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    2003年, 第23卷, 第4期 刊出日期:2003-10-06 上一期    下一期
    本期栏目: 论文 
    论文
    DECOMPOSITION OF BV FUNCTIONS IN CARNOT-CARATH´|EODORY SPACES
    宋迎清, 扬孝平, 刘振海
    数学物理学报(英文版). 2003 (4):  433. 
    摘要 ( 566 )   RICH HTML PDF(132KB) ( 1143 )   收藏

    The aim of this paper is to get the decomposition of distributional
     derivatives of functions with bounded
    variation in the framework of Carnot-Carath\'eodory
    spaces (C-C spaces in brievity) in which the vector fields are of
    Carnot type. For this purpose the approximate
    continuity of BV functions is discussed first, then  approximate
     differentials of $ L^1$ functions are defined in the case that vector
    fields are of Carnot type and finally the decomposition $Xu=\nabla u\cdot
     L^n+X^su$ is proved, where $ u\in BV_X(\Omega)$ and $\nabla u$
    denotes the approximate   differential of $u$.

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    ANALYSIS OF AN SI EPIDEMIC MODEL WITH NONLINEAR TRANSMISSION AND STAGE STRUCTURE 1
    陈忠华, 张淑京, 陈兰荪
    数学物理学报(英文版). 2003 (4):  440. 
    摘要 ( 670 )   RICH HTML PDF(114KB) ( 1651 )   收藏

    A disease transmission model of SI type with stage structure is formulated.
    The stability of disease free equilibrium, the existence and uniqueness of an endemic equilibrium,
    the existence of a global attractor are investigated.

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    REGULARITIES AND SINGULARITIES OF THE ENERGY MINIMIZERS OF THE HEISENBERG GROUP TARGETS
    贾高
    数学物理学报(英文版). 2003 (4):  447. 
    摘要 ( 697 )   RICH HTML PDF(119KB) ( 890 )   收藏

    In this paper, the properties of the maps for the
    Heisenberg group targets are studied. For $u \in W^{1,\alpha
    }(\Omega, {\bf H}^m)$,  some Poincar\'e type inequalities are proved.
    For the energy minimizers,  the $\epsilon$-regularity theorems
    and the singularity theorems are obtained.

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    EXACT EXPLICIT SOLUTIONS OF THE NONLINEAR SCHR¨|ODINGER EQUATION COUPLED TO THE BOUSSINESQ EQUATION
    姚若侠, 李志斌
    数学物理学报(英文版). 2003 (4):  453. 
    摘要 ( 634 )   RICH HTML PDF(118KB) ( 1086 )   收藏

    A system comprised of the nonlinear Schr¨odinger equation coupled to the
    Boussinesq equation (S-B equations) which dealing with the stationary propagation of coupled
    non-linear upper-hybrid and magnetosonic waves in magnetized plasma is proposed.
    To examine its solitary wave solutions, a reduced set of ordinary differential equations are
    considered by a simple traveling wave transformation. It is then shown that several new
    solutions (either functional or parametrical) can be obtained systematically, in addition to
    rederiving all known ones by means of our simple and direct algebra method with the help
    of the computer algebra system Maple.

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    TERATIVE SOLUTIONS FOR SYSTEMS OF NONLINEAR OPERATOR EQUATIONS IN BANACH SPACE
    宋光兴
    数学物理学报(英文版). 2003 (4):  461. 
    摘要 ( 660 )   RICH HTML PDF(90KB) ( 1298 )   收藏

    By using partial order method, the existence, uniqueness and iterative approximation
    of solutions for a class of systems of nonlinear operator equations in Banach
    space are discussed. The results obtained in this paper extend and improve recent results.

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    MULTIPLIERS AND RELATIVE COMPLETION IN WEIGHTED LORENTZ SPACES
    Cenap Duyar A. Turan G¨urkanli
    数学物理学报(英文版). 2003 (4):  467. 
    摘要 ( 706 )   RICH HTML PDF(145KB) ( 1456 )   收藏

    Let $G$ be a locally compact Abelian group with
    Haar measure $\mu $. In the present paper, first the authors
    discussed some properties of weighted Lorentz space. Then they
    defined the relative completion $\tilde {A}$ of a subspace $A$ of
    the weighted Lorentz space, and showed that the space of the
    multipliers from $L_{w}^{1} (G)$ to $A$ is algebrically isomorphic
    and homeomorphic to $\tilde {A}$.

