02 April 2008, Volume 24 Issue 2
    

  • Select all
    |
  • 论文
    Multiple Limit Cycles in an Immune System
    Xun-cheng Huang, Le-min Zhu, Minaya Villasana
    Acta Mathematicae Applicatae Sinica(English Series). 2008, 24(2): 177-184.
    Abstract ( )    Download PDF ( )   Knowledge map   Save
    The nonlinear oscillatory phenomenon has been observed in
    the system of immune response, which corresponds to the limit cycles
    in the mathematical models. We prove that the system simulating an
    immune response studied by Huang has at least three limit cycles in
    the system. The conditions for the multiple limit cycles are useful
    in analyzing the nonlinear oscillation in immune response.
  • 论文
    Procreating Tiles of Double Commutative-Step Digraphs
    Jian-qin Zhou
    Acta Mathematicae Applicatae Sinica(English Series). 2008, 24(2): 185-194.
    Abstract ( )    Download PDF ( )   Knowledge map   Save
    Double commutative-step digraph generalizes the
    double-loop digraph. A double commutative-step digraph can be
    represented by an $L$-shaped tile, which periodically tessellates
    the plane.
    Given an initial tile $L(l,h,x,y)$, Aguil$\acute{o}$ et al. define a discrete iteration
    $L(p)= L(l+2p, h+2p, x+p, y+p), p=0,1,2,\ldots $, over $L$-shapes
    (equivalently over double commutative-step digraphs), and obtain an
    orbit generated by $L(l,h,x,y)$, which is said to be a procreating
    $k$-tight tile if $L(p)( p=0,1,2,\cdots )$ are all $k$-tight tiles.
    They classify the set of $L$-shaped tiles by its behavior under the
    above-mentioned discrete dynamics and obtain some procreating tiles
    of double commutative-step digraphs.
    In this work, with an approach proposed by Li and Xu et al., we
    define some new discrete iteration over $L$-shapes and classify the
    set of tiles by the procreating condition. We also propose some
    approaches to find infinite families of realizable k-tight tiles
    starting from any realizable $k$-tight $L$-shaped tile $L(l , h, x,
    y), 0\le |y-x|\le 2k+2$. As an example, we present an infinite
    family of 3-tight optimal double-loop networks to illustrate our
    approaches.
  • 论文
    Ruin Probabilitiesin the Risk Process with Random Income
    Zhen-hua Bao, Zhong-xing Ye
    Acta Mathematicae Applicatae Sinica(English Series). 2008, 24(2): 195-202.
    Abstract ( )    Download PDF ( )   Knowledge map   Save
    We extend the classical risk model to the case in which
    the premium income process, modelled as a Poisson process, is no
    longer a linear function. We derive an analog of the Beekman
    convolution formula for the ultimate ruin probability when the
    inter-claim times are exponentially distributed. A defective
    renewal equation satisfied by the ultimate ruin probability is
    then given. For the general inter-claim times with zero-truncated
    geometrically distributed claim sizes, the explicit expression for
    the ultimate ruin probability is derived.
  • 论文
    A Note on an Open Problem about the First Painlev\'{e} Equation
    Hui-zeng Qin, You-min Lu
    Acta Mathematicae Applicatae Sinica(English Series). 2008, 24(2): 203-210.
    Abstract ( )    Download PDF ( )   Knowledge map   Save
    In this note, we apply numerical analysis to the first
    Painlev\'{e} equation, find the conditions for it to have
    oscillating solutions and therefore solve an open problem posed by
    Peter A. Clarkson.
  • 论文
    $\Large \pmb m$ Components-Admissible Solutions of Systems of Higher-OrderPartial Differential Equations on $\Large \pmb {C^n}$
    Ling-yun Gao
    Acta Mathematicae Applicatae Sinica(English Series). 2008, 24(2): 211-220.
    Abstract ( )    Download PDF ( )   Knowledge map   Save
    Using value distribution theory and techniques in several
    complex variables,we investigate the problem of existence of $m$
    components-admissible solutions
    of a class of systems of higher-order partial differential equations in several
    complex variables and estimate the number of admissible components of solutions. Some related results will also be obtained.
  • 论文
    Block Monotone Iterative Algorithms for VariationalInequalities with Nonlinear Operators
    Ming-hui Ren, Jin-ping Zeng
    Acta Mathematicae Applicatae Sinica(English Series). 2008, 24(2): 221-232.
