New moon from an old hand

The outcome of the Apollo lunar exploration program 1969-1974 was a model of lunar petrogenesis which ignored the probability of selective volatilisation of gases and alkalis from fire-fountaining lunar basalts. It overlooked the fact that the average compositions of the erupted basalts were those of plagioclase-saturated and low-pressure cotectic liquids on eruption, clearly indicating that they were not primary magmas. The basalts may have undergone evolution by gabbro fractionation within the lunar crust, perhaps in large lava lakes now solidified as the lunar maria. The existing model involving a global magma ocean and plagioclase flotation to form the lunar crust arises solely from the incorrect assumption that the basalts are primary magmas. The plagioclase flotation hypothesis requires the presence of a significant positive europium anomaly in the lunar highland crust, and was founded upon its alleged presence. However, that positive anomaly is neither established by the original data set nor by the much broader current data set. Critical observations, and experiments which will advance the debate are suggested, and alternative interpretations outlined.     

标准良序集

本文引进标准良序集概念并且证明了标准良序集的十个定理。     

关于Banach空间中连续自映射周期轨道存在问题

本文把[1]中的结论(5)推广到一般的Banach 空间;并且利用此结果证明:在半序Banach 空间中,如果它的一个连续的自映射满足一定的条件,那么它的全序的周期3轨道的存在蕴含着任何周期轨道的存在。     

Forecasting football results and the efficiency of fixed‐odds betting

An ordered probit regression model estimated using 10 years' data is used to forecast English league football match results. As well as past match results data, the significance of the match for end‐of‐season league outcomes, the involvement of the teams in cup competition and the geographical distance between the two teams' home towns all contribute to the forecasting model's performance. The model is used to test the weak‐form efficiency of prices in the fixed‐odds betting market. A strategy of selecting end‐of‐season bets with a favourable expected return according to the model appears capable of generating a positive return. Copyright © 2004 John Wiley & Sons, Ltd.     

有序Banach空间中一类时滞积分方程

考虑有序Ｂａｎａｃｈ空间中形如的时滞积分方程，给出了这类方程存在正周期解的若干充分条件。     

Measuring the influence of individual data points in a cluster analysis

The problem of measuring the impact of individual data points in a cluster analysis is examined. The purpose is to identify those data points that have an influence on the resulting cluster partitions. Influence of a single data point is considered present when different cluster partitions result from the removal of the element from the data set. The Hubert and Arabie (1985) corrected Rand index was used to provide numerical measures of influence of a data point. Simulated data sets consisting of a variety of cluster structures and error conditions were generated to validate the influence measures. The results showed that the measure of internal influence was 100% accurate in identifying those data elements exhibiting an influential effect. The nature of the influence, whether beneficial or detrimental to the clustering, can be evaluated with the use of the gamma and point-biserial statistics.     

BP算法中样本特性及参数α，β两阶段动态调整

从样本特性和参数调整出发，提出了三种改进的ＢＰ算法，并在ＸＯＲ等问题上进行了检验。     

灰色聚类法在湛江港冬季水质评价中的应用

2006年12月底,将湛江港划分为码头和七个断面,每个断面分为三个监测点进行调查,应用灰色聚类法对其水质测量结果进行综合评价。结果表明:从空间分布上看,各监测点水质状况好坏差别较大,断面Ⅰ、Ⅱ、Ⅲ,、Ⅶ为一类水质,断面Ⅳ、Ⅴ、Ⅵ、码头为三类水质,污染严重。     

基于模糊粗糙集的一种属性约简算法

将粗糙集理论与模糊集理论相结合,提出了一种基于模糊粗糙集的属性约简算法。该方法引入了模糊C均值聚类算法用以连续属性的模糊化;并通过聚类有效性分析来确定最佳分类数目;克服了目前属性模糊化方法需要人为规定划分类数,几乎不考虑信息系统的具体属性值等缺点。实例验证了此方法的有效性。