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SADDLE VALUES AND INTEGRABILITY CONDITIONS OF QUADRATIC DIFFERENTIAL SYSTEMS

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Chinese Annals of mathematics 1987年第4期8卷 466-478页

作者：朱德明 department of mathematics east china normal university shanghai china.

In the first section of the paper,the first three saddle values R1,R2,R3 of the realquadratic differential system（QDE） are computed by use of the method with which Poincaréresearchs on Hopf *** the second section,by applying the method and results ofDulac seeking integrability conditions of QDE it is proved that the system is integrable ifand only if R1=R2=R3=0,and it is also true when the system is *** integrabilityconditions given here can be applied much more easily then Dulac’*** the last part ofthe paper,it is pointed out that iR1,iR2,iR3 are the first three focal values of the weakfocus of the complex *** the formulae of R1,R2,R3 and the result in section 2,one can easily give the formulae of the focal values for the real QDE with Bautin formand give a new proof of Bautin’s famous result.

关键词：鲁一 Za SADDLE VALUES AND INTEGRABILITY CONDITIONS OF QUADRATIC DIFFERENTIAL SYSTEMS

Cholesterol oxidase biosensor based on a glassy carbon electrode modified with Nafion and methyl viologen

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Chinese Journal of Chemistry 1994年第4期12卷 343-347页

作者： JIN, Li-Tong ZHAO, Gui-zhu FANG, Yu-Zhidepartment of Chemistry, east china normal university, shanghai 200062, china department of Chemistry East China Normal University Shanghai 200062 China

Cholesterol oxidase biosensor has been constructed by using bovine serum albumin and glutaraldehyde as cross linker to immobilize cholesterol oxidase and cholesterol esterase on a glassy carbon electrode modified with Nafion and methyl viologen. The biosensor has been used to determine total cholesterol in blood. The linear range of the determination is 2.5×10~7 to 1.0×10-4 mol/L. The detection limit is about 5.0×10~8 mol/L. The response time is 12 s. This biosensor has the advantage of high selectivity, sensitivity and short response time.

关键词： Biosensor cholesterol oxidase enzyme electrode.

Checking for normality in linear mixed models

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Science china mathematics 2012年第4期55卷 787-804页

作者： WU Ping 1,,zhu LiXing 2,3 & FANG Yun 4 1 School of Finance and Statistics,east china normal university,shanghai 200241,china 2 School of Statistics and mathematics,Yunnan university of Finance and Economics,Yunnan 650221,china 3 The department of mathematics,Hong Kong Baptist university,Hong Kong 999077,china 4 mathematics and Science College,shanghai normal university,shanghai 200234,china School of Finance and Statistics East China Normal University Shanghai China School of Statistics and mathematics Yunnan University of Finance and Economics Yunnan China The department of mathematics Hong Kong Baptist University Hong Kong China mathematics and Science College Shanghai Normal University Shanghai China

Linear mixed models are popularly used to fit continuous longitudinal data, and the random effects are commonly assumed to have normal distribution. However, this assumption needs to be tested so that further analysis can be proceeded well. In this paper, we consider the Baringhaus-Henze-Epps-Pulley （BHEP） tests, which are based on an empirical characteristic function. Differing from their case, we consider the normality checking for the random effects which are unobservable and the test should be based on their predictors. The test is consistent against global alternatives, and is sensitive to the local alternatives converging to the null at a certain rate arbitrarily close to 1/V~ where n is sample size. ^-hlrthermore, to overcome the problem that the limiting null distribution of the test is not tractable, we suggest a new method： use a conditional Monte Carlo test （CMCT） to approximate the null distribution, and then to simulate p-values. The test is compared with existing methods, the power is examined, and several examples are applied to illustrate the usefulness of our test in the analysis of longitudinal data.

关键词： linear mixed models estimated best linear unbiased predictors BHEP tests conditional MonteCarlo test

Microbial flocculant and its application in environmental protection

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Journal of Environmental Sciences 1999年第1期11卷 5-16页

作者： Zhang Tong, Lin Zhe department of Environmental Engineering, east china university of Science and Technology, shanghai 200237, china zhu Huai lan department of Environmental Science, east china normal university, shanghai 200062, china

The microbial flocculant is a kind of natural bio polymer and has promising future to be used in the fermentation industry and wastewater treatment. It has been studied in details in many countries, such as U.S.A, Japan. This paper reviewed the development on microbial flocculant basic studies and applications, including flocculant production microorganisms, chemical and components of microbial flocculants, flocculation mechanism of microbial flocculants, capability of microbial flocculants and influence factors, and culture conditions for flocculant production. The application cases of microbial flocculants were also discussed.

