Maximal Subrings and Covering Numbers of Finite Semisimple Rings

We classify the maximal subrings of the ring of n×n matrices over a finite field, and show that these subrings may be divided into three types. We also describe all of the maximal subrings of a finite semisimple ring, and categorize them into two classes. As an application of these results, we calculate the covering number of a finite semisimple ring.     

基于重抽样分布的一类模糊累积和控制图

过程变量在代表产品或服务过程信息时并非完美，而使用模糊数可能是另一较好途径。文章进一步完善模糊累积和控制图，其中使用中心和扩展具有重抽样分布的模糊随机变量，并给出模拟例证。     

An Improved Composite Multiscale Fuzzy Entropy for Feature Extraction of MI-EEG

Motor Imagery Electroencephalography (MI-EEG) has shown good prospects in neurorehabilitation, and the entropy-based nonlinear dynamic methods have been successfully applied to feature extraction of MI-EEG. Especially based on Multiscale Fuzzy Entropy (MFE), the fuzzy entropies of the τ coarse-grained sequences in τ scale are calculated and averaged to develop the Composite MFE (CMFE) with more feature information. However, the coarse-grained process fails to match the nonstationary characteristic of MI-EEG by a mean filtering algorithm. In this paper, CMFE is improved by assigning the different weight factors to the different sample points in the coarse-grained process, i.e., using the weighted mean filters instead of the original mean filters, which is conductive to signal filtering and feature extraction, and the resulting personalized Weighted CMFE (WCMFE) is more suitable to represent the nonstationary MI-EEG for different subjects. All the WCMFEs of multi-channel MI-EEG are fused in serial to construct the feature vector, which is evaluated by a back-propagation neural network. Based on a public dataset, extensive experiments are conducted, yielding a relatively higher classification accuracy by WCMFE, and the statistical significance is examined by two-sample t-test. The results suggest that WCMFE is superior to the other entropy-based and traditional feature extraction methods.     

正规矩阵特征值扰动的新估计

设A,B均为正规矩阵,关于正规矩阵的特征值扰动,有结论 (n∑i=1︱μτ(i)-λi︱2)(1/2)≤n(1/2)‖E‖F,其中λi,μi分别为A,B的特征值.通过新的方法证明给出特征值扰动上界的新估计,并改进了以上结论.     

基于模糊控制的公路隧道通风控制系统

提出了一种新型的基于模糊控制的公路隧道通风控制系统,将CO浓度值和烟雾浓度值作为系统输入,风机数值作为系统输出。仿真结果显示,这种模糊通风控制系统用在隧道通风控制系统中可以缓解传统的分级式控制的风机频繁启停的问题。     

化学方程式配平的矩阵解法

基于矩阵解方程的理论，定义出了一个化学元素矩阵，从而找到了一种配平化学方程式的新方法，称之为矩阵解法。     

模糊关系运算的传递性

详细讨论模糊关系一元及二元运算的传递性性质。首先给定一个模糊关系具有某种传递性性质，讨论其余关系、逆关系、对偶关系的传递性性质；然后基于两个模糊关系具有某类传递性，讨论它僮的模并、模交运算的传递性性质。     

采场人员可靠性模糊综合分析

针对采场人—机—环境可靠性系统中,人是最主要的也是最脆弱的这一特点,根据可靠性理论,应用模糊数学理论与层次分析法,建立了一种新型的系统可靠性模糊数学分析模型,对采场人员可靠性进行综合分析和评价。该分析方法能够对采场人员系统可靠性给以直观、定量的描述。最后,以某磷矿为例,验证了模型的合理性。     

Existence of the uniformly minimum risk equivariant estimators of parameters in a class of normal linear models

In this paper, we study the existence of the uniformly minimum risk equivariant (UMRE) estimators of parameters in a class of normal linear models, which include the normal variance components model, the growth curve model, the extended growth curve model, and the seemingly unrelated regression equations model, and so on. The necessary and sufficient conditions are given for the existence of UMRE estimators of the estimable linear functions of regression coefficients, the covariance matrixV and (trV)^α, where α > 0 is known, in the models under an affine group of transformations for quadratic losses and matrix losses, respectively. Under the (extended) growth curve model and the seemingly unrelated regression equations model, the conclusions given in literature for estimating regression coefficients can be derived by applying the general results in this paper, and the sufficient conditions for non-existence of UMRE estimators ofV and tr(V) are expanded to be necessary and sufficient conditions. In addition, the necessary and sufficient conditions that there exist UMRE estimators of parameters in the variance components model are obtained for the first time.