    Abstract ( )    Download PDF ( )   Knowledge map   Save
    Some block iterative methods for solving variational
    inequalities with nonlinear operators are proposed. Monotone
    convergence of the algorithms is obtained. Some comparison
    theorems are also established. Compared with the
    research work in given by Pao in 1995 for nonlinear equations and research
    work in given by Zeng and Zhou in 2002
    for elliptic variational inequalities, the algorithms proposed in this paper are
    independent of the boundedness of the derivatives of the nonlinear
    operator.
  • 论文
    More Large Sets of Resolvable {MTS} and {DTS} with Even Orders
    Qing-de Kang, Rong-jia Xu
    Acta Mathematicae Applicatae Sinica(English Series). 2008, 24(2): 233-252.
    Abstract ( )    Download PDF ( )   Knowledge map   Save
    In this paper, we first introduce a special structure that
    allows us to construct a large set of resolvable Mendelsohn triple
    systems of orders $2q+2$, or LRMTS$(2q+2)$, where $q=6t+5$ is a
    prime power. Using a computer, we find examples of such structure
    for $t\in T=\{0,1,2,3,4,6,7,8,9,14,16,18,20,22,24\}$. Furthermore,
    by a method we introduced in [13], large set of resolvable directed
    triple systems with the same orders are obtained too. Finally, by
    the tripling construction and product construction for LRMTS and
    LRDTS introduced in [2, 20, 21], and by the new results for
    $LR$-design in [8], we obtain the existence for LRMTS$(v)$ and
    $LRDTS(v)$, where $v=12(t+1)\prod\limits_{m_i\geq0}(2\cdot7^{m_i}+1)
    \prod\limits_{n_i\geq0}(2\cdot13^{n_i}+1)$ and $t\in T$, which
    provides more infinite family for LRMTS and LRDTS of even orders.
  • 论文
    Existence of Three Positive Solutionsfor Some Second-Order M-Point Boundary Value Problems
    Liu Yang, Chun-fang Shen, Xi-ping Liu
    Acta Mathematicae Applicatae Sinica(English Series). 2008, 24(2): 253-264.
    Abstract ( )    Download PDF ( )   Knowledge map   Save
    By using fixed-point theorems, some new results for
    multiplicity of positive solutions for some second order m-point
    boundary value problems are obtained.The associated Green's function
    of these problems are also given.
  • 论文
    A Global Carleman Inequality and Exact Controllability of ParabolicEquations with Mixed Boundary Conditions
    Tujin Kim, Qian-shun Chang, Jing Xu
    Acta Mathematicae Applicatae Sinica(English Series). 2008, 24(2): 265-280.
    Abstract ( )    Download PDF ( )   Knowledge map   Save
    This paper establishes a global Carleman inequality of
    parabolic equations with mixed boundary conditions and an estimate
    of the solution. Further, we prove exact controllability of the
    equation by controls acting on an arbitrarily given subdomain or
    subboundary.
  • 论文
    The Existence of Even Cycles with Specific Lengths in Wenger's Graph
    Jia-yu Shao, Chang-xiang He, Hai-ying Shan
    Acta Mathematicae Applicatae Sinica(English Series). 2008, 24(2): 281-288.
    Abstract ( )    Download PDF ( )   Knowledge map   Save
    Wenger's graph $H_m(q)$ is a $q$-regular bipartite graph
    of order $2q^m$ constructed by using the $m$-dimensional vector
    space $F_q^m$ over the finite field $F_q$. The existence of the cycles of certain even length plays an important role
    in the study of the accurate order of the Turan number $ex(n;C_{2m})$ in extremal graph theory.
    In this paper, we use the algebraic methods of linear system of equations
    over the finite field and the ``critical zero-sum sequences" to
    show that: if $m \geq 3$, then for any integer $l$ with $l\neq 5, 4 \leq l \leq 2 {\rm ch}(F_q)$ (where \ ch$(F_q)$ is the character of
    the finite field $F_q$) and any vertex $v$ in the Wenger's graph $H_m(q)$, there is a cycle of length $2l$ in $H_m(q)$
    passing through the vertex $v$.
  • 论文
    Sharp Upper and Lower Bounds for the LaplacianSpectral Radius and the Spectral Radius of Graphs
    Ji-ming Guo
    Acta Mathematicae Applicatae Sinica(English Series). 2008, 24(2): 289-296.
