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Some results on numerical divided difference formulas

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Science China mathematics 2005年第11期48卷 1441-1450页

作者： Wang Xinghua,Wang Heyu & Ming-Jun Lai department of mathematics, Zhejiang university, Hangzhou 310028, China Computing Center, Zhejiang university, Hangzhou 310012, China department of mathematics, university of Georgia, Athens, GA 30602-7403, usa 1. department of mathematics Zhejiang University 310028 Hangzhou China 2. Computing Center Zhejiang University 310012 Hangzhou China 3. department of mathematics University of Georgia 30602-7403 Athens GA USA

The remainder estimates of numerical divided difference formula are given for the functions of lower and higher smoothness, respectively. Then several divided difference formulas with super-convergence are derived wit... 详细信息

关键词： numerical divided difference remainder estimate functions of lower smoothness sufficiently smooth functions super convergence.

NONOVERLAPPING DOMAIN DECOMPOSITION METHOD WITH MIXED ELEMENT FOR ELLIPTIC PROBLEMS

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Journal of Computational mathematics 1996年第4期14卷 291-300页

作者： H.X. Rui(mathematics department, Shandong university, Jinan) SHANDONG UNIV DEPT MATHJINAN 250100PEOPLES R CHINA

In this paper we consider the nonoverlapping domain decomposition method based on mixed element approximation for elliptic problems in two dimentional space. We give a kind of discrete domain decomposition iterative algorithm using mixed finite element, the subdomain problems of which can be implemented parallelly. We also give the existence, uniqueness and convergence of the approximate solution.

关键词： Zhang NONOVERLAPPING DOMAIN DECOMPOSITION METHOD WITH MIXED ELEMENT FOR ELLIPTIC PROBLEMS EV

L-R smash products for bimodule algebras

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Progress in Natural Science:Materials International 2006年第6期16卷 580-587页

作者： ZHANG Liangyun (department of mathematics, Nanjing Agricultural university, Nanjing 210095, China department of mathematics, Nanjing university, Nanjing 210008, China) [a] department of mathematics Nanjing Agricultural University Nanjing China [b] department of mathematics Nanjing University Nanjing China

In this paper, we prove that the L-R smash product A(?)H is exactly the twisted smash product A * H if H is a finite dimensional cocommutative Hopf algebra, and give a sufficient and necessary condition for L-R smash products to be bialgebras (Hopf algebras) . For any finite dimensional coquasitriangular Hopf algebra (H,σ), we prove that the L-R smash product H(?)H is semisimple Artinian if H is semisimple and H * is unimodular. In particular, the L-R smash product D(H)* (?)D(H)* semisimple Artinian if the Drin-fel'd double D(H) is semisimple.

关键词： bimodule algebras L-R smash products coquasitriangular Hopf algebras Long bialgebras.

Occupation Measures of Singularly Perturbed Markov Chains with Absorbing States

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Acta Mathematica Sinica,English Series 2000年第1期16卷 161-180页

作者： G.Yin~(1)) department of mathematics,Wayne State university,Detroit,MI 48202,usaQ.Zhang~(2)) department of mathematics,university of Georgia,Athens,GA 30602,usaG.Badowski~(3)) department of mathematics,Wayne State university,Detroit,MI 48202,usa department of mathematics Wayne State University Detroit MI 48202 USA department of mathematics University of Georgia Athens GA 30602 USA

This paper develops asymptotic properties of singularly perturbed Markov chains with inclusion of absorbing *** focuses on both unscaled and scaled occupation *** mild conditions,a mean-square estimate is *** averaging the fast components,we obtain an aggregated *** the aggregated process itself may be non-Markovian,its weak limit is a Markov chain with much smaller state ***,a suitably scaled sequence consisting of a component of scaled occupation measures and a component of the aggregated process is shown to converge to a pair of processes with a switching diffusion component.

关键词： Singularly perturbed Markov chain Occupation measure Aggregation Absorbing state Weak convergence Switching diffusion

Two-Dimensional Riemann Problems for the Compressible Euler System

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Chinese Annals of mathematics,Series B 2009年第6期30卷 845-858页

作者： Yuxi ZHENG Dedicated to Professor Andrew Majda for his 60th Birthday

Riemann problems for the compressible Euler system in two space dimensions are complicated and difficult,but a viable alternative remains *** author lists merits of one-dimensional Riemann problems and compares them with those for the current two-dimensional Riemann problems,to illustrate their ***-dimensional Riemann problems are approached via the methodology promoted by Andy Majda in the spirits of modern applied mathematics;that is,simplified model is built via asymptotic analysis,numerical simulation and theoretical analysis.A simplified model called the pressure gradient system is derived from the full Euler system via an asymptotic ***-of-the-art numerical methods in numerical simulations are used to discern small-scale structures of the solutions,e.g.,semi-hyperbolic *** methods are used to establish the validity of the structure revealed in the numerical *** entire process,used in many of Majda's programs,is shown here for the two-dimensional Riemann problems for the compressible Euler systems of conservation laws.