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    KERNEL ESTIMATION OF HIGHER DERIVATIVES OF DENSITY AND HAZARD RATE FUNCTION FOR TRUNCATED AND CENSORED DEPENDENT DATA
    陈清平, 戴永隆
    数学物理学报(英文版). 2003 (4):  477. 
    摘要 ( 660 )   RICH HTML PDF(143KB) ( 1522 )   收藏

    Based on left truncated and right censored dependent data, the estimators
    of higher derivatives of density function and hazard rate function are given by kernel
    smoothing method. When observed data exhibit -mixing dependence, local properties
    including strong consistency and law of iterated logarithm are presented. Moreover, when
    the mode estimator is defined as the random variable that maximizes the kernel density
    estimator, the asymptotic normality of the mode estimator is established.

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    SOME EXISTENCE RESULTS OF SOLUTIONS FOR p-LAPLACIAN
    陈志辉, 沈尧天, 姚仰新
    数学物理学报(英文版). 2003 (4):  487. 
    摘要 ( 680 )   RICH HTML PDF(151KB) ( 1233 )   收藏

    In this paper the Dirichlet problem for p-Laplacian (p > 1) is considered.
    Under suitable conditions and by using critical point theory the existence of solutions for
    the Dirichlet problem is studied, and some results in the literature are improved.

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    SOME SUBGROUPS OF EXTENDED HECKE GROUPS |$\bar{H}(\lambda _q)
    Recep Sahin, Osman Bizim
    数学物理学报(英文版). 2003 (4):  497. 
    摘要 ( 669 )   RICH HTML PDF(105KB) ( 1478 )   收藏

    The authors consider the extended Hecke groups $\overline{H}$($\lambda _q)$ generated
    by $T(z)=-1$ $/$ $z$, $S(z)=-1/(z+\lambda _q)$ and $R(z)=1$ $/$ $\overline{z}
    $ with $\lambda _q=2\cos (\pi /q)$ for $q\geq 3$ an integer$.$ In this
    paper, the even subgroup $\overline{H}_e$($\lambda _q),$ the second
    commutator subgroup $\overline{H}^{\prime \prime }$($\lambda _q)$ and the
    principal congruence subgroups $\overline{H}_p$($\lambda _q)$ of the
    extended Hecke groups $\overline{H}$($\lambda _q)$ are studied. Also,
     relations between them are given.

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    FINITELY GENERATED COMMUTATIVE RCHIMEDEAN SEMIGROUPS
    J.C. Rosales J.I. Garc′?a-Garc′?a
    数学物理学报(英文版). 2003 (4):  503. 
    摘要 ( 578 )   RICH HTML PDF(123KB) ( 1185 )   收藏

    In this work commutative Archimedean finitely generated semigroups are
    characterized in terms of ideal extensions.

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    A METHOD TO APPROACH OPTIMAL ESTORATION IN IMAGE RESTORATION ROBLEMS WITHOUT NOISE ENERGY NFORMATION
    曾三友, 丁立新, 康立山
    数学物理学报(英文版). 2003 (4):  512. 
    摘要 ( 597 )   RICH HTML PDF(119KB) ( 1082 )   收藏

    This paper proposes a new image restoration technique, in which the resulting
    regularized image approximates the optimal solution steadily. The affect of the regular-
    ization operator and parameter on the lower band and upper band energy of the residue
    of the regularized image is theoretically analyzed by employing wavelet transform. This
    paper shows that regularization operator should generally be lowstop and highpass. So this
    paper chooses a lowstop and highpass operator as regularization operator, and construct
    an optimization model which minimizes the mean squares residue of regularized solution
    to determine regularization parameter. Although the model is random, on the condition
    of this paper, it can be solved and yields regularization parameter and regularized solu-
    tion. Otherwise, the technique has a mechanism to predict noise energy. So, without noise
    information, it can also work and yield good restoration results.

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    AREA FUNCTIONS ON HARDY SPACESASSOCIATED TO SCHR¨|ODINGER OPERATORS
    朱月萍
    数学物理学报(英文版). 2003 (4):  521. 
    摘要 ( 669 )   RICH HTML PDF(136KB) ( 1213 )   收藏

    In this paper, the author gives a characterization of atomic Hardy spaces
    associated to Schr¨odinger operators by using area functions, and hence gets the dual spaces
    of atomic Hardy spaces.

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    WEIGHTED KOPPELMAN-LERAY-NORGUET FRMULAS ON A LOCAL q-CONCAVE WEDGE IN A COMPLEX MANIFOLD
    邱春晖, 姚宗元
    数学物理学报(英文版). 2003 (4):  531. 
    摘要 ( 630 )   RICH HTML PDF(166KB) ( 842 )   收藏

    A weighted Koppelman-Leray-Norguet formula of (r, s) differential forms on
    a local q-concave wedge in a complex manifold is obtained. By constructing the new
    weighted kernels, the authors give a new weighted Koppelman-Leray-Norguet formula with-
    out boundary integral of (r, s) differential forms, which is different from the classical one.
    The new weighted formula is especially suitable for the case of the local q-concave wedge
    with a non-smooth boundary, so one can avoid complex estimates of boundary integrals
    and the density of integral may be not defined on the boundary but only in the domain.
    Moreover, the weighted integral formulas have much freedom in applications such as in the
    interpolation of functions.

