20 October 2008, Volume 24 Issue 4
    

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  • Nonexistence and Existence of Multiple Positive Solutions for Superlinear Three-point Boundary Value Problems via Index Theory
    Bao-qiang Yan, Donal O'Regan, Ravi P. Agarwal
    Acta Mathematicae Applicatae Sinica(English Series). 2008, 24(4): 529-540.
    Abstract ( )    Download PDF ( )   Knowledge map   Save
    This paper discusses both the nonexistence of positive solutions for
    second-order three-point boundary value problems
    when the nonlinear term $f(t,x,y)$ is superlinear in $y$ at $y=0$
    and the existence
    of multiple positive solutions for second-order three-point boundary value
    problems when the nonlinear term $f(t,x,y)$ is superlinear in $x$ at
    $+\infty$.
  • 论文
    Analytic Study of Magnetohydrodynamic Flow and Boundary LayerControl Over a Wedge
    M. Chandrasekar, S. Baskaran
    Acta Mathematicae Applicatae Sinica(English Series). 2008, 24(4): 541-552.
    Abstract ( )    Download PDF ( )   Knowledge map   Save
    A genuine variational principle developed by Gyarmati, in the field of thermodynamics of irreversible processes
    unifying the theoretical requirements of technical, environmental and biological sciences is employed to study the effects of
    uniform suction and injection on MHD flow adjacent to an isothermal wedge with pressure gradient in the presence of a transverse
    magnetic field. The velocity distribution inside the boundary layer has been considered as a simple polynomial function and the
    variational principle is formulated. The Euler-Lagrange equation is reduced to a simple polynomial equation in terms of momentum
    boundary layer thickness. The velocity profiles, displacement thickness and the coefficient of skin friction are calculated for
    various values of wedge angle parameter $m$, magnetic parameter $\xi$ and suction/injection parameter $H$. The present results
    are compared with known available results and the comparison is found to be satisfactory. The present study establishes high
    accuracy of results obtained by this variational technique.
  • 论文
    The Nonlinear Singularly Perturbed NonlocalReaction Diffusion Systems
    Jia-qi Mo, Xiu Chen
    Acta Mathematicae Applicatae Sinica(English Series). 2008, 24(4): 553-562.
    Abstract ( )    Download PDF ( )   Knowledge map   Save
    In this paper the singularly perturbed initial boundary value
    problems for a nonlocal reaction diffusion system are considered. Using the
    iteration method and the comparison theorem, the existence and asymptotic
    behavior of solutions for the problem are studied.
  • 论文
    Stochastic Noise in Auto-regulatory Genetic Network: Model-dependence andStatistical Complication
    Ying-zi Shang
    Acta Mathematicae Applicatae Sinica(English Series). 2008, 24(4): 563-572.
    Abstract ( )    Download PDF ( )   Knowledge map   Save
    For the single gene network model, there are two basic
    types. For convenience, we call them Type I and Type II,
    respectively. The Type I model describes both the dynamics of mRNA
    and protein. The Type II model is a simplification of the Type I
    model based on the assumption that the change rate of mRNA is much
    faster than protein because the half-life of mRNA is short compared
    with that of protein. the Type II model describes only the dynamics
    of protein. The analysis of the Type I model is based on the
    assumption that the ratio of the protein decay rate to the mRNA
    decay rate is small enough. The main results for Type I model show
    that the Fano factor of the protein must be bigger than one if there
    is no negative feedback on the transcription. If there is negative
    feedback, the relative fluctuation strength in the number of
    proteins is determined by the size of the feedback regulation
    strength.
  • 论文
    The $ \large \pmb k$-point Exponent Set of Primitive Digraphswith Girth 2
    She-xi Chen, Wei-jun Liu, Jin-wang Liu
    Acta Mathematicae Applicatae Sinica(English Series). 2008, 24(4): 573-582.
    Abstract ( )    Download PDF ( )   Knowledge map   Save
    Let $D=(V, E)$ be a primitive digraph. The vertex exponent of $D$ at
    a vertex $v\in V$, denoted by $\exp_{D}(v)$, is the least integer $p$ such that
    there is a $v\rightarrow u$ walk of length $p$ for each $u\in V.$ Following
    Brualdi and Liu, we order the vertices of $D$ so that $\exp_{D}(v_{1})\leq
    \exp_{D}(v_{2})\leq \cdots \leq \exp_{D}(v_{n})$. Then $\exp_{D}(v_{k})$ is
    called the $k$-point exponent of $D$ and is denoted by $\exp_{D}(k),$ $1\leq
    k\leq n.$ In this paper we define $e(n,k):=\max\{\exp_D(k)|\, D\in PD(n,2)\}$
    and $E(n,k):=\{\exp_{D}(k)|\, D\in PD(n,2)\},$ where $PD(n,2)$ is the set of
    all primitive digraphs of order $n$ with girth $2$. We completely determine
    $e(n,k)$ and $E(n,k)$ for all $n,$ $k$ with $n\geq 3$ and $1\leq k\leq n.$
  • 论文
    A Remark on Partly Dissipative Reaction Diffusion Systems on \Large $\bf {I\! R}^n $
    Xue-ke Pu$^{}$, Xing-you Zhang
    Acta Mathematicae Applicatae Sinica(English Series). 2008, 24(4): 583-588.
