15 January 2007, Volume 23 Issue 1
    

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  • 论文
    Asymptotic Weighted-Periodicity of the Impulsive Parabolic Equation with Time Delay
    Jin-liang Wang
    Acta Mathematicae Applicatae Sinica(English Series). 2007, 23(1): 1-8.
    Abstract ( )    Download PDF ( )   Knowledge map   Save
    The main aim of this paper is to investigate the effects
    of the impulse and time delay on a type of parabolic equations. In
    view of the characteristics of the equation, a particular
    iteration scheme is adopted. The results show that Under certain
    conditions on the coefficients of the equation and the impulse,
    the solution oscillates in a particular manner---called
    ``asymptotic weighted-periodicity".
  • 论文
    Study on a Cross Diffusion Parabolic System
    Li Chen
    Acta Mathematicae Applicatae Sinica(English Series). 2007, 23(1): 9-28.
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    This paper considers a kind of strongly coupled cross
    diffusion parabolic system, which can be used as the
    multi-dimensional {\it Lyumkis} energy transport model in
    semiconductor science. The global existence and large time
    behavior are obtained for smooth solution to the initial boundary
    value problem. When the initial data are a small perturbation of
    an isothermal stationary solution, the smooth solution of the
    problem under the insulating boundary condition, converges to that
    stationary solution exponentially fast as time goes to infinity.
  • 论文
    The {\mathcal{UV}}$-Decomposition on a Class of D.C. Functions and Optimality Conditions
    Wei Wang
    Acta Mathematicae Applicatae Sinica(English Series). 2007, 23(1): 29-38.
    Abstract ( )    Download PDF ( )   Knowledge map   Save
    In this paper, the $\mathcal{UV}$-theory and
    P-differential calculus are
    employed to study second-order expansion of a class of D.C. functions and
    minimization problems. Under certain conditions, some properties of the ${\cal U}$-Lagrangian, the
    second-order expansion of this class of functions
    along some trajectories are formulated. Some first and
    second order optimality conditions for the class of D.C. optimization
    problems are given.
  • 论文
    Existence of Positive Periodic Solutions for Nonautonomous Predator-prey Systems with Discrete and Continuously Distributed Delays
    Yan Lv
    Acta Mathematicae Applicatae Sinica(English Series). 2007, 23(1): 39-48.
    Abstract ( )    Download PDF ( )   Knowledge map   Save
    By using the continuation theorem of coincidence degree
    theory, the sufficient conditions to guarantee the existence of
    positive periodic solutions are established for nonautonomous
    predator-prey systems with discrete and continuously distributed
    delays.
  • 论文
    Gevrey Class Regularity and Exponential Decay Property for Navier-Stokes-${\alpha}$ Equations
    Kai-tai Li
    Acta Mathematicae Applicatae Sinica(English Series). 2007, 23(1): 49-58.
    Abstract ( )    Download PDF ( )   Knowledge map   Save
    The Navier-Stokes-$\alpha$ equations subject to the
    periodic boundary conditions are considered. Analyticity in time
    for a class of solutions taking values in a Gevrey class of
    functions is proven. Exponential decay of the spatial Fourier
    spectrum for the analytic solutions and the lower bounds on the
    rate defined by the exponential decay are also obtained.
  • 论文
    Unification of Filled Function and Tunnelling Function in Global Optimization
    Wei Wang, Yong-jian Yang, Lian-sheng Zhang
    Acta Mathematicae Applicatae Sinica(English Series). 2007, 23(1): 59-66.
    Abstract ( )    Download PDF ( )   Knowledge map   Save
    In this paper, two auxiliary functions for global
    optimization are proposed. These two auxiliary functions possess
    all characters of tunnelling functions and filled functions under
    certain general assumptions. Thus, they can be considered as the
    unification of filled function and tunnelling function. Moreover,
    the process of tunneling or filling for global optimization can be
    unified as the minimization of such auxiliary functions. Result of
    numerical experiments shows that such two auxiliary functions are
    effective.
  • 论文
    Constructions for Anonymous Secret Sharing Schemes Using Combinatorial Designs
    Ying-pu Deng, Li-feng Guo, Mu-lan Liu
    Acta Mathematicae Applicatae Sinica(English Series). 2007, 23(1): 67-78.
    Abstract ( )    Download PDF ( )   Knowledge map   Save
    In an anonymous secret sharing scheme the secret can be
    reconstructed without knowledge of which participants hold which
    shares. In this paper some constructions of anonymous secret
    sharing schemes with 2 thresholds by using combinatorial designs
    are given. Let $v(t,w,q)$ denote the minimum size of the set of
    shares of a perfect anonymous $(t,w)$ threshold secret sharing
    scheme with $q$ secrets. In this paper we prove that
    $v(t,w,q)=\Theta(q)$ if $t$ and $w$ are fixed and that the lower
    bound of the size of the set of shares in [4] is not optimal under
    certain condition.
