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A Monte Carlo Evaluation Of A Nonparametric Technique For Estimating The Hazard Function, Sheng Jia Lin

All Graduate Plan B and other Reports, Spring 1920 to Spring 2023

This research is primarily concerned with the estimation of the Hazard functions, the Hazard function is the failure rate at time t, and is defined as -R '(t)/R(t), so it plays an important role in Reliability.

In order to compare and evaluate the estimation methods, it is convenient to select one distribution in this research. Since the Weibull distribution is a useful distribution in Reliability, the Weibull distribution is used in this paper.

Torus Knots, David S. Bradley

All Graduate Plan B and other Reports, Spring 1920 to Spring 2023

We have compiled here many interesting results concerning a particular collection of knots called torus knots. Torus knots are merely simple closed curves imbedded in an unknotted torus T² in E³. We show that the fundamental groups of T², π(T²), is the direct product of the additive group of integers with itself. The ordered pair (p, q) in Z x Z determines an equivalence class of loops on the torus, and we show in Section II that the class [(p, q)] contains a loop whose image is a simple closed curve if and …