fractional steps schemes are put forward. Some techniques, such as calculus of variations, commutative law of multiplication of difference operators, decomposition of high order difference operators, the theory of prior estimates and techniques are used. Optimal order estimates in $L^{{2}}$ norm are derived for the error in the approximate solution. This method has already been applied to the numerical simulation of seawater intrusion and migration-accumulation of oil resources.
    • 论文
  • The Erd\H{o}s-S\'{o}s Conjecture for Graphs Whose Complements Contain No $\large \pmb {C_4}$
    Jian-hua Yin, Jiong-sheng Li
    应用数学学报(英文版). 2004, 20(3): 397-406.
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    Erd\H{o}s and S\'{o}s conjectured in 1963 (see [1], Problem 12 in 247) that every graph $G$ on $n$ vertices with size $e(G)>\frac{1}{2}n(k-1)$ contains every tree $T$ of size $k$. In this paper, we prove the conjecture for graphs whose complements contain no cycles of length 4.
    • Original Articles
  • The Erd\H{o}s-S\'{o}s Conjecture for Graphs Whose Complements Contain No $\large \pmb {C_4}$
    Jian-hua Yin, Jiong-sheng Li
    应用数学学报(英文版). 2004, 20(3): 397-400.
    摘要 ( ) PDF全文 ( )   可视化   收藏
    Erd\H{o}s and S\'{o}s conjectured in 1963 (see [1], Problem 12 in 247) that every graph $G$ on $n$ vertices with size $e(G)>\frac{1}{2}n(k-1)$ contains every tree $T$ of size $k$. In this paper, we prove the conjecture for graphs whose complements contain no cycles of length 4.
    • 论文
  • The Model for Two-dimensional Layout Optimization Problem with Performance Constraints and Its Optimality Function
    Xu Zhang, En-min Feng
    应用数学学报(英文版). 2004, 20(3): 401-410.
    摘要 ( ) PDF全文 ( )   可视化   收藏
    This paper studies the two-dimensional layout optimization problem. An optimization model with performance constraints is presented. The layout problem is partitioned into finite subproblems in terms of graph theory, in such a way of that each subproblem overcomes its on-off nature optimal variable. A minimax problem is constructed that is locally equivalent to each subproblem. By using this minimax problem, we present the optimality function for every subproblem and prove that the first order necessary optimality condition is satisfied at a point if and only if this point is a zero of optimality function.
    • Original Articles
  • The Model for Two-dimensional Layout Optimization Problem with Performance Constraints and Its Optimality Function
    Xu Zhang, En-min Feng
    应用数学学报(英文版). 2004, 20(3): 401-410.
    摘要 ( ) PDF全文 ( )   可视化   收藏
    This paper studies the two-dimensional layout optimization problem. An optimization model with performance constraints is presented. The layout problem is partitioned into finite subproblems in terms of graph theory, in such a way of that each subproblem overcomes its on-off nature optimal variable. A minimax problem is constructed that is locally equivalent to each subproblem. By using this minimax problem, we present the optimality function for every subproblem and prove that the first order necessary optimality condition is satisfied at a point if and only if this point is a zero of optimality function.
  • An Efficient Algorithm for the Optimal Market Timing over Two Stocks
    Hui Li$^1$, Hong-zhi An$^2$, Guo-fu Wu$^2$
    应用数学学报(英文版). 2004, 20(3): 411-424.
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    In this paper, the optimal trading strategy in timing the market by switching between two stocks is given. In order to deal with a large sample size with a fast turnaround computation time, we propose a class of recursive algorithm. A simulation is given to verify the effectiveness of our method.
    • 论文
  • An Efficient Algorithm for the Optimal Market Timing over Two Stocks
    Hui Li$^1$, Hong-zhi An$^2$, Guo-fu Wu$^2$
    应用数学学报(英文版). 2004, 20(3): 411-424.
    摘要 ( ) PDF全文 ( )   可视化   收藏
    In this paper, the optimal trading strategy in timing the market by switching between two stocks is given. In order to deal with a large sample size with a fast turnaround computation time, we propose a class of recursive algorithm. A simulation is given to verify the effectiveness of our method.