  • 论文
    Multisplitting Iteration Schemes for Solving a Class of Nonlinear Complementarity Problems
    Chen-liang Li
    Acta Mathematicae Applicatae Sinica(English Series). 2007, 23(1): 79-90.
    Abstract ( )    Download PDF ( )   Knowledge map   Save
    We consider several synchronous and asynchronous
    multisplitting iteration schemes for solving a class of
    nonlinear complementarity problems with the system matrix being an $H-$matrix.
    We establish the convergence theorems for the schemes. The
    numerical experiments show that the schemes are efficient for
    solving the class of nonlinear complementarity problems.
  • 论文
    On Connectedness of Efficient Solution Sets for a Star Cone-Quasiconvex Vector Optimization Problem
    Wen Song$^1$, Bo-ying Wu$^2$, Jian-mei Zhang$^3$
    Acta Mathematicae Applicatae Sinica(English Series). 2007, 23(1): 91-98.
    Abstract ( )    Download PDF ( )   Knowledge map   Save
    In this note, we prove that the efficient solution set
    for a vector optimization problem with a continuous, star
    cone-quasiconvex objective mapping is connected under the
    assumption that the ordering cone is a $D$-cone. A $D$-cone
    includes any closed convex pointed cones in a normed space which
    admits strictly positive continuous linear functionals.
  • 论文
    Time Decay Rates of the Isotropic Non-Newtonian Flows in ${\pmb R}^n$
    Bo-Qing Dong
    Acta Mathematicae Applicatae Sinica(English Series). 2007, 23(1): 99-106.
    Abstract ( )    Download PDF ( )   Knowledge map   Save
    This paper is concerned with time decay rates
    for weak solutions to a class system of
    isotropic incompressible non-Newtonian fluid motion in
    $\R^n$. With the use of the spectral decomposition
    methods of Stokes operator, the optimal decay estimates of weak
    solutions in L${^2}$ norm are derived under the different
    conditions on the initial velocity. Moreover, the error
    estimates of the difference between non-Newtonian flow and
    Navier-Stokes flow are also investigated.
  • 论文
    Construction of $\large \pmb{2^{m-(m-k)}_{\rm III}}$ Designs with the Maximum Number of Clear Two-factor Interactions
    Gui-Jun Yang
    Acta Mathematicae Applicatae Sinica(English Series). 2007, 23(1): 107-112.
    Abstract ( )    Download PDF ( )   Knowledge map   Save
    It is useful to know the maximum number of clear
    two-factor interactions in a $2^{m-(m-k)}_{\rm III}$ design. This
    paper provides a method to construct a $2^{m-(m-k)}_{\rm III}$
    design with the maximum number of clear two-factor interactions.
    And it is proved that the resulting designs have more clear
    two-factor interactions than those constructed by Tang et
    al.$^{[6]}$. Moreover, the designs constructed are shown to have
    concise grid representations.
  • 论文
    The Boundedness for Commutators of Multipliers
    Wen-ming Li
    Acta Mathematicae Applicatae Sinica(English Series). 2007, 23(1): 113-122.
    Abstract ( )    Download PDF ( )   Knowledge map   Save
    Let $[b,T]$ be the commutator generated by a Lipschitz
    function $b\in \text{Lip}(\beta)(0<\beta<1)$ and multiplier $T$.
    The authors studied the boundedness
    of $[b,T]$ on the Lebesgue spaces and Hardy spaces.
  • 论文
    Large Sets and Overlarge Sets of Triangle-Decomposition
    Zi-hong Tian
    Acta Mathematicae Applicatae Sinica(English Series). 2007, 23(1): 123-132.
    Abstract ( )    Download PDF ( )   Knowledge map   Save
    There are six types of triangles: undirected triangle,
    cyclic triangle, transitive triangle, mixed-1 triangle, mixed-2
    triangle and mixed-3 triangle. The triangle-decompositions for the
    six types of triangles have already been solved. For the first
    three types of triangles, their large sets have already been
    solved, and their overlarge sets have been investigated. In this
    paper, we establish the spectrum of $LT_i(v,\lambda)$, $OLT_i(v)
    (i=1,2)$, and give the existence of $LT_3(v,\lambda)$ and
    $OLT_3(v,\lambda)$ with $\lambda$ even.
