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The Isometric Extension of the Into Mapping from the Unit Sphere S_1(E) to S_1(l~∞(Г))

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Acta Mathematica Sinica,English Series 2008年第9期24卷 1475-1482页

作者： Xiao Hong FU department of mathematics,Jiaying College,Meizhou 514015,p.r.china department of mathematics Jiaying College Meizhou 514015 P. R. China

This paper considers the isometric extension problem concerning the mapping from the unitsphere S(E)of the normed space E into the unit sphere S(l~∞(Γ)).We find a condition under whichan isometry from S,(E)into S1(l~∞(Γ))can be linearly and isometrically extended to the whole *** l~∞(Γ)is universal with respect to isometry for normed spaces,isometric extension problemson a class of normed spaces are *** precisely,if E and F are two normed spaces,and ifV:S(E)→S(F)is a surjective isometry,where c(Γ)■(Γ),then Vcan be extended tobe an isometric operator defined on the whole space.

关键词： l~∞(F) space isometric mapping isometric extension

On the Isomorphic Classes of Hopf-Galois Extensions with Normal Bases over a Commutative ring

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Acta Mathematica Sinica,English Series 1999年第4期15卷 515-524页

作者： Xiaolong Jiang department of mathematics,Zhongshan university,Guangzhou 510275,p.r.china E-mail:stdm@zsu.edu.cnYonghua Xu Institute of mathematics,Fudan university,Shanghai 200433,p.r.china E-mail:yxu@*** department of mathematics Zhongshan University Guangzhou P. R. China Institute of mathematics Fudan University Shanghai P. R. China

In this paper we consider the isomorphic classes of H-Galois extensions with the normal basis property over a fixed commutative ring B for a finite Hopf algebra *** result is that when H is cocommutative,then the above isomorphic classes and the 2-nd cohomology group H^2(L~*,U) are isomorphic as groups under the product defined in this paper,where L=BH,L~*=Hom_B(L,B).

关键词： Hopf-Galois extentions Cohomology group

CONVErGENCE OF THE pOINT VOrTEX METHODS FOr EULEr EQUATION ON HALF pLANE

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Journal of Computational mathematics 1996年第3期14卷 213-222页

作者： p.W. Zhang(department of mathematics, Beijing university, Beijing, china) BEIJING UNIV DEPT MATHBEIJING 100871PEOPLES R CHINA

In this paper, we study the point vortex method for 2-D Euler equation of incompressible how on the half plane, and the explicit Euler's scheme is considered with the reflection method handling the boundary condition.... 详细信息

关键词： Math CONVErGENCE OF THE pOINT VOrTEX METHODS FOr EULEr EQUATION ON HALF pLANE Zhang

The Existence of BIB Designs

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Acta Mathematica Sinica,English Series 2000年第1期16卷 103-112页

作者： Yanxun Chang Institute of mathematics,Northern Jiaotong university,Beijing 100044,p.r.china Institute of mathematics Northern Jiaotong University Beijing 100044 P.R. China

Given any positive integers k3 and λ,let c（k,λ）denote the smallest integer such that u ∈ B（k,λ）for every integer uc（k,λ）that satisfies the congruences λv（v-1）≡0（mod k（k-1））and λ（u-1）≡0（mod k-1）.In this article we make an improvement on the bound of c（k,λ）provided by Chang in[4]and prove that c（k,λ）exp{kp>3kp>6p>p>}.In particular,c（k,1）exp{kp>kp>2p>p>}.

关键词： Wilson’s theorem Balanced incomplete block design pBD-closed

When Closed Graph Manifolds are Finitely Covered by Surface Bundles Over S^1

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Acta Mathematica Sinica,English Series 1999年第1期15卷 11-20页

作者： Yan Wang Fengchun Yudepartment of mathematics,peking university,Beijing 100871 p.r.china department of mathematics Peking University Beijing P. R. China

The problem of deciding whether a graph manifold is finitely covered by a surface bundle over the circle is discussed in this paper.A necessary and sufficient condition in term of the solutions of a certain matrix equation is obtained,as well as a necessary condition which is easy to compute. Our results sharpen and extend the earlier results of ***,***,and ***-F. Yu in this topic.