  • Adaptive Unified Biased Estimators of Parameters in Linear Model
    Hu Yang$^{1}$, Li-xing Zhu
    应用数学学报(英文版). 2004, 20(3): 425-432.
    摘要 ( ) PDF全文 ( )   可视化   收藏
    To tackle multi collinearity or ill-conditioned design matrices in linear models, adaptive biased estimators such as the time-honored Stein estimator, the ridge and the principal component estimators have been studied intensively. To study when a biased estimator uniformly outperforms the least squares estimator, some sufficient conditions are proposed in the literature. In this paper, we propose a unified framework to formulate a class of adaptive biased estimators. This class includes all existing biased estimators and some new ones. A sufficient condition for outperforming the least squares estimator is proposed. In terms of selecting parameters in the condition, we can obtain all double-type conditions in the literature.
    • Original Articles
  • Adaptive Unified Biased Estimators of Parameters in Linear Model
    Hu Yang$^{1}$, Li-xing Zhu
    应用数学学报(英文版). 2004, 20(3): 425-432.
    摘要 ( ) PDF全文 ( )   可视化   收藏
    To tackle multi collinearity or ill-conditioned design matrices in linear models, adaptive biased estimators such as the time-honored Stein estimator, the ridge and the principal component estimators have been studied intensively. To study when a biased estimator uniformly outperforms the least squares estimator, some sufficient conditions are proposed in the literature. In this paper, we propose a unified framework to formulate a class of adaptive biased estimators. This class includes all existing biased estimators and some new ones. A sufficient condition for outperforming the least squares estimator is proposed. In terms of selecting parameters in the condition, we can obtain all double-type conditions in the literature.
    • 论文
  • Biharmonic Equation and an Improved Hardy Inequality
    Yang-xin Yao, Yao-tian Shen, Zhi-hui Chen
    应用数学学报(英文版). 2004, 20(3): 433-440.
    摘要 ( ) PDF全文 ( )   可视化   收藏
    An improved Hardy inequality will be proven in the present work. Using the improved Hardy inequality and variational techniques, we also discuss the existence of nontrivial solution for following the weighted eigenvalue problem: $$ \cases \Lap^2 u -\mu\dfrac{u}{|x|^4}= \la uf(x), \qquad &x\in\Om,\ u = \dfrac {\pd u}{\pd\nu}= 0, & x\in\bd\Om\endcases $$
    • Original Articles
  • Biharmonic Equation and an Improved Hardy Inequality
    Yang-xin Yao, Yao-tian Shen, Zhi-hui Chen
    应用数学学报(英文版). 2004, 20(3): 433-440.
    摘要 ( ) PDF全文 ( )   可视化   收藏
    An improved Hardy inequality will be proven in the present work. Using the improved Hardy inequality and variational techniques, we also discuss the existence of nontrivial solution for following the weighted eigenvalue problem: $$ \cases \Lap^2 u -\mu\dfrac{u}{|x|^4}= \la uf(x), \qquad &x\in\Om,\ u = \dfrac {\pd u}{\pd\nu}= 0, & x\in\bd\Om\endcases $$
    • 论文
  • Effects of Hard Limits on Bifurcation, Chaos and Stability
    Rui-qi Wang, Ji-cai Huang
    应用数学学报(英文版). 2004, 20(3): 441-456.
    摘要 ( ) PDF全文 ( )   可视化   收藏
    An SMIB model in the power systems, especially that concering the effects of hard limits on bifurcations, chaos and stability is studied. Parameter conditions for bifurcations and chaos in the absence of hard limits are compared with those in the presence of hard limits. It has been proved that hard limits can affect system stability. We find that (1) hard limits can change unstable equilibrium into stable one; (2) hard limits can change stability of limit cycles induced by Hopf bifurcation; (3) persistence of hard limits can stabilize divergent trajectory to a stable equilibrium or limit cycle; (4) Hopf bifurcation occurs before SN bifurcation, so the system collapse can be controlled before Hopf bifurcation occurs. We also find that suitable limiting values of hard limits can enlarge the feasibility region. These results are based on theoretical analysis and numerical simulations, such as condition for SNB and Hopf bifurcation, bifurcation diagram, trajectories, Lyapunov exponent, Floquet multipliers, dimension of attractor and so on.
