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Empirical likelihood confidence regions of the parameters in a partially linear single-index model

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Science china Mathematics 2005年第10期48卷 1333-1348页

作者： XUE Liugen~1 & ZHU Lixing~2.1. college of applied Sciences,{2. university of technology,{2. 10002.,china 2. Department of Mathematics,Hong Kong Baptist university,Hong Kong,china college of applied Sciences Beijing University of Technology Beijing China Department of Mathematics Hong Kong Baptist University Hong Kong China

In this paper, a partially linear single-index model is investigated, and three empirical log-likelihood ratio statistics for the unknown parameters in the model are suggested. It is proved that the proposed statistics are asymptotically standard chi-square under some suitable conditions, and hence can be used to construct the confidence regions of the parameters. Our methods can also deal with the confidence region construction for the index in the pure single-index model. A simulation study indicates that, in terms of coverage probabilities and average areas of the confidence regions, the proposed methods perform better than the least-squares method.

关键词： partially linear single-index model, empirical likelihood, confidence region, chi-square distribution, coverage probability.

Existence of solutions for the dynamic equation of ferrimagnets

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Progress in Natural Science:Materials International 2007年第11期17卷 1279-1283页

作者： Zeng Ming1, Guo Boling2.and Cheng Caozong1(1. college of applied Sciences,{2., beijing 10002., china 2. Center for Nonlinear Studies, Institute of applied Physics and Computational Mathematics, beijing 100088, china) college of applied Sciences Beijing University of Technology Beijing 100022 China

Ferrimagnet is a kind of basic and important multi-sublattice magnet material. It has attracted more and more attention of physicists and mathematicians. Many results of solitons and numerical computations on this topic have appeared. In this article, the dynamic equation for an isotropic ferrimagnet with two non-equivalent sublattices is studied, existence of weak solutions in multi dimension case is proved through the penalized method, the uniqueness and smoothness of the solution in one dimension case are also obtained by the relation between this equation and hyperbolic equation.

关键词： ferrimagnet weak solutions penalized method finite difference method

Simultaneous variable selection for heteroscedastic regression models

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Science china Mathematics 2011年第3期54卷 515-530页

作者： ZHANG ZhongZhan1 & WANG DaRong2.1college of applied Sciences,{2., beijing 10012., china 2.he Pilot college,{2., beijing 101101, china college of applied Sciences Beijing University of Technology The Pilot college Beijing University of Technology

In this paper, we propose a new criterion, named PICa, to simultaneously select explanatory variables in the mean model and variance model in heteroscedastic linear models based on the model structure. We show that the new criterion can select the true mean model and a correct variance model with probability tending to 1 under mild conditions. Simulation studies and a real example are presented to evaluate the new criterion, and it turns out that the proposed approach performs well.

关键词： variable selection heteroscedastic regression models adjusted profile log-likelihood AIC BIC

On some tests-based projection pursuit for elliptical symmetry of a high-dimensional distribution

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Chinese Science Bulletin 1998年第6期43卷 450-458页

作者： JING Ping 1 and ZHU Lixing 2.1. Mathematics Lab, china university of Mining & {2., beijing 100083, china 2. Probability Lab, Institute of applied Mathematics, Chinese Academy of Sciences, beijing 100080, china Mathematics Lab China University of Mining & Technology Beijing China Probability Lab Institute of Applied Mathematics Chinese Academy of Sciences Beijing China

Some test statistics of Kolmogorov type and Cramér-von Mises type based on projection pursuit technique are proposed for the testing problem of sphericity of a high-dimensional distribution. The limiting distributions of the test statistics are derived under the null hypothesis and under any fixed alternative. The asymptotic properties of bootstrap approximation are investigated. Furthermore, for computational reasons, an approximation for the statistics, based on the number theoretic method, is suggested.

关键词： bootstrap approximation projection pursuit type statistic elliptical symmetry.

