15 March 2001, Volume 17 Issue 3
    

  • Select all
    |
  • Original Articles
    Extreme solutions of initial value problems for nonlinear second order integrodifferential equations in Banach spaces
    Fang Qi Chen
    Acta Mathematicae Applicatae Sinica(English Series). 2001, 17(3): 289-295.
    Abstract ( )    Download PDF ( )   Knowledge map   Save
    In this paper,using the monotone iterative method,we study the existence of extreme solutions of initial value problems for nonlinear second order integrodifferential equations in Banach spaces.Some existence theorems of extreme solutions are obtained.
  • 论文
    Extreme solutions of initial value problems for nonlinear second order integrodifferential equations in Banach spaces
    Fang Qi Chen
    Acta Mathematicae Applicatae Sinica(English Series). 2001, 17(3): 289-295.
    Abstract ( )    Download PDF ( )   Knowledge map   Save
    In this paper,using the monotone iterative method,we study the existence of extreme solutions of initial value problems for nonlinear second order integrodifferential equations in Banach spaces.Some existence theorems of extreme solutions are obtained.
  • Original Articles
    General central path and the largest step general central path following algorithm for linear programming
    Wen Bao Ai, Ke Cun ZHANG
    Acta Mathematicae Applicatae Sinica(English Series). 2001, 17(3): 296-303.
    Abstract ( )    Download PDF ( )   Knowledge map   Save
    In this paper,we propose a general path following method,in which the starting point can be any feasible interior pair and each iteration uses a step with the largest possible reduction in duality gap.The algorithm maintains the O(〖KF(〗n〖KF)〗L) iteration complexity.It enjoys quadratic convergence if the optimal vertex is nondegenerate.
  • 论文
    General central path and the largest step general central path following algorithm for linear programming
    Wen Bao Ai, Ke Cun ZHANG
    Acta Mathematicae Applicatae Sinica(English Series). 2001, 17(3): 296-303.
    Abstract ( )    Download PDF ( )   Knowledge map   Save
    In this paper,we propose a general path following method,in which the starting point can be any feasible interior pair and each iteration uses a step with the largest possible reduction in duality gap.The algorithm maintains the O(〖KF(〗n〖KF)〗L) iteration complexity.It enjoys quadratic convergence if the optimal vertex is nondegenerate.
  • 论文
    Some results on comparison of maintenance policies
    Gui Mei LI, Ze Hui LI, Cheng Kui ZHONG, Ke Liu
    Acta Mathematicae Applicatae Sinica(English Series). 2001, 17(3): 304-309.
    Abstract ( )    Download PDF ( )   Knowledge map   Save
    In this paper,we study the stochastic comparisons of minimal repair replacement policies in repairable case.We give some results on comparisons of the same unit for different policies and on comparisons of the same policies for different units.
  • Original Articles
    Some results on comparison of maintenance policies
    Gui Mei LI, Ze Hui LI, Cheng Kui ZHONG, Ke Liu
    Acta Mathematicae Applicatae Sinica(English Series). 2001, 17(3): 304-309.
    Abstract ( )    Download PDF ( )   Knowledge map   Save
    In this paper,we study the stochastic comparisons of minimal repair replacement policies in repairable case.We give some results on comparisons of the same unit for different policies and on comparisons of the same policies for different units.
  • Original Articles
    The integrability and parametric representation of a hierarchy of soliton equations
    Lei ZHANG, Qi Yan SHI
    Acta Mathematicae Applicatae Sinica(English Series). 2001, 17(3): 310-316.
    Abstract ( )    Download PDF ( )   Knowledge map   Save
    The parametric representation for finite-band solutions of a stationary soliton equation is discussed.This parametric representation can be represented as a Hamiltonian system which is integrable in Liouville sense.The nonconfocal involutive integral representations {F_m} are obtained also.The finite-band solutions of the soliton equation can be represented as the solutions of two set of ordinary differential equations.
  • 论文
    The integrability and parametric representation of a hierarchy of soliton equations
    Lei ZHANG, Qi Yan SHI
    Acta Mathematicae Applicatae Sinica(English Series). 2001, 17(3): 310-316.
