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Continuous Method for Describing Dendrite Evolution During Solidification

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Chinese Physics Letters 2004年第1期21卷 143-145页

作者：李强郭巧懿李殿中钱百年李大明李若张平文 InstituteofMetalResearch ChineseAcademyofSciencesShenyang110016 ShenyangInstituteofTechnology Shenyang110168 schoolofmathematicalscience PekingUniversityBeijing100871

A continuous method is presented to deal with the discontinuous physical properties on both sides of solid/liquid interface during the solidification process. Then single dendrite evolution in two and three dimensions is simulated by using this method. Multi-grain evolution is also simulated during solidification by the method. The method is easy to be understood and does not need all details of dendrite. The simulated results can reflect the random characteristic of dendrite evolution and the micro-segregation of solute.

关键词： Solidification

REPRESENTATIONS OF SOLVABLE LIE GROUPSAND GEOMETRIC QUANTIZATION

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Chinese Annals of Mathematics,Series B 1999年第3期20卷 351-362页

作者： ZHAOQIANG XIAOLI schoolofmathematicalscience PekingUniversityBeijlng100871China DepartmentofMathematics NorthwestNormalUniversityLanzhou730070China.

Representations of solvable Lie groups are realized and classified by geometric quantization of coadjoint orbits through positive polarizations.

关键词：可解李群表示法几何量子化配极变换余伴随轨迹

Baeicklund Transformation and Multiple Soliton Solutions for （3＋1）-Dimensional Potential-YTSF Equation

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Communications in Theoretical Physics 2004年第6X期42卷 827-830页

作者： BAICheng-Lin LIUXi-Qiang ZHAOHong DepartmentofCommunicationEngineering LiaochengUniversityLiaocheng252059China schoolofmathematicalscience LiaochengUniversityLiaocheng252059China

We study an approach to constructing multiple soliton solutions of the (3+1)-dimensional nonlinear evolution equation. We take the (3+1)-dimensional potential- YTSF equation as an example. Using the extended homogeneous balance method, one can find a Backlund transformation to decompose the (3+1)-dimensional potential-YTSF equation into a set of partial differential equations. Starting from these partial differential equations, some multiple soliton solutions for the (3+1)-dimensional potential-YTSF equation are obtained by introducing a class of formal solutions.

关键词：孤波解奇次平衡展开法 YTSF势能方程非线性偏微分

PARAMETER ESTIMATION FOR A DISCRETELY OBSERVED STOCHASTIC VOLATILITY MODEL WITH JUMPS IN THE VOLATILITY

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Chinese Annals of Mathematics,Series B 2003年第2期24卷 227-238页

作者： JIANGWENJIANG J.PEDERSEN schoolofmathematicalscience YunnanNormalUniversityKunming650092China. InstituteofMathematicalSciences UniversityofAarhusAarhusDenmark.

In this paper a stochastic volatility model is considered. That is, a log price process Y whichis given in terms of a volatility process V is studied. The latter is defined such that the logprice possesses some of the properties empirically observed by Barndorff-Nielsen & Jiang[6]. Inthe model there are two sets of unknown parameters, one set corresponding to the marginaldistribution of V and one to autocorrelation of V. Based on discrete time observations ofthe log price the authors discuss how to estimate the parameters appearing in the marginaldistribution and find the asymptotic properties.

关键词：参数估计随机挥发模型中心极限定理大数定律 Levy过程 NIG分布 Ornstein-Uhlenbeck过程证券价格 Brown运动边缘分布

Tracking control and synchronization of chaotic systems based upon sampled—data feedback

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Chinese Physics B 2002年第3期11卷 233-237页

作者：陈士华刘杰等 schoolofmathematicalscience WuhanUniversityWuhan430072China

A novel tracking control and synchronization method is proposed based upon sampled-data feedback. This methodcan make a chaotic system approach any desired smooth orbit and synchronize the driving system and the responsesystem, both in the same structure and in diverse structures. Finally, a numerical simulation with a Lorenz system isprovided for the purpose of illustration and verification.

关键词： synchronization chaos Lorenz system

POSITIVE SOLUTIONS FOR SINGULAR BOUNDARY VALUE PROBLEM OF SECOND ORDER

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Chinese Annals of Mathematics,Series B 2004年第3期25卷 383-392页

作者： LIUJIAQUAN ZENGPING＇AN XIONGMING schoolofmathematicalscience PekingUniversityBeijing100871China SchoolofMathematlcalScience PekingUniversityBeijing100871China DepartmentofMathematics DaliUniversity（HehuaCampus）Dali671000YunnanChina

Some results of existence of positive solutions for singular boundary value problems{-u″(t) = p(t)f(u(t)), t ∈ (0, 1),u(0) = u(1) = 0are given, where the function p(t) may be singular at t = 0,1.

关键词：奇异边界值单一性正解变化法函数