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14 July 2003, Volume 23 Issue 3 Previous Issue    Next Issue

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THE UNIVERSAL DUAL COMODULE OF MODULE IN HOPF ALGEBRAS HAO Zhi-Feng, FENG Liang-Gui Acta mathematica scientia,Series B. 2003, 23 (3):  289.  Abstract ( 585 )   RICH HTML PDF (137KB) ( 1232 )   Save The purpose of this paper is to present some dual properties of dual  comodule. It turns out that dual comodule has universal property (cf.Theorem 2). Since $((\ )^*,(\ )^{o})$ is an adjoint pair (cf.Theorem 3),  some nice properties of functor ( )$^{o}$ are obtained. Finally Theoram 4 provides that the cotensor product is the dual of the tensor product by $(M \otimes _A N)^o \cong M^o \Box _{A^o} N^o$. Moreover, the result Hom$_A (M,N) \cong {\rm Com} _{A^o}  (N^o,M^o)$ is proved for finite related modules $M,N$ over a reflexive algebra $A$. References | Related Articles | Metrics

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INFLUENCE ANALYSIS ON EXPONENTIAL NONLINEAR MODELS WITH RANDOM EFFECTS ZONG Xu-Beng, DIAO Dun, WANG Hai-Bin, HUI Bo-Cheng Acta mathematica scientia,Series B. 2003, 23 (3):  297.  Abstract ( 653 )   RICH HTML PDF (145KB) ( 1133 )   Save his paper presents a unified diagnostic method for exponential nonlinear models with random effects based upon the joint likelihood given by Robinson in 1991. The authors show that the case deletion model is equivalent to mean shift outlier model. From this point of view, several diagnostic measures, such as Cook distance, score statistics are derived. The local influence measure of Cook is also presented. Numerical example illustrates that our method is available. References | Related Articles | Metrics

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REPRESENTATIONS OF THE TWO PARAMETER DEFORMATION OF THE VIRASORO ALGEBRA ZHANG Zi-Long, ZHANG Geng-Sheng, GU Yu-Ting Acta mathematica scientia,Series B. 2003, 23 (3):  309.  Abstract ( 609 )   RICH HTML PDF (111KB) ( 1002 )   Save This paper constructs a class of Harish-Chandra modules with multiplicity  1 of the two parameter deformation of Virasoro algebra and proves a classification theorem. References | Related Articles | Metrics

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A REMARK ON THE ATTRACTORS OF NON-NEWTONIAN FLUIDS HAO Bai-Lin, LIN Guo-An Acta mathematica scientia,Series B. 2003, 23 (3):  316.  Abstract ( 733 )   RICH HTML PDF (99KB) ( 906 )   Save This paper corrects some mistakes in the proof of absorbing sets theorem of at- tractors of non-Newtonian fluids, and establishes again the existence of bounded absorbing sets. References | Related Articles | Metrics

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LINEAR SEARCH FOR A BROWNIAN TARGET MOTION A. B. El-Rayes1 Abd El-Moneim A. Mohamed1 Hamdy M. Abou Gabal2 Acta mathematica scientia,Series B. 2003, 23 (3):  321.  Abstract ( 602 )   RICH HTML PDF (106KB) ( 1383 )   Save A target is assumed to move according to a Brownian motion on the real line. The searcher starts from the origin and moves in the two directions from the starting point. The object is to detect the target. The purpose of this paper is to find the conditions under which the expected value of the first meeting time of the searcher and the target is finite, and to show the existence of a search plan which made this expected value minimum. References | Related Articles | Metrics

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APPLICATIONS OF HERZ-TYPE TRIEBEL-LIZORKI SPACES XU Jing-Shi, YANG Da-Chun Acta mathematica scientia,Series B. 2003, 23 (3):  328.  Abstract ( 730 )   RICH HTML PDF (157KB) ( 1182 )   Save In this paper, the authors first establish the connections between the Herz- type Triebel-Lizorkin spaces and the well-known Herz-type spaces; the authors then study the pointwise multipliers for the Herz-type Triebel-Lizorkin spaces and show that pseudo- differential operators are bounded on these spaces by using pointwise multipliers. References | Related Articles | Metrics

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EXCESS FUNCTIONS OF RAYS ON COMPLETE NONCOMPACT MANIFOLDS XU Sen-Lin, XU Xu Acta mathematica scientia,Series B. 2003, 23 (3):  339.  Abstract ( 577 )   RICH HTML PDF (97KB) ( 1007 )   Save This paper gives an estimate of excess functions of rays on complete noncom- pact manifolds. By using this estimation, they can get the results in [3] as corollaries, which asserts that a complete manifold is diffeomorphic to Rn under some curvature and pinching conditions. At last, they obtain a refinement of them with extra Ricci condition. References | Related Articles | Metrics