    Abstract ( )    Download PDF ( )   Knowledge map   Save
    The parametric representation for finite-band solutions of a stationary soliton equation is discussed.This parametric representation can be represented as a Hamiltonian system which is integrable in Liouville sense.The nonconfocal involutive integral representations {F_m} are obtained also.The finite-band solutions of the soliton equation can be represented as the solutions of two set of ordinary differential equations.
  • 论文
    Attractors for generalized Ginzburg-Landau-BBM equations in an unbounded domain
    Mu Rong JIANG, Bo Ling GUO
    Acta Mathematicae Applicatae Sinica(English Series). 2001, 17(3): 317-325.
    Abstract ( )    Download PDF ( )   Knowledge map   Save
    By the interpolation inequality and a priori estimates in the weighted space,the existence of global solutions for generalized Ginzburg-Landau equation coupled with BBM equation in an unbounded domain is considered,and the existence of the maximal attractor is obtained.
  • Original Articles
    Attractors for generalized Ginzburg-Landau-BBM equations in an unbounded domain
    Mu Rong JIANG, Bo Ling GUO
    Acta Mathematicae Applicatae Sinica(English Series). 2001, 17(3): 317-325.
    Abstract ( )    Download PDF ( )   Knowledge map   Save
    By the interpolation inequality and a priori estimates in the weighted space,the existence of global solutions for generalized Ginzburg-Landau equation coupled with BBM equation in an unbounded domain is considered,and the existence of the maximal attractor is obtained.
  • Original Articles
    Simple proof of a large deviation result
    Zhi Xiang Zhang
    Acta Mathematicae Applicatae Sinica(English Series). 2001, 17(3): 326-331.
    Abstract ( )    Download PDF ( )   Knowledge map   Save
    In this note we prove a large deviation result for a perturbed discontinuous inhomogeneous system which complements.
  • 论文
    Simple proof of a large deviation result
    Zhi Xiang Zhang
    Acta Mathematicae Applicatae Sinica(English Series). 2001, 17(3): 326-331.
    Abstract ( )    Download PDF ( )   Knowledge map   Save
    In this note we prove a large deviation result for a perturbed discontinuous inhomogeneous system which complements.
  • 论文
    Mixed finite element methods based on Riesz-representing operators for the shell problem
    Huo Yuan Duan , Da Li ZHANG
    Acta Mathematicae Applicatae Sinica(English Series). 2001, 17(3): 332-339.
    Abstract ( )    Download PDF ( )   Knowledge map   Save
    To solve the shell problem,we propose a mixed finite element method with bubble-stabilization term and discrete Riesz-representation operators.It is shown that this new method is coercive,implying the well-known K-ellipticity and the Inf-Sup condition being circumvented,and the resulting linear system is symmetrically positively definite,with a condition number being at most O(h~(-2)).Further,an optimal error bound is attained.
  • Original Articles
    Mixed finite element methods based on Riesz-representing operators for the shell problem
    Huo Yuan Duan , Da Li ZHANG
    Acta Mathematicae Applicatae Sinica(English Series). 2001, 17(3): 332-339.
    Abstract ( )    Download PDF ( )   Knowledge map   Save
    To solve the shell problem,we propose a mixed finite element method with bubble-stabilization term and discrete Riesz-representation operators.It is shown that this new method is coercive,implying the well-known K-ellipticity and the Inf-Sup condition being circumvented,and the resulting linear system is symmetrically positively definite,with a condition number being at most O(h~(-2)).Further,an optimal error bound is attained.
  • 论文
    Positive solutions for a Dirichlet problem
    Huan Song Zhou
    Acta Mathematicae Applicatae Sinica(English Series). 2001, 17(3): 340-349.
    Abstract ( )    Download PDF ( )   Knowledge map   Save
    In this paper,we study a nonlinear Dirichlet problem on a smooth bounded domain,in which the nonlinear term is asymptotically linear,not superlinear,at infinity and sublinear near the origin.By using Mountain Pass Theorem,we prove that there exist at least two positive solutions under suitable assumptions on the nonlinearity.
