矩阵方程AXB=C在对称矩阵类中有解的充要条件

对称矩阵是一类很重要的矩阵.矩阵微分方程、数学物理问题经离散后一般得到对称形式线性方程，文中讨论矩阵方程AXB=C在对称矩阵类中求解问题.     

对称群Sn的极小生成集

本文给出了Sn的几个子集，并证明了它们均可极小生成Sn。     

一类对称统计量的强相合性

考虑了一类有如下形式的对称统计量Tn=k(n-k) k(k-1)2-1∑n-ki=1∑i kj=i 1φ(Xi,Xj) ∑n-1i=n-k 1∑nj=i 1φ(Xi,Xj),这里φ(Xi,Xj)为一对称函数,其中k为不大于n的自然数.这一表达形式是一类统计量,当k=n-1时,它就是一U统计量.在假定E(φ2(Xi,Xj)≤M<∞下,研究了Tn的强相合性.     

对称反循环矩阵的逆矩阵

讨论了求对称反循环矩阵逆矩阵的一般方法,并根据反循环矩阵与对称反循环矩阵的特殊关系给出几类特殊对称反循环矩阵的逆矩阵.     

Output feedback stabilization for symmetric control systems

This work is devoted to the study of symmetric control systems. It establishes a relation between internal symmetry and external one for a linear invariant control system having n real simple poles. The symmetric stabilization problem is studied using a symmetric feedback gain such that the output control stabilizes the closed-loop system. A necessary and sufficient condition is given to solve this stabilization problem for a symmetric control system (A,B,C) and a generalized symmetric control system (E,A,B,C).     

二次插值对称点算法求解一维搜索问题

插值法是一类用插值多项式来逼近未知或复杂函数的方法。本文基于二次插值,将插值多项式的极小点和其对称点作为搜索区间的两个探索点,通过不断缩小搜索区间,求解一维搜索问题的最优解。本文给出了二次插值对称点的算法,并用0.618法进行了数值比较。结果表明,新算法比0.618法效果好。     

用格林函数法求解双层球面间的非对称电场问题

用格林函数法求出了双层球面间的非对称电场的第一类边值问题的解析解，它概括了常见教材、文献中关于格林函数法往往限于“简单”、“接地”、“轴对称”等特殊情况。     

局部对称空间中具有平行平均曲率向量的子流行

设Nn p为n p维局部对称的完备流行,Mn为Nn p中具有平行平均曲率向量的紧致子流行。本文作者给出此类子流行的两个拼挤定理。     

A novel personality detection method based on high-dimensional psycholinguistic features and improved distributed Gray Wolf Optimizer for feature selection

Existing personality detection methods based on user-generated text have two major limitations. First, they rely too much on pre-trained language models to ignore the sentiment information in psycholinguistic features. Secondly, they have no consensus on the psycholinguistic feature selection, resulting in the insufficient analysis of sentiment information. To tackle these issues, we propose a novel personality detection method based on high-dimensional psycholinguistic features and improved distributed Gray Wolf Optimizer (GWO) for feature selection (IDGWOFS). Specifically, we introduced the Gaussian Chaos Map-based initialization and neighbor search strategy into the original GWO to improve the performance of feature selection. To eliminate the bias generated when using mutual information to select features, we adopt symmetric uncertainty (SU) instead of mutual information as the evaluation for correlation and redundancy to construct the fitness function, which can balance the correlation between features–labels and the redundancy between features–features. Finally, we improve the common Spark-based parallelization design of GWO by parallelizing only the fitness computation steps to improve the efficiency of IDGWOFS. The experiments indicate that our proposed method obtains average accuracy improvements of 3.81% and 2.19%, and average F1 improvements of 5.17% and 5.8% on Essays and Kaggle MBTI dataset, respectively. Furthermore, IDGWOFS has good convergence and scalability.     

求解奇异线性方程组的双逐次投影法

用双逐次投影迭代法来求解奇异线性方程组,当线性方程组的系数矩阵是对称半正定时,给出了不同情形时有关参量的选取以及相应的算法,并就收敛结果分别与雅可比迭代法和Gauss-Seidel迭代法进行了比较,数值结果表明,该方法对求解奇异线性方程组是很有效的.