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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

Nonautonomous bright solitons and soliton collisions in a nonlinear medium with an external potential

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Chinese Physics B 2012年第5期21卷 145-152页

作者：李画眉葛龙何俊荣 department of Physics Zhejiang Normal University

We present exact bright multi-soliton solutions of a generalized nonautonomous nonlinear Schroinger equation with time-and space-dependent distributed coefficients and an external potential which describes a pulse propagating in nonlinear media when its transverse and longitudinal directions are nonuniformly *** solutions exist in certain constraint conditions on the coefficients depicting dispersion,nonlinearity,and gain（loss）.Various shapes of bright solitons and interesting interactions between two solitons are *** applications of interest to the field and stability of the solitons are discussed.

关键词： generalized nonautonomous nonlinear Schrodinger equation multi-soliton solution,Fourier-synthesized optical lattice potential flying bird potential

JACOBI SPECTRAL APPROXIMATIONS TO DIFFERENTIALEQUATIONS ON THE HALF LINE

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Journal of Computational mathematics 2000年第1期18卷 95-112页

作者： Ben-yu Guo(department of mathematics, Shanghai normal university, Shanghai 200234, china)(COM2MAC, Pohang university of Science and Technology, Pohang, Korea) 上海师范大学上海 200234

Presents a study which investigated some Jacobi approximations which are used for numerical solutions of differential equations on the half line. Application of the approximations to problems on unbounded domains; Alg... 详细信息

关键词： Jacobi spectral approximations differential equations on the half line stability and convergence

CONTINUITY AND LINEARITY OF ADDITIVE DERIVATIONS OF NEST ALGEBRAS ON BANACH SPACES

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Chinese Annals of mathematics,Series B 1996年第2期17卷 227-236页

作者： HAN DEGUANG department of mathematics, Qufa normal university, Qufu 273165, Shandong, china. QUFA normal UNIV DEPT MATHQUFU 273165SHANDONGPEOPLES R CHINA

This paper discusses the problem concerning the continuity and linearity of additive derivation of nest algebras on normed spaces. It is proved that every linear derivation of a nest algebraalgN is continuous provided that one of the following conditions is satisfied: (1) 0+ (?) 0. (2)X_ (?) X. (3) there exists a non-trivial idempotent p in algN such that the range of p belongsto N. It is also proved that every additive derivation of a nest algebra is automatically linearif the underlying normed space is infinite dimemnsional.

关键词： Nest algebra Derivation Continuity Linearity Banach space

Estimates for eigenvalues of Laplacian operator with any order

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Science china mathematics 2007年第8期50卷 1078-1086页

作者： Fa-en WU~(1+) Lin-fen CAO~2 1 department of mathematics,Beijing Jiaotong university,Beijing 100044,china 2 department of mathematics,Henan normal university,Xinxiang 453007,china department of mathematics Beijing Jiaotong University Beijing 100044 China department of mathematics Henan Normal University Xinxiang 453007 China

Let D be a bounded domain in an n-dimensional Euclidean space ? n . Assume that $$0 < \lambda _1 \leqslant \lambda _2 \leqslant \cdots \leqslant \lambda _k \leqslant \cdots $$ are the eigenvalues of the Dirichlet Laplacian operator with any order l: $$\left\{ \begin{gathered} ( - \vartriangle )^l u = \lambda u, in D \hfill \\ u = \frac{{\partial u}}{{\partial \vec n}} = \cdots = \frac{{\partial ^{l - 1} u}}{{\partial \vec n^{l - 1} }} = 0, on \partial D \hfill \\ \end{gathered} \right.$$ . Then we obtain an upper bound of the (k+1)-th eigenvalue λ k+1 in terms of the first k eigenvalues. $$\sum\limits_{i = 1}^k {(\lambda _{(k + 1)} - \lambda _i )} \leqslant \frac{1}{n}[4l(n + 2l - 2)]^{\tfrac{1}{2}} \left\{ {\sum\limits_{i = 1}^k {(\lambda _{(k + 1)} - \lambda _i )^{\tfrac{1}{2}} \lambda _i^{\tfrac{{l - 1}}{l}} \sum\limits_{i = 1}^k {(\lambda _{(k + 1)} - \lambda _i )^{\tfrac{1}{2}} \lambda _i^{\tfrac{1}{l}} } } } \right\}^{\tfrac{1}{2}} $$ . This ineguality is independent of the domain D. Furthermore, for any l ? 3 the above inequality is better than all the known results. Our rusults are the natural generalization of inequalities corresponding to the case l = 2 considered by Qing-Ming Cheng and Hong-Cang Yang. When l = 1, our inequalities imply a weaker form of Yang inequalities. We aslo reprove an implication claimed by Cheng and Yang.

关键词： Dirichlet problem eigenvalue estimate Laplacian operator 35P15 58G25

Moment bounds for IID sequences under sublinear expectations

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Science china mathematics 2011年第10期54卷 2155-2160页

作者： HU Feng1,2 1department of mathematics,Qufu normal university,Qufu 273165,china 2School of mathematics,Shandong university,Jinan 250100,china 1. department of mathematics Qufu Normal University Qufu 273165 China2. School of Mathematics Shandong University Jinan 250100 China

With the notion of independent identically distributed(IID) random variables under sublinear expectations introduced by Peng,we investigate moment bounds for IID sequences under sublinear expectations. We obtain a moment inequality for a sequence of IID random variables under sublinear expectations. As an application of this inequality,we get the following result:For any continuous functionsatisfying the growth condition |(x) | C(1 + |x|p) for some C > 0,p 1 depending on ,the central limit theorem under sublinear expectations obtained by Peng still holds.

关键词： moment bound sublinear expectation IID random variables G-normal distribution central limit theorem

Uniquely ergodic property of minimal probability measure in positive definite Lagrangian systems

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Science china mathematics 2006年第12期49卷 1864-1866页

作者： CHEN Jing & BAI Yuzhen department of mathematics, Nanjing university, Nanjing 210093, china department of mathematics, Qufu normal university, Qufu 273165, china 1. department of mathematics Nanjing University Nanjing 210093 China 2. department of mathematics Qufu Normal University Qufu 273165 China

Mane conjectured that every minimal measure in the generic Lagrangian systems is uniquely ergodic. In this paper, we will show that the answer to the Mane's conjecture is negative by analyzing the structure of the sup... 详细信息

关键词： minimal probability measure,uniquely ergodic,Mather theory,Lagrangian systems.

Decomposition of integrable holomorphic quadratic differential on Riemann surface of infinite type

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Science china mathematics 2010年第8期53卷 2039-2044页

作者： CHENG Tao department of mathematics,East china normal university,Shanghai 200241,china 1. department of mathematics East China Normal University Shanghai 200241 China

In this paper,decomposition of the integrable holomorphic quadratic differential on Riemann surface of infinite type is ***,Schleicher and Shishikura gave a thick-thin decomposition on Riemann surface of finite type with an integrable holomorphic quadratic differential and they thought their result might be generalized to arbitrary hyperbolic Riemann surface of infinite *** confirm what they thought is right and give a proposition(Proposition 2.2) of its own interest.

关键词： holomorphic quadratic differential decomposition collar