Solutions and improved perturbation analysis for the matrix equation X-A^{*}X^{-p}A=Q (p>0)

In this paper the nonlinear matrix equation X-A^{*}X^{-p}A=Q with p>0 is investigated. We consider two cases of this equation: the case p>1 and the case 01, a new sufficient condition for the existence of a unique positive definite solution for the matrix equation is obtained. A perturbation estimate for the positive definite solution is derived. Explicit expressions of the condition number for the positive definite solution are given. In the case 0<p<1, a new sharper perturbation bound for the unique positive definite solution is evaluated. A new backward error of an approximate solution to the unique positive definite solution is obtained. The theoretical results are illustrated by numerical examples.Comment: 17 pages. arXiv admin note: substantial text overlap with arXiv:1208.3672, arXiv:1208.351

China\u27s New Labor Contract Law and Protection of Workers

This Comment will discuss the labor conditions in China that prompted many provisions in the recently enacted Labor Contract Law, and how the new law responds to deficiencies of China\u27s Labor Law to address various labor problems. Part I of this Comment contains a brief presentation of the historical and economic background of the emergence of migrant workers. Part I also examines the causes of the main problems faced by migrant workers, in particular the insufficiencies of China\u27s Labor Law in protecting migrant workers. Part II looks into the legislation\u27s background and specific provisions of China\u27s new Labor Contract Law that supplement the Labor Law and stress the protection of laborers. Many provisions of the new law specifically address labor abuses faced by migrant workers. Finally, Part III discusses the insufficiencies and likely effects of the new Labor Contract Law