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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 43.072.China 2. Laboratory of Computational Physics,institute 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.

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, Academy of mathematics and System {3., chinese Academy of {3., 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.

LOCAL ASYMPTOTIC PROPERTIES OF HAZARD RATE ESTIMATORS FOR TRUNCATED AND CENSORED DATA

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Journal of systems science & Complexity 2001年第4期14卷 413-424页

作者： SUN Liuquan, WU Guofu, WEI Xianhua (institute of applied {2., Academy of {2. and systems science, chinese Academy of sciences, beijing 100080, China) 中科院应用数学所北京 100080

Functional laws of the iterated logarithm are obtained for cumulative hazard processes in the neighborhood of a fixed point when the data are subject to left truncation and right censorship. On the basis of these results the exact rates of pointwise almost sure convergence for various types of kernel hazard rate estimators are derived.

关键词： Truncated and censored data hazard rate kernel estimation nearest neighbor estimation law of the iterated logarithm.

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. University of Technology, {2. 10002., China 2. Center for Nonlinear Studies, institute of applied Physics and Computational mathematics, {2. 100088, China) College of applied sciences Beijing University of Technology Beijing 100022 China Center for Nonlinear Studies Institute of Applied Physics and Computational Mathematics Beijing 100088 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

Intermediate processes and critical phenomena: Theory, method and progress of fractional operators and their applications to modern mechanics

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science China(Physics,Mechanics & Astronomy) 2006年第3期49卷 257-272页

作者： XU Mingyu1 & TAN Wenchang2.1. institute of applied {2., School of Math & System science, Shandong University, Jinan 2.0100, China 2. State Key Laboratory of Turbulence and Complex systems & Department of Mechanics and Engineering science, Peking University, beijing 100871, China 1. institute of applied {2. School of Math & System Science Shandong University Jinan 250100 China 2. State Key Laboratory of Turbulence and Complex systems & Department of Mechanics and Engineering science Peking University Beijing 100871 China

From point of view of physics, especially of mechanics, we briefly introduce fractional operators (with emphasis on fractional calculus and fractional differential equa- tions) used for describing intermediate processes and critical phenomena in physics and mechanics, their progress in theory and methods and their applications to modern me- chanics. Some authors’ researches in this area in recent years are included. Finally, prospects and evaluation for this subject are made.

关键词： fractional operators,intermediate processes,critical phenomena,modern mechanics

A CRITERION FOR TESTING WHETHER A DIFFERENCE IDEAL IS PRIME

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Journal of systems science & Complexity 2009年第4期22卷 627-635页

作者： Chunming YUAN Xiao-Shan GAO Key Laboratory of mathematics Mechanization,institute of {2. {3. Academy of mathematics and {2. {3.,chinese Academy of sciences,beijing 100190,China. Key Laboratory of mathematics Mechanization Institute of Systems Science Beijing China Academy of mathematics and systems {2. Chinese Academy of Sciences Beijing 100190 China

This paper presents a criterion for testing the irreducibility of a polynomial over an algebraicextension *** this criterion and the characteristic set method,the authors give a criterion fortesting whether certain difference ascending chains are strong irreducible,and as a consequence,whetherthe saturation ideals of these ascending chains are prime ideals.

关键词： Characteristic set difference prime ideal irreducibility strong irreducibility.

Analysis for twinning and slip in face-centered cubic crystals under axisymmetric co-deformation

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science China(Technological sciences) 2006年第5期49卷 521-536页

作者： CHEN Zhiyong1,2. CAI Hongnian1, ZHANG Xinming2. WANG Fuchi1 & TAN Chengwen1,3.1. School of Material science and Engineering, {3. {2. of Technology, {3. 100081, China 2. School of Material science and Engineering, Central South University, Changsha 410083. China 3. School of Material science and Engineering, {3. University of Aeronautics and Astronautics, {3. 100083. China 1. School of Material science and Engineering Beijing Institute of Technology Beijing 100081 China 2. School of Material science and Engineering Central South University Changsha 410083 China 3. School of Material science and Engineering Beijing University of Aeronautics and Astronautics Beijing 100083 China

