含稀疏度约束的非负张量分解算法及其在故障诊断中的应用(英文)

针对双谱分析在应用于机械设备故障诊断过程中面临的问题,提出了含有稀疏度约束的非负张量分解算法及基于此的二次故障特征提取方法.首先,改进已有的非负张量分解算法,加入稀疏度控制策略;其次,将机械振动信号的双谱图像堆叠为一个三阶张量;然后利用改进后的分解算法对该张量进行二次故障特征提取,得到代表局部特征的"基图像";最后,通过计算得出基图像在构成原双谱图像中所占的权重,并将得到的权重向量用于故障分类.将该方法应用于齿轮箱故障诊断的结果表明,从齿轮箱振动信号的双谱中提取出来的二次特征不仅能够反映出系统中存在的一些非线性特征,而且二次特征与故障特征频率之间有直观的对应关系,从而为解释齿轮箱故障与对应双谱之间的关系提供了很大的方便.     

a尺度紧支撑双正交多小波的提升格式

提升格式是由Sweldens和Daubechies提出的一种构造第二代小波的方法．它也可以被用来构造第一代小波．文章在已知构造方法的基础上，提出了一种新的构造a尺度紧支撑双正交多小波提升格式的方法，从最基本的概念出发，给出了构造a尺度紧支撑双正交多小波的提升格式的推导过程、分解形式及其证明，最后得到一种有效的构造算法．     

一类图的伴随多项式基于挖补定理的因式分解及色性

通过研究L-类图簇的伴随多项式因式分解,给出并证明了这类图的补图的色等价图的结构性质和非色唯一性.     

Leveraging personality information to improve community recommendation in e-learning platforms

E-learning platforms are becoming more and more important and they are gradually changing people’s learning ways. In the e-learning platforms, users actively create and join their favorite communities to share their questions and ideas. With the increase of users of e-learning platforms, the number of communities is increasing dramatically. In this context, it has become difficult for users to find learning communities that match their interests and preferences. Therefore, how to effectively recommend the learning community for users has become an urgent need. However, compared to learning item recommendation, there is relatively limited work on learning community recommendation, and the existing research on community recommendation often ignores the personality information. Personality is considered one of the primary factors that influence human behavior and social relationships, as it affects how people react and interact with others. Several studies have demonstrated that people with similar personality tend to have similar interests. Furthermore, homophily theory also states that social interactions between similar individuals occur at a higher rate than among dissimilar ones. Since interests and interactions are important driving forces for users to join the learning communities, personality has an important impact on users’ choices of communities. Therefore, this paper aims at shedding some light on the impact of personality information on the accuracy of community recommendations. Particularly, we propose three enhanced matrix factorization models based on the Big Five personality framework. To evaluate the effectiveness of our proposed models, we conducted extensive experiments on myPersonality datasets. The results prove that the personality information can improve the performance of the learning community recommendation model and alleviate the data sparsity problem.     

矩阵的广义逆与线性方程组

讨论用矩阵的广义逆求相容的线性方程组的通解,得到一些有用的结果和易行的计算方法。     

一个具有恢复消息的数字签名方案的安全性分析及其改进

分析了卢-陈提出的具有消息恢复的数字签名方案,发现他们的方案是不安全的,任何人知道了系统公布的参数,就可以伪造数字签名.最后,给出了一个改进方案,改进的方案是安全的.     

再论单位根的应用

单位根除在多项式整除性中的应用外，还在多项式因式分解、三角等试证明，行列式计算，几何命题证明等方面有着广泛的应用。     

大整数分解的二次筛法及其微机实现

二次筛法是８０年代中期以来用来分解没有小因子的大整数的“通用算法”，其有效性不依赖于被分解大整数的因子性质．本文详细描述二次筛法的思想和算法，并给出在４８６微机上实现的一些数据结果     

J-次酉矩阵的分解

在J-次酉矩阵分块形式的基础上,给出J-次酉矩阵的几类特殊分解形式,得出了一些新的结果．     

11-9双正交小波的构造与提升分解

构造了一种分解与重构分别为11和9的对称双正交小波(11-9小波)；利用提升的思想，对其进行了提升分解，并对提升分解的系数进行了二进制取整(k／2^r，k，r∈Z)，从而实现了只需移位和整数加法的11-9小波快速算法(12个移位和19个整数加法)．