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The evolution and morphological stability of a spherical crystal

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Science china(Technological sciences) 2008年第3期51卷 225-243页

作者： CHEN MingWen1,2, WANG ZiDong2 & XU JianJun3,4 1 school of Applied sciences, university of Science and Technology Beijing, Beijing 100083, china 2 school of Materials Science and Engineering, university of Science and Technology Beijing, Beijing 100083, china 3 school of mathematical sciences, nankai university, tianjin 300071, china 4 Department of Mathematics and Statistics, McGill university, Montreal H3A 2K6, Canada 1. school of Applied sciences University of Science and Technology Beijing Beijing 100083 China 2. school of Materials Science and Engineering University of Science and Technology Beijing Beijing 100083 China 3. school of mathematical sciences Nankai University Tianjin 300071 China 4. Department of Mathematics and Statistics McGill University Montreal H3A 2K6 Canada

The growth model of a spherical crystal in the undercooled melt including the surface energy, interfacial kinetics and convective flow is established. The effect of the convective flow induced by a small far field flow on the evolution and morphological stability of the interface of the spherical crystal is studied. The interface shape of the spherical crystal, which is affected by the far field flow, and the dispersion relation of the growth rate of amplitude of the perturbed interface are derived. It is shown that the convection induced by the far field flow makes the interface of the growing spherical crystal further grow in the upstream direction of the far field flow and inhibit growth in the downstream direction; the interface of the decaying spherical crystal further decays in the upstream direction and inhibits decay in the downstream direction. The theoretical result suggests that both the growth of the sphere in the upstream direction and the decay of the sphere in the downstream direction make the spherical crystal tend to evolve into an oval; the morphological stability of the interface depends on a certain radius R c such that the spherical crystal is unstable when its radius is greater than R c and stable when its radius is less than R c . The surface energy and interfacial kinetics have strong stabilizing effects on the growth of the spherical crystal. In the meantime interfacial kinetics is a table factor of the interface when the interface of the sphere is growing; it is an unstable factor of the interface when the interface is decaying.

关键词： solid-liquid interface spherical crystal convective flow crystal growth morphological stability

MAXIMUM INFORMATION AND OPTIMUM ESTIMATING FUNCTION

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Chinese Annals of Mathematics,Series B 2003年第3期24卷 349-358页

作者： LIN Lu Department of Statistics, school of mathematical sciences, nankai university, tianjin 300071, china. nankai Univ Sch Math Sci Dept Stat Tianjin 300071 Peoples R China

In order to construct estimating functions in some parametric models, this paper introducestwo classes of information matrices. Some necessary and sufficient conditions for the informationmatrices achieving their upper bounds are given. For the problem of estimating the median,some optimum estimating functions based on the information matrices are acquired. Undersome regularity conditions, an approach to carrying out the best basis function is introduced. Innonlinear regression models, an optimum estimating function based on the information matricesis obtained. Some examples are given to illustrate the results. Finally, the concept of optimumestimating function and the methods of constructing optimum estimating function are developedin more general statistical models.

关键词： Quasi (pseudo) Fisher information Estimating function Quasi score Nonlinear regression model Median regression model

On isometric extension problem between two unit spheres

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Science china Mathematics 2009年第10期52卷 2069-2083页

作者： Ding GuangGui school of mathematical sciences and LPMC, nankai university, tianjin 300071, china 1. school of mathematical sciences and LPMC Nankai University Tianjin 300071 China

In this paper we introduce the isometric extension problem of isometric mappings between two unit spheres. Some important results of the related problems are outlined and the recent progress is mentioned.

关键词： normed space isometric extension isometric mapping 1-Lipschitz mapping 46A22 46B02 46B04 46B20 46B22

Brake subharmonic solutions of first order Hamiltonian systems

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Science china Mathematics 2010年第10期53卷 2719-2732页

作者： LI Chong & LIU ChunGen school of mathematical sciences and LPMC,nankai university,tianjin 300071,china 1. school of mathematical sciences and LPMC Nankai University Tianjin 300071 China

In this paper,we mainly use the Galerkin approximation method and the iteration inequalities of the L-Maslov type index theory to study the properties of brake subharmonic solutions for the first order non-autonomous Hamiltonian *** prove that when the positive integers j and k satisfy the certain conditions,there exists a jT-periodic nonconstant brake solution zj such that zj and zkj are distinct.

