A comparison of transformation methods for evaluating two‐dimensional weakly singular integrals

Accurate numerical evaluation of integrals arising in the boundary element method is fundamental to achieving useful results via this solution technique. In this paper, a number of techniques are considered to evaluate the weakly singular integrals which arise in the solution of Laplace's equation in three dimensions and Poisson's equation in two dimensions. Both are two‐dimensional weakly singular integrals and are evaluated using (in a product fashion) methods which have recently been used for evaluating one‐dimensional weakly singular integrals arising in the boundary element method. The methods used are based on various polynomial transformations of conventional Gaussian quadrature points where the transformation polynomial has zero Jacobian at the singular point. Methods which split the region of integration into sub‐regions are considered as well as non‐splitting methods. In particular, the newly introduced and highly accurate generalized composite subtraction of singularity and non‐linear transformation approach (GSSNT) is applied to various two‐dimensional weakly singular integrals. A study of the different methods reveals complex relationships between transformation orders, position of the singular point, integration kernel and basis function. It is concluded that the GSSNT method gives the best overall results for the two‐dimensional weakly singular integrals studied. Copyright © 2002 John Wiley & Sons, Ltd.     

等离子体刻蚀工艺控制模型分析

讨论了主因素分析法以及神经网络法在等离子体刻蚀工艺中的应用.结果表明主元素分析法可以实现对数据的压缩,而神经网络算法则显示出比传统的统计过程控制算法更好的准确性.     

一种变步长D-Rake多用户检测器

在时变多径衰落信道下,接收到的CDMA信号功率变化较大,此时D-Rake盲自适应多用户检测器性能显著下降,将变步长LMS算法与基于主分量的相干合并引入到D-Rake(DecorrelatingRake)检测器中,构成一种变步长D-Rake,称之为VD-Rake(Variablestep-sizeDecorrelatingRake)检测器。该检测器能克服原D-Rake检测器对信号功率变化较敏感等缺点,有效地改善了D-Rake检测器的性能。     

中国古典园林三维造型研究

论述了采用层次结构化及参数化三维造型方法，建立一个以造型函数库为核心，从而构造各类、各级园林景观构件表面模型的方法和过程。对于某些非建筑类的园林配景构件，采用了Ｆｒａｃｔａｌ方法进行造型。     

The Cooperative Molecular Field Effect

Two‐dimensional arrangements of molecules can show remarkable cooperative electronic effects. Such effects can serve to achieve direct electronic sensing of chemical and physical processes via electrostatic effects, i.e., without transfer of charge or matter between the locus of sensing and that of detection.     

Application of annexation principle of thermodynamic property of In-Pb-Sb and In-Bi-Pb melts

Based on the principle of annexation and phase diagrams, the structural units of In-Pb-Sb and In-Bi-Pb melts were determined, and their calculating models of mass action concentrations were formulated. Calculated results agree well with practical values, which in turn show that the models deduced can reflect the structural realities of corresponding melts and the principle of annexation is applicable not only to some binary metallic melts, but also to ternary metallic melts.     

Synthesis, Characterization, and Formation Process of Na-X Zeolite from Coal Fly Ash

Using the SiO₂ and Al₂O₃ components of the amorphous phase in coal fly ash (Fa), Fa was converted to Na-X zeolites in NaOH-NaAlO₂ solutions by stirring at 35°C for 72 hr and then aging at 85°C for a given period. The molar ratio SiO₂/Al₂O₃ of the starting materials was controlled from 2.0 to 13.2. The resulting materials were characterized by various means. Increasing the SiO₂/Al₂O₃ ratio of the starting material increased the degree of crystallinity of faujasite, exhibiting a maximum at SiO₂/Al₂O₃ = 8.0. The faujasite formed was identified as Na-X zeolite with Si/Al = 1.20. The amorphous phase in Fa was dissolved during the stirring to form a precursor of zeolite, such as amorphous aluminosilicate. The Na-X zeolite was formed by aging for 24 hr, and the degree of crystallinity of this material was increased with the increasing aging period. The cation exchange capacity and specific surface area were increased with the increasing degree of crystallinity of the Na-X zeolites.     

Introduction of a nonlinearity measure for principal component models

Although principal component analysis (PCA) is an important tool in standard multivariate data analysis, little interest has been devoted to assessing whether the underlying relationship within a given variable set can be described by a linear PCA model or whether nonlinear PCA must be utilized. This paper addresses this deficiency by introducing a nonlinearity measure for principal component models. The measure is based on the following two principles: (i) the range of recorded process operation is divided into smaller regions; and (ii) accuracy bounds are determined for the sum of the discarded eigenvalues. If this sum is within the accuracy bounds for each region, the process is assumed to be linear and vice versa. This procedure is automated through the use of cross-validation. Finally, the paper shows the utility of the new nonlinearity measure using two simulation studies and with data from an industrial melter process.