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    NORMAL FAMILY OF COMPOSITIONS OF HOLOMORPHIC FUNCTIONS AND THEIR HIGH ORDER DERIVATIVES
    邓方文
    数学物理学报(英文版). 2003 (4):  544. 
    摘要 ( 633 )   RICH HTML PDF(94KB) ( 1010 )   收藏

    A weighted Koppelman-Leray-Norguet formula of $(r,s)$
    differential forms on a local $q$-concave wedge  in a complex
    manifold is obtained. By constructing the new weighted kernels,
    the authors give a new weighted Koppelman-Leray-Norguet formula
    without boundary integral of $(r,s)$ differential forms,
    which is different from the  classical one.
    The new weighted formula is especially suitable for the case
    of the local $q$-concave wedge with a non-smooth boundary, so
    one can  avoid complex  estimates of  boundary
    integrals and the density of integral may be not defined on the
    boundary but only in the domain.
    Moreover, the weighted integral formulas have much freedom
    in applications such as in the interpolation of functions.

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    DIMENSION OF POLAR SETS FOR BROWNIAN SHEET
    陈振龙, 刘三阳
    数学物理学报(英文版). 2003 (4):  549. 
    摘要 ( 694 )   RICH HTML PDF(157KB) ( 1092 )   收藏

    Let $W\hat{=}\{W(t);t\in
    R^N_+\}$ be the $d$-dimensional $N$-parameter Brownian Sheet.
    Sufficient conditions for a compact set $F\subset R^d\setminus
    \{0\}$ to be a polar set for $W$ are proved. It is also proved
    that if $2N\leq d$, then for any compact set $ E\subset R^N_>$,
    $$
    \inf\{{\rm dim} F:F\in {\cal B}(R^d), P\{W(E)\cap F\not= \phi\}>0\}
    =d-2{\rm Dim}E,
    $$
    and if $2N>d$, then for any compact set $F\subset R^d\setminus \{0\}$,
    $$
    \inf\{{\rm dim}E:E\in {\cal B}(R^N_>), P\{W(E)\cap F\not= \phi\}>0\}
    =\frac{d}{2}-\frac{{\rm Dim}F}{2},
    $$
    where ${\cal B}(R^d)$ and ${\cal B}(R^N_>)$ denote the Borel
    $\sigma$-algebra in $R^d$ and  $R^N_>$ respectively, and
    dim and Dim are Hausdorff dimension and Packing dimension
    respectively.

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    EXTENDED CES´ARO OPERATORS ON THE BLOCH SPACE IN THE UNIT BALL OF C_{n}
    胡璋剑
    数学物理学报(英文版). 2003 (4):  561. 
    摘要 ( 671 )   RICH HTML PDF(115KB) ( 1347 )   收藏

    The paper defines an extended Ces\`{a}ro operator
    $T_g$ with holomorphic  symbol $g$ in the unit ball $\bf B$ of $C^n$ as
    $$
         T_g(f)(z)=\int_0^1f(tz)\Re g(tz)\frac{{\rm d}t}{t},
     \verb#       # f\in H({\bf B}),z\in \bf B. $$
    Where $\Re g(z)= \sum_{j=1}^{n} z_j\fr{\partial g}
    {\partial z_j}$ is  the radial
     derivative of $g$. In this paper, the author
     characterizes  $g$ for which $T_g$ is
     bounded (or compact) on the Bloch space ${\cal B}$
     and the little Bloch space ${\cal B}_0 $.

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    VISCOSITY METHOD OF A NON-HOMOGENEOUS BURGERS EQUATION
    丁夏畦, 丁毅
    数学物理学报(英文版). 2003 (4):  567. 
    摘要 ( 568 )   RICH HTML PDF(123KB) ( 1089 )   收藏

    In [1], Ding et al. studied the nonhomogeneous Burgers equation
    $$ u_t+uu_x=\mu u_{xx}+4x.\eqno{(1.1)}$$

    This paper  will
     prove that when $\mu\to 0$ the solution of (1.1) will approach the
    generalized solution of
    $$ u_t+uu_x=4x.\eqno{(1.2)}$$
    The authors notice that the equation (1.2) is beyond the scope of
    investigations by Oleinik O. in [2]. The solutions here are
    unbounded in general.

    The paper also studies the $\d$-wave phenomenon when (1.2) is jointed with
    some other equation.

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