关键词： Surface bundle Covering Graph manifolds

Contribution of an Auxin to the Uptake of Nickel and Cadmium in Maize Seedlings

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Biomedical and Environmental Sciences 1999年第3期12卷 170-176页

作者： GUO DONG-SHENG XI Yv-YINC WANG AI-YING ZHANG JUN AND YUAN XIAO-YING(department of Environmentel Science, shanxi university, Taiyuan, china Analyzingand Detecting Center, shanxi university, Taiyuan, china) department of Environmentel Science Shanxi University Taiyuan China

Maize seedlings were cultured in nickel or cadmium contaminated sand treated with α-naphthylacetic acid (NAA). The effeets of NAA on nickel and cadmium uptake in roots, shoots, and subcellular fractions (cell wall, nuclei and remained parts of seedling cells) were determined. The data showed growth promotion when NAA was applied at low concentrations and inhibition at high concentrations. Uptake of nickel and cadmium content increased concurmntly in roots and shoots. In thesubcellular fraction, nickel and cadmium was greatest in the cell wall. The changes in growth had greatest cormlation Wtih nickel and cadmium content in the subeellular fraction.

关键词： Ni Contribution of an Auxin to the Uptake of Nickel and Cadmium in Maize Seedlings

Empirical Likelihood for Semiparametric Varying-Coefficient Heteroscedastic partially Linear Models

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Journal of Mathematical research with Applications 2012年第1期32卷 95-107页

作者： Guo Liang FAN 1,2,Hong Xia XU 1,1.School of mathematics & physics,Anhui polytechnic university,Anhui 241000,p.r.china 2.department of mathematics,Tongji university,Shanghai 200092,p.r.china School of mathematics & physics Anhui Polytechnic University Anhui 241000

Consider the semiparametric varying-coefficient heteroscedastic partially linear model Y i = Xτiβ + Zτiα(Ti) + σiei,1 ≤ i ≤ n,where σ 2 i = f(Ui),β is a p × 1 column vector of unknown parameter,(Xi,Zi,Ti,Ui) are random design points,Y i are the response variables,α(·) is a q-dimensional vector of unknown functions,e i are random *** both cases that f(·) is known and unknown,we propose the empirical log-likelihood ratio statistics for the parameter β.For each case,a nonparametric version of Wilks' theorem is *** results are then used to construct confidence regions of the *** studies are carried out to assess the performance of the empirical likelihood method.

关键词： Empirical likelihood heteroscedastic partially linear model varying-coefficient model local linear method confidence region.

A New Almost periodic Type Solution of First Order Neutral Delay Differential Equations with piecewise Constant Argument

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Acta Mathematica Sinica,English Series 2001年第3期17卷 403-412页

作者： rong YUAN department of mathematics,Beijing Normal university,Beijing 100875,p.r.china E-mail:ryuan@*** department of mathematics Beijing Normal University Beijing 100875 P. R. China

In this paper,we introduce a new class of ergodic sequences,pseudo almost periodic sequences,and study the existence of pseudo almost periodic sequences to difference *** the basis of these,we investigate the existence of pseudo almost periodic solutions for neutral delay differential equations with piecewise constant argument, d/(dt)(y(t)+py(t-1))=qy(2[(t+1)/2])+g(t,y(t),([t])).

关键词： pseudo almost periodic solutions pseudo almost periodic sequences Neutral delay equation piecewise constant argument

population-size-dependent branching processes in Markovian random environments

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Chinese Science Bulletin 1998年第8期43卷 635-638页

作者： WANG Hanxing 1 and DAI Yonglong 2 1. department of mathematics, Shanghai university, Shanghai 201800, china 2. department of mathematics, Zhongshan university, Guangzhou 510275, china department of mathematics Shanghai University Shanghai China department of mathematics Zhongshan University Gunngzhou China

A branching model {Z n} n≥0is considered where the offspring distribution of the population’s evolution is not only dependent on the population size, but also controlled by a Markovian environmental process {ξ n} n≥0. For this model, asymptotic behaviour is studied such as limn→∞Z n and limn→∞Z n/m n in the case that the mean m k, θof the offspring distribution converges to m>1 as the population size k grows to ∞. In the case that {ξ n} n≥0is an irreducible positive recurrent Markov chain, certain extinction (i.e. p(Z n=0 for some n)=1) and noncertain extinction (i.e. p(Z n=0 for some n)re studied.

关键词： Markov chains in random environments stochastic population models branching processes.