Table of Content

06 October 2003, Volume 23 Issue 4 Previous Issue    Next Issue

For Selected:

View Abstracts

Download Citations EndNote Reference Manager ProCite BibTeX RefWorks

Toggle Thumbnails

Articles

Select

DECOMPOSITION OF BV FUNCTIONS IN CARNOT-CARATH´|EODORY SPACES SONG Ying-Qing, YANG Xiao-Beng, LIU Zhen-Hai Acta mathematica scientia,Series B. 2003, 23 (4):  433.  Abstract ( 568 )   RICH HTML PDF (132KB) ( 1155 )   Save 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 $u$. References | Related Articles | Metrics

Select

ANALYSIS OF AN SI EPIDEMIC MODEL WITH NONLINEAR TRANSMISSION AND STAGE STRUCTURE 1 CHEN Zhong-Hua, ZHANG Chu-Jing, CHEN Lan-Sun Acta mathematica scientia,Series B. 2003, 23 (4):  440.  Abstract ( 675 )   RICH HTML PDF (114KB) ( 1677 )   Save 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. References | Related Articles | Metrics

Select

REGULARITIES AND SINGULARITIES OF THE ENERGY MINIMIZERS OF THE HEISENBERG GROUP TARGETS GU Gao Acta mathematica scientia,Series B. 2003, 23 (4):  447.  Abstract ( 701 )   RICH HTML PDF (119KB) ( 899 )   Save 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. References | Related Articles | Metrics

Select

EXACT EXPLICIT SOLUTIONS OF THE NONLINEAR SCHR¨|ODINGER EQUATION COUPLED TO THE BOUSSINESQ EQUATION TAO Re-Xia, LI Zhi-Bin Acta mathematica scientia,Series B. 2003, 23 (4):  453.  Abstract ( 639 )   RICH HTML PDF (118KB) ( 1110 )   Save 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. References | Related Articles | Metrics

Select

TERATIVE SOLUTIONS FOR SYSTEMS OF NONLINEAR OPERATOR EQUATIONS IN BANACH SPACE SONG Guang-Xin Acta mathematica scientia,Series B. 2003, 23 (4):  461.  Abstract ( 665 )   RICH HTML PDF (90KB) ( 1319 )   Save 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. References | Related Articles | Metrics

Select

MULTIPLIERS AND RELATIVE COMPLETION IN WEIGHTED LORENTZ SPACES Cenap Duyar A. Turan G¨urkanli Acta mathematica scientia,Series B. 2003, 23 (4):  467.  Abstract ( 712 )   RICH HTML PDF (145KB) ( 1478 )   Save 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 $\tilde {A}$. References | Related Articles | Metrics

Select

KERNEL ESTIMATION OF HIGHER DERIVATIVES OF DENSITY AND HAZARD RATE FUNCTION FOR TRUNCATED AND CENSORED DEPENDENT DATA CHEN Qing-Beng, DAI Yong-Long Acta mathematica scientia,Series B. 2003, 23 (4):  477.  Abstract ( 662 )   RICH HTML PDF (143KB) ( 1550 )   Save 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. References | Related Articles | Metrics

Select

SOME EXISTENCE RESULTS OF SOLUTIONS FOR p-LAPLACIAN CHEN Zhi-Hui, CHEN Yao-Tian, TAO Ang-Xin Acta mathematica scientia,Series B. 2003, 23 (4):  487.  Abstract ( 687 )   RICH HTML PDF (151KB) ( 1281 )   Save 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. References | Related Articles | Metrics

Select

SOME SUBGROUPS OF EXTENDED HECKE GROUPS |$\bar{H}(\lambda _q) Recep Sahin, Osman Bizim Acta mathematica scientia,Series B. 2003, 23 (4):  497.  Abstract ( 698 )   RICH HTML PDF (105KB) ( 1510 )   Save 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. References | Related Articles | Metrics

Select

FINITELY GENERATED COMMUTATIVE RCHIMEDEAN SEMIGROUPS J.C. Rosales J.I. Garc′?a-Garc′?a Acta mathematica scientia,Series B. 2003, 23 (4):  503.  Abstract ( 581 )   RICH HTML PDF (123KB) ( 1194 )   Save In this work commutative Archimedean finitely generated semigroups are characterized in terms of ideal extensions. References | Related Articles | Metrics

Select

A METHOD TO APPROACH OPTIMAL ESTORATION IN IMAGE RESTORATION ROBLEMS WITHOUT NOISE ENERGY NFORMATION CENG San-You, DING Li-Xin, KANG Li-Shan Acta mathematica scientia,Series B. 2003, 23 (4):  512.  Abstract ( 600 )   RICH HTML PDF (119KB) ( 1101 )   Save 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. References | Related Articles | Metrics

Select

AREA FUNCTIONS ON HARDY SPACESASSOCIATED TO SCHR¨|ODINGER OPERATORS ZHU Yue-Ping Acta mathematica scientia,Series B. 2003, 23 (4):  521.  Abstract ( 671 )   RICH HTML PDF (136KB) ( 1221 )   Save 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. References | Related Articles | Metrics

Select

WEIGHTED KOPPELMAN-LERAY-NORGUET FORMULAS ON A LOCAL q-CONCAVE WEDGE IN A COMPLEX MANIFOLD QIU Chun-Hui, TAO Zong-Yuan Acta mathematica scientia,Series B. 2003, 23 (4):  531.  Abstract ( 631 )   RICH HTML PDF (166KB) ( 849 )   Save 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. References | Related Articles | Metrics

Select

NORMAL FAMILY OF COMPOSITIONS OF HOLOMORPHIC FUNCTIONS AND THEIR HIGH ORDER DERIVATIVES DENG Fang-Wen Acta mathematica scientia,Series B. 2003, 23 (4):  544.  Abstract ( 636 )   RICH HTML PDF (94KB) ( 1057 )   Save 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. References | Related Articles | Metrics

Select

DIMENSION OF POLAR SETS FOR BROWNIAN SHEET CHEN Zhen-Long, LIU San-Yang Acta mathematica scientia,Series B. 2003, 23 (4):  549.  Abstract ( 697 )   RICH HTML PDF (157KB) ( 1110 )   Save 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. References | Related Articles | Metrics

Select

EXTENDED CES´ARO OPERATORS ON THE BLOCH SPACE IN THE UNIT BALL OF C_{n} HU Zhang-Jian Acta mathematica scientia,Series B. 2003, 23 (4):  561.  Abstract ( 675 )   RICH HTML PDF (115KB) ( 1385 )   Save 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 ${\cal B}_0$. References | Related Articles | Metrics

Select

VISCOSITY METHOD OF A NON-HOMOGENEOUS BURGERS EQUATION DING Jia-Qi, DING Yi Acta mathematica scientia,Series B. 2003, 23 (4):  567.  Abstract ( 570 )   RICH HTML PDF (123KB) ( 1099 )   Save 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. References | Related Articles | Metrics