The maximum work principle of Bishop-Hill was developed to analyze the axisymmetric co-deformation in face-centered cubic crystals (f.c.c.) for twinning on {111} 112.and slip on {111} 110 systems. The influence of ξ , the ratio of critical re- solved shear stress for twinning to slip, on the yield stress states and corresponding active slip or/and twinning systems for orientations in the standard stereographic triangle of cubic crystal was investigated systematically. The Taylor factors and the anisotropy of yield strength for three important orientations [100], [110] and [111] in orientation space were analyzed. It is found that the yield strength asymmetry for the case of axisymmetric de- formation of tension and compression can be explained based on the microscopic theory of crystal plasticity. The concept of orientation factor for twinning ability was proposed and the deformation mechanism map in the orientation space was established for the case of axisymmetric deformation. The deformation texture formation and development of f.c.c. crystals with low stacking fault energy for axisymmetric tension can be explained qualita- tively on the basis of analyzed results.

关键词： twinning slip face-centered cubic crystals axisymmetric co-deformation Bishop-Hill maximum work principle yield strength anisotropy

A land surface model incorporated with soil freeze/thaw and its application in GAME/Tibet

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science China Earth sciences 2006年第12期49卷 1311-1322页

作者： HU Heping1, YE Baisheng2. ZHOU Yuhua3.& TIAN Fuqiang1 1. Department of Hydraulic Engineering, Tsinghua University, beijing 100084, China 2. Cold and Arid Regions Environmental and Engineering Research {3., {2. Academy of sciences, Lanzhou 73.000, China 3. Department of Civil Engineering, Massachusetts {3. of Technology, USA 1. Department of Hydraulic Engineering Tsinghua University Beijing 100084 China 2. Cold and Arid Regions Environmental and Engineering Research institute Chinese Academy of Sciences Lanzhou 730000 China 3. Department of Civil Engineering Massachusetts Institute of Technology USA

Land surface process is of great importance in global climate change, moisture and heat exchange in the interface of the earth and atmosphere, human impacts on the environment and eco- system, etc. Soil freeze/thaw plays an important role in cold land surface processes. In this work the diurnal freeze/thaw effects on energy partition in the context of GAME/Tibet are studied. A sophisti- cated land surface model is developed, the particular aspect of which is its physical consideration of soil freeze/thaw and vapor flux. The simultaneous water and heat transfer soil sub-model not only reflects the water flow from unfrozen zone to frozen fringe in freezing/thawing soil, but also demon- strates the change of moisture and temperature field induced by vapor flux from high temperature zone to low temperature zone, which makes the model applicable for various circumstances. The modified Picard numerical method is employed to help with the water balance and convergence of the numerical scheme. Finally, the model is applied to analyze the diurnal energy and water cycle char- acteristics over the Tibetan Plateau using the Game/Tibet datasets observed in May and July of 1998. Heat and energy transfer simulation shows that: (i) There exists a negative feedback mechanism between soil freeze/thaw and soil temperature/ground heat flux; (ii) during freezing period all three heat fluxes do not vary apparently, in spite of the fact that the negative soil temperature is higher than that not considering soil freeze; (iii) during thawing period, ground heat flux increases, and sensible heat flux decreases, but latent heat flux does not change much; and (iv) during freezing period, soil temperature decreases, though ground heat flux increases.

关键词： land surface model,soil freeze/thaw,GAME/Tibet,simultaneous liquid,vapor and heat transfer.

ANALYSIS OF A PRODUCTION-INVENTORY MODEL WITH ERLANGIAN DEMAND ARRIVAL PROCESS

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Journal of systems science & Complexity 2003年第2期16卷 184-190页

作者： WANG Jinting CAO Jinhua LIU Bin(institute of applied {2., Academy of {2. and systems sciences, chinese Academy of sciences, beijing 100080, China) institute of applied {2. Academy of Mathematics and Systems Sciences Chinese Academy of Sciences Beijing 100080 China

We study a production-inventory system having a machine, a storage facility. The demand for the product is governed by an Erlangian demand arrival process, where demand sizes are independent and identically distributed random variables. A two-criticalnumber policy (m, M) is used to control a machine's setups and shutdowns, namely, a machine is shut down whenever the inventory level reaches M, and resumes operating only when the inventory level falls below the critical number m(m ≤ M). We obtain the steady state distribution of the inventory process and some performance measures of the process.

关键词： erlangian demand arrival process production-inventory system