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Automorphisms with order three of affine Lie algebras

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Chinese Science Bulletin 1998年第21期43卷 1793-1798页

作者： JIN Quanqin 1,2 and HOU Zixin 2 1. department of mathematics, hebei university, Baoding 071002, china 2. department of mathematics, Nankai university, tianjin 300071, china department of mathematics Hebei University Baoding China department of mathematics Nankai University Tianjin China

Some properties of automorphisms of affine Lie algebras are presented. Automorphisms with order three are classified up to conjugacy, and their fixed point sets are also computed. As a corollary, it is proved that two... 详细信息

关键词： affine Lie algebra automorphism of order three first (second) kind of automorphism.

LOCAL ARTIFICIAL BOUNDARY CONDITIONS FOR THEINCOMPRESSIBLE VISCOUS FLOW IN A SLIP CHANNEL

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Journal of Computational mathematics 1997年第4期15卷 335-344页

作者： Wei-zhu Bao Hou-de Han (department of applied mathematics, Tsinghua university, Beijing, china) 清华大学应用数学系北京

In this paper we consider numerical simulation of incompressible viscous flow in a infinite slip channel. Local artificial boundary conditions at an artificial boundary are derived by the continuity of velocity and normal stress at the segment artificial boundary. The the original problem is reduced to a boundary value problem on a bounded computational domain. Numerical example shows that our artificial boundary conditions are very effective.

关键词： Boundary value problems Computational methods Computer simulation Navier Stokes equations Numerical methods Viscous flow

TRACE AVERAGING DOMAIN DECOMPOSITION METHOD WITH NONCONFORMING FINITE ELEMENTS

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Journal of Computational mathematics 1996年第1期14卷 40-53页

作者： J. Gu X. Hu(department of applied mathematics, Tsinghua university, Beijing, china) 清华大学应用数学系北京

We consider, in this paper, the trace averaging domain decomposition method for the second order self-adjoint elliptic problems discretized by a class of nonconforming finite elements, which is only continuous at the nodes of the quasi-uniform mesh. We show its geometric convergence and present the dependence of the convergence factor on the relaxation factor, the subdomain diameter H and the mesh parameter h. In essence;, this method is equivalent to the simple iterative method for the preconditioned capacitance equation. The preconditioner implied in this iteration is easily invertible and can be applied to preconditioning the capacitance matrix with the condition number no more than O((1 + In H/h)max(1 + H-2, 1 + In H/h)).

关键词： Math TRACE AVERAGING DOMAIN DECOMPOSITION METHOD WITH NONCONFORMING FINITE ELEMENTS

REDUCTIONS OF ADJOINT REPRESENTATIONS TO LAX REPRESENTATIONS FOR CONSTRAINED FLOWS

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Chinese Annals of mathematics,Series B 1996年第2期17卷 187-198页

作者： ZENG YUNBO department of applied mathematics, Tsinghua university, Beijing 100084, china. 清华大学应用数学系北京

Within framework of zero-curvature representation theory, the Lax representations for x- andtn-constrained flows of soliton hierarchy are obtained from reductions of adjoint representationsof the auxiliary linear problems. This method is applied to the third order spectral problem bytaking modified Boussinesq hierarchy as an illustrative example.

关键词： Constrained flow Lax representation Adjoint representation Soliton hierarchy

ON THE DOMAIN DECOMPOSITION METHOD FOR MORLEYELEMENT-FROM WEAK OVERLAP TO NONOVERLAP

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Journal of Computational mathematics 1999年第6期17卷 615-628页

作者： Jian-guo Huang(department of applied mathematics, Shanghai Jiao Tong university, Shanghai 200240,china) 上海交通大学应用数学系上海 200240

In this paper, following our original ideas[9], we first consider a weakly overlapping additive Schwarz preconditioner according to the framework of [2] for Morley element and show that its condition number is quasi-optimal; we then analyze in detail the structure of this preconditioner, and after proper choices of the inexact solvers, we obtain a quasi-optimal nonoverlapping domain decomposition preconditioner in the last. Compared with [12], [13], it seems that according to this paper's procedure we can make out more thoroughly the relationship between overlapping and nonoverlapping domain decomposition methods for nonconforming plate elements, and certainly, we have also proposed another formal and simple strategy to construct nonoverlapping domain decomposition preconditioners for nonconforming plate elements.

关键词： Morley element domain decomposition weak overlap

ON THE EXISTENCE OF SOLUTIONS TO A TYPE OF NONLINEAR DIFFERENTIAL-ITERATIVE EQUATIONS

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Chinese Annals of mathematics,Series B 2000年第2期21卷 217-224页

作者： GE WEIGAO(department of applied mathematics, Beijing Institute of technology, Beijing 100081, china.) LI CUIZHE(department of applied mathematics, Beijing Institute of technology, Beijing 100081, china.) YU YUANHONG(Inditute of applied mathematics, Acad department of applied mathematics Beijing Institute of Technology Beijing 100081 China Institute of applied mathematics Academia Sinica Beijing 100080 China

Under the assumption that h(z) is strictly monotone the existence of solutions to a type of nonlinear differential-iterative equations in the form of x’(t) = g(x(t)) -h(x(x(t))) is discussed according to the behavior... 详细信息

关键词： Differential-iterative equation Quasi-isoclinic curve Fixed point

THE SCHWARZ CHAOTIC RELAXATION METHOD WITH INEXACT SOLVERS ON THE SUBDOMAINS

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Journal of Computational mathematics 1999年第2期17卷 125-132页

作者： Jian-guo Huang(department of applied mathematics, Shanghai Jiao Tong university,Shanghai 200240, china) 上海交通大学应用数学系上海

In this paper, a S-CR method with inexact solvers on the subdomains is presented, and then its convergence property is proved under very general conditions. This result is important because it guarantees the effective... 详细信息

关键词： S-CR method chaotic algorithm inexact solvers

THE INVARIANT CONTINUOUS-TRACE C*-ALGEBRAS BY THE ACTIONS OF COMPACT ABELIAN GROUPS

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Chinese Annals of mathematics,Series B 1998年第4期19卷 489-498页

作者： FANG XIAOCHUN (department of applied mathematics, Tonaii university, Shanghai, 200092, china.) 同济大学应用数学系上海

The author studies the relation of continuous-trace property between C*-algebra A and the fixed point C*-algebra Aα in certain C*-dynamic system (A, G, α) by introducing an α-invariant　continuous trace property. For separable C*-dynamic system (A, G, α) with G compact and　abelian,A liminal, αt ∈ AutCb(A) (A) and pointwise unitary, the necessary and sufficient condition for A to be continuous-trace, which contains Aα continuousitrace, is obtained.

关键词： Continuous-Trace Action of Group C*-Algebra

GLOBAL CONVERGENCE RESULTS OF A THREE TERM MEMORY GRADIENT METHOD WITH A NON-MONOTONE LINE SEARCH TECHNIQUE

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Acta Mathematica Scientia 2005年第1期25卷 170-178页

作者：孙清滢 department of applied mathematics university of Petroleum Dongying 257061 China Department of Applied Mathematics Dalian University of Technology Dalian 116024 China

In this paper, a new class of three term memory gradient method with non-monotone line search technique for unconstrained optimization is presented. Global convergence properties of the new methods are discussed. Combining the quasi-Newton method with the new method, the former is modified to have global convergence property. Numerical results show that the new algorithm is efficient.

关键词： Non-linear programming three term memory gradient method convergence non-monotone line search technique numerical experiment