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Some Fundamental Results of Calculus on Fractal Sets

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Communications in Nonlinear Science and Numerical Simulation 1998年第1期3卷 22-26页

作者： Huikun JIANG and Weiyi SU (Dept.of Mathematics,nanjing university,210008,china) department of Mathematics Nanjing University Nanjing 210008 China

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关键词： s set s derivatives s integrals

Free Quadratic Bialgebra

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Acta Mathematica Sinica,English Series 1996年第3期12卷 244-248页

作者： Hao Zhifeng, department of Applied Mathematics South china university of Technology Guangzhou, 510641 chinaTong Wenting, department of Mathematics nanjing university nanjing, 210008 china department of Applied Mathematics South China University of Technology Guangzhou China department of Mathematics Nanjing University Nanjing China

In this paper, we obtain the following main theorem for a free quadratic bialgebra J: (a) For p≠0, J is a pointed cosemisimple coalgebra. For p=0, J is a hyperalgebra. (b) For p≠0 and q≠0, J has antipode S iff p·q+2=0 and S(x)=x. Forp=0 or q=0, J has antipode and S(x)=-x. (c) All left J*-modules are rational. Also, we give some applications in homological theory and algebraic K-theory.

关键词： Free quadratic bialgebra Antipode Cosemisimple Rational module

Luminosity function of optically-selected type II QSOs

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Science china(physics,Mechanics & Astronomy) 2010年第S1期53卷 191-195页

作者： BIAN WeiHao & ZHANG ShiYan department of physics,nanjing Normal university,nanjing 210097,china department of physics Nanjing Normal University Nanjing China

For a sample of 411 type II QSOs with redshifts less then 0.3,we use the Balmer decrements to do the reddening correction of the [O III] luminosities and then derive the intrinsic [O III] luminosity *** find that the host reddening correction of the [O III] 5007 luminosity for type II QSOs cannot be *** median Balmer decrement of Hα/Hβ=4.0 corresponds to an extinction of 0.94 mag for the [O III] 5007 line,which is consistent with the result derived from the median Hβ/Hγ.Comparing the intrinsic luminosity function of type II QSOs with that of type I QSOs,we find that the upper limit of the type II QSO’s fraction in the total QSOs is 80% for type II QSOs with z < 0.3 and 8.6≤log(L[O III]/L)≤9.4.

关键词： type II QSOs luminosity function emission lines Balmer decrements

One-step estimation for varying coefficient models

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Science china Mathematics 2005年第2期48卷 198-213页

作者： TANG Qingguo & WANG Jinde department of Mathematics, nanjing university, nanjing 210093, china Institute of Sciences, PLA university of Science and Technology, nanjing 210007, china department of Mathematics Nanjing University Nanjing China Institute of Sciences PLA University of Science and Technology Nanjing China

A one-step method is proposed to estimate the unknown functions in the varying coefficient models, in which the unknown functions admit different degrees of smoothness. In this method polynomials of different orders are used to approximate unknown functions with different degrees of smoothness. As only one minimization operation is employed, the required computation burden is much less than that required by the existing two-step estimation method. It is shown that the one-step estimators also achieve the optimal convergence rate. Moreover this property is obtained under conditions milder than that imposed in the two-step estimation method. More importantly, as only one minimization operation is employed, the full asymptotic properties, not only the asymptotic bias and variance, but also the asymptotic distributions of the estimators can be derived. The asymptotic distribution results will play a key role for making statistical inference.

关键词： varying coefficient model, one-step estimation, asymptotic distribution, optimal convergence rate.

