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13 July 2004, Volume 24 Issue 1 Previous Issue    Next Issue

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MORE ABOUT MELLIN TRANSFORM IN WEAK FUNCTIONS AND M¨UNTS FORMULA Ding-Jia-Qi, LUO Pei-Zhu Acta mathematica scientia,Series B. 2004, 24 (1):  1-8.  Abstract ( 577 )   RICH HTML PDF (102KB) ( 804 )   Save This paper is a further continuation of the paper [1]. In the present paper Mellin transform and M¨unts formula of weak functions in complex domain will be treated. References | Related Articles | Metrics

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ON QUADRATURE FORMULAE FOR SINGULAR |INTEGRALS OF ARBITRARY ORDER DU Jin-Yuan Acta mathematica scientia,Series B. 2004, 24 (1):  9-27.  Abstract ( 546 )   RICH HTML PDF (182KB) ( 1187 )   Save t Some quadrature formulae for the numerical evaluation of singular integrals of arbitrary order are established and both the estimate of remainder and the convergence of each quadrature formula derived here are also given. References | Related Articles | Metrics

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LOCAL MEDIAN ESTIMATION OF VARIANCE FUNCTION YANG Ying, W. C. Ip, Y. K. Kwan Acta mathematica scientia,Series B. 2004, 24 (1):  28-38.  Abstract ( 575 )   RICH HTML PDF (141KB) ( 968 )   Save This paper considers local median estimation in fixed design regression prob- lems. The proposed method is employed to estimate the median function and the variance function of a heteroscedastic regression model. Strong convergence rates of the proposed estimators are obtained. Simulation results are given to show the performance of the proposed methods. References | Related Articles | Metrics

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HYPERSURFACES IN SPACE FORMS WITH SCALAR CURVATURE CONDITIONS XU Sen-Lin, ZHANG Yun-Chao Acta mathematica scientia,Series B. 2004, 24 (1):  39-44.  Abstract ( 544 )   RICH HTML PDF (104KB) ( 994 )   Save Let $\ f:M^n$ $\hookrightarrow$ $S^{n+1}$ $\subset$ $R^{n+2}$ be an $n$-dimensional complete oriented Riemannian manifold minimally immersed in an $(n+1)$-dimensional  unit sphere $S^{n+1}$. Denote by $S^{n+1}_+$ the upper closed hemisphere. If $f(M^n)\subseteq S_{+}^{n+1}$, then under some curvature conditions the authors can get that the isometric immersion is a totally embedding. They also generalize a theorem of Li Hai Zhong  on hypersurface of space form with costant scalar curvature. References | Related Articles | Metrics

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A RECOGNITION OF SIMPLE GROUPS PSL(3, q) BY THEIR ELEMENT ORDERS M. R. Darafsheh;A. R. Moghaddamfar A.R. Zokay Acta mathematica scientia,Series B. 2004, 24 (1):  45-51.  Abstract ( 607 )   RICH HTML PDF (127KB) ( 2147 )   Save For any group G, denote by e(G) the set of orders of elements in G. Given a finite group G, let h(e(G)) be the number of isomorphism classes of finite groups with the same set e(G) of element orders. A group G is called k-recognizable if h(e(G)) = k < 1, otherwise G is called non-recognizable. Also a 1-recognizable group is called a recognizable (or characterizable) group. In this paper the authors show that the simple groups PSL(3, q), where 3 < q  ±2 (mod 5) and (6, (q − 1)/2) = 1, are recognizable. References | Related Articles | Metrics

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ON THE GROWTH OF SOLUTIONS OF A CLASS OF HIGHER ORDER DIFFERENTIAL EQUATIONS CHEN Zong-Xuan, SUN Guang-Gao Acta mathematica scientia,Series B. 2004, 24 (1):  52-60.  Abstract ( 618 )   RICH HTML PDF (141KB) ( 1652 )   Save In this paper, authors investigate the order of growth and the hyper order of solutions of a class of the higher order linear differential equation, and improve results of M. Ozawa[6], G. Gundersen[7] and J.K. Langley[8], Li Chun-hong[11] References | Related Articles | Metrics

