中文摘要：

本文结合传统T函数理论与非阿基米德T函数理论,深入研究T函数的性质特点,重点讨论一致可微T函数的单圈性及最高位序列的保熵性.首次利用参数的概念建立传统T函数理论中单字T函数单圈性判定条件与非阿基米德T函数理论中单圈性判定条件的联系,说明了两类判定条件的适用范围.定义了对T函数生成序列进行压缩变换的保熵性概念,讨论了一致可微T函数最高位序列的保熵性,说明了一致可微的T函数保熵性具有传递性,给出了T函数最高位序列保熵性的判定条件.

英文摘要：

Combining conventional theory with non-Archimedean theory, we study the properties of T-functions. We focus on the criteria of single cycle T-functions and entropy preservability of the most significant bit output sequence genera- ted by T-functions. Utilizing the parameters, the connection between criteria of single cycle T-functions in two different theo- ries is established. The situation each criterion is suited for is cleared. On the other hand, we define the notion of entropy pre- servability of T-functions. We talk about the entropy preservability of most significant bit output sequences generated by T- functions with uniform differentiability. We present the condition for entropy preservability of most significant bit output se- auences and show the transitivity.