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EXISTENCE OF LIMIT CYCLES IN A MULTIPLY-CONNECTED REGION

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Chinese Annals of mathematics,Series B 1999年第2期20卷 169-172页

作者： ZHANG XIANG(department of mathematics, Naming normal university, Naming 210097, china.) department of mathematics Nanjing Normal University Nanjing 210097 China

In this paper,a conjecture about the existence of limit cycles in a multiply-connected regionproposed by Ye Yanqian is proved.

关键词： Multiply-connected region Annulus theorem Limit cycle

The　θ－Methods　in　Numerical　Solution　of　Systems　of　Differential　Equations　with　Two　Delay　Terms

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Journal of Systems Engineering and Electronics 1994年第3期5卷 32-40页

作者： Tian Hongjiong & Kuang Jiaoxun (department of mathematics, Shanghai normal university, Shanghai 200234, china) department of mathematics Shanghai Normal University Shanghai 200234 China

This paper deals with the numerical solution of initial value problems for systems of differential equations with two delay terms. We investigate the stability of adaptations of the θ-methods in the numerical solution of test equations u'(t) = a 11 u(t) + a12v(t) + b11 u(t - τ1) + b12v(t-τ2,v'(t) = a21 u(t) + a22 v(t) + b21 u(t -τ1,) + b22 v(t -τ2), t>0,with initial conditionsu(t)=u0(t),v(t) =v0(t), t≤*** aij, bij∈C, τj >0, i,j = 1,2,, and u0(t), v0(t)are continuous and complex valued. Sufficient conditions for the asymptotic stability of test equation are derived. Furthermore, with respect to an appropriate definition of stability for the numerical method, it is proved that the linear θ-method is stable if and only if 1/2≤θ≤1 and the one-leg θ-method is stable if and only if θ= 1.

关键词： Delay differential equations Numerical solution θ-methods Asymptotic stability Schur polynomial.

ON THE RANGE OF RANDOM WALKS IN RANDOM ENVIRONMENT　

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Chinese Annals of mathematics,Series B 1995年第1期16卷 131-138页

作者： ZHOU XIANYIN(department of mathematics, Beijing normal university, Beijing 100875, china.) 北京师范大学北京 100875

The range of random walk on Z￣d in symmetric random environment is investigated. As results, it is proved that the strong law of large numbers for the range of random walk on Zdin some random environments holds if d... 详细信息

关键词： Law of large numbers Ergodic theorem Range of random walk Random environment Effective resistance.

An equality on Hochschild homology groups

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Chinese Science Bulletin 1997年第8期42卷 624-627页

作者： ZHANG Pu and LIU Shaoxue1. department of mathematics, university of Science and Technology of china, Hefei 230026, china 2. department of mathematics, Beijing normal university, Beijing 100875, china department of mathematics University of Science and Technology of China Hefei China department of mathematics Beijing Normal University Beijing China

LET A be finite-dimensional algebra over field k,and Ae the enveloping algebra of A,i.e.Ae=A kAop,where Aop is the opposite algebra of *** A-bimodule has a natural left Ae-module structure as follows:

关键词： finite-dimensional algebra Hochschild homology groups dimensions.

Pairing problem of generators in Kac-Moody algebras

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Chinese Science Bulletin 1998年第22期43卷 1872-1879页

作者： LU Caihui department of mathematics, Capital normal university, Beijing 100037, china department of mathematics Capital Normal University Beijing China

The following result is proved: in any Kac Moody algebra g(A) , (ⅰ) given any non central element h in the Cartan subalgebra  , or (ⅱ) given any real root vector x β, β∈Δ re . There exists y∈g(A) such that th... 详细信息

关键词： generator root system real root vector.

Analysis of the cause of crack in cold rolling of QSn6.5-0.1 strip

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Journal of Central South university of Technology 2001年第2期8卷 94-98页

作者： ZHANG Sheng hua 1,QIN Ye xia 1,LOU Hua fen 2,LU Jun pan 2,ZHONG Wei jia 2 (1 department of Materials Science and Engineering, Central South university, Changsha 410083, china 2.luoyang Copper Processing Company, luoyang 471000, china) department of Materials Science and Engineering Central South University Changsha China luoyang Copper Processing Company Luoyang China

