Analysis of finite dimensional approximations to a class of partial differential equations

In this paper, a unified approach for analysing finite dimensional approximations to a class of partial differential equations boundary value problems (second‐kind Fredholm differential equations) is introduced. The approach is shown to be general despite of its extremely simple form. In particular, it is expected to be useful in the convergence analysis of finite element methods for solving PDE problems. Three specific examples are presented to illustrate the broad applicability of the approach. Copyright © 2004 John Wiley & Sons, Ltd.     

微全分析系统检测方法的研究进展

综述了不同类型的检测方法在微全分析系统的应用，并简述了各类型的检测方法的优缺点。引用文献92篇。     

美式期权定价中非局部问题的有限元方法

在本文中 ,我们关心的是美式期权的有限元方法 .首先 ,根据 [4 ]我们对所讨论的问题引进一个新奇的实用的方法 ,它涉及到对原问题重新形成准确的数学公式 ,使得数值解的计算可以在非常小的区域上进行 ,从而该算法计算速度快精度高 .进而 ,我们利用超逼近分析技术得到了有限元解关于 L2 -模的最优估计 .     

Krylov subspaces and the analytic grade

Typical behaviour of the solution of a linear system of equations obtained iteratively by Krylov methods can be characterized by three stages. Initially the residual diminishes steadily; this is followed by stagnation and finally rapid convergence near the algebraic grade. This study examines this behaviour in terms of the concepts of approximately invariant subspace and what we have called the analytic grade of a Krylov sequence. It is shown how the small Ritz values play a vital role in the convergence and how this knowledge helps in the construction of an effective preconditioner. Copyright © 2004 John Wiley & Sons, Ltd.     

Space time-index plots for probing dynamical nonstationarity

We propose a simple method to efficiently probe dynamical nonstationarity in observed time series. In a space time-index plot, the density distributions as a function of normalized time-index are V-shaped due to nonstationarity. We show that this method is workable for short data sets and typical examples are illustrated.     

层次分析中广义最小偏差法的性质

广义最小偏差法（GLDM）是层次分析中一种重要的排序方法．本文讨论了广义最小偏差法的性质和灵敏度分析问题．     

几种国际通用统计软件的比较

汤旦林，王松柏．几种国际通用统计软件的比较，数理统计与管理，１９９７，１６（１），４８～５３．本文对七种著名的国际通用统计软件作了扼要的介绍，并从用户的角度对它们的性能进行了具体的比较     

Generalization of the Gram-Charlier/Edgeworth Series and Application to Time-Frequency Analysis

We derive a general equation relating probability densities and as special cases we the obtain Gram-Charlier and Edgeworth series. This allows us to generalize these methods and clarify a number of issues pertaining to both probability theory and time-frequency analysis. In particular we show how the Gram-Charlier and Edgeworth series are related to the kernel method of time-frequency analysis. The approach allows us to construct densities that satisfy given constraints such as joint moments or conditional moments. Also, we show that the kernel has to be signal dependent and that to obtain a proper distribution it should be the ratio of two characteristic functions.     

The “Essential Tension” at Work in Qualitative Analysis: A Case Study of the Opposite Points of View of Poincaré and Enriques on the Relationships between Analysis and Geometry

An analysis of the different philosophic and scientific visions of Henri Poincaré and Federigo Enriques relative to qualitative analysis provides us with a complex and interesting image of the “essential tension” between “tradition” and “innovation” within the history of science. In accordance with his scientific paradigm, Poincaré viewed qualitative analysis as a means for preserving the nucleus of the classical reductionist program, even though it meant “bending the rules” somewhat. To Enriques's mind, qualitative analysis represented the affirmation of a synthetic, geometrical vision that would supplant the analytical/quantitative conception characteristic of 19th-century mathematics and mathematical physics. Here, we examine the two different answers given at the turn of the century to the question of the relationship between geometry and analysis and between mathematics, on the one hand, and mechanics and physics, on the other.Copyright 1998 Academic Press.Un'analisi delle diverse posizioni filosofiche e scientifiche di Henri Poincaré e Federigo Enriques nei riguardi dell'analisi qualitativa fornisce un'immagine complessa e interessante della “tensione essenziale” tra “tradizione” e “innovazione” nell'ambito della storia della scienza. In linea con il proprio paradigma scientifico, Poincaré vedeva nell'analisi qualitativa un mezzo per preservare il nucleo del programma riduzionista calssico, anche se cio comportava una lieve “distorsione delle regole”. Nella mente di Enriques, l'analisi qualitativa rappresentava l'affermazione di un punto di vista sintetico e geometrico che avrebbe soppiantato la concezione analitico-quantitativa caratteristica della matematica e della fisica matematica del 19° secolo. Il nostro scopo principale è di esaminare due diverse risposte date a cavallo del secolo alla questione dei rapporti tra geometria e analisi e tra matematica da un lato e meccanica e fisica dall'altro.Copyright 1998 Academic Press.AMS subject classification: 01A55     

SINGULAR BOUNDARY PROPERTIES OF HARMONIC FUNCTIONS AND FRACTAL ANALYSIS

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