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Theory of optimal blocking for fractional factorial split-plot designs

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Science china mathematics 2005年第5期48卷 649-656页

作者： Al Mingyao & HE Shuyuan key Laborartory of Pure and applied mathematics, school of mathematical sciences, peking university, beijing 100871, china 1. key Laborartory of Pure and applied mathematics School of Mathematical Sciences Peking University 100871 Beijing China

The issue of optimal blocking for fractional factorial split-plot (FFSP) designs is considered under the two criteria of minimum aberration and maximum estimation capacity. The criteria of minimum secondary aberration (MSA) and maximum secondary estimation capacity (MSEC) are developed for discriminating among rival nonisomorphic blcoked FFSP designs. A general rule for identifying MSA or MSEC blocked FFSP designs through their blocked consulting designs is established.

关键词： blocking consulting design estimation capacity minimum secondary aberration fractional factorial split-plot design.

VARIABILITY SETS AND HAMILTON SEQUENCES

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Chinese Annals of mathematics,Series B 2005年第4期26卷 543-550页

作者： SUN NA WU SHENGJIAN key laboratory of Pure and applied mathematics School of Mathematical Sciences Peking University Beijing 100871 China.

This paper studies extremal quasiconformal mappings. Some properties of the variability set are obtained and the Hamilton sequences which are induced by point shift differentials are also discussed.

关键词： Quasiconformal mapping Point shift differentials Hamilton sequence Extremal mapping

Global Classical Solutions to Partially Dissipative Quasilinear Hyperbolic Systems

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Chinese Annals of mathematics,Series B 2011年第5期32卷 771-780页

作者： Yi ZHOU 11 key laboratory of mathematics for Nonlinear sciences,ministry of education,china Shanghai key laboratory for Contemporary applied mathematics school of mathematical sciences,Fudan university,Shanghai 200433,china. key laboratory of mathematics for Nonlinear sciences Ministry of Education China Shanghai Key Laboratory for Contemporary Applied Mathematics School of Mathematical Sciences Fudan University Shanghai 200433 China

The author considers the Cauchy problem for quasilinear inhomogeneous hyperbolic *** the assumption that the system is weakly dissipative,Hanouzet and Natalini established the global existence of smooth solutions for small initial data (in *** ***.,Vol.169,2003,pp.89-117).The aim of this paper is to give a completely different proof of this result with slightly different assumptions.

关键词： Cauchy problem Global classical solution Partially dissipativequasilinear hyperbolic system

DISCRIMINANT ANALYSIS BASED ON STATISTICAL DEPTH

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Journal of Systems Science & Complexity 2010年第2期23卷 362-371页

作者： Jiao JIN·Hengjian CUI school of mathematical sciences,key laboratory of mathematics and Complex Systems,ministry of education, beijing Normal university,beijing 100875,china. school of mathematical sciences Key Laboratory of Mathematics and Complex Systems Ministry of Education

In the past two decades,many statistical depth functions seemed as powerful exploratoryand inferential tools for multivariate data analysis have been *** this paper,a new depthfunction family that meets four properties mentioned in Zuo and Serfling(2000)is *** aclassification rule based on the depth function family is *** classification parameter b couldbe modified according to the type-Ⅰ error α,and the estimator of b has the consistency and achievesthe convergence rate n^(-1/2).With the help of the proper selection for depth family parameter c,theapproach for discriminant analysis could minimize the type-Ⅱ error β.A simulation study and a realdata example compare the performance of the different discriminant methods.

关键词： Depth discriminant analysis location parameter MVE scatter matrix.

An eSnake model for medical image segmentation

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Progress in Natural Science:Materials International 2005年第5期15卷 424-429页

作者： Lv Hongyu1, YUAN Kehong2, BAO Shanglian1, ZU Donglin1 and DUAN Chaijie1*(1. The Research Center for Tumor Diagnosis and Therapeutical Physics & beijing key laboratory of Medical Physics and Engineering, beijing 100871, china 2. key laboratory of Pure and applied mathematics, school of mathematical sciences, peking university, beijing 100871, china) The Research Center for Tumor Diagnosis and Therapeutical Physics & beijing key laboratory of Medical Physics and Engineering Beijing 100871 China key laboratory of Pure and applied mathematics School of Mathematical Sciences Peking University Beijing 100871 China

A novel scheme of external force for detecting the object boundary of medical image based on Snakes (active contours) is introduced in the paper. In our new method, an electrostatic field on a template plane above the original image plane is designed to form the map of the external force. Compared with the method of Gradient Vector Flow (GVF), our approach has clear physical meanings. It has stronger ability to conform to boundary concavities, is simple to implement, and reliable for shape segmenting. Additionally, our method has larger capture range for the external force and is useful for medical image preprocessing in various applications. Finally, by adding the balloon force to the electrostatic field model, our Snake is able to represent long tube-like shapes or shapes with significant protrusions or bifurcations, and it has the specialty to prevent Snake leaking from large gaps on image edge by using a two-stage segmentation technique introduced in this paper. The test of our models proves that our methods are robust, precise in medical image segmentation.

关键词： image segmentation eSnake external force electrostatic field balloon force.