In order to know the cause of cracks in cold rolling of QSn6.5 0.1 copper alloy strip, a lot of experiments and analysis were done. The microstructure changes of QSn6.5 0.1 were investigated by means of metallurgical microscope. The morphology of cracks and surface defects were examined using scanning electron microscope. Macroscopic residual stresses produced in every process during manufacturing in the QSn6.5 0.1 strip were measured by X ray diffraction method and hole drilling method. The results show that the cracks in the QSn6.5 0.1 cold rolling strip were caused due to the derivation of metallurgical defects, such as SnO 2, S, fine looses,the inverse segregation unable to clear up when milling, and the accumulation of all kinds of resi dual stresses. When the accumulation of the residual stress reaches the material′s breaking strength, the cracks will be generated. Several measures to avoid the development of these kinds of cracks were put forward, such as: controlling the casting technology, improving homogenization annealing procedure (680 ℃/7 h) and milling quality(using the second milling when necessary), working out a more reasonable rolling technology to ensure intermediate annealing in time.

关键词： QSn6.5 0.1 cold rolling strip crack metallurgical defect residual stress

Approach to synthesis and structure of chiral multi-functionalized organophosphorus derivatives

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Science Bulletin 2003年第4期48卷 323-328页

作者： FU Yuqin, FAN Xue, WANG Jiange, KANG Haixia & CHEN Qinghua department of Chemistry, luoyang normal College, luoyang 47102., china Correspondence should be addressed to Chen Qinghua department of Chemistry Luoyang Normal College Luoyang 471022 China

The diastereomerically pure organophosphorus derivatives containing multiple chiral centers 5 and 5 were obtained, respectively, in 62%-84% yields with ≥98% de (diastereomeric excess) via asymmetric reaction of the chiron, 3-bromo-2(5H)-furanone 4 with racemic diethyl a-hydroxyl- substituted-phosphonates 3 + 3 and further through the separation of the diastereomeric mixture by chromatography. The structures of the chiral organophosphorus derivatives were identified on the basis of their elementary and spectro-scopic data, such as IR, 1H NMR, 13C NMR, MS and X-ray crystallography. In this report, the synthetic methods of the active organophosphorus substrates, the structure charac-terization and resolution, the optical purity and the stereo-chemistry of the chiral products were discussed. These re-sults provide a new idea and a good method for synthesizing some natural organophosphorus compounds and approach-ing their biological activities, also a facile route to the appli-cation of organophosphorus substrates.

关键词： diastereomerically pure organophosphorus derivatives tandem asymmetric reaction racemic diethyl a-hydroxyl-substi- tuted-phosphonate biological activity.

On quasi-convex mappings of order α in the unit ball of a complex Banach space

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Science china mathematics 2006年第11期49卷 1451-1457页

作者： LIU Taishun & XU Qinghua department of mathematics, Huzhou Teachers College, Huzhou, 313000, china department of mathematics, Jiangxi normal university, Nanchang, 330022, china department of mathematics Huzhou Teachers College Huzhou China department of mathematics Jiangxi Normal University Nanchang China

In this paper, a class of biholomorphic mappings named quasi-convex mapping of order a in the unit ball of a complex Banach space is introduced. When the Banach space is confined to Cn, we obtain the relation between this class of mappings and the convex mappings. Furthermore, the growth and covering theorems of this class of mappings are given on the unit ball of a complex Banach space X. Finally, we get the second order terms coefficient estimations of the homogeneous expansion of quasi-convex mapping of order a defined on the polydisc in Cn and on the unit ball in a complex Banach space, respectively.

关键词： coefficient estimation the homogeneous expansion quasi-convex mapping quasi-convex mapping of order a.

Existence and Application of Optimal Markovian Coupling with Respect to Non-Negative Lower Semi-Continuous Functions

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Acta Mathematica Sinica,English Series 2000年第2期16卷 261-270页

作者： Shaoyi Zhangdepartment of mathematics.Beijing normal university,Beijing 100875,P.R.china department of mathematics,Hubei normal university,Huangshi 435002,P.R.china department of mathematics Beijing Normal University Beijing 100875 P. R. China department of mathematics Hubei Normal University Huangshi 435002 P. R. China

In this paper,for two given transition probabilities,the existence of the optimal Markovian coupling with respect to a non-negative lower semi-continuous function is *** an application of this result,the well-known Strassen’s theorem is ***,it is proved that the existence of an order-preserving Markovian coupling of two given jump processes is equivalent to their stochastical comparability.

关键词： Transition probability Markovian coupling Jump process