    • Original Articles
  • Effects of Hard Limits on Bifurcation, Chaos and Stability
    Rui-qi Wang, Ji-cai Huang
    应用数学学报(英文版). 2004, 20(3): 441-456.
    摘要 ( ) PDF全文 ( )   可视化   收藏
    An SMIB model in the power systems, especially that concering the effects of hard limits on bifurcations, chaos and stability is studied. Parameter conditions for bifurcations and chaos in the absence of hard limits are compared with those in the presence of hard limits. It has been proved that hard limits can affect system stability. We find that (1) hard limits can change unstable equilibrium into stable one; (2) hard limits can change stability of limit cycles induced by Hopf bifurcation; (3) persistence of hard limits can stabilize divergent trajectory to a stable equilibrium or limit cycle; (4) Hopf bifurcation occurs before SN bifurcation, so the system collapse can be controlled before Hopf bifurcation occurs. We also find that suitable limiting values of hard limits can enlarge the feasibility region. These results are based on theoretical analysis and numerical simulations, such as condition for SNB and Hopf bifurcation, bifurcation diagram, trajectories, Lyapunov exponent, Floquet multipliers, dimension of attractor and so on.
    • 论文
  • Dynamical Behavior and Singularities of a Single-machine Infinite-bus Power System
    Jin-liang Wang$^{1}$, Sheng-wei Mei$^{2}$, Qiang Lu$^{2}$, Teo Kok-lay$^{3}$
    应用数学学报(英文版). 2004, 20(3): 457-476.
    摘要 ( ) PDF全文 ( )   可视化   收藏
    This paper uses the geometric singular perturbation theory to investigate dynamical behaviors and singularities in a fundamental power system presented in a single-machine infinite-bus formulation. The power system can be approximated by two simplified systems S and F, which correspond respectively to slow and fast subsystems. The singularities, including Hopf bifurcation (HB), saddle-node bifurcation (SNB) and singularity induced bifurcation (SIB), are characterized. We show that SNB occurs at $P_{Tc}=3.4382$, SIB at $P_{T0}=2.8653$ and HB at $P_{Th}=2.802$ for the singular perturbation system. It means that the power system will collapse near SIB which precedes SNB and that the power system will oscillate near HB which precedes SIB. In other words, the power system will lose its stability by means of oscillation near the HB which precedes SIB and SNB as $P_T$ is increasing to a critical value. The boundary of the stability region of the system can be described approximately by a combination of boundaries of the stability regions of the fast subsystem and slow subsystem.
    • Original Articles
  • Dynamical Behavior and Singularities of a Single-machine Infinite-bus Power System
    Jin-liang Wang$^{1}$, Sheng-wei Mei$^{2}$, Qiang Lu$^{2}$, Teo Kok-lay$^{3}$
    应用数学学报(英文版). 2004, 20(3): 457-476.
    摘要 ( ) PDF全文 ( )   可视化   收藏
    This paper uses the geometric singular perturbation theory to investigate dynamical behaviors and singularities in a fundamental power system presented in a single-machine infinite-bus formulation. The power system can be approximated by two simplified systems S and F, which correspond respectively to slow and fast subsystems. The singularities, including Hopf bifurcation (HB), saddle-node bifurcation (SNB) and singularity induced bifurcation (SIB), are characterized. We show that SNB occurs at $P_{Tc}=3.4382$, SIB at $P_{T0}=2.8653$ and HB at $P_{Th}=2.802$ for the singular perturbation system. It means that the power system will collapse near SIB which precedes SNB and that the power system will oscillate near HB which precedes SIB. In other words, the power system will lose its stability by means of oscillation near the HB which precedes SIB and SNB as $P_T$ is increasing to a critical value. The boundary of the stability region of the system can be described approximately by a combination of boundaries of the stability regions of the fast subsystem and slow subsystem.
