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.     

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.     

环的弱正则性

首先引入弱正则理想的概念,得到了弱正则理想的一些性质,接着讨论了半群环的弱正则性.     

群决策的交互式TOPSIS方法及其应用

建立了一种多轮交互逐步逼近满意解的多属性群体决策的综合方法,对决策方案采用扩展的 TOPSIS(technique for order preference by similarity to ideal solution)法进行定性评价排序,以克服一类难以建立解析模型,分析求解困难的多属性群决策问题;设计了群体满意度等软指标来分析计算,判断群体一致性的达成,最终得出群体满意的方案排序.通过应用实例,说明了该方法的有效性和可行性,初步提出了可作为建立一类实际的群决策支持系统的方法和技术框架.     

一类n-Lie代数的最小理想问题

研究了n+k维n-Lie代数一些结构性质,并且证明了对于具有性质:任意非零理想其维数都大于或等于k的n+k维n-Lie代数一定存在最小理想.     

一种新的门限秘密共享方案

一个(k,n)门限秘密共享方案允许把一个秘密S分成n份Si(1≤i≤n),每一份交由一个用户Pi,使得任意k个或多于k个用户联合起来可以恢复秘密S,而任意少于k个用户却不能。在现实生活中,它有着非常广泛的应用。文章介绍了Shamir秘密共享方案,并设计了一种新的基于线性方程组求解的门限秘密共享方案。该方案满足完备、理想特性;与Shamir门限方案相比,其安全性相当;但在计算、重构以及更新共享时更有效。     

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。     

弹性半空间-理想流体层中Stoneley波的动力特性

为了解弹性半空一理想流体层中Stoneley波的动力特性,并为进一步开发利用海洋资源提供调查方法,根据弹性固体与理想流体动力学方程,推导了弹性半空间一理想流体层中Stoneley波的特征方程、基于该特征方程,分析了固液两介质的物理特性对流体动压力的影响,以及固体和流体介质的位移分布情况．结果表明,该体系中Stoneley波在固体中的位移分布类似于半空间Rayleigh波,而在流体中的位移分布有明显的规律性;弹性半空一理想流体层中Stoneley波具有频散性,且其波速小于弹性半空间中Rayleigh波的波速．     

PMS-代数的同余理想

给出PMS-代数L的主同余θ（0,b）及θ（a,1）的一个新的刻划,利用这个刻划,得到理想I=（d]是同余理想的充要条件,从而断定L的同余理想只能是正则理想．     

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.