    Abstract ( )    Download PDF ( )   Knowledge map   Save
    In this paper, sharp upper bounds for the Laplacian
    spectral radius and the spectral radius of graphs are given, respectively.
    We show that some known bounds can be obtained from our bounds. For
    a bipartite graph $G$, we also present sharp lower bounds for the
    Laplacian spectral radius and the spectral radius, respectively.
  • 论文
    A Lower Semicontinuity Result for Some Integral Functionals in the Space SBD
    Zhong-xue L\"{u}, Xiao-ping Yang, Min-ling Zheng
    Acta Mathematicae Applicatae Sinica(English Series). 2008, 24(2): 297-304.
    Abstract ( )    Download PDF ( )   Knowledge map   Save
    In this paper, we obtain a lower semicontinuity result with respect
    to the strong $L^{1}-$convergence of the integral functionals
    $$
    F(u,\Omega)=\int_{\Omega}f\big(x,u(x),{\cal {E}} u(x)\big)dx
    $$
    defined in the space $SBD$ of special functions with bounded
    deformation.
    Here ${\cal {E}} u$ represents the absolutely continuous part of the
    symmetrized distributional derivative $Eu$. The integrand $f$
    satisfies the standard growth assumptions of order $p>1$ and some
    other conditions. Finally, by using this result,we discuss the
    existence of an constrained variational problem.
  • 论文
    The Optimal Preconditioner of Strictly DiagonallyDominant $\large \pmb Z$-matrix
    Ji-cheng Li, Wei Li
    Acta Mathematicae Applicatae Sinica(English Series). 2008, 24(2): 305-312.
    Abstract ( )    Download PDF ( )   Knowledge map   Save
    In this paper, we present a series of new
    preconditioners with parameters of strictly diagonally dominant
    $Z$-matrix, which contain properly two kinds of known
    preconditioners as special cases. Moreover, we prove the
    monotonicity of spectral radiuses of iterative matrices with
    respect to the parameters and some comparison theorems. The
    results obtained show that the bigger the parameter $k$ is(i.e.,
    we select the more upper right diagonal elements to be the
    preconditioner), the less the spectral radius of iterative matrix
    is. A numerical example generated randomly is provided to
    illustrate the theoretical results.
  • 论文
    Bifurcations of Limit Cycles in A Perturbed QuinticHamiltonian System with Six Double Homoclinic Loops
    Yong-xi Gao, Yu-hai Wu, Li-xin Tian
    Acta Mathematicae Applicatae Sinica(English Series). 2008, 24(2): 313-328.
    Abstract ( )    Download PDF ( )   Knowledge map   Save
    This paper concerns with the number and distributions of limit cycles of a quintic subject to a
    seven-degree perturbation. With the aid of numeric integral computation provided by Mathematica 4.1, at least
    45 limit cycles are found in the above system by applying the method of double homoclinic loops bifurcation,
    Hopf bifurcation and qualitative analysis. The four configurations of 45 limit cycles of the system are also shown.
    The results obtained are useful to the study of the weakened 16th Hilbert Problem.
  • 论文
    A Local Limit Theorem for Solutions of BSDEs with Mao's non-LipschitzGenerator
    Yu-chun Liu, Long Jiang, Ying-ying Xu
    Acta Mathematicae Applicatae Sinica(English Series). 2008, 24(2): 329-336.
    Abstract ( )    Download PDF ( )   Knowledge map   Save
    This paper establishes a local limit theorem for
    solutions of backward stochastic differential equations with Mao's
    non-Lipschitz generator, which is similar to the limit theorem
    obtained by [3] under the Lipschitz assumption.
  • 论文
    A Difference Scheme for Solving the Timoshenko Beam Equations with Tip Body
    Fu-le Li, Zi-ku Wu, Kai-mei Huang
    Acta Mathematicae Applicatae Sinica(English Series). 2008, 24(2): 337-352.
    Abstract ( )    Download PDF ( )   Knowledge map   Save
    In this article, a Timoshenko beam with tip body and
    boundary damping is considered. A linearized three-level
    difference scheme of the Timoshenko beam equations on uniform
    meshes is derived by the method of reduction of order. The unique
    solvability, unconditional stability and convergence of the
    difference scheme are proved. The convergence order in maximum
    norm is of order two in both space and time. A numerical example
    is presented to demonstrate the theoretical results.
Journal Online
News More