On a new family of high‐order iterative methods for the matrix pth root

The main goal of this paper is to approximate the principal pth root of a matrix by using a family of high‐order iterative methods. We analyse the semi‐local convergence and the speed of convergence of these methods. Concerning stability, it is well known that even the simplified Newton method is unstable. Despite it, we present stable versions of our family of algorithms. We test numerically the methods: we check the numerical robustness and stability by considering matrices that are close to be singular and badly conditioned. We find algorithms of the family with better numerical behavior than the Newton and the Halley methods. These two algorithms are basically the iterative methods proposed in the literature to solve this problem. Copyright © 2015 John Wiley & Sons, Ltd.     

Decreasing case on characteristic endpoints question for iterative roots of PM functions

For PM functions of height 1, the existence of continuous iterative roots of any order was obtained under the characteristic endpoints condition. A natural open question about iterative roots without that condition was raised. This question was answered partially in the case that the function is increasing on its characteristic interval. In this paper, to the opposite, we consider the decreasing case and give the existence and nonexistence results for their iterative roots.     

Sufficient embedding conditions for three-state discrete-time Markov chains with real eigenvalues

Within the set of discrete-time Markov chains, a Markov chain is embeddable in case its transition matrix has at least one root that is a stochastic matrix. The present paper examines the embedding problem for discrete-time Markov chains with three states and with real eigenvalues. Sufficient embedding conditions are proved for diagonalizable transition matrices as well as for non-diagonalizable transition matrices and for all possible configurations regarding the sign of the eigenvalues. The embedding conditions are formulated in terms of the projections and the spectral decomposition of the transition matrix.     

黑胡椒根萜类化合物的分析

报道了用蒸馏 萃取法提取黑胡椒根中挥发性物质,测得黑胡椒根挥发油的质量分数为3.1%,用GC/MS法从黑胡椒根挥发油中分离并确定出28种化学成分。其中主要成分为萜类化合物,占总检出量的82.48%。     

用标准化变量方法简化介绍线性模型

用标准化变量方法,对线性回归模型的描述进行了简化,使其统计模型变得直观和容易理解.     

压气机叶片前缘分离流动

用实验方法研究了压气机叶片前缘分离流动结构。实验是在低速叶栅风洞中完成的。考察了分别具有圆形和椭圆形前缘的NACA65叶型和CDA叶型前缘附近的流动情况。给出了细致的叶片前缘和分离区内的压力分布情况以及叶片前缘附近流动结构。     

一类二阶微分方程的简化待定特解

给出了简化一类二阶微分方程的待定特解形式的两种方法.     

Are per capita incomes of MENA countries converging or diverging?

This study considers the issue of income convergence among the MENA (Middle East and North African) countries by using real per capita incomes over the period 1950-2006. We employed (Kapetanios et al. 2003) [21] unit root test by incorporating an additive constant and a trend component as Chong et al. (2008) [20] did in their study and found most of the MENA countries diverging during the sample period.     

非负不可约矩阵Perron根的上界序列

给出了非负不可约矩阵Perron根的新上界序列,并指出该序列是收敛到Perron根的,最后给出两个数值例子加以说明,并与文献[1,3,6]中的结论进行了比较．     

多部门动态宏观经济模型及其均衡增长研究

本文运用投入产出分析法建立了一类动态宏观经济模型 ,推广了华罗庚教授提出的“正特征矢量法”,讨论了投资递增条件下 ,开放的宏观经济系统均衡增长的充分必要条件 .