A Note on Menon Difference Sets

证明了具有同态象Ｚ４×Ｚｐ的４ｐ２阶群中不存在Ｍｅｎｏｎ差集（ｐ≥５，ｐ≡３（ｍｏｄ４）），并指出在某些情形下Ｔｕｒｙｎ的指数界可以改善。     

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。     

L—fuzzy拓扑空间中的I型强连通性

利用准闭集和Ｐ远域引入和研究了Ｌｆｕｚｙ拓扑空间中的Ｉ＊型强连通性概念,它保持了一般拓扑空间连通集的若干重要性质．     

相容粗糙集在音频检索中的应用

针对数字技术的发展促使个人的多媒体数据资料量越来越大,给人们的使用造成很大的不便,人们迫切需要能对这些资料进行检索和管理的工具,提出了利用相容粗糙集理论对音频数据进行预检索的新方法,即在相容类的近似空间中对音频数据进行预检索.实验结果表明,该方法可以有效地克服等价粗糙集在音频检索方面的限制,对提高检索效率具有一定的作用.     

权重分析系统

本文利用加权模糊区间统计方法,对决策指标权重进行了讨论,并引入关联度的概念讨论了各专家的偏离度及一致性。     

粗糙极大算子交换子有界性的一个注记

本文给出一类粗糙核极大算子与ＢＭＯ函数产生的高阶交换子的加权（Ｌｐ，Ｌｑ）有界性     

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。     

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.     

关于闭集的距离及分离性的讨论

章主要指出[1]中一种不确切的说法，并就R^D中闭集的距离及分离分有界和无界情形进行了讨论，同时给出了较直观的证明。