25 January 2008, Volume 24 Issue 1
    

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  • 论文
    Convergence of Solutions of Discrete Reflected Backward SDE's and Simulations
    Jean M\'emin, Shi-ge Peng, Ming-yu Xu
    Acta Mathematicae Applicatae Sinica(English Series). 2008, 24(1): 1-18.
    Abstract ( )    Download PDF ( )   Knowledge map   Save
    The objective of this paper is to introduce elementary
    discrete reflected backward equations and to give a simple method
    to discretize in time a (continuous) reflected backward equation.
    A presentation of numerical simulations is also described.
  • 论文
    The Global Attractors for the Dissipative Generalized Hasegawa-Mima Equation
    Rui-feng Zhang
    Acta Mathematicae Applicatae Sinica(English Series). 2008, 24(1): 19-28.
    Abstract ( )    Download PDF ( )   Knowledge map   Save
    The long time behavior of solutions of the generalized
    Hasegawa-Mima equation with dissipation term is considered. The
    existence of global attractors of the periodic initial
    value problem is proved, and the estimate of the upper bound of the Hausdorff
    and fractal dimensions for the global attractors is obtained by means of uniform
    a priori estimates method.
  • 论文
    Optimal Control Problem Governed bySemilinear Parabolic Equation and its Algorithm
    Chun-fa Li, Xue Yang, En-min Feng
    Acta Mathematicae Applicatae Sinica(English Series). 2008, 24(1): 29-40.
    Abstract ( )    Download PDF ( )   Knowledge map   Save
    In this paper, an optimal control problem governed by semilinear
    parabolic equation which involves the control variable acting on forcing term
    and coefficients appearing in the higher order derivative terms is formulated
    and analyzed. The strong variation method, due originally to Mayne et al to
    solve the optimal control problem of a lumped parameter system, is extended to
    solve an optimal control problem governed by semilinear parabolic equation, a
    necessary condition is obtained, the strong variation algorithm for this
    optimal control problem is presented, and the corresponding convergence result
    of the algorithm is verified.
  • 论文
    A Symmetric Characteristic Finite Volume Element Scheme for NonlinearConvection--Diffusion Problems
    Min Yang, Yi-rang Yuan
    Acta Mathematicae Applicatae Sinica(English Series). 2008, 24(1): 41-54.
    Abstract ( )    Download PDF ( )   Knowledge map   Save
    In this paper, we implement alternating direction
    strategy and construct a symmetric FVE scheme for nonlinear
    convection--diffusion problems. Comparing to general FVE methods,
    our method has two advantages. First, the coefficient matrices of
    the discrete schemes will be symmetric even for nonlinear
    problems. Second, since the solution of the algebraic equations at
    each time step can be inverted into the solution of several
    one-dimensional problems, the amount of computation work is
    smaller. We prove the optimal $H^1$-norm error estimates of order
    $O(\Delta t^2+h)$ and present some numerical examples at the end
    of the paper.
  • 论文
    AVDTC Numbers of Generalized Halin Graphs with MaximumDegree at Least 6
    Xiang-en Chen, Zhong-fu Zhang
    Acta Mathematicae Applicatae Sinica(English Series). 2008, 24(1): 55-58.
    Abstract ( )    Download PDF ( )   Knowledge map   Save
    In a paper by Zhang and Chen et al.(see [11]),
    a conjecture was made concerning the minimum number of colors $\chi_{at}(G)$ required
    in a proper total-coloring of $G$ so that any two adjacent vertices have
    different color sets, where the color set of a vertex $v$ is the set composed of
    the color of $v$ and the colors incident to $v$. We find the exact values
    of $\chi_{at}(G)$ and thus
    verify the conjecture when $G$ is a Generalized Halin graph with maximum
    degree at least $6$. A generalized Halin graph is a 2-connected
    plane graph $G$ such that removing all the edges of the boundary
    of the exterior face of $G$ (the degrees of the vertices in the
    boundary of exterior face of $G$ are all three) gives a tree.
