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On the coupled NBEM and FEM for a class of nonlinear exterior Dirichlet problem in R^(2.)

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Science China mathematics 2004年第z1期47卷 181-189页

作者： WU Zhengpeng, KANG Tong & YU Dehaoinstitute of Computational mathematics and Scientific/Engineering Computing, {2. of mathematics and System sciences, chinese academy of sciences, beijing 100080, China Department of applied mathematics, beijing Broadcasting institute, beijing 10002., China Combinatorial and Computational mathematics Center, Pohang University of Science and Technology, Phoang 790-784, Republic of Korea chinese Acad Sci Acad Math & Syst Sci Inst Computat Math & Sci Engn Comp Beijing 100080 Peoples R China beijing Broadcasting Inst Dept Appl Math Beijing 100024 Peoples R China Pohang Univ Sci & Technol Combinatorial & Computat Math Ctr Phoang 790784 South Korea

In this paper, based on the natural boundary reduction advanced by Feng and Yu, we couple the finite elementapproach with the natural boundary element method to study theweak solvability and Galerkin approximation of a class ofnonlinear exterior boundary value problems. The analysis is mainlybased on the variational formulation with *** provethe error estimate of the finite element solution and obtain theasymptotic rate of convergence. Finally, we also give anumerical example.

关键词： natural boundary integral method, finite element method, coupling method, error estimate.

Cleaning of Chromate Manufacture Process

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International Journal of Minerals,Metallurgy and Materials 2000年第2期14卷 132-134页

作者： Xing Zou Yi Zhang(applied Science School, University of Science and Technology beijing, beijing 100083, China)(institute of Engineering Chemistry and Metallurgy, chinese academy of sciences, beijing 100080, China) applied Science School University of Science and Technology Beijing Beijing 100083 China institute of Engineering Chemistry and Metallurgy Chinese Academy of Sciences Beijing 100080 China

Sodium chromate solubility is determined in the range of NaOH concentrations from 450 to 810 g/L andsolution temperatUres from 30 to 110℃. The optimized conditions to separate sodium chromate from NaOH inleached solution are resolved. It is first found the method to efficiently separate sbdium chromate from NaOH andsodium altuninate in crude sodium chromate. Bench-scale studies on the separating are performed. Finally, goodseparation results are achieved.

关键词： chromate separation clean process

Spectrophotometric determination of cationic surfactants by formation of ternary complexes with Fe(Ⅲ) and chrome azurol S

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chinese Journal of Chemistry 1996年第3期14卷 228-234页

作者： SONG, Ming LIANG, Shu-Quan institute of Chemistry, chinese academy of sciences,{2., China institute of Chemistry Chinese Academy of Sciences Beijing 100080 China

An extraction-free spectrophotometric method for the determination of cationic surfactants, such as cetylpyridinium chloride, cetyltrimethylammonium bromide and zephiramine is proposed, which is based on the formation of ternary complexes with Fe(Ⅲ) and chrome azurol S. The molar ratio of the complex is 2.1:1 (Fe(Ⅲ):chrome azurol S:cationic surfactant). The method is simple, rapid and sensitive, giving an apparent molar absorptivity of 4.5×104 ***-1 and a linear range of 0.1-6.0 umol/L cationic surfactants. The total cationic surfactant content can be determined directly in aqueous solutions by measuring the absorbance at 680 nm (pH 5.8). The method has been successfully applied to water samples.

关键词： Cationic surfactant determination spectrophotometry ternary complex Fe(Ⅲ) chrome azurol S

On exactness and unbiasedness of confidence bands for a continuous distribution function

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Science China mathematics 2010年第10期53卷 2665-2678页

作者： DING XiaoBo1,2.XU XingZhong2.& ZHAO ShuRan3 1institute of applied {2.,academy of {2. and Systems Science,chinese academy of sciences,beijing 100190,China 2.epartment of {2.,beijing institute of Technology,beijing 100081,China 3School of Economics,Ocean University of China,Qingdao 2.6071,China 1. institute of applied mathematics Academy of Mathematics and Systems Science Chinese Academy of Sciences Beijing 100190 China2. Department of Mathematics Beijing Institute of Technology Beijing 100081 China3. School of Economics Ocean University of China Qingdao 266071 China

We define a class of confidence bands for distribution functions,named simple confidence *** class of bands includes the common step bands and continuous bands,some of which may perform better than the smoothed bands not belonging to the class,e.g.,the kernel smoothed *** is shown that under some mild assumptions,the simple bands with exact coverage for continuous distribution functions are all step *** unbiasedness problem of the step bands is also *** is proved that most of two-sided step bands are biased and one-sided step bands are unbiased.

关键词： exact coverage goodness of fit kernel smoothing simple confidence bands unbiasedness

Bifurcation and Chaos in a Weakly Nonlinear System Subjected to Combined Parametric and External Excitation

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Acta Mathematicae Applicatae Sinica 2002年第3期18卷 501-512页

作者： Wei Li, Peng-cheng Xuinstitute of mathematics, {2. University of Chemical Technology, {2. 10002., Chinainstitute of applied mathematics, academy of mathematics and System sciences, chinese academy of sciences, beijing 100080, China institute of mathematics Beijing University of Chemical Technology Beijing China institute of applied {2. Academy of Mathematics and System Sciences Chinese Academy of Science Beijing China

In this paper the dynamics of a weakly nonlinear system subjected to combined parametric and external excitation are discussed. The existence of transversal homoclinic orbits resulting in chaotic dynamics and bifurcation are established by using the averaging method and Melnikov method. Numerical simulations are also provided to demonstrate the theoretical analysis.

