In the fourth and fifth chapters of this paper , we discuss the schwarzian derivatives of analytic functions , the nehari families and the extremal set of schwarzian derivatives , and apply the obtained results to determine the inner radius of univalence of rectangles and hexagons with equal angles 在第四章和第五章中，对解析函数的schwarz导数和nehari族以及schwarz导数的极值集作了深入细致的研究，并且利用所得到的结果研究了矩形、等角六边形的单叶性内径问题。
The dynamics is described by the glauber - type stochastic progress with the single - spin transition meehanism and disposed approximately by weighted average method in which we add a corresponding weight to each possible configuration . we obtain not only the exact analytical solutions of the time dependent magnetization and equal time spin - pair correlation functions , but also the analytical temperature dependent dynamical relaxation function 通过采用加权平均的近似处理方法，也就是对各种可能出现的跃迁几率赋一个相应的权重，我们不仅可以得到随时间演化的磁化强度和等时对关联的解析解，还得到了系统驰豫时间的温度解析函数。
We compare the approximation of an analytic function f by its taylor polynomial and its poisson partial sum with the same number of terms and illustrate that for functions with limit zero at infinity and for bounded functions the poisson expansion provides a better approximation to the function than the taylor expansion 在第三章中，介绍了rb曲线与poisson曲线的概念以及基本的几何性质，指出了poisson基函数与有理bernstein基函数之间存在的关系，并且将解析函数的taylor逼近与poisson逼近进行比较。实例表明，对于在无穷远处极限为0的函数以及有界函数， poisson逼近比taylor逼近效果要好。
The theory of schwarzian derivatives has great significance in determining whether a conformal mapping has quasiconformal extensions , in estimating the inner radius of uni - valence of a domain and in discussing the properties of some conformal mapping families . the study of these key problems will be very important to the development of the theory of quasiconformal mappings Schwarz导数在判定共形映射能否拟共形延拓、估计区域的单叶性内径以及探讨一些解析函数族的性质方面有非常重要的作用，对这些热点问题的研究将对拟共形映射理论的发展起着积极的作用。