    • 论文
  • Iterative Algorithm for Finding Approximate Solutions of a Class of Mixed Variational-like Inequalities
    Liu-chuan Zeng
    应用数学学报(英文版). 2004, 20(3): 477-486.
    摘要 ( ) PDF全文 ( )   可视化   收藏
    The purpose of this paper is to investigate the iterative algorithm for finding approximate solutions of a class of mixed variational-like inequalities in a real Hilbert space, where the iterative algorithm is presented by virtue of the auxiliary principle technique. On one hand, the existence of approximate solutions of this class of mixed variational-like inequalities is proven. On the other hand, it is shown that the approximate solutions converge strongly to the exact solution of this class of mixed variational-like inequalities.
    • Original Articles
  • Iterative Algorithm for Finding Approximate Solutions of a Class of Mixed Variational-like Inequalities
    Liu-chuan Zeng
    应用数学学报(英文版). 2004, 20(3): 477-486.
    摘要 ( ) PDF全文 ( )   可视化   收藏
    The purpose of this paper is to investigate the iterative algorithm for finding approximate solutions of a class of mixed variational-like inequalities in a real Hilbert space, where the iterative algorithm is presented by virtue of the auxiliary principle technique. On one hand, the existence of approximate solutions of this class of mixed variational-like inequalities is proven. On the other hand, it is shown that the approximate solutions converge strongly to the exact solution of this class of mixed variational-like inequalities.
    • 论文
  • On a Class of Vector-Valued Sequences Associated with Multiplier Sequences
    Binod Chandra Tripathy$^1$, Sabita Mahanta$^2$
    应用数学学报(英文版). 2004, 20(3): 487-494.
    摘要 ( ) PDF全文 ( )   可视化   收藏
    In this article we introduce the vector valued sequence space $m(E_k, \phi, \Lambda)$, associated with the multiplier sequence $\Lambda=(\lambda_k)$ of non-zero complex numbers, and the terms of the sequence are chosen from the seminormed spaces $E_k$, seminormed by $f_k$ for all $k \in N$. This generalizes the sequence space $m(\phi)$ introduced and studied by Sargent$^{[10]}$. We study some of its properties like solidity, completeness, and obtain some inclusion results. We also characterize the multiplier problem and obtain the corresponding spaces dual to $m(E_k, \phi, \Lambda)$. We prove some general results too.
    • Original Articles
  • On a Class of Vector-Valued Sequences Associated with Multiplier Sequences
    Binod Chandra Tripathy$^1$, Sabita Mahanta$^2$
    应用数学学报(英文版). 2004, 20(3): 487-494.
    摘要 ( ) PDF全文 ( )   可视化   收藏
    In this article we introduce the vector valued sequence space $m(E_k, \phi, \Lambda)$, associated with the multiplier sequence $\Lambda=(\lambda_k)$ of non-zero complex numbers, and the terms of the sequence are chosen from the seminormed spaces $E_k$, seminormed by $f_k$ for all $k \in N$. This generalizes the sequence space $m(\phi)$ introduced and studied by Sargent$^{[10]}$. We study some of its properties like solidity, completeness, and obtain some inclusion results. We also characterize the multiplier problem and obtain the corresponding spaces dual to $m(E_k, \phi, \Lambda)$. We prove some general results too.
  • Explicit Expressions for the Ruin Probabilities of Erlang Risk Processes with Pareto Individual Claim Distributions
    Li Wei$^1$, Hai-liang Yang$^2$
    应用数学学报(英文版). 2004, 20(3): 495-506.
    摘要 ( ) PDF全文 ( )   可视化   收藏
    In this paper we first consider a risk process in which claim inter-arrival times and the time until the first claim have an Erlang (2) distribution. An explicit solution is derived for the probability of ultimate ruin, given an initial reserve of $u$ when the claim size follows a Pareto distribution. Follow Ramsay$^{[8]}$, Laplace transforms and exponential integrals are used to derive the solution, which involves a single integral of real valued functions along the positive real line, and the integrand is not of an oscillating kind. Then we show that the ultimate ruin probability can be expressed as the sum of expected values of functions of two different Gamma random variables. Finally, the results are extended to the Erlang(n) case. Numerical examples are given to illustrate the main results.