A new DNA algorithm to solve graph coloring problem

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Progress in Natural Science:Materials International 2007年第6期17卷 733-738页

作者： Jiang Xingpeng1, Li Yin2. Meng Ya3 and Meng Dazhi2.1. National Laboratory of Pattern Recognition,Institute of Automation, Chinese Academy of Sciences, beijing 100080, china 2. {2. of applied Sciences, beijing university of technology, beijing 10002., china 3. School of Science, beijing Institute of technology, beijing 100081, china) National Laboratory of Pattern Recognition Institute of Automation Chinese Academy of Sciences Beijing 100080 China National High Magnetic Field Laboratory Florida State University 1800 East Paul Dirac Drive Tallahassee Florida 32306 USA

Using a small quantity of DNA molecules and little experimental time to solve complex problems successfully is a goal of DNA computing. Some NP-hard problems have been solved by DNA computing with lower time complexity than conventional computing. However, this advantage often brings higher space complexity and needs a large number of DNA encoding molecules. One example is graph coloring problem. Current DNA algorithms need exponentially increasing DNA encoding strands with the growing of problem size. Here we propose a new DNA algorithm of graph coloring problem based on the proof of four-color theorem. This algorithm has good properties of needing a relatively small number of operations in polynomial time and needing a small number of DNA encoding molecules (we need only 6R DNA encoding molecules if the number of regions in a graph is R).

关键词： DNA computing NP-hard problem graph coloring problem.

Existence of the solutions and the attractors for the large-scale atmospheric equations

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Science china Earth Sciences 2006年第6期49卷 650-660页

作者： HUANG Haiyang1 & GUO Boling2.1. Department of Mathematics, beijing Normal university, beijing 100875, china 2. Institute of applied Physics and Computational Mathematics, beijing 100080, china Department of Mathematics Beijing Normal University Beijing China Institute of applied Physics and Computational Mathematics Beijing China

In this paper, firstly, the proper function space is chosen, and the proper expression of the operators is introduced such that the complex large-scale atmospheric motion equations can be described by a simple and abstract equation, by which the definition of the weak solution of the atmospheric equations is made. Secondly, the existence of the weak solution for the atmospheric equations and the steady state equations is proved by using the Galerkin method. The existence of the non-empty global attractors for the atmospheric equations in the sense of the Chepyzhov-Vishik’s definition is obtained by constructing a trajectory attractor set of the atmospheric motion equations. The result obtained here is the foundation for studying the topological structure and the dynamical behavior of the atmosphere attractors. Moreover, the methods used here are also valid for studying the other atmospheric motion models.

关键词： atmosphere equations, weak solution, trajectory attractor, global attractor, equilibrium.

The study of two-color excitation upconversion of Pr(0.5)Yb(3):ZBLAN

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Science china(Physics,Mechanics & Astronomy) 2006年第2期49卷 169-177页

作者： CHEN Xiaobo1 & SONG Zengfu2.1. applied Optics beijing Area Major Laboratory, Analysis and testing center, beijing Normal university, beijing 100875, china 2. Peking university, Physics School, beijing 100871, china applied Optics beijing Area Major Laboratory Analysis and testing center Beijing Normal University Beijing China Physics School Peking University Beijing China

The excited state absorption upconversion of Pr(0.5)Yb(3):ZBLAN glass material, under two-color excitation of the 960 nm semiconductor laser and the Xe lamp light simultaneously, is reported in this article. It was found that the upconversion emission spectra of 480.1, 519.0, 601.9 and 631.8 nm coincide with the common emission spectra. Meanwhile, the upconversion-excitation spectrum has three obvious peaks under two-color excitation, and they respectively correspond to the 856.0 nm upconversion ex-citation transition [1G4(Pr3+)→1I6(Pr3+) and 1G4(Pr3+)→3P1(Pr3+)], the 789.0 nm upconver-sion excitation transition 1G4(Pr3+)→3P2.Pr3+), and the 803.7 nm upconversion excitation transition 3H6(Pr3+)→1D2.Pr3+). The upconversion excitation transition 1G4(Pr3+)→1I6(Pr3+) is strong because its oscillator strength f = 2..040×10?6 is large, which results in a large peak appearing in the upconversion excitation spectrum. That is just the new interesting two-color excitation upconversion luminescence phenomenon of Pr(0.5)Yb(3):ZBLAN induced by one laser and one continuous normal light simultaneously.