    Abstract ( )    Download PDF ( )   Knowledge map   Save
    The long time behavior of the solutions of some partly
    dissipative reaction diffusion systems is studied. We prove the
    existence of a compact $(L^2\times L^2-H^1\times L^2)$ attractor for
    a partly dissipative reaction diffusion system in $R^n$. This
    improves a previous result obtained by A. Rodrigues-Bernal and B.
    Wang concerning the existence of a compact $(L^2\times L^2-L^2\times
    L^2)$ attractor for the same system.
  • 论文
    Positive Solutions for a Competition Model with an Inhibitor Involved
    Bin Chen
    Acta Mathematicae Applicatae Sinica(English Series). 2008, 24(4): 589-598.
    Abstract ( )    Download PDF ( )   Knowledge map   Save
    In the paper, we study the positive solutions of a
    diffusive competition model with an inhibitor involved subject to
    the homogeneous Dirichlet boundary condition. The existence,
    uniqueness, stability and multiplicity of positive solutions are
    discussed. This is mainly done by using the local and global
    bifurcation theory.
  • 论文
    Homoclinic and Heteroclinic Flows in Global Attractor for Davey-stewartson II Equation
    Zheng-de Dai, Shao-lin Li
    Acta Mathematicae Applicatae Sinica(English Series). 2008, 24(4): 599-612.
    Abstract ( )    Download PDF ( )   Knowledge map   Save
    By the variable transformation and generalized Hirota method, exact
    homoclinic and heteroclinic solutions for Davey-Stewartson II (DSII) equation
    are obtained. For perturbed DSII equation, the existence of a global attractor
    is proved. The persistence of homoclinic and heteroclinic flows is
    investigated, and the special homoclinic and heteroclinic structure in
    attractors is shown.
  • 论文
    Adaptive Wavelet Solution to the Stokes Problem
    Ying-chun Jiang, Youming Liu
    Acta Mathematicae Applicatae Sinica(English Series). 2008, 24(4): 613-626.
    Abstract ( )    Download PDF ( )   Knowledge map   Save
    This paper deals with the design and analysis of adaptive wavelet
    method for the Stokes problem. First, the limitation of Richardson iteration
    is explained and the multiplied matrix $M_0$ in the paper of Bramble and
    Pasciak is proved to be the simplest possible in an appropiate sense. Similar
    to the divergence operator, an exact application of its dual is shown; Second,
    based on these above observations, an adaptive wavelet algorithm for the Stokes
    problem is designed. Error analysis and computational complexity are given;
    Finally, since our algorithm is mainly to deal with an elliptic and positive
    definite operator equation, the last section is devoted to the Galerkin
    solution of an elliptic and positive definite equation. It turns out that the
    upper bound for error estimation may be improved.
  • 论文
    Positive Periodic Solution of a Discrete Predator-prey Patch-system
    Shu-yuan Shen, Pei-xuan Weng
    Acta Mathematicae Applicatae Sinica(English Series). 2008, 24(4): 627-642.
    Abstract ( )    Download PDF ( )   Knowledge map   Save
    A periodic difference predator-prey
    model with Holling-$(m+1)(m>2)$ type functional response and
    impulses is established. Sufficient conditions are derived for the
    existence of periodic solutions by using a continuation theorem in
    coincidence degree.
  • 论文
    The Existence of $\Large \pmb {(v, 4, 1)}$ Disjoint Difference Families with $\Large\pmb v$a Prime Power
    Dian-hua Wu, Jian-xiao Yang, Bi-chang Huang
    Acta Mathematicae Applicatae Sinica(English Series). 2008, 24(4): 643-648.
    Abstract ( )    Download PDF ( )   Knowledge map   Save
    A $(v, k, \lambda)$ difference family ($(v, k,
    \lambda)$-DF in short) over an abelian group $G$ of order $v$, is a
    collection ${\cal F}=\{B_i| i\in I\}$ of $k$-subsets
    of $G$, called base blocks, such that any nonzero element of $G$
    can be represented in precisely $\lambda$ ways as a difference of
    two elements lying in some base blocks in ${\cal F}$. A $(v, k, \lambda)$-DDF
    is a difference family with disjoint blocks. In this paper, by
    using Weil's theorem on character sum estimates, it is proved that
    there exists a $(p^n, 4, 1)$-DDF, where $p\equiv 1 \ (mod \ 12)$ is
    a prime number and $n\geq 1$.
  • 论文
    The Ruin Probability in the Presence of Extended Regular Variationand Optimal Investment
    Li Wei
    Acta Mathematicae Applicatae Sinica(English Series). 2008, 24(4): 649-654.
    Abstract ( )    Download PDF ( )   Knowledge map   Save
    Considering the classical model with risky investment, we are
    interested in the ruin probability that is minimized by a suitably chosen
    investment strategy for a capital market index. For claim sizes with common
    distribution of extended regular variation, starting from an
    integro-differential equation for the maximal survival probability, we find
    that the corresponding ruin probability as a function of the initial surplus is
    also extended regular variation.