  • Original Articles
    Positive solutions for a Dirichlet problem
    Huan Song Zhou
    Acta Mathematicae Applicatae Sinica(English Series). 2001, 17(3): 340-349.
    Abstract ( )    Download PDF ( )   Knowledge map   Save
    In this paper,we study a nonlinear Dirichlet problem on a smooth bounded domain,in which the nonlinear term is asymptotically linear,not superlinear,at infinity and sublinear near the origin.By using Mountain Pass Theorem,we prove that there exist at least two positive solutions under suitable assumptions on the nonlinearity.
  • 论文
    Topological and metrical conditions for Collel-Eckmann unimodal maps
    Lan Yu WANG
    Acta Mathematicae Applicatae Sinica(English Series). 2001, 17(3): 350-360.
    Abstract ( )    Download PDF ( )   Knowledge map   Save
    In this paper we prove that Sands' topological condition for Collet-Eckmann maps implies Tsujii's metrical condition;on the other hand,if a Collet-Eckmann map satisfies Tsujii's metrical condition,then it satisfies Sands' topological condition.Thus we obtain three different versions of Benedicks-Carleson Theorem by using topological conditions.
  • Original Articles
    Topological and metrical conditions for Collel-Eckmann unimodal maps
    Lan Yu WANG
    Acta Mathematicae Applicatae Sinica(English Series). 2001, 17(3): 350-360.
    Abstract ( )    Download PDF ( )   Knowledge map   Save
    In this paper we prove that Sands' topological condition for Collet-Eckmann maps implies Tsujii's metrical condition;on the other hand,if a Collet-Eckmann map satisfies Tsujii's metrical condition,then it satisfies Sands' topological condition.Thus we obtain three different versions of Benedicks-Carleson Theorem by using topological conditions.
  • 论文
    Outpaths of arcs in multipartite tournaments
    Guo Fei Zhou
    Acta Mathematicae Applicatae Sinica(English Series). 2001, 17(3): 361-365.
    Abstract ( )    Download PDF ( )   Knowledge map   Save
    A k-outpath of an arc xy in a multipartite tournament is a directed path with length k starting from xy such that x does not dominate the end vertex of the directed path.This concept is a generalization of a directed cycle.We show that if T is an almost regular n-partite (n≥8) tournament with each partite set having at least two vertices,then every arc of T has a k-outpath for all k,3≤k≤n-1.
  • Original Articles
    Outpaths of arcs in multipartite tournaments
    Guo Fei Zhou
    Acta Mathematicae Applicatae Sinica(English Series). 2001, 17(3): 361-365.
    Abstract ( )    Download PDF ( )   Knowledge map   Save
    A k-outpath of an arc xy in a multipartite tournament is a directed path with length k starting from xy such that x does not dominate the end vertex of the directed path.This concept is a generalization of a directed cycle.We show that if T is an almost regular n-partite (n≥8) tournament with each partite set having at least two vertices,then every arc of T has a k-outpath for all k,3≤k≤n-1.
  • 论文
    A splitting method for quadratic programming problem
    Zi Luan WEI
    Acta Mathematicae Applicatae Sinica(English Series). 2001, 17(3): 366-374.
    Abstract ( )    Download PDF ( )   Knowledge map   Save
    A matrix splitting method is presented for minimizing a quadratic programming (QP) problem,and a general algorithm is designed to solve the QP problem and generates a sequence of iterative points.We prove that the sequence generated by the algorithm converges to the optimal solution and has an R-linear rate of convergence if the QP problem is strictly convex and nondegenerate,and that every accumulation point of the sequence generated by the general algorithm is a KKT point of the original problem under the hypothesis that the value of the objective function is bounded below on the constrained region,and that the sequence converges to a KKT point if the problem is nondegenerate and the constrained region is bounded.
  • Original Articles
    A splitting method for quadratic programming problem
    Zi Luan WEI
    Acta Mathematicae Applicatae Sinica(English Series). 2001, 17(3): 366-374.
