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Journal of Computational mathematics 2000年第5期18卷 521-540页

作者： Lan-chieh Huang (institute of Computational mathematics and Scientific/Engineering Computing,{2., beijing 100080, china) 中科院计算数学与科学工程计算所北京 100080

In this paper, the Crank-Nicholson + component-consistent pressure correction method for the numerical solution of the unsteady incompressible Navier-Stokes equation of [1] on the rectangular half-Staggered mesh has been extended to the curvilinear half-Staggered mesh. The discrete projection, both for the projection step in the solution procedure and for the related differential-algebraic equations, has been carefully studied and verified. It is proved that the proposed method is also unconditionally (in t) nonlinearly stable on the curvilinear mesh, provided the mesh is not too skewed. It is seen that for problems with an outflow boundary, the half-Staggered mesh is especially advantageous. Results of preliminary numerical experiments support these claims.

关键词： Unsteady incompressible Navier-Stokes equations Curvilinear half- staggered mesh Discrete projection.

STABILITY ANALYSIS OF FINITE ELEMENT METHODS FORTHE ACOUSTIC WAVE EQUATION WITH ABSORBINGBOUNDARY CONDITIONS (PART I)

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Journal of Computational mathematics 1999年第3期17卷 293-306页

作者： Xiu-min Shao Zhi-ling Lan(institute of mathematics, {2. of sciences, beijing 100080, china) 中科院数学所北京

In Part I and Part II of this paper initial-boundary value problems of the acoustic wave equation with absorbing boundary conditions are considered. Their finite element-finite difference computational schemes are proposed. The stability of the schemes is discussed and the corresponding stability conditions are given. Part I and Part II concern the first- and the second-order absorbing boundary conditions, respectively. Finally, numerical results are presented in Part II to show the correctness of theoretical analysis. (Author abstract) 7 Refs.

关键词： stability finite element methods wave equation absorbing boundary conditions

A global solution of the Ein-stein-Yang-Mills equation on the conformal space

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chinese Science Bulletin 2001年第6期46卷 460-461页

作者： LU Qikenginstitute of mathematics,{2., beijing 100080, china institute of mathematics Chinese Academy of Sciences Beijing China

A global solution of the Einstein-Yang-Mills (EYM) equation on the conformal space is constructed. This solution is conformal invariant under the conformal group.

关键词： Einstein-Yang-Mills equation $12.2.-connection confor- mal space.

On factorizable solution of the differential equation(f')~2.a_0(z)(f-a)1(z))~2.

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chinese Science Bulletin 1997年第21期42卷 1779-1782页

作者： YUAN Wenjun and HE Yuzaninstitute of mathematics,{2., beijing 100080, china institute of mathematics Chinese Academy of Sciences Beijing 100080 China

If the coefficients are transcendental, Bergweiler et al. proved that in all possible non-trivialfactorization f(z)=h(g(z)), the growth of the right factor g(z) can be controlled by thegrowth of the coefficients. In ref. [2., He and Laine proved a similar conclusion for two othertypical kinds of nonlinear differential equations. But for the following equation:

关键词： factorization growth order meromorphic function ordinary differential equation.

The asymptotic stability of multistep multiderivative methods for systems of delay differential equations

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Communications in Nonlinear Science and Numerical Simulation 2000年第1期5卷 24-26页

作者： Chengming HUANG and Qianshun CHANG institute of applied {2., chinese academy of sciences, P. O. Box 2.34, beijing 100080, china institute of applied {2. Chinese Academy of Sciences P. O. Box 2734 Beijing 100080 China

This paper deals with the asymptotic stability of multistep multiderivative methods for systems of delay differential equations. In particular, it is shown that A-stability of multistep multiderivative methods for ord... 详细信息

关键词： delay differential equation stability multistep multiderivative methods

ON THE ERROR ESTIMATE OF LINEAR FINITE ELEMENT APPROXIMATION TO THE ELASTIC CONTACT PROBLEM WITH CURVED CONTACT BOUNDARY

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Journal of Computational mathematics 2000年第6期18卷 561-566页

作者： Lie-heng Wang (State Key Laboratory of Scientific and Engineering Computing, institute of Computational mathematics, {2. of mathematics and System sciences, chinese academy of sciences, beijing 100080, china) 中科院计算数学所科学与工程计算国家重点实验室北京 100080

In this paper, the linear finite element approximation to the elastic contact problem with curved contact boundary is considered. The error bound O(h[sup ?]) is obtained with requirements of two times continuously differentiable for contact boundary and the usual regular triangulation, while *** et. al. Obtained the error bound O(h[sup ?]) with requirements of three times continuously differentiable for contact boundary and extra regularities of triangulation (c.f. [2.). [ABSTRACT FROM AUTHOR]