  • 论文
    On the Distributions of Two Classes of Multiple DependentAggregate Claims
    Rong-ming Wang, Kam C. Yuen, Li-xing Zhu
    Acta Mathematicae Applicatae Sinica(English Series). 2008, 24(4): 655-668.
    Abstract ( )    Download PDF ( )   Knowledge map   Save
    In this paper we examine two classes of correlated aggregate claims
    distributions, with univariate claim counts and multivariate claim sizes.
    Firstly, we extend the results of Hesselager [ASTIN Bulletin, 24: 19--32(1994)]
    and Wang $\&$ Sobrero's [ASTIN Bulletin, 24: 161--166 (1994)] concerning
    recursions for compound distributions to a multivariate situation where each
    claim event generates a random vector. Then we give a multivariate continuous
    version of recursive algorithm for calculating a family of compound
    distribution. Especially, to some extent, we obtain a continuous version of the
    corresponding results in Sundt [ASTIN Bulletin, 29: 29--45 (1999)] and
    Ambagaspitiya [Insurance: Mathematics and Economics, 24: 301--308 (1999)].
    Finally, we give an example and show how to use the algorithm for aggregate
    claim distribution of first class to compute recursively the compound
    distribution.
  • 论文
    Some Results on Fractional Brownian Sheets and TheirLocal Times
    Zong-mao Cheng, Zheng-yan Lin
    Acta Mathematicae Applicatae Sinica(English Series). 2008, 24(4): 669-676.
    Abstract ( )    Download PDF ( )   Knowledge map   Save
    Let $B_{0}^{H}=\{B_{0}^{H}(t), t\in R_{+}^{N}\}$ be a
    real-valued fractional Brownian sheet.
    Define
    the $(N,d)-$ Gaussian random field $B^{H}$ by
    $$B^{H}(t)=\big(B_{1}^{H}(t), \cdots, B_{d}^{H}(t)\big)\qquad t\in R_{+}^{N} ,$$ where $B_{1}^{H},
    \cdots, B_{d}^{H}$ are independent copies of $B_{0}^{H}$. The
    existence and joint continuity of local times of $B^{H}$ is proven
    in some given conditions in [22]. We then study further properties
    of the local times of $B^{H},$ such as the moments of increments of
    local times, the large increments and the maximum moduli of
    continuity of local times and as a result, we answer the questions
    posed in [22].
  • 论文
    Short Cycle Structure of Graphs on Surfaces (1) -- the Uniqueness Theorems
    Han Ren, Mo Deng
    Acta Mathematicae Applicatae Sinica(English Series). 2008, 24(4): 677-680.
    Abstract ( )    Download PDF ( )   Knowledge map   Save
    In this paper we investigate cycle base structures of a (weighted)
    graph and show that much information of short cycles is contained in a MCB
    (minimum cycle base). After setting up a {\it Hall type theorem} for
    base-transformation, we give a sufficient and necessary condition for a cycle
    base to be a MCB. Further more, we show that the structure of MCB in a
    (weighted) graph is unique. In the case of nonnegative weight, every pair of
    MCB have the same number of $k-$cycles for each integer $k\geq 3$. The property
    is also true for those having longest length (although much work has been down
    in evaluating MCB, little is known for those having longest length).
  • 论文
    A Robust Algorithm for Blind Total Variation Restoration
    Jing Xu, Qian-shun Chang
    Acta Mathematicae Applicatae Sinica(English Series). 2008, 24(4): 681-690.
    Abstract ( )    Download PDF ( )   Knowledge map   Save
    Image restoration is a fundamental problem in image processing. Blind
    image restoration has a great value in its practical application. However, it
    is not an easy problem to solve due to its complexity and difficulty. In this
    paper, we combine our robust algorithm for known blur operator with an
    alternating minimization implicit iterative scheme to deal with blind
    deconvolution problem, recover the image and identify the point spread
    function(PSF). The only assumption needed is satisfy the practical physical
    sense. Numerical experiments demonstrate that this minimization algorithm is
    efficient and robust over a wide range of PSF and have almost the same results
    compared with known PSF algorithm.
  • 论文
    Exact Solitary-wave Solutions and Periodic Wave Solutionsfor Generalized Modified Boussinesq Equation and the Effect of Wave Velocity on Wave Shape
    Wei-guo Zhang, Shao-wei Li, Wei-zhong Tian, Lu Zhang
    Acta Mathematicae Applicatae Sinica(English Series). 2008, 24(4): 691-704.
    Abstract ( )    Download PDF ( )   Knowledge map   Save
    By means of the undetermined assumption method, we obtain some new
    exact solitary-wave solutions with hyperbolic secant function fractional form
    and periodic wave solutions with cosine function form for the generalized
    modified Boussinesq equation. We also discuss the boundedness of these
    solutions. More over, we study the correlative characteristic of the
    solitary-wave solutions and the periodic wave solutions along with the
    travelling wave velocity's variation.
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