关键词： upconversion volumetric three-dimensional display two-color excitation.

Effect and mechanism of stresses on rock permeability at different scales

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Science china Earth Sciences 2006年第7期49卷 714-723页

作者： YIN Shangxian1 & WANG Shangxu2.1. Safety Engineering college, North china Institute of Science and {2., Yanjiao, beijing 101601, china 2. Key Laboratory of Geophysics Exploration, china university of Petroleum, beijing 100083, china Safety Engineering college North China Institute of Science and Technology Yanjiao Beijing China Key Laboratory of Geophysics Exploration China University of Petroleum Beijing China

The effect of geo-stress fields on macroscopic hydro-geological conditions or micro-cosmic permeability of water-bearing media should follow some laws or principles. Cases study and tests show that: (1) At macro-geologic large scale, deformed and crashed rocks which were induced by geo-stress fields changing provided space for groundwater storage and flow. Groundwater adjusts water-bearing space and dilatants fractures by flowing and press transferring. Coupling of liquid and solid can be implemented for rocks and groundwater. Although tectonic fields witness several times of change and build-up in geological time, stress fields forming regional tectonic framework are coherent with seepage fields, orientation of the maximum horizontal stress demonstrates main seepage direc-tions. (2. At macro-geologic middle scale, zones of stresses changing sharply, quite low stresses, stress or shear concentration can be used to show locations and types of main fractures, zones of geo-stresses changing equably can be acted as normal base media zones of tri-porosity media. (3) At micro-geologic small scale, tri-porosity media include fractured rocks, porous rocks and capillary rocks. Investigations indicate that porosity or permeability is functions of effective stresses, and po-rosity or permeability changing rules of porous rocks with variation of effective stresses can be de-scribed as the index model, the model of power exponent functions is suitable for those of fractured rocks, the model of the second power parabola for capillary rocks. The porosity and permeability loss in fractured rocks, which are greater than that in porous rocks, are shown by calculation of effective compressive coefficient and closing pressure in cracks. The calculations can also explain the mecha-nism why porosity changes are always larger than permeability changes. It is proved by the thick wall cylinder theory that the second power parabola relation between porosity or permeability loss and effective

关键词： geo-stress fields, seepage fields, tri-porosity media, effective stresses, permeability, porosity,scale.

Pattern phenomena in an rf discharge dusty plasma system

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Science china(Physics,Mechanics & Astronomy) 2006年第5期49卷 588-596页

作者： HUANG Feng1,2. YE Maofu2.& WANG Long2.1. college of Science, china Agricultural {2., beijing 100083, china 2. Institute of Physics, Chinese Academy of Sciences, beijing 100080, china college of Science China Agricultural University Beijing China Institute of Physics Chinese Academy of Sciences Beijing China

Various dust patterns are observed in an rf discharge dusty plasma system. According to the dust growth process from small to large in size, the formation of different dust patterns can be divided into two stages: the small-particle stage (or dust cloud stage), and the large-particle stage (or dust crystal stage). The evolution relations between different dust patterns with gas pressure changing are investigated. Dust voids, dust acoustic waves and strong turbulence modes are presented at the small-particle stage. The self-organized dust lattices and dust clusters are investigated at the large-particle stage. The static structure of a dust lattice is characterized by means of the pair correlation function. Dust clusters formed by particles with different numbers and the regular evolution of the clusters with gas pressure are also investigated. The packing sequences of dust clusters are verified through two-dimensional confined molecular dynamics simulations.

关键词： dusty plasma dust patterns