向量空间的模结构分解

将数域F上n维向量空间视为数域F上多项式环F[s]上的模，给出了向量空间的模结构分解，指出任一数域上的向量空间都可表示为若干多项式环上循环模的直和形式，特别讨论了复数域和实数域上向量空间的分解情形，引入了变换(或矩阵)的特征值对应的生成根向量的定义，得到了循环模的生成元与变换的生成根向量之间的关系。     

Adaptive synchronization of fractional‐order complex networks via pinning control

Adaptive synchronization of a class of fractional‐order complex networks is investigated in this paper. On the basis of the fractional‐order system stability theory, adaptive synchronization criteria of fractional‐order complex networks with 0 < q < 1 is achieved. Furthermore, pinning control method is then suggested to control the networks, and adaptive strategy is employed to tune the control gains and coupling strength. Because the nodes with high degree may not be the center of the networks, a new attempt to choose the pinned nodes on the basis of the closeness centrality scheme is proposed. Finally, numerical simulations are given to verify the effectiveness of the proposed approach based on the closeness centrality scheme. Copyright © 2012 John Wiley & Sons, Ltd.     

Eigenvectors of tridiagonal matrices of Sylvester type

Eigenvectors of the tridiagonal matrices of Sylvester type are explicitly determined. These are closely related to orthogonal polynomials named after Krawtchouk, (dual) Hahn and Racah as well as to q-Racah polynomials.      

Detecting community structure in networks by representative energy

Network community has attractedmuch attention recently, but the accuracy and efficiency in finding a community structure is limited by the lower resolution of modularity. This paper presents a new method of detecting community based on representative energy. The method can divide the communities and find the representative of community simultaneously. The communities of network emerges during competing for the representative among nodes in network, thus we can sketch structure of the whole network. Without the optimizing by modularity, the community of network emerges with competing for representative among those nodes. To obtain the proximate relationships among nodes, we map the nodes into a spectral matrix. Then the top eigenvectors are weighted according to their contributions to find the representative node of a community. Experimental results show that the method is effective in detecting communities of networks.     

复杂河流网络节点重要度分析

流域中,具有一定水力联系的河流、交叉口、水利工程设施等纵横交错地构成了一个复杂的河流网络.应用复杂网络理论,建立了河流网络模型,并描述了节点的重要度.将该网络模型应用于海河流域,建立了含有565个节点的海河流域网络.计算了海河流域网络节点的度指标和介数指标,并分别划分为8个等级和12个等级,对不同等级的节点进行节点重要度分析.通过对比分析节点的度指标和介数指标,证明了介数指标更能准确刻画河流网络节点的重要性.复杂网络中节点重要度分析可以为水利规划提供理论依据.     

基于小波和矩的图像字符特征提取方法研究

提取稳定而有代表性的特征是视频图像字符识别的核心问题之一。文章提出了一种基于小波和矩的图像字符特征向量提取方法。通过对字符图像的不同小波分解子图求取不同的矩特征，构造出字符的特征向量。该方法将小波对图像结构精细特征的把握能力强的优点与矩所具有的平移，缩放和旋转不变及抗噪性强的特性有机地结合起来，特征向量稳定、识别准确率高、算法快、抗噪性能强，且特征提取方法具有类人视觉特点。     

基于最大信噪比的盲源分离算法的修正与比较

对基于最大信噪比的盲源分离算法进行了修正,解决了原算法在一些情况下失效的问题,并且比较分析了以上算法和全局最优盲源分离算法的分离性能。仿真结果表明,修正了的基于最大信噪比的盲源分离算法和全局最优盲源分离算法经常在分离性能上很相近,且都解决了修正前算法在一些情况下失效的问题。     

社交网络节点中心性测度

研究节点影响力以及扩大节点影响力的范围在社交网络传播中具有重大意义。为了综合分析节点自身影响力与其潜在影响力,提出了PPI（Personal-Potential Influence,PPI）算法,用介数中心性值,紧密中心性值及k-shell值加权来评估节点自身影响力,再通过节点间的相互影响来评估其潜在影响力。实验结果表明PPI算法在评估节点影响力上有较好的准确性。     

Parameterized ABD preconditioning technique for time-periodic convection–diffusion problems

In this paper, a parameterized additive block diagonal (PABD) preconditioning technique is present for solving the nine-point approximations of the time-periodic convection–diffusion problems. The explicit expressions for the eigenvalues and eigenvectors of the corresponding preconditioned matrices are presented. The range of the optimal parameters is derived. Numerical experiments show that the generalized minimal residual method preconditioned by the PABD preconditioner with the experimental optimal parameters or some special values is effective for a wide range of problem sizes.