    Abstract ( )    Download PDF ( )   Knowledge map   Save
    A matrix splitting method is presented for minimizing a quadratic programming (QP) problem,and a general algorithm is designed to solve the QP problem and generates a sequence of iterative points.We prove that the sequence generated by the algorithm converges to the optimal solution and has an R-linear rate of convergence if the QP problem is strictly convex and nondegenerate,and that every accumulation point of the sequence generated by the general algorithm is a KKT point of the original problem under the hypothesis that the value of the objective function is bounded below on the constrained region,and that the sequence converges to a KKT point if the problem is nondegenerate and the constrained region is bounded.
  • 论文
    Bifurcation of periodic solution in a three-unit neural network with delay
    Yi Ping LIN, Roland Lemmert, Peter Volkmann
    Acta Mathematicae Applicatae Sinica(English Series). 2001, 17(3): 375-381.
    Abstract ( )    Download PDF ( )   Knowledge map   Save
    A system of three-unit networks with no-self-connection is investigated,the general formula for bifuraction direction of Hopf bifurcation is calculated,and the estimation formula of the period for periodic solution is given.
  • Original Articles
    Bifurcation of periodic solution in a three-unit neural network with delay
    Yi Ping LIN, Roland Lemmert, Peter Volkmann
    Acta Mathematicae Applicatae Sinica(English Series). 2001, 17(3): 375-381.
    Abstract ( )    Download PDF ( )   Knowledge map   Save
    A system of three-unit networks with no-self-connection is investigated,the general formula for bifuraction direction of Hopf bifurcation is calculated,and the estimation formula of the period for periodic solution is given.
  • 论文
    A characterization of N-dimensional Daubechies type tensor product wavelet
    Deng Long LI, Si Long Peng
    Acta Mathematicae Applicatae Sinica(English Series). 2001, 17(3): 382-392.
    Abstract ( )    Download PDF ( )   Knowledge map   Save
    In this paper,we consider the problem of the existence of general non-separable variate orthonormal compactly supported wavelet basis when the symbol function has a special form.We prove that the general non-separable variate orthonormal wavelet basis doesn't exist if the symbol function possesses a certain form.This helps us to explicate the difficulty of constructing the non-separable variate wavelet basis and to hint how to construct non-separable variate wavelet basis.
  • Original Articles
    A characterization of N-dimensional Daubechies type tensor product wavelet
    Deng Long LI, Si Long Peng
    Acta Mathematicae Applicatae Sinica(English Series). 2001, 17(3): 382-392.
    Abstract ( )    Download PDF ( )   Knowledge map   Save
    In this paper,we consider the problem of the existence of general non-separable variate orthonormal compactly supported wavelet basis when the symbol function has a special form.We prove that the general non-separable variate orthonormal wavelet basis doesn't exist if the symbol function possesses a certain form.This helps us to explicate the difficulty of constructing the non-separable variate wavelet basis and to hint how to construct non-separable variate wavelet basis.
  • Original Articles
    On the uniqueness of the unbounded classical solution of the evolution system describing geophysical flow within the earth and its associated systems
    Kai Tai LI, Chunshan Zhao
    Acta Mathematicae Applicatae Sinica(English Series). 2001, 17(3): 393-397.
    Abstract ( )    Download PDF ( )   Knowledge map   Save
    The uniqueness for unbounded classical solutions of the evolution system describing geophysical flow within the earth and its associated systems is investigated.Under suitable growth conditions,it is shown that the solution to the initial value problem is unique.Moreover,a counterexample is given if the growth conditions are not satisfied.
  • 论文
    On the uniqueness of the unbounded classical solution of the evolution system describing geophysical flow within the earth and its associated systems
    Kai Tai LI, Chunshan Zhao
    Acta Mathematicae Applicatae Sinica(English Series). 2001, 17(3): 393-397.
    Abstract ( )    Download PDF ( )   Knowledge map   Save
    The uniqueness for unbounded classical solutions of the evolution system describing geophysical flow within the earth and its associated systems is investigated.Under suitable growth conditions,it is shown that the solution to the initial value problem is unique.Moreover,a counterexample is given if the growth conditions are not satisfied.