  • 论文
    The Survival Analysis of a Non-autonomous N-dimensional Volterra Mutualistic System in a Polluted Environment
    Xiao-jian Li$^{1*}$, Ke Wang$^{2\dagger}$
    Acta Mathematicae Applicatae Sinica(English Series). 2007, 23(1): 133-140.
    Abstract ( )    Download PDF ( )   Knowledge map   Save
    In this paper, we extend the autonomous n-Dimensional
    Volterra Mutualistic System to a non-autonomous system. The
    condition of persistence and extinction is obtained for each
    population, and the threshold is established for asymptotically
    autonomous system.
  • 论文
    On Ekeland’s Variational Principle for Set-Valued Mappings
    Sheng-jie Li, Wen-yan Zhang
    Acta Mathematicae Applicatae Sinica(English Series). 2007, 23(1): 141-148.
    Abstract ( )    Download PDF ( )   Knowledge map   Save
    In this paper, we derive a general vector Ekeland
    variational principle for set-valued mappings, which has a closed
    relation to $\varepsilon k^0$ -efficient points of set-valued
    optimization problems. The main result presented in this paper is
    a generalization of the corresponding result in [3].
  • 论文
    Existence of Arrow-Debreu Equilibrium with S-shaped Utility Function
    Yang Xi
    Acta Mathematicae Applicatae Sinica(English Series). 2007, 23(1): 149-154.
    Abstract ( )    Download PDF ( )   Knowledge map   Save
    This paper characterizes the optimal solution of
    subjective expected utility with S-shaped utility function, by
    using the prospect theory (PT). We also prove the existence of
    Arrow-Debreu equilibrium.
  • 论文
    On the Upper Bounds of the Numbers of Perfect Matchings in Graphs with Given Parameters
    Hong Lin, Xiao-feng Guo
    Acta Mathematicae Applicatae Sinica(English Series). 2007, 23(1): 155-160.
    Abstract ( )    Download PDF ( )   Knowledge map   Save
    Let $\phi (G)$, $\kappa (G)$, $\alpha (G)$, $\chi (G)$,
    $cl(G)$, diam$(G)$ denote the number of perfect matchings,
    connectivity, independence number, chromatic number, clique number
    and diameter of a graph $G$, respectively. In this note, by
    constructing some extremal graphs, the following extremal problems
    are solved:\\
    1. max $\{\phi (G)$: $|V(G)|=2n$, $\kappa (G)\leq
    k\}=k[(2n-3)!!]$,\\
    2. max$\{\phi (G)$: $|V(G)|=2n$, $\alpha (G)\geq
    k\}=\Big[\prod\limits_{i=0}^{k-1}(2n-k-i)\Big][(2n-2k-1)!!]$,\\
    3. max$\{\phi (G)$: $|V(G)|=2n$, $\chi (G)\leq k\}=\phi
    (T_{k,2n})$ \ $T_{k,2n}$ is the Tur$\acute{a}$n graph, that is a
    complete $k$-partite graph on $2n$ vertices in which all parts are
    as equal in size as possible,\\
    4. max$\{\phi (G)$: $|V(G)|=2n$, $cl(G)=2\}=n!$,\\
    5. max$\{\phi (G)$: $|V(G)|=2n$, diam$(G)\geq
    2\}=(2n-2)(2n-3)[(2n-5)!!]$,\\
    max$\{\phi (G)$: $|V(G)|=2n$, diam$(G)\geq
    3\}=(n-1)^2[(2n-5)!!]$.
  • 论文
    Structure-Preserving Algorithms for a Class of Dynamical Systems
    Ling-shu Wang
    Acta Mathematicae Applicatae Sinica(English Series). 2007, 23(1): 161-176.
    Abstract ( )    Download PDF ( )   Knowledge map   Save
    In this paper, we study structure-preserving algorithms
    for dynamical systems defined by ordinary differential equations
    in $R^n$. The equations are assumed to be of the form
    $\dot{y}=A(y)+D(y)+R(y)$, where $A(y)$ is the conservative part
    subject to $\langle A(y), y\rangle=0$; $D(y)$
    is the damping part or the part describing the coexistence of damping and
    expanding; $R(y)$ reflects strange phenomenon of the system. It
    is shown that the numerical solutions generated by the symplectic
    Runge-Kutta(SRK) methods with $b_{i}>0\;(\;i=1,\cdots,s)$ have
    long-time approximations to the exact ones, and these methods can
    describe the structural properties of the quadratic energy for
    these systems. Some numerical experiments and backward error
    analysis
    also show that these methods are better than other methods
    including the general algebraically stable
    Runge-Kutta(RK)methods.
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