15 August 2007, Volume 23 Issue 3
    

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  • 论文
    Parametric Duality Models for Semi-infinite Discrete Minmax Fractional Programming Problems Involving Generalized (η,ρ)-Invex Functions
    G.J. Zalmai, Qing-hong Zhang
    Acta Mathematicae Applicatae Sinica(English Series). 2007, 23(3): 353-376.
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    A semi-infinite programming problem is a mathematical programming problem with a finite number of variables and infinitely many constraints. Duality theories and generalized convexity concepts are important research topics in mathematical programming. In this paper, we discuss a fairly large number of parametric duality results under various generalized (η, ρ)-invexity assumptions for a semi-infinite minmax fractional programming problem.

  • 论文
    An Optimal Control Problem of a Coupled Nonlinear Parabolic Population System
    Chao-hua Jia, De-xing Feng
    Acta Mathematicae Applicatae Sinica(English Series). 2007, 23(3): 377-388.
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    An optimal control problem for a coupled nonlinear parabolic population system is considered. The existence and uniqueness of the positive solution for the system is shown by the method of upper and lower solutions. An explicit prior bound of solutions to the system is given by considering an auxiliary coupled linear system. The existence of the optimal control is proved and the characterization of the optimal control is established.

  • 论文
    Some Properties of Bent Functions
    Ying Zhao
    Acta Mathematicae Applicatae Sinica(English Series). 2007, 23(3): 389-394.
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    First, this paper discusses and sums up some properties of a pair of functions p(x), q(x) that makes (y +1)p(x)+yq(x) into a bent function. Then it discusses the properties of bent functions. Also, the upper and lower bounds of the number of bent functions on GF(2)2k are discussed.

  • 论文
    A New Superlinearly Convergent SQP Algorithm for Nonlinear Minimax Problems
    Jin-bao Jian, Ran Quan, Qing-jie Hu
    Acta Mathematicae Applicatae Sinica(English Series). 2007, 23(3): 395-410.
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    In this paper, the nonlinear minimax problems are discussed. By means of the Sequential Quadratic Programming (SQP), a new descent algorithm for solving the problems is presented. At each iteration of the proposed algorithm, a main search direction is obtained by solving a Quadratic Programming (QP) which always has a solution. In order to avoid the Maratos effect, a correction direction is obtained by updating the main direction with a simple explicit formula. Under mild conditions without the strict complementarity, the global and superlinear convergence of the algorithm can be obtained. Finally, some numerical experiments are reported.

  • 论文
    Impulsive Boundary Value Problems for First-order Ordinary Differential Inclusions
    Yi-cheng Liu, Jun Wu, Zhi-xiang Li
    Acta Mathematicae Applicatae Sinica(English Series). 2007, 23(3): 411-420.
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    In this paper, we investigate the existence of solutions for impulsive first order ordinary differential inclusions which admitting nonconvex valued right hand side. We present two classes of results. In the first one, we rely on a fixed point theorem for contraction multivalued maps due to Covitz and Nadler, and for the second one, we use Schaefer’s fixed point theorem combined with lower semi-continuous multivalued operators with decomposable values under weaker conditions.

  • 论文
    An Extension Landau-Lifshitz Model in Studying Soft Ferromagnetic Films
    Jing-na Li, Xiao-feng Wang, Zheng-an Yao
    Acta Mathematicae Applicatae Sinica(English Series). 2007, 23(3): 421-432.
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    In this paper, we propose a model in studying soft ferromagnetic films, which is readily accessible experimentally. By using penalty approximation and compensated compactness, we prove that the dynamical equation in thin film has a local weak solution. Moreover, the corresponding linear equation is also dealt with in great detail.

  • 论文
    Vertex Distinguishing Equitable Total Chromatic Number of Join Graph
    Zhi-wen Wang, Li-hong Yan
    Acta Mathematicae Applicatae Sinica(English Series). 2007, 23(3): 433-438.
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    A vertex distinguishing equitable total coloring of graph G is a proper total coloring of graph G such that any two distinct vertices’ coloring sets are not identical and the difference of the elements colored by any two colors is not more than 1. In this paper we shall give vertex distinguishing equitable total chromatic number of join graphs Pn∨Pn,Cn∨Cn and prove that they satisfy conjecture 3, namely, the chromatic numbers of vertex distinguishing total and vertex distinguishing equitable total are the same for join graphs Pn ∨Pn and Cn ∨ Cn.

