正方形编码下 Appell 级数 F_1 的多元 Padé 逼近

多元超几何级数即Ａｐｐｅｌ级数，由于其在物理学、统计学中的应用十分广泛而成为数值逼近领域中的热门话题之一。对这类级数研究的手段之一就是采用多元Ｐａｄé逼近的方法。采用正方形编码方式穷举二元Ｐａｄé逼近中所涉及到的三个指标集Ｎ、Ｄ和Ｅ中的元素，并利用二元Ｐａｄé逼近的行列式公式，给出了Ａｐｐｅｌ级数Ｆ１［１；１，１；２；ｘ，ｙ］的二元Ｐａｄé逼近式，为了说明逼近效果也给出了诸ＭＰＡｓ在点（０．７５，０．７５）处的数值结果。     

二型Fuzzy集代数结构的若干性质

本文指出了文[4]的一个错误,改进了此文中的一个结果。此外,我们还得到了关于二型Fuuy集的许多有用的代数性质。     

从定积分的角度看粗糙集

对于粗糙集的定义及其基本性质,从定积分的角度,给出了一种全新的描述.     

基于集合覆盖的异构有向传感网寿命优化策略

在由感知半径、感知角度和携带能量不同的有向传感器节点组成的异构有向传感器网络中,对满足优先级不同的监测目标有不同覆盖要求条件下的网络寿命最大化问题进行研究。利用集合覆盖的思想,将有向传感器节点划分为满足目标覆盖要求的集合,通过集合之间的切换来达到延长网络寿命的目的。首先证明本文问题是NP-hard问题,然后利用改进的和声搜索算法进行求解,一方面引入带有混沌参数的微分变异因子,改进种群的多样性;另一方面,与模拟退火算法结合增强算法的局部搜索能力。同时为对比算法性能,提出一种贪婪算法。仿真结果显示:较之原始和声搜索算法和贪婪算法,改进和声搜索算法能有效延长网络的寿命,证明了改进算法的有效性。     

应用模糊模型预测高压电网中的闭合过电压

在接通较长的无负载支路时 ,会出现幅度较大的闭合过电压。本文利用前人得到的数据 ,设计了一些模糊规则 ,并以此建立了一个可以预测有关过电压信息的模糊模型 ,同时给出了应用该模型的两个例子。     

非完全竞争的买方行为

将消费者行为理论推广到非完全竞争的买方行为。首先证明了预算映射和需求映射的连续性，并得到了需求集单值的条件；接着推广了数学规划的对偶性；最后证明了支付集的连续性和可微性。     

一种新的模糊线性规划方法

本文详细研究了约束带有模糊系数型线性规划的模糊约束集的定义方法，给出了其隶属函数的规定原则和应满足的条件，并建议了两种具体的定义形式，从而得到了求解这种规划的新方法。     

利用马氏链来分析粗集的动态变动

将马氏链的方法用于分析粗集的动态变动过程，为数据的动态处理提供了一种较为恰当的方法，最后给出了应用的实际背景及实例．     

Rough sets bankruptcy prediction models versus auditor signalling rates

Both international and US auditing standards require auditors to evaluate the risk of bankruptcy when planning an audit and to modify their audit report if the bankruptcy risk remains high at the conclusion of the audit. Bankruptcy prediction is a problematic issue for auditors as the development of a cause–effect relationship between attributes that may cause or be related to bankruptcy and the actual occurrence of bankruptcy is difficult. Recent research indicates that auditors only signal bankruptcy in about 50% of the cases where companies subsequently declare bankruptcy. Rough sets theory is a new approach for dealing with the problem of apparent indiscernibility between objects in a set that has had a reported bankruptcy prediction accuracy ranging from 76% to 88% in two recent studies. These accuracy levels appear to be superior to auditor signalling rates, however, the two prior rough sets studies made no direct comparisons to auditor signalling rates and either employed small sample sizes or non‐current data. This study advances research in this area by comparing rough set prediction capability with actual auditor signalling rates for a large sample of United States companies from the 1991 to 1997 time period. Prior bankruptcy prediction research was carefully reviewed to identify 11 possible predictive factors which had both significant theoretical support and were present in multiple studies. These factors were expressed as variables and data for 11 variables was then obtained for 146 bankrupt United States public companies during the years 1991–1997. This sample was then matched in terms of size and industry to 145 non‐bankrupt companies from the same time period. The overall sample of 291 companies was divided into development and validation subsamples. Rough sets theory was then used to develop two different bankruptcy prediction models, each containing four variables from the 11 possible predictive variables. The rough sets theory based models achieved 61% and 68% classification accuracy on the validation sample using a progressive classification procedure involving three classification strategies. By comparison, auditors directly signalled going concern problems via opinion modifications for only 54% of the bankrupt companies. However, the auditor signalling rate for bankrupt companies increased to 66% when other opinion modifications related to going concern issues were included. In contrast with prior rough sets theory research which suggested that rough sets theory offered significant bankruptcy predictive improvements for auditors, the rough sets models developed in this research did not provide any significant comparative advantage with regard to prediction accuracy over the actual auditors' methodologies. The current research results should be fairly robust since this rough sets theory based research employed (1) a comparison of the rough sets model results to actual auditor decisions for the same companies, (2) recent data, (3) a relatively large sample size, (4) real world bankruptcy/non‐bankruptcy frequencies to develop the variable classifications, and (5) a wide range of industries and company sizes. Copyright © 2003 John Wiley & Sons, Ltd.     

Banach空间中变分法和单调非线性算子理论

本文在 Banach 空间中给出了单调算子方程理论、变分法和单调算子不等式理论在凸集上的统一扩张。