矩阵Drazin逆的一种算法

矩阵A的Drazin逆可表为A的多项式。为降低多项式的次数，利用Jordan标准形理论分析了矩阵Drazin逆的结构，再由矩阵最小多项式的系数，给出了一个最低次多项式d（A）的算法，使d（A）为的Drazin的逆。该算法简化了已有的矩阵Drazin逆算法。     

Jordan导子的内导性

主要研究Jordan导子的内导性,从而得到套代数上任何一个导子都是内导子.     

n-李代数导子的Jordan-Chevalley分解

利用n-李代数导子性质和一般线性变换的Jordan-Chevalley分解，得到，n-李代数的导子也可以进行Jordan—Chevalley分解．     

三角代数上Lie积为平方零元的非线性Jordan高阶可导映射

设U是一个 2-无挠的三角代数,D ={d_n}_n∈N是U上一个Lie积为平方零元的非线性Jordan高阶可导映射。证明了三角代数U上的每一个Lie积为平方零元的非线性Jordan高阶可导映射都是高阶导子。作为结论的应用,得到套代数或 2-无挠的上三角分块矩阵代数上的每一个Lie积为平方零元的非线性Jordan高阶可导映射都是高阶导子。     

广义BabyTKK代数的Boson-fermion场下的不可约模

研究对应于欧式空间中最小（非格）半格S的babyTKK李代数^g（T（S））的泛中心扩张广义babyTKK代数^g（T（S））的一类boson-fenmion场下的不可约表示，这里T（S）为半格S∈R^υ（υ=2）上的Jordan代数。     

交换环上辛代数和正交代数的抛物子代数的导子

设R是有1的交换环,L是R上的辛代数或正交代数,h是L的极大环面子代数,b是L中包含h的标准Borel子代数.在2∈R可逆的条件下,本文详细描述了b与L之间的中间李代数,并且证明这些中间李代数的导子都是内导子.     

Jordan标准形定理的一个矩阵证明

运用矩阵的初等运算重新证明了Jordan标准形定理.     

Neural network structure identification in inflation forecasting

Neural networks (NNs) are appropriate to use in time series analysis under conditions of unfulfilled assumptions, i.e., non‐normality and nonlinearity. The aim of this paper is to propose means of addressing identified shortcomings with the objective of identifying the NN structure for inflation forecasting. The research is based on a theoretical model that includes the characteristics of demand‐pull and cost‐push inflation; i.e., it uses the labor market, financial and external factors, and lagged inflation variables. It is conducted at the aggregate level of euro area countries from January 1999 to January 2017. Based on the estimated 90 feedforward NNs (FNNs) and 450 Jordan NNs (JNNs), which differ in variable parameters (number of iterations, learning rate, initial weight value intervals, number of hidden neurons, and weight value of the context unit), the mean square error (MSE), and the Akaike Information Criterion (AIC) are calculated for two periods: in‐the‐sample and out‐of‐sample. Ranking NNs simultaneously on both periods according to either MSE or AIC does not lead to the selection of the ‘best’ NN because the optimal NN in‐the‐sample, based on MSE and/or AIC criteria, often has high out‐of‐sample values of both indicators. To achieve the best compromise solution, i.e., to select an optimal NN, the preference ranking organization method for enrichment of evaluations (PROMETHEE) is used. Comparing the optimal FNN and JNN, i.e., FNN(4,5,1) and JNN(4,3,1), it is concluded that under approximately equal conditions, fewer hidden layer neurons are required in JNN than in FNN, confirming that JNN is parsimonious compared to FNN. Moreover, JNN has a better forecasting performance than FNN.     

广义酉矩阵和广义(斜)Hermite矩阵的约当标准形

文章给出了P-内积的定义,利用P-内积的概念详细讨论了广义酉矩阵和广义(斜)Hermite矩阵的特征值以及广义特征向量的各种性质,并且利用这些性质解决了广义酉矩阵和广义(斜)Hermite矩阵的约当标准形。     

交换半环上广义矩阵代数的Jordan导子

研究交换半环上加法可消的广义矩阵代数的Jordan导子、导子和反导子,给岀了广义矩阵代数的Jordan导子、导子和反导子的刻画,进而证明了在某些条件下广义矩阵代数的每一个Jordan导子都可表示为一个导子和一个反导子之和.