关键词： Bifurcation chaos transversal homoclinic orbit

Research on the method for retrieving soil moisture using thermal inertia model

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Science China Earth sciences 2006年第5期49卷 539-545页

作者： LIU Zhenhua1 & ZHAO Yingshi2.1. Information College, South China Agricultural University, Guangzhou 510642. China 2. Graduate University of chinese academy of sciences, beijing 100049, China 1. Information College South China Agricultural University Guangzhou 510642 China 2. Graduate University of chinese academy of sciences Beijing 100049 China

In order to improve accuracy of soil moisture inversion using remote sensing, a new thermal inertia model is proposed in this paper. The improved model needs only surface maximum temperature as the temperature parameter input instead of input of the surface temperature difference, as well as the surface sensible and latent fluxes are introduced into boundary conditions of thermal conductivity equation. Furthermore, surface soil conductive heat transfer equation of two-layer model is used to solve the soil thermal inertia so that the remote sensing thermal inertia method can be ap- plied to regions with better-covered vegetation, but usually only for the bare areas or worse vegetation covered areas. The model has been tested at several locations in the area of west Inner Mongolia. Comparing the simulation of the new model with the measurements obtained by apparent thermal inertia and by field test, the result shows that the inertia thermal model can be used to estimate soil moisture in more reasonable accuracy.

关键词： thermal model, thermal conductivity equation, soil initial, sensible flux, latent flux, two-layer model.

STRONG REPRESENTATIONS OF THE SURVIVAL FUNCTION ESTIMATOR ON INCREASING SETS FOR TRUNCATED AND CENSORED DATA

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Acta Mathematica Scientia 1999年第3期19卷 251-260页

作者：孙六全郑忠国 chinese Acad Sci Inst Appl Math Beijing 100080 Peoples R China Peking Univ Dept Stat & Probabil Beijing 100871 Peoples R China

In this paper, based on random left truncated and right censored data, the authors derive strong representations of the cumulative hazard function estimator and the product-limit estimator of the survival function. which are valid up to a given order statistic of the observations. A precise bound for the errors is obtained which only depends on the index of the last order statistic to be included.

关键词： truncated and censored data cumulative hazard function product-limit estimator strong representations

Convergence analysis of the adaptive finite element method with the red-green refinement

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Science China mathematics 2010年第2期53卷 499-512页

作者： ZHAO XuYing 1, 3 , HU Jun 2.? & SHI ZhongCi 1 1 State Key laboratory of Scientific and Engineering Computing, institute of Computational {2. and Scientific/Engineering Computing, {2. of {2. and Systems Science, chinese academy of sciences, beijing 100190, China 2.Key laboratory of {2. and applied {2. (Peking University), Ministry of Education and School of Mathematical sciences, Peking University, beijing 100871, China 3 Graduate University of chinese academy of sciences, beijing 100190, China 1. State Key laboratory of Scientific and Engineering Computing Institute of Computational Mathematics and Scientific/Engineering Computing Academy of Mathematics and Systems Science Chinese Academy of Sciences Beijing 100190 China3. Graduate University of Chinese Academy of Sciences Beijing 100190 China2. Key Laboratory of Mathematics and Applied Mathematics (Peking University) Ministry of Education and School of Mathematical Sciences Peking University Beijing 100871 China

In this paper, we analyze the convergence of the adaptive conforming P 1 element method with the red-green refinement. Since the mesh after refining is not nested into the one before, the Galerkin-orthogonality does not hold for this case. To overcome such a difficulty, we prove some quasi-orthogonality instead under some mild condition on the initial mesh (Condition A). Consequently, we show convergence of the adaptive method by establishing the reduction of some total error. To weaken the condition on the initial mesh, we propose a modified red-green refinement and prove the convergence of the associated adaptive method under a much weaker condition on the initial mesh (Condition B).

关键词： red-green refinement adaptive finite element method convergence non-nested local refinement

Mathematical stencil and its application in finite difference approximation to the Poisson equation

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Science China mathematics 2005年第10期48卷 1421-1429页

作者： FENG Hui~1 ZHANG Baolin~(1,2. & LIU Yang~1 1. Department of mathematics,Wuhan University,Wuhan 430072.China 2. laboratory of Computational Physics,{2. of {2. Physics and Computational mathematics,beijing 100088. China 1. Department of mathematics Wuhan University 430072 Wuhan China 2. laboratory of Computational Physics Institute of Applied Physics and Computational Mathematics 100088 Beijing China

The concept of mathematical stencil and the strategy of stencil elimination for solving the finite difference equation is presented, and then a new type of the iteration algorithm is established for the Poisson equation. The new algorithm has not only the obvious property of parallelism, but also faster convergence rate than that of the classical Jacobi iteration. Numerical experiments show that the time for the new algorithm is less than that of Jacobi and Gauss-Seidel methods to obtain the same precision, and the computational velocity increases obviously when the new iterative method, instead of Jacobi method, is applied to polish operation in multi-grid method, furthermore, the polynomial acceleration method is still applicable to the new iterative method.

关键词： mathematical stencil, stencil elimination, Poisson equation, finite difference, iterative algorithm,parallelism.