关键词： microorganism flocculant flocculation.

MELNIKOV VECTOR WITH HIGHER ORDER

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Annals of Differential Equations 1996年第3期12卷 371-379页

作者： zhu deming(east china normal university,200062) east china normal university 200062

By using the geometrical method, the higher order Melnikov vector and the associatedcriteria for the persistence, transversality and tangency of homoclinic and heteroclinic orbits are established. Examples of applicat... 详细信息

关键词： invariant manifold,tangent space heteroclinic orbit transversality exponential dichotomy.

SEMIPOSITONE PROBLEM FOR THE nTH-ORDER DELAYED DIFFERENTIAL SYSTEM

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Annals of Differential Equations 2008年第3期24卷 299-305页

作者： Lu Qiuying, zhu deming (Dept. of Math., east china normal university, shanghai 200062)

In this paper, we are concerned with the existence of positive solutions to the superlinear semipositone problem of the nth-order delayed differential system. The main result in this paper generalizes the corresponding result on the second order de-layed differential equation. Our proofs are based on the well-known Guo-Krasnoselskii fixed-point theorem.

关键词： positive solutions nonlinear nth-order delayed differential system cone fixed-point theorem boundary value problems semipositone problem

OSCILLATION FOR NONLINEAR SECOND-ORDER DYNAMIC EQUATIONS ON TIME SCALES

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Annals of Differential Equations 2008年第4期24卷 457-469页

作者： Xu Yancong (College of Science, Hangzhou normal university, Hangzhou 310036) zhu deming (Dept. of Math., east china normal university, shanghai 200062)

Through the use of generalized Riccati transformation techniques, we establish some oscillation criteria for one type of nonlinear dynamic equation on time scales. Several examples, including a semilinear dynamic equation and a nonlinear Emden-Fowler dynamic equation, are also given to illustrate these criteria and to improve the results obtained in some references.

关键词： oscillation dynamic equations time scales Riccati technique

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三点粗异宿环分支

数学学报（中文版） 2004年第6期47卷 1237-1242页

作者：金银来朱德明临沂师范学院数学系临沂276005 华东师范大学数学系上海200062

本文研究高维系统连接三个鞍点的粗异宿环的分支问题.在一些横截性条件和非扭曲条件下,获得了Γ附近的1-异宿三点环, 1-异宿两点环、 1-同宿环和1-周期轨的存在性,唯一性和不共存性.同时给出了分支曲面和存在域.上述结果被进一步推广到... 详细信息

本文研究高维系统连接三个鞍点的粗异宿环的分支问题.在一些横截性条件和非扭曲条件下,获得了Γ附近的1-异宿三点环, 1-异宿两点环、 1-同宿环和1-周期轨的存在性,唯一性和不共存性.同时给出了分支曲面和存在域.上述结果被进一步推广到连接l个鞍点的异宿环的情况,其中l≥2.

关键词：局部坐标异宿环同宿环

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史景迁史学探要

史学月刊 2009年第1期 99-110页

作者：朱政惠华东师范大学历史系

中国人作史强调一个史义,崇尚史识。史景迁史学影响大,最根本的还是他的史学思想和史学理念。他对明清史长时段演变问题的探究,对历史底层人物命运的追问等,都是试图对历史奥密进行洞察。他还希望究明东西方文化交流的历史,也期待自己... 详细信息

中国人作史强调一个史义,崇尚史识。史景迁史学影响大,最根本的还是他的史学思想和史学理念。他对明清史长时段演变问题的探究,对历史底层人物命运的追问等,都是试图对历史奥密进行洞察。他还希望究明东西方文化交流的历史,也期待自己成为不同文明交流大潮中的弄潮儿。长期的史学实践造就了他对过往历史、史学潮流、学术前沿的不凡洞察力,并以华美的历史文笔和精彩叙事去完善其治史的美好愿景。诚然,他的研究也有"局外人"的局限问题,在充分肯定史景迁的史学成就时,也要注意对这类问题的思考。

关键词：美国中国学史景迁史学理念