马氏正态过程在教育质量评价中的应用

本文首先利用正态分布给出状态空间的划分方法,然后将马氏正态过程离散化为马氏链,并给出一步转移矩阵的计算方法．根据不同的状态划分,给出对应的权矩阵,并使用加权平均确定出教学效率的指标,从而给出一种评价教学效率的新方法,并用实例验证其可行性及有效性．     

自共轭四元数矩阵的特征及迹不等式的两个充要条件

研究自共轭四元数矩阵的性质,给出了自共轭四元数矩阵的一个判别法和对角线上元素的特征;证明了自共轭四元数矩阵迹不等式的两个充要条件.     

“关灯”游戏的数学建模与求解

对互联网上的一个数学游戏的控制问题,进行了一般性推广,运用数学建模的方法给出了其基于有限域上的线性方程组的数学模型及求解．     

高等代数方法在中学数学中的应用

讨论利用行列式知识证明四点共圆、利用齐次线性方程组解的理论解有关应用题、利用正定与半正定矩阵知识证明不等式等高等代数方法在中学数学中的应用。     

关于r-循环矩阵的若干性质

文章给出了r-循环矩阵的定义,讨论了r-循环矩阵的一些等价刻画、对角化、可逆性等性质.     

图的控制研究

从关联矩阵和邻接矩阵出发,给出了自关联矩阵、自邻接矩阵和对图的顶点相关分割的定义,然后利用顶点的相关分割解决图的控制问题.结果表明,该方法是解决这类问题的一种简单而实用的方法.     

ONTHEPROPERTIESOFZCIRCULANTMATRICES

本文给出了Ｚ循环矩阵的一些性质     

线性方程组的求解

由于线性方程组在各学科的广泛应用,其重要性是显而易见的,有必要对线性方程组的求解及特殊类型的无穷线性方程组求解进行讨论.     

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.     

基于谱聚类与多信息特征融合的图像分割算法

为了改善传统基于聚类的图像分割算法对噪声敏感以及仅使用单一特征无法精确描述目标特性等问题,提出了一种基于区域的多特征图像分割算法。首先,使用 Meanshift 算法对原图像进行预分割,获得一组区域块;其次,提取每个区域块的颜色特征和纹理特征,使用 FCM 算法分别对每个特征进行聚类,针对每个特征获得一个类标签邻接矩阵;再次,将多个邻接矩阵叠加,形成多特征邻接矩阵;最后,使用 NCUT 算法对叠加邻矩阵进行聚类,获得最终分割图像。实验结果表明,基于区域多特征的分割算法优于对比算法,融合多特征对图像分割可以更准确地识别不同的目标结构,具有更好的分割效果。