  • 论文
    A Score Type Test for General Autoregressive Models in Time Series
    Jian-hong Wu, Li-xing Zhu
    Acta Mathematicae Applicatae Sinica(English Series). 2007, 23(3): 439-450.
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    This paper is devoted to the goodness-of-fit test for the general autoregressive models in time series. By averaging for the weighted residuals, we construct a score type test which is asymptotically standard chi-squared under the null and has some desirable power properties under the alternatives. Specifically, the test is sensitive to alternatives and can detect the alternatives approaching, along a direction, the null at a rate that is arbitrarily close to n-1/2. Furthermore, when the alternatives are not directional, we construct asymptotically distribution-free maximin tests for a large class of alternatives. The performance of the tests is evaluated through simulation studies.

  • 论文
    Bifurcation and Isochronicity at Infinity in a Class of Cubic Polynomial Vector Fields
    Qin-long Wang, Yi-rong Liu
    Acta Mathematicae Applicatae Sinica(English Series). 2007, 23(3): 451-466.
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    In this paper, we study the appearance of limit cycles from the equator and isochronicity of infinity in polynomial vector fields with no singular points at infinity. We give a recursive formula to compute the singular point quantities of a class of cubic polynomial systems, which is used to calculate the first seven singular point quantities. Further, we prove that such a cubic vector field can have maximal seven limit cycles in the neighborhood of infinity. We actually and construct a system that has seven limit cycles. The positions of these limit cycles can be given exactly without constructing the Poincar′e cycle fields. The technique employed in this work is essentially different from the previously widely used ones. Finally, the isochronous center conditions at infinity are given.

  • 论文
    A Shrinkage Estimator for Combination of Bioassays
    Jian Xiong, D.G. Chen
    Acta Mathematicae Applicatae Sinica(English Series). 2007, 23(3): 467-476.
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    A shrinkage estimator and a maximum likelihood estimator are proposed in this paper for combination of bioassays. The shrinkage estimator is obtained in closed form which incorporates prior information just on the common log relative potency after the homogeneity test for combination of bioassays is accepted. It is a practical improvement over other estimators which require iterative procedure to obtain the estimator for the relative potency. A real data is also used to show the superiorities for the newly-proposed procedures.

  • 论文
    Optimal Proportional Reinsurance for Controlled Risk Process which is Perturbed by Diffusion
    Zhi-bin Liang
    Acta Mathematicae Applicatae Sinica(English Series). 2007, 23(3): 477-488.
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    In this paper, we study optimal proportional reinsurance policy of an insurer with a risk process which is perturbed by a diffusion. We derive closed-form expressions for the policy and the value function, which are optimal in the sense of maximizing the expected utility in the jump-diffusion framework. We also obtain explicit expressions for the policy and the value function, which are optimal in the sense of maximizing the expected utility or maximizing the survival probability in the diffusion approximation case. Some numerical examples are presented, which show the impact of model parameters on the policy. We also compare the results under the different criteria and different cases.

  • 论文
    Fixed Points for Mean Non-expansive Mappings
    Chun-xue Wu, Li-juan Zhang
    Acta Mathematicae Applicatae Sinica(English Series). 2007, 23(3): 489-494.
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    For a Banach Space X Garcia-Falset introduced the coefficient R(X) and showed that if R(X) < 2 then X has a fixed point. In this paper, we define a mean non-expansive mapping T on X in the sense that then T has a fixed point in X.

  • 论文
    Strong Laws of Large Numbers for Random Walks in Random Sceneries
    Wen-sheng Wang
    Acta Mathematicae Applicatae Sinica(English Series). 2007, 23(3): 495-500.
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    In this paper, we study strong laws of large numbers for random walks in random sceneries. Some mild sufficient conditions for the validity of strong laws of large numbers are obtained.

  • 论文
    One Dimensional Stochastic Differential Equations with Distributional Drifts
    Kai He, Xi-cheng Zhang
    Acta Mathematicae Applicatae Sinica(English Series). 2007, 23(3): 501-512.
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    In this paper we study the existence, pathwise uniqueness and homeomorphism flow of strong solutions to a class of one dimensional SDEs driven by infinitely many Brownian motions, and with Yamada- Watanabe diffusion coefficients and distributional drift coefficients.

  • 论文
    On Comparison Theorem and Solutions of BSDEs for Lévy Processes
    Qing Zhou
    Acta Mathematicae Applicatae Sinica(English Series). 2007, 23(3): 513-522.
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    In this paper, we consider backward stochastic differential equations driven by a Lévy process. A comparison theorem and an existence and uniqueness theorem of BSDEs with non-Lipschitz coefficients are obtained.

  • 论文
    Global Attractivity of Positive Periodic Solutions for a Survival Model of Red Blood Cells
    Xin-min Wu, Jing-wen Li
    Acta Mathematicae Applicatae Sinica(English Series). 2007, 23(3): 523-528.
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    In this paper, we deal with a model for the survival of red blood cells with periodic coefficients A new sufficient condition for global attractivity of positive periodic solutions of Eq.(*) is obtained. Our criterion improves corresponding result obtained by Li and Wang in 2005.

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