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In 1980s, Thurston established a topological characterization theorem for postcritically finite rational maps. In this paper, a decomposition theorem for a class of postcritically infinite branched covering termed Herman map is developed. It's shown that every Herman map can be decomposed along a stable multicurve into finitely many Siegel maps and Thurston maps, such that the combinations and rational realizations of these resulting maps essentially dominate the original one. This result is motivated by a non-expanding version of McMullen's problem, and Thurston's theory on characterization of rational maps. It enables us to prove a Thurston-type theorem for rational maps with Herman rings.  相似文献
2.
Comparison of two-sample heteroscedastic single-index models, where both the scale and location functions are modeled as single-index models, is studied in this paper. We propose a test for checking the equality of single-index parameters when dimensions of covariates of the two samples are equal. Further, we propose two test statistics based on Kolmogorov–Smirnov and Cramér–von Mises type functionals. These statistics evaluate the difference of the empirical residual processes to test the equality of mean functions of two single-index models. Asymptotic distributions of estimators and test statistics are derived. The Kolmogorov–Smirnov and Cramér–von Mises test statistics can detect local alternatives that converge to the null hypothesis at a parametric convergence rate. To calculate the critical values of Kolmogorov–Smirnov and Cramér–von Mises test statistics, a bootstrap procedure is proposed. Simulation studies and an empirical study demonstrate the performance of the proposed procedures.  相似文献
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The main objective of this paper is to propose a product approximation for the Gamma function in the form of continued fraction, via the Tri-gamma function. The importance of this new formula is that the convergence of the corresponding asymptotic series is faster than other recently discovered asymptotic series, and some new inequalities related to the new formula are also established.  相似文献
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变点危险率模型已受到广泛关注.它不仅可以更加直接地显示治疗效果或医学上的突破,也可以提供这些事件发生的时间点.在这篇文章中,我们提出当前状态数据下的单边点危险率治愈模型并探讨了这个模型的估计方法.我们建立了估计的大样本理论并通过模拟评估有限样本下的估计.  相似文献
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