关键词： brake subharmonic solution L-Maslov type index Hamiltonian systems

A Four-filtrated May Spectral Sequence and Its Applications

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Acta Mathematica Sinica,English Series 2008年第9期24卷 1507-1524页

作者： Xiu Gui LIU Xiang Jun WANG school of mathematical sciences and LPMC,nankai university,tianjin 300071,P.R.china school of mathematical sciences and LPMC Nankai University Tianjin 300071 P. R. China

In this paper, we introduce a four-filtrated version of the May spectral sequence (MSS), from which we study the general properties of the spectral sequence and give a collapse theorem. We also give an efficient method to detect generators of May E 1-term E 1 s,t,b,* for a given (s, t, b, *). As an application, we give a method to prove the non-triviality of some compositions of the known homotopy elements in the classical Adams spectral sequence (ASS).

关键词： stable homotopy groups of spheres Adams spectral sequence May spectral sequence

Totally geodesic submanifolds of maximal rank in symmetric spaces

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Science china Mathematics 2004年第2期47卷 264-271页

作者： ZHU Fuhai & LIANG Keschool of mathematical sciences and LMAM, Peking university, Beijing 100871, china College of mathematical sciences and LPMC, nankai university, tianjin 300071, china 1.school of mathematical sciences and LMAM Peking University 100871 Beijing China 2.College of Mathematical Sciences and LPMC Nankai University 300071 Tianjin China

We gave a complete list of totally geodesic submanifolds of maximal rank in symmetric spaces of noncompact type. The compact cases can be obtained by the duality.

关键词： totally geodesic submanifold, Lie triple system, maximal rank.

Stochastic Fractional Anderson Models with Fractional Noises

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Chinese Annals of Mathematics,Series B 2010年第1期31卷 101-118页

作者： Yiming JIANG Kehua SHI Yongjin WANG school of mathematical sciences and LPMC Nankai University Tianjin 300071 China school of mathematical sciences and LPMC Nankai University Tianjin 300071 China

The authors are concerned with a class of one-dimensional stochastic Anderson models with double-parameter fractional noises, whose differential operators are fractional. A unique solution for the model in some appropriate Hilbert space is constructed. Moreover, the Lyapunov exponent of the solution is estimated, and its HSlder continuity is studied. On the other hand, the absolute continuity of the solution is also discussed.

关键词： Anderson models Fractional noises Lyapunov exponent Holder continuity Absolute continuity

A NEW FAMILY OF FILTRATION s+6 IN THE STABLE HOMOTOPY GROUPS OF SPHERES

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Acta Mathematica Scientia 2006年第2期26卷 193-201页

作者：刘秀贵 school of mathematical sciences and LMPC nankai university Tianjin 300071China

In the year 2002, Lin detected a nontrivial family in the stable homotopy groups of spheres ;π-6S which is represented by hngoγ^-3 ∈ Ext^6tA（Zp, Zp） in the Adams spectral sequence, where t = 2p^n（p- 1）＋ 6（p^2 ＋p ＋ 1）（p- 1） and p ≥ 7 is a prime number. This article generalizes the result and proves the existence of a new nontrivial family of filtration s ＋ 6 in the stable homotopy groups of spheres πt1-8-6S which is represented by bygoγ^s＋3 ∈ Ext^s＋6＋t1Atl （Zp, Zp） in the Adams spectral sequence, where n≥ 4, 0 ≤ s 〈 p - 4, t1 = 2p^n（p- 1）＋ 2（p- 1）（（s ＋ 3）p^2 ＋（s ＋ 3）p ＋（s ＋ 3））＋ s.

关键词： Stable homotopy groups of spheres Adams spectral sequence Toda-Smith spectrum May spectral sequence

Weak minimum aberration and maximum number of clear two-factor interactions in 2_(IV)^(m-p)designs

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Science china Mathematics 2005年第11期48卷 1479-1487页

作者： YANG Guijun,LIU Minqian & ZHANG Runchu Department of Statistics, tianjin university of Finance and Economics, tianjin 300222, china Department of Statistics, school of mathematical sciences and LPMC, nankai university, tianjin 300071, china 1. Department of Statistics Tianjin University of Finance and Economics 300222 Tianjin China 2. Department of Statistics School of Mathematical Sciences and LPMC Nankai University 300071 Tianjin China

Both the clear effects and minimum aberration criteria are the important rules for the design selection. In this paper, it is proved that some 2IVm-p designs have weak minimum aberration, by considering the number of clear two-factor interactions in the designs. And some conditions are provided, under which a 2IVm-p design can have the maximum number of clear two-factor interactions and weak minimum aberration at the same time. Some weak minimum aberration 2IVm-p designs are provided for illustrations and two non-isomorphic weak minimum aberration 2IV13-6 designs are constructed at the end of this paper.

关键词： clear weak minimum aberration resolution wordlength pattern.