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On c-equivalence

Science China mathematics 2009年第12期52卷 2389-2396页

作者： LI Xia department of mathematics,Nanjing university,Nanjing 210093,China department of mathematics Nanjing University Nanjing China

In this paper,we propose some c-equivalence specifically for autonomous Lagrangian systems and show how to construct connecting orbits in energy surface based on this c-equivalence.

关键词： c-equivalence autonomous Lagrangian systems connecting orbits 37K14

Asymptotic Properties of Self-Consistent Estimatorswith Doubly-Censored Data

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Acta Mathematica Sinica,English Series 2001年第4期17卷 581-594页

作者： Qi Qing YU Lin Xiong LI mathematics department, SUNY at Binghamton, Binghamton, NY 13902, usa mathematics department. Zhongshan university, Guangzhou 510275, P. R. China department of mathematics. university of New Orleans, New Orleans, LA 70148, usa mathematics department SUNY at Binghamton Binghamton USA mathematics department Zhongshan University Guangzhou 510275 P. R. China department of mathematics University of New Orleans New Orleans USA

The asyrmptotic properties of the self-consistent estimator (SCE) of a distribution function F of a random variable X with doubly-censored data are examined by several authors under the asstumption that X is observable everywhere in the interval [a, b], where a=inf{x: F(x)>0} and b=sup{x: F(x)gap in the proofs of the existing results in the literature due to the definition of the SCE.

关键词： Asymptotic normality Generalized MLE Right censoring Self-consistent algorithm Strong consistency

L~∞ CONVERGENCE OF TRUNC ELEMENT FOR THE BIHARMONIC EQUATION

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Journal of Computational mathematics 1997年第1期15卷 14-22页

作者： M. Wang(department of mathematics, Beijing university, Beijing, China) 北京大学数学系北京

The paper considers the L∞ convergence for TRUNC finite elements solving the boundary value problems of the biharmonic equation. The nearly optimal L∞ estimates for the error of first order derivatives are *** TRUNC plate element is proposed and developed by Argyris et al.. The numerical experiences show that the element has very good .***,[1l2]. The mathematicalproof of convergence of the TRUNC element is given by Shi Zong-ci in paper [3]. Thispaper will consider the L~∞ convergence for the TRUNC plate element.

关键词：双谐波方程边值问题收敛性有限元法

DESIGN AND ANALYSIS OF HIGH-THROUGHPUT SCREENING EXPERIMENTS

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Journal of Systems Science & Complexity 2011年第4期24卷 711-724页

作者： Xianggui QU department of mathematics and Statistics Oakland University Rochester MI 48309 USA.

Saturated row-column designs are studied to eliminate positional effects in primary high- throughput screening experiments. Compared to designs currently used in practice, all compounds in the designs considered are comparable within each microplate in spite of the existence of row and column effects. The designs considered in this paper also have the maximum number of compounds arranged in each microplate. Two statistical methods are used to choose leading compounds in the designs considered. These two methods take full advantages of effect sparsity in primary screening. Simulation studies are carried out to compare the two statistical methods with two ad hoc methods in selecting active compounds. A method that maintains balanced false positives and false negatives is recommended.

关键词： Bscore high-throughput screening row-column design saturated design Zscore.

RESERVOIR DESCRIPTION BY USING A PIECEWISE CONSTANT LEVEL SET METHOD

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Journal of Computational mathematics 2008年第3期26卷 365-377页

作者： Hongwei Li Center for Integrated Petroleum Research,university of Bergen,Norway department of mathematics,Capital Normal university,Beijing 100037,China Xuecheng Tai department of mathematics,university of Bergen,Norway Division of Mathematical Sciences,School of Physical and Mathematical Sciences,Nanyang Technological university,Singapore Sigurd Ivar Aanonsen Center for Integrated Petroleum Research,university of Bergen,Norway department of mathematics,university of Bergen,Norway Center for Integrated Petroleum Research University of Bergen Norway department of mathematics Capital Normal University Beijing 100037 China department of mathematics University of Bergen Norway Division of Mathematical Sciences School of Physical and Mathematical Sciences Nanyang Technological University Singapore

We consider the permeability estimation problem in two-phase porous media flow. We try to identify the permeability field by utilizing both the production data from wells as well as inverted seismic data. The permeability field is assumed to be piecewise constant, or can be approximated well by a piecewise constant function. A variant of the level set method, called Piecewise Constant Level Set Method is used to represent the interfaces between the regions with different permeability levels. The inverse problem is solved by minimizing a functional, and TV norm regularization is used to deal with the ill-posedness. We also use the operator-splitting technique to decompose the constraint term from the fidelity term. This gives us more flexibility to deal with the constraint and helps to stabilize the algorithm.