  • 论文
    Precise Asymptotics of Error Variance Estimator in Partially Linear Models
    Shao-jun Guo, Min Chen, Feng Liu
    Acta Mathematicae Applicatae Sinica(English Series). 2008, 24(1): 59-74.
    Abstract ( )    Download PDF ( )   Knowledge map   Save
    In this paper, we focus our attention on the precise
    asymptotics of error variance estimator in partially linear
    regression models, $y_i=x_i^\tau \beta+g(t_i)+\e_i,1\le i \le n$,
    $ \{\e_i, i=1,\cdots, n\}$ are $i.i.d$ random errors with mean 0
    and positive finite variance $\sigma^2$. Following the ideas of
    Allan Gut and Aurel Sp$\breve{a}$taru$^{[7,8]}$ and
    Zhang$^{[21]}$, on precise asymptotics in the Baum-Katz and Davis
    laws of large numbers and precise rate in laws of the iterated
    logarithm, respectively, and subject to some regular conditions,
    we obtain the corresponding results in partially linear
    regression models.
  • 论文
    On the Asymptotic Behavior of theStorage Process Fed by a Markov Modulated Brownian Motion
    Xiao-yu Xing, Xue-qiang Wang
    Acta Mathematicae Applicatae Sinica(English Series). 2008, 24(1): 75-84.
    Abstract ( )    Download PDF ( )   Knowledge map   Save
    Consider a storage model fed by a Markov modulated
    Brownian motion. We prove that the stationary distribution of the
    model exits and that the running maximum of the storage process
    over the interval $[0, t]$ grows asymptotically like $\log t$ as
    $t\rightarrow \infty$.
  • 论文
    A longitudinal study of the effects of family background factors on mathematics achievements using quantile regression
    Xi-zhi Wu; Mao-zai Tian
    Acta Mathematicae Applicatae Sinica(English Series). 2008, 24(1): 85-98.
    Abstract ( )    Download PDF ( )   Knowledge map   Save
    Quantile regression is gradually emerging as a powerful tool for estimating models of conditional quantile functions, and therefore research in this area has vastly increased in the past two decades. This paper, with the quantile regression technique, is the first comprehensive longitudinal study on mathematics participation data collected in Alberta, Canada. The major advantage of longitudinal study is its capability to separate the so-called cohort and age effects in the context of population studies. One aim of this paper is to study whether the family background factors alter performance on the mathematical achievement of the strongest students in the same way as that of weaker students based on the large longitudinal sample of 2000, 2001 and 2002 mathematics participation longitudinal data set. The interesting findings suggest that there may be differential family background factor effects at different points in the mathematical achievement conditional distribution.
  • 论文
    Testing Serial Correlation in Semiparametric Varying-Coefficient Partially LinearEV Models
    Xue-mei Hu, Zhi-zhong Wang, Feng Liu
    Acta Mathematicae Applicatae Sinica(English Series). 2008, 24(1): 99-106.
    Abstract ( )    Download PDF ( )   Knowledge map   Save
    This paper studies estimation and serial correlation
    test of a semiparametric varying-coefficient partially linear EV
    model of the form $Y=X^{\tau}\beta+Z^{\tau}\alpha(T)+\varepsilon,
    \xi= X+\eta$ with the identifying condition
    $E[(\varepsilon,\eta^{\tau})^{\tau}]=0,$
    Cov$[(\varepsilon,\eta^{\tau})^{\tau}]=\sigma^{2}I_{p+1}$. The
    estimators of interested regression parameters $\beta$ , and the
    model error variance $\sigma^{2}$, as well as the nonparametric
    components $\alpha(T)$, are constructed. Under some regular
    conditions, we show that the estimators of the unknown vector
    $\beta$ and the unknown parameter $\sigma^{2}$ are strongly
    consistent and asymptotically normal and that the estimator of
    $\alpha(T)$ achieves the optimal strong convergence rate of the
    usual nonparametric regression. Based on these estimators and
    asymptotic properties, we propose the $V_{N,p}$ test statistic and
    empirical log-likelihood ratio statistic for testing serial
    correlation in the model. The proposed statistics are shown to
    have asymptotic normal or chi-square distributions under the null
    hypothesis of no serial correlation. Some simulation studies are
    conducted to illustrate the finite sample performance of the
    proposed tests.