    • 论文
  • Explicit Expressions for the Ruin Probabilities of Erlang Risk Processes with Pareto Individual Claim Distributions
    Li Wei$^1$, Hai-liang Yang$^2$
    应用数学学报(英文版). 2004, 20(3): 495-506.
    摘要 ( ) PDF全文 ( )   可视化   收藏
    In this paper we first consider a risk process in which claim inter-arrival times and the time until the first claim have an Erlang (2) distribution. An explicit solution is derived for the probability of ultimate ruin, given an initial reserve of $u$ when the claim size follows a Pareto distribution. Follow Ramsay$^{[8]}$, Laplace transforms and exponential integrals are used to derive the solution, which involves a single integral of real valued functions along the positive real line, and the integrand is not of an oscillating kind. Then we show that the ultimate ruin probability can be expressed as the sum of expected values of functions of two different Gamma random variables. Finally, the results are extended to the Erlang(n) case. Numerical examples are given to illustrate the main results.
    • Original Articles
  • A Result On the Probability Measures Dominated by ${\pmb g}$-Expectation
    Long Jiang$^{}$, Zeng-jing Chen
    应用数学学报(英文版). 2004, 20(3): 507-512.
    摘要 ( ) PDF全文 ( )   可视化   收藏
    It is proved that a probability measure is dominated by $g$-expectation ${\cal E}_{\mu}[\cdot]$ if and only if it can be generated by Girsanov transformation via a process which is uniformly bounded by $\mu$.
    • 论文
  • A Result On the Probability Measures Dominated by ${\pmb g}$-Expectation
    Long Jiang$^{}$, Zeng-jing Chen
    应用数学学报(英文版). 2004, 20(3): 507-512.
    摘要 ( ) PDF全文 ( )   可视化   收藏
    It is proved that a probability measure is dominated by $g$-expectation ${\cal E}_{\mu}[\cdot]$ if and only if it can be generated by Girsanov transformation via a process which is uniformly bounded by $\mu$.
  • Bifurcations and Stability Boundary of a Power System
    Ying-hui Gao
    应用数学学报(英文版). 2004, 20(3): 513-532.
    摘要 ( ) PDF全文 ( )   可视化   收藏
    A single-axis flux decay model including an excitation control model proposed in [12,14,16] is studied. As the bifurcation parameter $P_{m}$ (input power to the generator) varies, the system exhibits dynamics emerging from static and dynamic bifurcations which link with system collapse. We show that the equilibrium point of the system undergoes three bifurcations: one saddle-node bifurcation and two Hopf bifurcations. The state variables dominating system collapse are different for different critical points, and the excitative control may play an important role in delaying system from collapsing. Simulations are presented to illustrate the dynamical behavior associated with the power system stability and collapse. Moreover, by computing the local quadratic approximation of the 5-dimensional stable manifold at an order 5 saddle point, an analytical expression for the approximate stability boundary is worked out.
    • Original Articles
  • Bifurcations and Stability Boundary of a Power System
    Ying-hui Gao
    应用数学学报(英文版). 2004, 20(3): 513-532.
    摘要 ( ) PDF全文 ( )   可视化   收藏
    A single-axis flux decay model including an excitation control model proposed in [12,14,16] is studied. As the bifurcation parameter $P_{m}$ (input power to the generator) varies, the system exhibits dynamics emerging from static and dynamic bifurcations which link with system collapse. We show that the equilibrium point of the system undergoes three bifurcations: one saddle-node bifurcation and two Hopf bifurcations. The state variables dominating system collapse are different for different critical points, and the excitative control may play an important role in delaying system from collapsing. Simulations are presented to illustrate the dynamical behavior associated with the power system stability and collapse. Moreover, by computing the local quadratic approximation of the 5-dimensional stable manifold at an order 5 saddle point, an analytical expression for the approximate stability boundary is worked out.
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