INFINITE ELEMENT METHOD FOR THE EXTERIOR PROBLEMS OF THE HELMHOLTZ EQUATIONS

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Journal of Computational mathematics 2000年第6期18卷 657-672页

作者： Lung-an Ying (school of mathematical sciences, peking university, beijing 100871, china) 北京大学北京 100871

There are two cases of the exterior problems of the Helmholtz equation. If λ ≥ 0 the bilinear form is coercive, and if λ < 0 it is the scattering problem. We give a new approach of the infinite element method, which enables us to solve these exterior problems as well as corner problems. A numerical example of the scattering problem is given. [ABSTRACT FROM AUTHOR]

关键词： Helmholtz equation exterior problem infinite element method

Simulation of nuclei morphologies for binary alloy

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Science china mathematics 2010年第11期53卷 2927-2936页

作者： LI DaMing1, & ZHANG PingWen2 1Department of mathematics, Shanghai Jiaotong university, Shanghai 200240, china 2key Lab of mathematics and applied mathematics, Center for applied Physics and Technology and school of mathematical sciences, peking university, beijing 100871, china 1. Department of mathematics Shanghai Jiaotong University Shanghai 200240 China2. Key Lab of Mathematics and Applied Mathematics Center for Applied Physics and Technology and School of Mathematical Sciences Peking University Beijing 100871 China

We study the critical nuclei morphologies of a binary alloy by the string method. The dynamic equation of the string, connecting the metastable phase (liquid) and stable phase (solid), is governed by Helmholtz free energy for the binary alloy system at a given temperature. The stationary string through the critical nucleus (saddle point) is obtained if the relaxation time of the string is su?ciently large. The critical nucleus radius and energy barrier to nucleation of a pure alloy with isotropic interface energy in two and three dimensions are calculated, which are consistent with the classical nucleation theory. The critical nuclei morphologies are sensitive to the anisotropy strength of interface energy and interface thickness of alloy in two and three dimensions. The critical nucleus and energy barrier to nucleation become smaller if the anisotropy strength of the interface energy is increased, which means that it is much easier to form a stable nucleus if the anisotropy of the interface energy is considered.

关键词： nucleation crystal morphology string method

Sieve M-estimation for semiparametric varying-coefficient partially linear regression model

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Science china mathematics 2010年第8期53卷 1995-2010页

作者： HU Tao 1,2 & CUI HengJian 1,2 1 school of mathematical sciences,beijing Normal university,laboratory of mathematics and Complex Systems,ministry of education,beijing 100875,china 2 school of mathematical sciences,Capital Normal university,beijing 100048,china 1. school of mathematical sciences Beijing Normal University Laboratory of Mathematics and Complex Systems Ministry of Education Beijing 100875 China2. School of Mathematical Sciences Capital Normal University Beijing 100048 China

This article considers a semiparametric varying-coefficient partially linear regression *** semiparametric varying-coefficient partially linear regression model which is a generalization of the partially linear regression model and varying-coefficient regression model that allows one to explore the possibly nonlinear effect of a certain covariate on the response variable.A sieve M-estimation method is proposed and the asymptotic properties of the proposed estimators are *** main object is to estimate the nonparametric component and the unknown parameters *** is easier to compute and the required computation burden is much less than the existing two-stage estimation ***,the sieve M-estimation is robust in the presence of outliers if we choose appropriate ρ(·).Under some mild conditions,the estimators are shown to be strongly consistent;the convergence rate of the estimator for the unknown nonparametric component is obtained and the estimator for the unknown parameter is shown to be asymptotically normally *** experiments are carried out to investigate the performance of the proposed method.

关键词： partly linear model varying-coefficient robustness optimal convergence rate asymptotic normality

Sharpness on the Lower Bound of the Lifespan of Solutions to Nonlinear Wave Equations

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Chinese Annals of mathematics,Series B 2011年第4期32卷 521-526页

作者： Yi ZHOU 1 Wei HAN 2 1 Nonlinear mathematical Modeling and Methods laboratory Shanghai key laboratory for Contem- porary applied mathematics school of mathematical sciences, Fudan university, Shanghai 200433, china. 2 school of mathematical sciences, Fudan university, Shanghai 200433, china Department of mathematics, North university of china, Taiyuan 030051, china. Nonlinear mathematical Modeling and Methods laboratory Shanghai Key Laboratory for Contemporary Applied Mathematics School of Mathematical Sciences Fudan University Shanghai 200433 China

This paper is devoted to proving the sharpness on the lower bound of the lifespan of classical solutions to general nonlinear wave equations with small initial data in the case n = 2 and cubic nonlinearity （see the results of T. T. Li and Y. M. Chen in 1992）. For this purpose, the authors consider the following Cauchy problem： { where □=δt^2-∑i=1n δx^^2 is the wave operator, g（x）（≡/） 0 is a smooth non-negative function with compact support, and ε 〉 0 is a small parameter. It is shown that the solution blows up in a finite time, and the lifespan T（ε） of solutions has an upper bound T（ε） ≤ exp（Aε-2） with a positive constant A independent of ε, which belongs to the same kind of the lower bound of the lifespan.

关键词： Nonlinear wave equation Cauchy problem Lifespan