Some Questions on Pei's "Giant Ape"

Some Questions on Unique

The simplest type of integral extension of a unique factorization domain B is obtained by adjoining to B an n-th root of one of its elements; that is, by forming the ring Bn = B[z]=(z n g), where n 2 Z and g 2 B. When n = 1, Bn = B. When n 2 it is natural to ask for what g 2 B will unique factorization be preserved? The case where B is a polynomial ring over an algebraically closed eld k immedi...

Some Questions

These are some questions I am every interested in. Your solution to any question in this draft would be welcome. I keep updating this draft. 1. Classical recursion theory We use R to denote the partial ordering of r.e. degrees and Dn to denote the partial ordering of n-r.e. degrees. Yang and I proved thatR is not a Σ1-substructure of Dn. Question 1.1 (Khoussainov). For n > 1, is there a functio...

E-Learning: some unanswered questions

Giant Chloroviruses: Five Easy Questions

Chloroviruses are large, icosahedral, dsDNA-containing viruses that replicate in certain unicellular, chlorella-like green algae [1,2]. They exist in freshwater throughout the world with titers as high as thousands of plaque-forming units (PFU) per ml of indigenous water although titers are typically 1–100 PFU/ml. Titers fluctuate during the year with the highest titers typically occurring in t...

On Some Questions of Rationality and Decidability

In this note we begin by resolving (in the negative) a question posed by Paz [6, Open Problem 1, p. 65] concerning the existence of an effective procedure for determining whether a recursively specified "probabilistie input-output relation" is of finite rank. To show that such an algorithm does not exist, it is enough to prove the undecidability of the corresponding problem for "probabilistic w...