SOLVING TRUST REGION PROBLEM IN LARGE SCALEOPTIMIZATION

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Journal of Computational Mathematics 2000年第1期18卷 1-12页

作者： Bing-sheng He(department of Mathematics, nanjing university, Naming 210093, china) 南京大学江苏南京 210093

Presents a study which introduced a method for solving trust region problem in scale minimization. Review of the conjugate gradient method (CG) and the projection and contraction (PC) method; Convergence behavior of t... 详细信息

关键词： trust region problem conjugate gradient method projection and contraction method

Completely regular paracompact reflection of locales

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Science china Mathematics 2006年第6期49卷 820-826页

作者： HE Wei & LUO Maokang department of Mathematics, nanjing Normal university, nanjing 210097, china department of Mathematics, Sichuan university, Chengdu 610064, china department of Mathematics Nanjing Normal University Nanjing China department of Mathematics Sichuan University Chengdu China

We give an explicit construction of the completely regular paracompact reflection pL of a completely regular locale L described as a sublocale of the Stone-tech compactification βL of L.

关键词： completely regular paracompact locale, nucleus.

Evolution of chlorite composition in the Paleogene prototype basin of Jiyang Depression, Shandong, china, and its implication for paleogeothermal gradient

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Science china Earth Sciences 2007年第11期50卷 1645-1654页

作者： ZHAO Ming1, CHEN XiaoMing1, JI JunFeng1, ZHANG Zhe1 & ZHANG Yun2 1 State Key Laboratory for Mineral Deposits Research, department of Earth Sciences, nanjing university, nanjing 210093, china 2 Jiangsu Survey Institute of Engineering and physics, nanjing 210008, china State Key Laboratory for Mineral Deposits Research Department of Earth Sciences Nanjing University Nanjing China Jiangsu Survey Institute of Engineering and physics Nanjing China

The Dongying Basin, Huimin Basin, and Zhanhua Basin constitute the Jiyang Depression in Shandong Province. They are major oil and gas exploring districts within the depression. Through reconstructions of the paleotemperature of the three basins facilitated with the chlorite geothermometry, the thermal history of the Paleogene prototype basin in Jiyang Depression and its geologic significance were explored. This study reveals that the Si^(4+) component in chlorites reduces gradually as its buried depth increases, while the AI~Ⅳ component increases accordingly. The chlorite type changes from silicon-rich diabantite to silicon-poor ferroamesite and prochlorite. The prochlorite in this district only appears in the deep buried depth, high temperature, and relatively old stratigraphies; while the diabantite appears in the shallower buried, low temperature, and newly formed strata; the ferroamesite exists in the conditions between prochlorite and diabantite formation. The diagenetic temperatures of the chlorites in these Paleogene basins are 171 — 238℃ for the Dongying Basin, 160—202℃ for the Huimin Basin, and 135—180℃ for the Zhanhua Basin. The differences of the chlorite diagenetic temperatures in the three basins were controlled by the duration time of the structural depressing processes. Higher temperature indicates longer depression time. The relationship between the chlorite diagenetic temperature and its buried depth indicates that the average paleogeothermal gradient is about 38.3℃ /km in the Paleogene prototype basin of Jiyang Depression. It was higher than the present geothermal gradient (29—30℃/km). This phenomenon was attributed to the evolution of the structural dynamics in the depression basin.

关键词： Paleogene,Jiyang depression,chlorite component,chlorite geothermometry,paleotemperature,paleogeothermal gradient

Some new results on planar harmonic mappings

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Science china Mathematics 2010年第3期53卷 597-604页

作者： CHEN HuaiHui department of Mathematics, nanjing Normal university, nanjing 210097, china department of Mathematics Nanjing Normal University

This survey paper contains some new results on the Landau theorem, Bloch theorem and Schwarz-Pick lemma for planar harmonic mappings.

关键词： harmonic mapping Landau theorem Bloch constant Schwarz-Pick lemma quasi-regularity

A POSTERIORI ERROR ESTIMATES OF FINITEELEMENT METHOD FOR PARABOLIC PROBLEMS

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Acta Mathematica Scientia 1999年第4期19卷 449-456页

作者：陈艳萍 department of Mathematics Xiangtan University Xiangtan 411105 China department of Mathematics Nanjing University Nanjing 210008 China

This paper deals with a-posteriori error estimates for piecewise linear finite element approximations of parabolic problems in two space dimensions. The analysis extends previous results for elliptic problems to the p... 详细信息

关键词： Aposteriori error estimates finite element method parabolic problem