Padé approximant related to the Wallis formula
AbstractBased on the Padé approximation method, in this paper we determine the coefficients aj$a_{j}$ and bj$b_{j}$ such that 
 π=((2n)!!(2n−1)!!)2{nk+a1nk−1+⋯+aknk+1+b1nk+⋯+bk+1+O(1n2k+3)},n→∞,$$ \pi= \biggl(\frac{(2n)!!}{(2n-1)!!} \biggr)^{2} \biggl\{ \frac {n^{k}+a_{1}n^{k-1}+\cdots+a_{k}}{n^{k+1}+b_{1}n^{k}+\cdots+b_{k+1}}+O \biggl(\frac{1}{n^{2k+3}} \biggr) \biggr\} ,\quad n\to\infty, $$ where k≥0$k\geq0$ is any given integer. Based on the obtained result, we establish a more accurate formula for approximating π, which refines some known results.
Padé approximant related to remarkable inequalities involving trigonometric functions
In this paper we, respectively, give simple proofs of some remarkable trigonometric inequalities, based on the Padé approximation method. We also obtain rational refinements of these inequalities. We are convinced that the Padé approximation method offers a general framework for solving many other similar inequalities.
In-services and empty threats: The roles of organizational practices and workplace experiences in shaping U.S. educators' understandings of students' rights.
This paper applies theoretical frameworks from organizational sociology and sociolegal studies to examine factors associated with educators' conceptions of students' rights to due process in disciplinary actions. We analyze a unique representative data set of 402 teachers and 200 administrators in U.S. high schools to investigate how educators understand the rights to due process articulated in the Supreme Court case of Goss v. Lopez (1975). We then examine whether individual characteristics and participation in organizational processes are associated with educators' understandings of students' due process rights. Findings suggest that educators' understandings of students' entitlements to due process vary with educators' level of education, experience of school-related legal threats, and participation in district or diocese in-service training programs on students' rights. Results point to organizational climate as a key factor in shaping educators' rights conceptions and the role of law in American schools.