关键词： Inverse problem Level set method Piecewise constant Operator splitting,Reservoir description

On Holomorphic Automorphisms of a Class of Non-homogeneous Rigid Hypersurfaces in C^(N+1)

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Chinese Annals of mathematics,Series B 2010年第2期31卷 201-210页

作者： Qingyan WU department of mathematics,Linyi Normal university,Linyi 276005,Shandong,China department of mathematics,Zhejiang university,Hangzhou 310027,China department of mathematics Linyi Normal University Linyi China department of mathematics Zhejiang University Hangzhou China

The author determines the real-analytic infinitesimal CR automorphisms of a class of non-homogeneous rigid hypersurfaces in CN+1 near the origin,and the connected component containing the identity transformation of al... 详细信息

关键词： Real-analytic infinitesimal CR automorphisms Rigid hypersurfaces Holomorphic automorphisms

Numerical Dynamics of Coupled System of J-JType

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Communications in Nonlinear Science and Numerical Simulation 1997年第3期2卷 3-5页

作者： Wen Xin QIN (department of mathematics, Suzhou university) department of mathematics Suzhou University USA

ＮｕｍｅｒｉｃａｌＤｙｎａｍｉｃｓｏｆＣｏｕｐｌｅｄＳｙｓｔｅｍｏｆＪＪＴｙｐｅＷｅｎＸｉｎＱＩＮ（ＤｅｐａｒｔｍｅｎｔｏｆＭａｔｈｅｍａｔｉｃｓ，ＳｕｚｈｏｕＵｎｉｖｅｒｓｉｔｙ）Ａｂｓｔｒａｃｔ：Ｉｎｔｈｉｓ... 详细信息

ＮｕｍｅｒｉｃａｌＤｙｎａｍｉｃｓｏｆＣｏｕｐｌｅｄＳｙｓｔｅｍｏｆＪＪＴｙｐｅＷｅｎＸｉｎＱＩＮ（ＤｅｐａｒｔｍｅｎｔｏｆＭａｔｈｅｍａｔｉｃｓ，ＳｕｚｈｏｕＵｎｉｖｅｒｓｉｔｙ）Ａｂｓｔｒａｃｔ：Ｉｎｔｈｉｓｐａｐｅｒｗｅｃｏｎｓｉｄｅｒｔｈ...

关键词： Coupled System of J J Type Global Attractor Numerical Dynamics Approximation

CONVERGENCE OF VORTEX WITH BOUNDARY ELEMENT METHODS

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Journal of Computational mathematics 1997年第2期15卷 127-137页

作者： P.W. Zhang(department of mathematics, Peking university) 北京大学数学系北京

In this work, the vortex methods for Euler equations with initial boundary value problem is considered, Poisson equations are solved using boundary element methods which can be seen to require less operations to compute the velocity field from the vorticity by Chorin([6]). We prove that the rate of convergence of the boundary element schemes can be independent of the vortex blob parameters.

关键词： Math CONVERGENCE OF VORTEX WITH BOUNDARY ELEMENT METHODS Zhang

Tree wavelet approximations with applications

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Science China mathematics 2005年第5期48卷 680-702页

作者： XU Yuesheng & ZOU Qingsong department of mathematics, Syracuse university, Syracuse, NY 13244, usa Institute of mathematics, Academy of mathematics and System Sciences, Chinese Academy of Sciences, Beijing 100080, China department of Scientific Computing and Computer Science, Zhongshan university, Guangzhou 510275, China department of mathematics Syracuse University Syracuse USA Institute of mathematics Academy of Mathematics and System Sciences Chinese Academy of Sciences Beijing China department of Scientific Computing and Computer Science Zhongshan University Guangzhou China

We construct a tree wavelet approximation by using a constructive greedy scheme (CGS). We define a function class which contains the functions whose piecewise polynomial approximations generated by the CGS have a prescribed global convergence rate and establish embedding properties of this class. We provide sufficient conditions on a tree index set and on bi-orthogonal wavelet bases which ensure optimal order of convergence for the wavelet approximations encoded on the tree index set using the bi-orthogonal wavelet bases. We then show that if we use the tree index set associated with the partition generated by the CGS to encode a wavelet approximation, it gives optimal order of convergence.

关键词： greedy algorithms tree wavelet approximations Besov spaces.