  • 论文
    Asymptotic behavior and oscillations of second order difference equations with delay depending on the unknown function
    Jiao Wan LUO, Zhu Jun JING
    Acta Mathematicae Applicatae Sinica(English Series). 2001, 17(3): 398-406.
    Abstract ( )    Download PDF ( )   Knowledge map   Save
    The asymptotic behavior of the nonoscillatory solutions of the difference equations Δ[r(n)Δx(n)]+f(n,x(n),x(τ(n,x(n))))=0 (1) is considered.In the case when f is a strongly sublinear (superlinear) function,conditions for oscillations of (1) are also found.
  • Original Articles
    Asymptotic behavior and oscillations of second order difference equations with delay depending on the unknown function
    Jiao Wan LUO, Zhu Jun JING
    Acta Mathematicae Applicatae Sinica(English Series). 2001, 17(3): 398-406.
    Abstract ( )    Download PDF ( )   Knowledge map   Save
    The asymptotic behavior of the nonoscillatory solutions of the difference equations Δ[r(n)Δx(n)]+f(n,x(n),x(τ(n,x(n))))=0 (1) is considered.In the case when f is a strongly sublinear (superlinear) function,conditions for oscillations of (1) are also found.
  • 论文
    (Statistical inferences for varying-coefficient models based on locally weighted regression technique)
    Chang Lin MEI, Wen Xiu ZHANG, Yi LIANG
    Acta Mathematicae Applicatae Sinica(English Series). 2001, 17(3): 407-417.
    Abstract ( )    Download PDF ( )   Knowledge map   Save
    Some fundamental issues on statistical inferences relating to varying-coefficient regression models are addressed and studied.An exact testing procedure is proposed for checking the goodness of fit of a varying-coefficient model fited by the locally weighted regression technique versus an ordinary linear regression model.Also,an appropriate statistic for test variation of model parameters over the locations where the observations are collected is constructed and a formal testing approach which is essential to exploring spatial non-stationarity in geography science is suggested.
  • Original Articles
    (Statistical inferences for varying-coefficient models based on locally weighted regression technique)
    Chang Lin MEI, Wen Xiu ZHANG, Yi LIANG
    Acta Mathematicae Applicatae Sinica(English Series). 2001, 17(3): 407-417.
    Abstract ( )    Download PDF ( )   Knowledge map   Save
    Some fundamental issues on statistical inferences relating to varying-coefficient regression models are addressed and studied.An exact testing procedure is proposed for checking the goodness of fit of a varying-coefficient model fited by the locally weighted regression technique versus an ordinary linear regression model.Also,an appropriate statistic for test variation of model parameters over the locations where the observations are collected is constructed and a formal testing approach which is essential to exploring spatial non-stationarity in geography science is suggested.
  • 论文
    On the upper generalized exponents of ministrong digraphs
    Bo ZHOU
    Acta Mathematicae Applicatae Sinica(English Series). 2001, 17(3): 426-429.
    Abstract ( )    Download PDF ( )   Knowledge map   Save
  • Original Articles
    On the upper generalized exponents of ministrong digraphs
    Bo ZHOU
    Acta Mathematicae Applicatae Sinica(English Series). 2001, 17(3): 426-429.
    Abstract ( )    Download PDF ( )   Knowledge map   Save
  • 论文
    Superlinear convergence of the DFP algorithm without exact line search
    Ding Guo PU
    Acta Mathematicae Applicatae Sinica(English Series). 2001, 17(3): 430-432.
    Abstract ( )    Download PDF ( )   Knowledge map   Save
    In this paper,we give some conditions for line search,and prove that under these line search conditions the DFP algorithm is globally convergent and Q-superlinearly convergent.We show that the conditions are weaker than those in [6].
  • Original Articles
    Superlinear convergence of the DFP algorithm without exact line search
    Ding Guo PU
    Acta Mathematicae Applicatae Sinica(English Series). 2001, 17(3): 430-432.
    Abstract ( )    Download PDF ( )   Knowledge map   Save
    In this paper,we give some conditions for line search,and prove that under these line search conditions the DFP algorithm is globally convergent and Q-superlinearly convergent.We show that the conditions are weaker than those in [6].
Journal Online
News More