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 generated by T-functions.Utilizing the parameters

the connection between criteria of single cycle T-functions in two different theories is established.The situation each criterion is suited for is cleared.On the other hand

we define the notion of entropy preservability 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 sequences and show the transitivity.