关键词： Characteristic decomposition Guderley reflection Hodograph transform Pressure gradient system Self-similar Semi-hyperbolic wave Triple point paradox Riemann problem Riemann variable

L~∞ CONVERGENCE OF TRUNC ELEMENT FOR THE BIHARMONIC EQUATION

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Journal of Computational mathematics 1997年第1期15卷 14-22页

作者： M. Wang(department of mathematics, Beijing university, Beijing, China) 北京大学数学系北京

The paper considers the L∞ convergence for TRUNC finite elements solving the boundary value problems of the biharmonic equation. The nearly optimal L∞ estimates for the error of first order derivatives are *** TRUNC plate element is proposed and developed by Argyris et al.. The numerical experiences show that the element has very good .***,[1l2]. The mathematicalproof of convergence of the TRUNC element is given by Shi Zong-ci in paper [3]. Thispaper will consider the L~∞ convergence for the TRUNC plate element.

关键词： Biharmonic equations Convergent boundaries Shape functions Vertices Interpolation Weighting functions Integers

DESIGN AND ANALYSIS OF HIGH-THROUGHPUT SCREENING EXPERIMENTS

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Journal of Systems Science & Complexity 2011年第4期24卷 711-724页

作者： Xianggui QU department of mathematics and Statistics Oakland University Rochester MI 48309 USA.

Saturated row-column designs are studied to eliminate positional effects in primary high- throughput screening experiments. Compared to designs currently used in practice, all compounds in the designs considered are comparable within each microplate in spite of the existence of row and column effects. The designs considered in this paper also have the maximum number of compounds arranged in each microplate. Two statistical methods are used to choose leading compounds in the designs considered. These two methods take full advantages of effect sparsity in primary screening. Simulation studies are carried out to compare the two statistical methods with two ad hoc methods in selecting active compounds. A method that maintains balanced false positives and false negatives is recommended.

关键词： Bscore high-throughput screening row-column design saturated design Zscore.

Littlewood-Paley operators with variable kernels

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Science China mathematics 2006年第5期49卷 639-650页

作者： CHEN Jiecheng, DING Yong & FAN Dashan department of mathematics, Zhejiang university (Xixi Campus), Hangzhou 310028, China School of Mathematical Sciences, Beijing Normal university, Beijing 100875, China department of mathematics, university of Wisconsin-Milwaukee, Milwaukee WI 53201, usa department of mathematics, Central China Normal university, Wuhan 430074, China department of mathematics Zhejiang University [Xixi Campus] Hangzhou 310028 China School of Mathematical Sciences Beijing Normal University Beijing 100875 China department of mathematics University of Wisconsin-Milwaukee Milwaukee WI 53201 USA department of mathematics Central China Normal University Wuhan 430074 China

In this paper we study a certain directional Hilbert transform and the boundedness on some mixed norm spaces. As one of applications, we prove the Lp-boundedness of the Littlewood-Paley operators with variable kernels... 详细信息

关键词： directional Hilbert transform, Sobolev spaces, Littlewood-Paley operator,variable kernel.

Asymptotic Properties of Self-Consistent Estimatorswith Doubly-Censored Data

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Acta Mathematica Sinica,English Series 2001年第4期17卷 581-594页

作者： Qi Qing YU Lin Xiong LI mathematics department, SUNY at Binghamton, Binghamton, NY 13902, usa mathematics department. Zhongshan university, Guangzhou 510275, P. R. China department of mathematics. university of New Orleans, New Orleans, LA 70148, usa mathematics department SUNY at Binghamton Binghamton USA mathematics department Zhongshan University Guangzhou 510275 P. R. China department of mathematics University of New Orleans New Orleans USA

The asyrmptotic properties of the self-consistent estimator (SCE) of a distribution function F of a random variable X with doubly-censored data are examined by several authors under the asstumption that X is observable everywhere in the interval [a, b], where a=inf{x: F(x)>0} and b=sup{x: F(x)<1}. Such an assumption does not allow the situation that X is discrete and the situation that X is only observable in a nontrivial subinterval of [a, b]. However, often in practice this assumption is not satisfied. In this manuscript we establish strong uniform consistency, asymptotic normality and asymptotic efficiency of the SCE under a set of assumptions that allow the situation that X is discrete and the situation that X is only observable in a nontrivial subinterval of [a, b]. Finally, we point out a gap in the proofs of the existing results in the literature due to the definition of the SCE.

关键词： Asymptotic normality Generalized MLE Right censoring Self-consistent algorithm Strong consistency