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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

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

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

The pointwise dimension of self-similar measures

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Chinese Science Bulletin 1999年第23期44卷 2136-2140页

作者： CHEN Ercai and XIONG Jincheng department of mathematics , Nanjing normal university , Nanjing 210097, china department of mathematics , South china normal university, Guangzhou 510631 , china department of mathematics Nanjing Normal University Nanjing China department of mathematics South China Normal University Guangzhou China

The problem about the existence of pointwise dimension of self-similar measure has been discussed. The Hausdorff dimension of the set of those points for which the pointwise dimension does not exist equals the dimenti... 详细信息

关键词： self-similar measure point wise dimension Hausdorff dimension multifractal symbolic space.

THE SECOND EXPONENT SET OF PRIMITIVE DIGRAPHS

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Chinese Annals of mathematics,Series B 2000年第2期21卷 233-236页

作者： MIAO ZHENGKE(department of mathematics, Nanjing university, Nanjing 210093, china.)(department of mathematics, Xuzhou normal university, Xuzhou 221009, china.) ZHANG KEMIN(department of mathematics, Nanjing university, Nanjing 210093, china.) department of mathematics Nanjing University Nanjing 210093 China department of mathematics Xuzhou Normal University Xuzhou 221009 China

Let D = (V, E) be a primitive digraph. The exponent of D, denoted byγ(D), is the least integer k such that for any u, v∈ V there is a directed walk of length k from u to v. The local exponent of D at a vertex u∈ V, denoted by exp_D (u), is the least integer k such that there is a directed walk of length k from u to v for each v ε V. Let V = {1,2,….,n}. Following [1], the vertices of V are ordered so that exp_D (1) ≤exp_D (2) ≤…≤exp_D(n) =λ(D). Let E_n(i):= {exp_D (i) ∈D PD_n}, where PD_n is the set of all primitive digraphs of order n. It is known that E_n(n) = {γ(D) D∈PD_n} has been completely settled by [7]. In 1998, E_n(1) was characterized by [5]. In this paper, the authors describe E_n(2) for all n≥2.

关键词： Primitive digraph Local exponent Gap

The best quadrature based on given Hermite information for the Sobolev class KW^r[a,b]

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Science china mathematics 2006年第8期49卷 1146-1152页

作者： WANG Xinghua & YANG Shijun department of mathematics, Zhejiang university, Hangzhou 310028, china department of mathematics, Hangzhou normal College, Hangzhou 310036, china department of mathematics Zhejiang University Hangzhou 310028 China department of mathematics Hangzhou Normal College Hangzhou 310036 China

As usual, denote by KWr[a,b] the Sobolev class consisting of every function whose (r-1)th derivative is absolutely continuous on the interval [a,b] and rth derivative is bounded by K a.e. In [a,b]. For a function f ∈ KWr[a,b], its values and derivatives up to r-1 order at a set of nodes x are known. These values are said to be the given Hermite *** work reports the results on the best quadrature based on the given Hermite information for the class KWr[a,b]. Existence and concrete construction issue of the best quadrature are settled down by a perfect spline interpolation. It turns out that the best quadrature depends on a system of algebraic equations satisfied by a set of free nodes of the interpolation perfect spline. From our another new result, it is shown that the system can be converted in a closed form to two single-variable polynomial equations, each being of degree approximately r/2. As a by-product,the best interpolation formula for the class KWr[a,b] is also obtained.

关键词： Sobolev class, Hermite information, perfect spline, optimal recovery, best quadrature.