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ASYMPTOTIC NORMALITY OF KERNEL ESTIMATES OF A DENSITY FUNCTION UNDER ASSOCIATION DEPENDENCE LIN Zheng-Tan Acta mathematica scientia,Series B. 2003, 23 (3):  345.  Abstract ( 692 )   RICH HTML PDF (110KB) ( 1428 )   Save Let {X_{n}, n>=1 1} be a strictly stationary sequence of random variables, which are either associated or negatively associated, f(·) be their common density. In this paper, the author shows a central limit theorem for a kernel estimate of f(·) under certain regular conditions. References | Related Articles | Metrics

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ON THE COMMUTATIVITY OF MULTIPLE SERIES AND BASIC SEQUENCE YANG Chang-Sen Acta mathematica scientia,Series B. 2003, 23 (3):  351.  Abstract ( 562 )   RICH HTML PDF (92KB) ( 785 )   Save Let $X$ be a Banach space and $\{e_j\}^{\oo}_{j=1}$ be a sequence  in $X$. The author shows  that $\{e_j\}^{\oo}_{j=1}$ is a basic sequence if and only if $\sum^{\oo}_{n=1}r_n \a_{nj}$  converges for every  $j\>1$ and $\sum^{\oo}_{n=1}r_n\sum^{\oo}_{j=1}\a_{nj}e_j= \sum^{\oo}_{j=1}(\sum^{\oo}_{n=1}r_n\a_{nj})e_j$ holds for every choice of scalar variables $\{\a_{nj}\}$ such that $\sum^{\oo}_{j=1}\a_{nj}e_j$ converges for each  $n\>1$  and any choice of scalar variables $\{r_n\}$ such that $\sum^{\oo}_{n=1} \sum^{\oo}_{j=1}r_n\a_{nj}e_j$ converges.  Moreover,  some applications about the result are given. References | Related Articles | Metrics

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A DIRECT APPROACH TO THE SOLITON PERTURBATION FOR KdV-MKdV EQUATION BO Liu-Xian, YA Jia-Ren, ZHOU Guang-Hui Acta mathematica scientia,Series B. 2003, 23 (3):  356.  Abstract ( 642 )   RICH HTML PDF (93KB) ( 936 )   Save The authors develop a direct approach to the soliton perturbation based on the separation of variables. With the aid of approach, the first-order effects of perturbation on a KdV-MKdV soliton are derived, both the slow time-dependence of the soliton parameters and the first-order correction are obtained. References | Related Articles | Metrics

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QUENCHING ON BOUNDARY TO THE NEWTON FILTRATION EQUATION DUAN Zhi-Wen, XIE Chun-Gong, LEI Wei-Meng Acta mathematica scientia,Series B. 2003, 23 (3):  361.  Abstract ( 677 )   RICH HTML PDF (116KB) ( 1063 )   Save In this paper discuss authors the global existence and quenching of the solution to the Newton filtration equation with the nonlinear boundary condition. They also discuss the profile of the quenching solution in the quenching time and obtain the quenching rate of the quenching solution. References | Related Articles | Metrics

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B¨ACKLUND TRANSFORMATION ON SURFACES WITH CONSTANT MEAN CURVATURE IN R TIAN Chou, ZHOU Kou-Hua, TIAN Chong-Bei Acta mathematica scientia,Series B. 2003, 23 (3):  369.  Abstract ( 709 )   RICH HTML PDF (111KB) ( 1081 )   Save In this paper, the authors obtain the B¨acklund transformation on time-like surfaces with constant mean curvature in R2,1. Using this transformation, families of surfaces with constant mean curvature from known ones can be constructed. References | Related Articles | Metrics

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A CLASS OF NONLINEAR SINGULARLY PERTURBED PROBLEMS FOR REACTION DIFFUSION EQUATIONS MO Jia-Qi Acta mathematica scientia,Series B. 2003, 23 (3):  377.  Abstract ( 685 )   RICH HTML PDF (110KB) ( 1183 )   Save A class of nonlinear singularly perturbed problems for reaction diffusion equa- tions are considered. Under suitable conditions, by using the theory of differential inequal- ities, the asymptotic behavior of solutions for the initial boundary value problems are studied, reduced problems of which possess two intersecting solutions. References | Related Articles | Metrics

