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METHOD OF NONCONFORMING MIXED FINITE ELEMENT FOR SECOND ORDER ELLIPTIC PROBLEMS METHOD OF NONCONFORMING MIXED FINITE ELEMENT FOR SECOND ORDER ELLIPTIC PROBLEMS

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Journal of Computational mathematics 2000年第5期18卷 449-456页

作者： Zhen-dong Luo (department of mathematics, Capital normal university, Beijing 100057, china) 首都师范大学北京 100037

In this paper, the method of non-conforming mixed finite element for second order elliptic problems is discussed and a format of real optimal order for the lowest order error estimate.

关键词： Non-conforming mixed finite element Error estimate Second order elliptic problems.

K-uniformly rotund spaces and k-uniformly smooth spaces

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Chinese Science Bulletin 1998年第2期43卷 92-95页

作者： Suyalatu 1 and WU Congxin 2 1. department of mathematics,Inner Mongolia normal university, Huhhot 010022, china 2. department of mathematics, Harbin Institute of Technology, Harbin 150006, china department of mathematics Inner Mongolia Normal University Huhhot China department of mathematics Harbin Institute of Technology Harbin China

The conception of k_uniform smoothness (KUS) is introduced. It is the extension of the conception of uniform smoothness. It is proved that the k_uniform smoothness and Sullivan’s K_uniform rotundity (KUR) are the daul notions. X+* is a KUR space if and only if X is a KUS space, X+* is a KUS space if and only if X is a KUR space. If X is a KUS space, then X is a (K+1)US space. It is also proved that the KUS space includes the Nan’s k_strongly smooth space.

关键词： K_uniform smoothness K_uniform convexity.

DERIVATIONS ON DIFFERENTIAL OPERATOR ALGEBRA AND WEYL ALGEBRA

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Chinese Annals of mathematics,Series B 1996年第2期17卷 199-212页

作者： CHEN CAOYU department of mathematics, Shanghai normal university, Shanghai 200234, china. 上海师范大学数学系上海

Let L be an n-dimensional nilpotent Lie algebra with a basis {x1,…,xn}, and every xiacts as a locally nilpotent derivation on algebra A. This paper shows that there exists a setof derivations {y1,…,yn} on U(L) such that (A#U(L))#k[yi,…,yn] is isomorphic to theWeyl algebra An(A). The author also uses the derivations to obtain a necessary and sufficientcondition for a finite dimensional Lie algebra to be nilpotent.

关键词： Crossed porduct Smash product Derivation Nilpotent Lie algebra Weyl algebra

Recovery of functions via their irregular sampling values

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Chinese Science Bulletin 1998年第4期43卷 268-271页

作者： FANG Gensun department of mathematics, Beijing normal university, Beijing 100875, china department of mathematics Lkijing Normal University Beijing China

It is proved that if a function can be completely reconstructed by tempered splines which satisfy the real Kiesz basis condition as the degree of spline goes to infinity, then the function is band limited.

关键词： band limited function cardinal splines irregular sampling.

Image space analysis for variational inequalities with cone constraints and applications to traffic equilibria

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Science china mathematics 2012年第4期55卷 851-868页

作者： LI Jun 1,& HUANG NanJing 2 1 College of mathematics and Information,china West normal university,Nanchong 637009,china 2.department of mathematics,Sichuan university,Chengdu 610064,china College of mathematics and Information China West Normal University Nanchong China department of mathematics Sichuan University Chengdu China

In this paper,the image space analysis (for short,ISA) is employed to investigate variational in- equalities (for short,VI) with cone *** separation for VI with cone constraints is characterized by using the normal cone to a regularization of the image,and saddle points of the generalized Lagrangian func- ***-type necessary and sufficient optimality conditions for VI with cone constraints are presented by using a separation *** functions and weak sharpness for VI with cone constraints are also investi- ***,the obtained results are applied to standard and time-dependent traffic equilibria introduced by Daniele,Maugeri and Oettli.

关键词： variational inequality image space analysis linear separation necessary and sufficient optimalitycondition traffic equilibrium

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Science china mathematics 2004年第5期47卷 659-674页

作者： SHI Peihu & WANG Mingxindepartment of mathematics, Southeast university, Nanjing 210018, china department of mathematics, Xuzhou normal university, Xuzhou 221116, china department of mathematics Southeast University Nanjing China department of mathematics Xuzhou Normal University Xuzhou China

This paper is devoted to study the classification of self-similar solutions to the quasilinear parabolic equations with nonlinear gradient termsu t = Δ(u m) - uq∣Δu∣ p withm ≥ 1,p,q > 0 andp +q >m. Form = 1, it is shown that the very singular self-similar solution exists if and only ifnq + (n +1)p 2, and in case of existence, such solution is unique. Form > 1, it is shown that very singular self-similar solutions exist if and only if 1 2 andnq + (n + 1)p 2 +mn, and such solutions have compact support if they exist. Moreover, the interface relation is obtained.

关键词： quasilinear parabolic equations, self-similar solutions, very singular solution, classification.

SUPERCONVERGENCE ANALYSIS FOR CUBIC TRIANGULARELEMENT OF THE FINITE ELEMENTSUPERCONVERGENCE ANALYSIS FOR CUBIC TRIANGULARELEMENT OF THE FINITE ELEMENT

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Journal of Computational mathematics 2000年第5期18卷 541-550页

作者： Qi-ding Zhu (department of mathematics, Hunan normal university, Changsha 410081, china ) 湖南师范大学湖南长沙 410081

In this paper, we construct a projection interpolation for cubic triangular element by using othogonal expansion triangular method. We show two fundamental formulas of estimation on a special partion and obtain a superconvergence result of 1- ∈order higher for the placement function and its tangential derivative on the third order Lobatto points and Gauss points on each edge of triangular element.

关键词： Finite element Superconvergence Projection interpolation.

ON THE GENERALIZED INVERSE NEVILLE-TYPE MATRIX-VALUED RATIONAL INTERPOLANTS

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Journal of Computational mathematics 2003年第2期21卷 157-166页

作者： Zhibing Chen9+(department of mathematics, normal College, Shenzhen university, Shenzhen 518060, china) department of mathematics Normal College Shenzhen University Shenzhen 518060

A new kind of matrix-valued rational interpolants is recursively established by means of generalized Samelson inverse for matrices, with scalar numerator and matrix-valued denominator. In this respect, it is essentially different from that of the previous works [7, 9], where the matrix-valued rational interpolants is in Thiele-type continued fraction form with matrix-valued numerator and scalar denominator. For both univariate and bivariate cases, sufficient conditions for existence, characterisation and uniqueness in some sense are proved respectively, and an error formula for the univariate interpolating function is also given. The results obtained in this paper are illustrated with some numerical examples.

关键词： Generalized inverse for matrices Neville-type Rational interpolants.

Neural Network for Solving Monotone LinearComplementary Problems

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Communications in Nonlinear Science and Numerical Simulation 1999年第2期4卷 128-132页

作者： Xingban GAO(department of mathematics, Shaanxi normal university, Xi’an 710062, china) department of mathematics Shanxi Normal University Xi'an 710062 China

A neural network for solving monotone linear complementary problem isproposed. It has not involved any parameter and is proven to be uniformly, asymptoticallyand stably convergent to an exact solution of the linear co... 详细信息

关键词： linear complementary problems neural network asymptotical stability