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BOOTSTRAP WAVELET IN THE NONPARAMETRIC REGRESSION MODEL WITH WEAKLY DEPENDENT PROCESSES LIN Lu, ZHANG Run-Chu Acta mathematica scientia,Series B. 2004, 24 (1):  61-70.  Abstract ( 536 )   RICH HTML PDF (131KB) ( 896 )   Save This paper introduces a method of bootstrap wavelet estimation in a non- parametric regression model with weakly dependent processes for both fixed and random designs. The asymptotic bounds for the bias and variance of the bootstrap wavelet estima- tors are given in the fixed design model. The conditional normality for a modified version of the bootstrap wavelet estimators is obtained in the fixed model. The consistency for the bootstrap wavelet estimator is also proved in the random design model. These results show that the bootstrap wavelet method is valid for the model with weakly dependent processes. References | Related Articles | Metrics

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LOCAL REGULARITY RESULT FOR SOLUTIONS OF OBSTACLE PROBLEMS GAO Gong-E, TIAN Hui-Yang Acta mathematica scientia,Series B. 2004, 24 (1):  71-74.  Abstract ( 597 )   RICH HTML PDF (97KB) ( 1250 )   Save This paper gives the local regularity result for solutions to obstacle problems of $A$-harmonic equation $\mbox {div} A(x, \bigtriangledown u(x))=0$, $|A(x, \xi )|\approx |\xi|^{p-1}$, when $1<p<n$ and the obstacle function $\psi \geq 0$. References | Related Articles | Metrics

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ON THE BOREL DIRECTION OF K-QUASIMEROMORPHIC MAPPINGS YANG Yan, LIU Ming-Sheng Acta mathematica scientia,Series B. 2004, 24 (1):  75-82.  Abstract ( 572 )   RICH HTML PDF (120KB) ( 1034 )   Save For the K-quasimeromorphic mappings, a precise fundamental inequality for the angular domain is established. From this, the Borel direction of the K-quasimeromorphic mappings of zero order is derived. References | Related Articles | Metrics

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MEROMORPHIC FUNCTIONS THAT SHARE TWO SETS, II YI Hong-Xun, LV Wei-Ran Acta mathematica scientia,Series B. 2004, 24 (1):  83-90.  Abstract ( 651 )   RICH HTML PDF (110KB) ( 1189 )   Save his paper deals with the problem of uniqueness of meromorphic functions,  and gets the following result: There exists a set $S$ with $13$ elements such that any two non-constant meromorphic functions $f$ and $g$ satisfying $\overline{E}(S,f)=\overline{E}(S,g)$  and $\overline{E}(\{\infty\},f)=\overline{E}(\{\infty\},g)$ must be identical. This is  the best result on this question until now. References | Related Articles | Metrics

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FORWARD-BACKWARD STOCHASTIC DIFFERENTIAL EQUATIONS WITH STOPPING TIME TUN Zhen Acta mathematica scientia,Series B. 2004, 24 (1):  91-99.  Abstract ( 642 )   RICH HTML PDF (126KB) ( 1694 )   Save The existence and uniqueness results of fully coupled forward-backward sto- chastic differential equations with stopping time (unbounded) is obtained. One kind of comparison theorem for this kind of equations is also proved.   References | Related Articles | Metrics

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BILINEAR FORMS AND LINEAR CODES GAO Ying Acta mathematica scientia,Series B. 2004, 24 (1):  100-106.  Abstract ( 528 )   RICH HTML PDF (110KB) ( 915 )   Save Abraham Lempel et al[1] made a connection between linear codes and systems of bilinear forms over finite fields. In this correspondence, a new simple proof of a theorem in [1] is presented; in addition, the encoding process and the decoding procedure of RS codes are simplified via circulant matrices. Finally, the results show that the correspondence between bilinear forms and linear codes is not unique. References | Related Articles | Metrics

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CONFIDENCE REGIONS IN TERMS OF STATISTICAL CURVATURE FOR AR(q) NONLINEAR REGRESSION MODELS 1 LIU Ying-An, HUI Bo-Cheng Acta mathematica scientia,Series B. 2004, 24 (1):  107-117.  Abstract ( 580 )   RICH HTML PDF (141KB) ( 864 )   Save This paper constructs a set of confidence regions of parameters in terms of statistical curvatures for AR(q) nonlinear regression models. The geometric frameworks are proposed for the model. Then several confidence regions for parameters and parameter subsets in terms of statistical curvatures are given based on the likelihood ratio statistics and score statistics. Several previous results, such as [1] and [2] are extended to AR(q) nonlinear regression models. References | Related Articles | Metrics

