Ekeland变分原理及其应用

本文将Ekeland变分原理作了推广，并将理论结果应用到正则约束最优化问题上．     

Preparation and characterization of three-dimen-sionally ordered macroporous polystyrene via atom-transfer radical polymerization

Three-dimensionally ordered macroporous polystyrene(3DOM PS) with pore size of 350 nm was fabricated using Cp2Co/Ethyl 2-bromoisobutyrate(EBiB) catalytic system by ATRP.The resulting polymers were detected by FT-IR,1H-NMR,SEM,and GPC.The microstructure of 3DOM PS was confirmed by FT-IR and 1H-NMR.SEM micrographs show that both silica spheres within the templates and pores in the 3DOM polystyrene are arranged in highly ordered fashion,and the shrinkage of the pores in the 3DOM PS is 24%.GPC curves show that the 3DOM PS possesses slightly lower Mn and narrow MWD compared with bulk one.This result indicats that living polymerization is different from non-living polymerizationin in the confined space.     

The generation of random,binary unordered trees

Several techniques are given for the uniform generation of trees for use in Monte Carlo studies of clustering and tree representations. First, general strategies are reviewed for random selection from a set of combinatorial objects with special emphasis on two that use random mapping operations. Theorems are given on how the number of such objects in the set (e.g., whether the number is prime) affects which strategies can be used. Based on these results, methods are presented for the random generation of six types of binary unordered trees. Three types of labeling and both rooted and unrooted forms are considered. Presentation of each method includes the theory of the method, the generation algorithm, an analysis of its computational complexity and comments on the distribution of trees over which it samples. Formal proofs and detailed algorithms are in appendices.     

An error variance approach to two-mode hierarchical clustering

A new agglomerative method is proposed for the simultaneous hierarchical clustering of row and column elements of a two-mode data matrix. The procedure yields a nested sequence of partitions of the union of two sets of entities (modes). A two-mode cluster is defined as the union of subsets of the respective modes. At each step of the agglomerative process, the algorithm merges those clusters whose fusion results in the smallest possible increase in an internal heterogeneity measure. This measure takes into account both the variance within the respective cluster and its centroid effect defined as the squared deviation of its mean from the maximum entry in the input matrix. The procedure optionally yields an overlapping cluster solution by assigning further row and/or column elements to clusters existing at a preselected hierarchical level. Applications to real data sets drawn from consumer research concerning brand-switching behavior and from personality research concerning the interaction of behaviors and situations demonstrate the efficacy of the method at revealing the underlying two-mode similarity structure.     

广义Volterra型积分方程与积分不等式

考虑一定有序局部紧空间上形如x(t)=w(t)+∫~tK(t,s)x(s)ds+(?)∫~tf(t,s,x(s))ds的Volterra型积分方程,并由此导出了相应的积分不等式结果.     

四值非全序R0命题逻辑上的随机伪度量

 通过引入随机化映射和真度权函数等概念,在四值非全序R₀命题逻辑系统中提出了公式的可变随机真度,得到可变随机真度的一些基本性质,提出了2公式间的随机相似度和随机伪度量,建立了四值非全序R₀命题逻辑系统上的随机逻辑伪度量空间,为在四值非全序命题逻辑系统上进行近似推理提供了一种可能的框架.     

基于DBSCAN算法的电信客户分类的应用研究

为了在激烈的市场竞争中取胜,电信企业意识到必须将客户分类,针对不同的客户研究相应的营销策略,DBSCAN算法能够实现客户分类,但对初始参数E和MinPts的取值非常敏感,不同的取值将产生不同的聚类结果,通过对DBSCAN算法进行改进,实现了更加准确和全面的客户分类。     

有样本缺失的稀疏交叉视图的多重集典型相关分析

从融合多组特征的角度出发,以多重集典型相关分析算法(MCCA)为研究基础,通过稀疏保持自适应选择样本局部信息,然后通过在同类样本之间计算权重矩阵,将样本类别信息嵌入到算法中,再利用多种视图之间的交叉相关项,克服不同视图样本必须成对出现的局限,提出一种有样本缺失的稀疏交叉视图的多重集典型相关分析算法(multiset canonical sparse cross-view correlation analysis with missing samples,CSMCCAM)。在手写体数据集和CENPARMI数据库上验证本文的算法,得到CSMCCAM算法分类精确度优于LPMCCAM等典型相关分析算法,并且对缺失样本数目不敏感。     

基于非均衡模糊近似支持向量机的P2P网贷借款人信用风险评估及应用

现实中P2P网贷平台可信用户和违约用户的样本分布具有非均衡性,且投资者对分类错误持有不同接受程度.本文通过使用双边权重误差测量方法和映射距离选择正负样本误差项的隶属度,构建了基于非均衡模糊近似支持向量机(DFPSVM)的P2P网贷借款人信用风险评估模型.然后,提出了借款人信用评分及评级方法.最后,借助人人贷平台借款人信用信息进行了实证分析,结果表明所构建的模型与其他模型相比具有更好的适应能力和较高的分类准确度,能有效减少样本非均衡性对分类结果的影响,显著增加负类样本分类的准确率.获得的人人贷平台借款人的信用得分、信用等级及违约率分布能够为平台控制违约风险及投资者决策提供帮助.     

一种新的样本选择算法及其在文本分类中的应用

在保证分类性能的前提下,如何从大量的训练样本集合中选择重要样本子集,是模式分类中的一个重要问题.基于该问题提出了一种新的样本选择算法,并将该算法应用于文本分类,在标准文档集Reuters-21578、复旦文档集和20newsGroup新闻组文档集上进行了实验.实验结果表明:该方法能有效地选取边界样本,且采用SVM和KNN分类能得到较好的分类结果,尤其是在不均衡文档集上效果更佳.