  • 论文
    Ruin Probabilities of a Surplus Process Described by PDMPs
    Jing-min He, Rong Wu, Hua-yue Zhang
    Acta Mathematicae Applicatae Sinica(English Series). 2008, 24(1): 117-128.
    Abstract ( )    Download PDF ( )   Knowledge map   Save
    In this paper we mainly study the ruin probability of a surplus
    process described by a piecewise deterministic Markov process (PDMP). An
    integro-differential equation for the ruin probability is derived. Under a
    certain assumption, it can be transformed into the ruin probability of a risk
    process whose premiums depend on the current reserves. Using the same argument
    as that in Asmussen and Nielsen$^{[2]}$, the ruin probability and its upper
    bounds are obtained. Finally, we give an analytic expression for ruin
    probability and its upper bounds when the claim-size is exponentially
    distributed.
  • 论文
    Time-periodic Solution to a Nonlinear ParabolicType Equation of Higher Order
    Yan-ping Wang, You-lin Zhang
    Acta Mathematicae Applicatae Sinica(English Series). 2008, 24(1): 129-140.
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    In this paper, the existence and uniqueness of
    time-periodic generalized solutions and time-periodic
    classical solutions to a class of parabolic type equation of
    higher order are proved by Galerkin method.
  • 论文
    A Notion of Stochastic Input-to-StateStability and Its Application to Stability ofCascaded Stochastic Nonlinear Systems
    Shu-jun Liu, Ji-feng Zhang, Zhong-ping Jiang
    Acta Mathematicae Applicatae Sinica(English Series). 2008, 24(1): 141-156.
    Abstract ( )    Download PDF ( )   Knowledge map   Save
    In this paper, the property of practical input-to-state
    stability and its application to stability of cascaded nonlinear
    systems are investigated in the stochastic framework. Firstly, the
    notion of (practical) stochastic input-to-state stability with
    respect to a stochastic input is introduced, and then by the
    method of changing supply functions, (a) an (practical)
    SISS-Lyapunov function for the overall system is obtained from the
    corresponding Lyapunov functions for cascaded (practical) SISS
    subsystems.
  • 论文
    An Iterative Algorithm for Angle-limited Three-dimensional Image Reconstruction
    Gang-rong Qu, Yong-sheng Lan, Ming Jiang
    Acta Mathematicae Applicatae Sinica(English Series). 2008, 24(1): 157-166.
    Abstract ( )    Download PDF ( )   Knowledge map   Save
    We establish an improved GP iterative algorithm for the
    extrapolation of band-limited function to fully 3-dimensional
    image reconstruction by the convolution-backprojection algorithm.
    Numerical experiments demonstrate that the image resolving power
    of IGP algorithm is better than that of the original GP algorithm
    for noisy data.
  • 论文
    The Same Distribution of Limit Cycles in a Hamiltonian Systemwith Nine Seven-order Perturbed Terms
    Tao Jiang, Zhi-yan Yang
    Acta Mathematicae Applicatae Sinica(English Series). 2008, 24(1): 167-176.
    Abstract ( )    Download PDF ( )   Knowledge map   Save
    Using qualitative analysis and numerical simulation, we
    investigate the number and distribution of limit cycles for a
    cubic Hamiltonian system with nine different seven-order perturbed
    terms. It is showed that these perturbed systems have the same
    distribution of limit cycles. Furthermore, these systems have 13,
    11 and 9 limit cycles for some parameters, respectively. The
    accurate positions of the 13, 11 and 9 limit cycles are obtained
    by numerical exploration, respectively.
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