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NON-NEWTON FILTRATION EQUATION WITH SPECIAL MEDIUM VOID TAN Zhong Acta mathematica scientia,Series B. 2004, 24 (1):  118-128.  Abstract ( 557 )   RICH HTML PDF (142KB) ( 1151 )   Save This paper  considers the existence and asymptotic estimates of global solutions and finite time blowup of local solution of non-Newton filtration equation with special  medium void of the following form: $$\left\{ \begin{array}{ll} \displaystyle \frac{u_t}{|x|^2}-\bigtriangleup_p u=u^q, &  (x,t)\in\Omega\times (0,T),\\[2mm] u(x,t)=0, & (x,t)\in\partial\Omega\times (0,T),\\ u(x,0)=u_0(x), & u_0(x)\geq 0, u_0(x)\not\equiv 0, \end{array}\right.$$ where $\bigtriangleup_pu={\rm div} \left(|\bigtriangledown u|^{p-2}\bigtriangledown u\right)$, $\Omega$ is a smooth bounded domain in $R^N(N\geq 3$), $0\in\Omega$, $2<p<N$, $p-1<q<\frac{Np}{N-p}-1$. The result of asymptotic estimate of global solution depends on the best constant in Hardy inequality. References | Related Articles | Metrics

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A FINITE VOLUME ELEMENT METHOD FOR THERMAL CONVECTION PROBLEMS RUI Hong-Xin Acta mathematica scientia,Series B. 2004, 24 (1):  129-138.  Abstract ( 581 )   RICH HTML PDF (179KB) ( 1127 )   Save Consider the finite volume element method for the thermal convection problem with the infinite Prandtl number. The author uses a conforming piecewise linear function on a fine triangulation for velocity and temperature, and a piecewise constant function on a coarse triangulation for pressure. For general triangulation the optimal order H1 norm error estimates are given. References | Related Articles | Metrics

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A CLASS OF STATIONARY MODELS OF SINGULAR STOCHASTIC CONTROL LIU Kun-Hui, QIN Meng-Da, LIU Chuan-Lai Acta mathematica scientia,Series B. 2004, 24 (1):  139-150.  Abstract ( 591 )   RICH HTML PDF (149KB) ( 994 )   Save A class of stationary models of singular stochastic control has been studied, in which the state is extended to solution of a class of S.D.E. from Wiener process. The existence of optimal control has been proved in all cases under some weaker conditions, and the structure of optimal control may be characterized. References | Related Articles | Metrics

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PERIODIC SOLUTIONS FOR GENERALIZED PREDATOR-PREY SYSTEMS WITH TIME DELAY AND DIFFUSION LI Bi-Wen Acta mathematica scientia,Series B. 2004, 24 (1):  151-160.  Abstract ( 684 )   RICH HTML PDF (131KB) ( 833 )   Save A set of easily verifiable sufficient conditions are derived for the existence of positive periodic solutions for delayed generalized predator-prey dispersion system $$\begin{array}{l} x'_{1}(t)=x_1(t)g_1(t,x_1(t))-a_1(t)y(t)p_1(x_1(t))+ D_1(t)(x_2(t)-x_1(t)),\\ x'_{2}(t)=x_2(t)g_2(t,x_2(t))-a_2(t)y(t)p_2(x_2(t))+ D_2(t)(x_1(t)-x_2(t)),\\ y'(t)=y(t)\left[-h(t,y(t))+b_1(t)p_1(x_1(t-\tau_1))+ b_2(t)p_2(x_2(t-\tau_2)) \right], \end{array}$$ where $a_i(t),b_i(t)$ and $D_i(t)(i=1,2)$ are positive continuous $T$-periodic functions, $g_i(t,x_i)$ $(i=1,2)$ and $h(t,y)$ are continuous and $T$-periodic with respect to $t$ and $h(t,y)>0$ for $y>0,t,y\in R,p_i(x)(i=1,2)$ are continuous and monotonously increasing functions, and $p_i(x_i)>0$ for $x_i>0$. References | Related Articles | Metrics