关键词： contact problem finite element approximation

A class of additive-accelerated means regression models for recurrent event data

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Science china mathematics 2010年第12期53卷 3139-3151页

作者： LIU Li 1, MU XiaoYun 2.& SUN LiuQuan 2.1 School of mathematics and Statistics, Wuhan University, Wuhan 430072. china 2.{2. of applied mathematics, academy of mathematics and Systems Science, chinese academy of sciences, beijing 100080, china 1. School of mathematics and Statistics Wuhan University Wuhan 430072 China2. Institute of Applied Mathematics Academy of Mathematics and Systems Science Chinese Academy of Sciences Beijing 100080 China

In this article, we propose a class of additive-accelerated means regression models for analyzing recurrent event data. The class includes the proportional means model, the additive rates model, the accelerated failure time model, the accelerated rates model and the additive-accelerated rate model as special cases. The new model offers great flexibility in formulating the effects of covariates on the mean functions of counting processes while leaving the stochastic structure completely unspecified. For the inference on the model parameters, estimating equation approaches are derived and asymptotic properties of the proposed estimators are established. In addition, a technique is provided for model checking. The finite-sample behavior of the proposed methods is examined through Monte Carlo simulation studies, and an application to a bladder cancer study is illustrated.

关键词： additive-accelerated means model counting process marginal model model checking recurrent events

Adaptive computation for convection dominated diffusion problems

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Science china mathematics 2004年第z1期47卷 22-31页

作者： CHEN Zhiming & Jl GuanghuaLSEC, institute of Computational mathematics, {2. of mathematics and System sciences, chinese academy of sciences, beijing 100080, china institute of Computational mathematics, {2. of mathematics and System sciences, chinese academy of sciences, beijing 100080, china (email:ghji@***) 1. LSEC Institute of Computational Mathematics Academy of Mathematics and System Sciences Chinese Academy of Sciences 100080 Beijing China 2. institute of Computational mathematics Academy of Mathematics and System Sciences Chinese Academy of Sciences 100080 Beijing China

We derive sharp L∞(L1) a posteriori error estimate for the convection dominated diffusion equations of the formThe derived estimate is insensitive to the diffusion parameter ε→0. The problem is dis-cretized implicitly in time via the method of characteristics and in space via continuous piecewise linear finite elements. Numerical experiments are reported to show the competitive behavior of the proposed adaptive method.

关键词： a posteriori error estimator, characteristics, adaptive.

MULTIVARIATE FOURIER SERIES OVER A CLASS OF NON TENSOR-PRODUCT PARTITION DOMAINS

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Journal of Computational mathematics 2003年第1期21卷 53-62页

作者： Jiachang Sun(Parallel Computing Division, institute of Software, chinese academy of sciences,{2., china) Parallel Computing Division Institute of Software Chinese Academy of Sciences 北京 100080

This paper finds a way to extend the well-known Fourier methods, to so-called n+1 directions partition domains in n-dimension. In particular, in 2.D and 3-D cases, we study Fourier methods over 3-direction parallel hexagon partitions and 4-direction parallel parallelogram dodecahedron partitions, respectively. It has pointed that, the most concepts and results of Fourier methods on tensor-product case, such as periodicity,orthogonality of Fourier basis system, partial sum of Fourier series and its approximation behavior, can be moved on the new non tensor-product partition case.

关键词： Multivariate Fourier methods Non tensor-product partitions Multivariate Fourier series

Stability of proton and maximally symmetric minimal unification model for basic forces and building blocks of matter

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Science china(Physics,Mechanics & Astronomy) 2007年第3期50卷 303-310页

作者： WU YueLiang institute of Theoretical Physics, chinese academy of sciences,{2., china 1. institute of Theoretical Physics Chinese Academy of Sciences Beijing 100080 China

With the hypothesis that all independent degrees of freedom of basic building blocks should be treated equally on the same footing and correlated by a possible maximal symmetry, we arrive at a 4-dimensional space-time unification model. In this model the basic building blocks are Majorana fermions in the spinor repre- sentation of 14-dimensional quantum space-time with a gauge symmetry GM4D = SO(1,3)×SU(32.×U(1)A×SU(3)F. The model leads to new physics including mirror particles of the standard model. It enables us to issue some fundamental questions that include: why our living space-time is 4-dimensional, why parity is not con- served in our world, how the stability of proton is, what the origin of CP violation is and what the dark matter can be.

关键词： gauge symmetry space-time symmetries beyond standard model and unification