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IMPLICIT-EXPLICIT MULTISTEP FINITE ELEMENT-MIXED FINITE ELEMENT METHODS FOR THE TRANSIENT BEHAVIOR OF A SEMICONDUCTOR DEVICE CHEN Wei Acta mathematica scientia,Series B. 2003, 23 (3):  386.  Abstract ( 677 )   RICH HTML PDF (150KB) ( 1177 )   Save The transient behavior of a semiconductor device consists of a Poisson equa- tion for the electric potential and of two nonlinear parabolic equations for the electron density and hole density. The electric potential equation is discretized by a mixed finite element method. The electron and hole density equations are treated by implicit-explicit multistep finite element methods. The schemes are very efficient. The optimal order error estimates both in time and space are derived. References | Related Articles | Metrics

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THE GEL’FAND n-WIDTHS OF MULTIVARIATE PERIODIC BESOV CLASSES XU Gui-Qiao, TU Chun-Wu Acta mathematica scientia,Series B. 2003, 23 (3):  399.  Abstract ( 792 )   RICH HTML PDF (119KB) ( 1091 )   Save The Gel’fand n-widths of Besov classes are considered. The weak asymptotic behavior is established for the corresponding quantity. References | Related Articles | Metrics

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UNIQUENESS OF STATIONARY SOLUTIONS WITH VACUUM OF EULER-POISSON EQUATIONS DENG Yin-Bin, GUO Yu-Jin Acta mathematica scientia,Series B. 2003, 23 (3):  405.  Abstract ( 724 )   RICH HTML PDF (126KB) ( 1042 )   Save \small\begin{quote}\bf Abstract\quad \rm In this paper, the uniqueness of stationary solutions with vacuum of Euler-Poisson equations is considered.  Through a nonlinear transformation which is a function of density and entropy, the corresponding problem can be reduced to a semilinear elliptic equation with a nonlinear source term consisting of  a power function, for which the classical theory$^{[4],[9]}$  of the elliptic equations leads us to the uniqueness result under some assumptions on  the entropy function $S(x)$. As an example, the authors  get the uniqueness of stationary solutions with vacuum of Euler-Poisson equations for $S(x) = |x|^\theta $ and $\theta \in \left \{0 \right \} \cup [2(N-2), +\infty)$. References | Related Articles | Metrics

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SOME REMARKS ON QUASIMEROMORPHIC MAPPINGS DING Jia-Qi, LUO Pei-Zhu Acta mathematica scientia,Series B. 2003, 23 (3):  413.  Abstract ( 550 )   RICH HTML PDF (91KB) ( 1002 )   Save In this paper, the authors introduce some Mellin transforms in weak functions and discuss their applications to M¨unts formula of the Riemann zeta-function. References | Related Articles | Metrics

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SOME REMARKS ON QUASIMEROMORPHIC MAPPINGS DENG Fang-Wen Acta mathematica scientia,Series B. 2003, 23 (3):  419.  Abstract ( 645 )   RICH HTML PDF (102KB) ( 1221 )   Save In this paper,the Nevanlinna direction, Borel direction and exceptional value of quasimeromorphic mapping are discussed and some results are obtained. References | Related Articles | Metrics

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THE VALUE DISTRIBUTION OF RANDOM DIRICHLET SERIES ON THE RIGHT HALF PLANE (II) TIAN Fan-Ji, LIN Yao-Feng Acta mathematica scientia,Series B. 2003, 23 (3):  426.  Abstract ( 847 )   RICH HTML PDF (130KB) ( 1073 )   Save Kahane has studied the value distribution of the Gauss-Taylor series $\sum\limits^\infty_{n=0}a_nX_nz^n$,  where $\{X_n\}$  is a complex Gauss sequence and $\sum\limits^\infty_{n=1}|a_n|^2=\infty$. In this paper, by  transforming the  right half plane into the unit disc and setting up some important inequalities,  the value distribution of the Dirichlet series $\sum\limits^\infty_{n=0}X_n{\rm e}^{-\lambda_nS}$  is studied where $\{X_n\}$ is a sequence of some non-degenerate independent random variable satisfying conditions: $EX_n=0; \sum\limits^\infty_{n=0}E|X_n|^2=+\infty; \forall n\in N, X_n$ or Re$X_n$ or Im$X_n$ of bounded density. There exists $\alpha>0$ such that $\forall n:\alpha^2E|X_n|^2\leq E^2 |X_n|<+\infty$  (the classic Gauss and Steinhaus random variables are special cases of such random variables). The important results are obtained that every point on the line Re$s=0$ is a Picard point of the series without finite exceptional value a.s.. References | Related Articles | Metrics