We study the definability of ultrafilter bases on $$\omega $$ in sense descriptive set theory. As a main result we show that there is no coanalytic base for Ramsey ultrafilter, while L can construct $$\Pi ^1_1$$ P-point and Q-point bases. also existence $${\varvec{\Delta }}^1_{n+1}$$ equivalent to $${\varvec{\Pi }}^1_n$$ base, $$n \in \omega . Moreover introduce Borel version classical number m...

p. 1 Redundancy Criteria for Constrained Completion p. 2 Bi-rewriting, a Term Rewriting Technique for Monotonic Order Relations p. 17 A Case Study of Completion Modulo Distributivity and Abelian Groups p. 32 A Semantic Approach to Order-Sorted Rewriting p. 47 Distributing Equational Theorem Proving p. 62 On the Correctness of a Distributed Memory Grobner Basis Algorithm p. 77 Improving Transfor...

the hydration of biomolecules is vitally important in molecular biology, so in this paper thesolvation energy and radial distribution function of dna bases have been calculated by themonte carlo simulation.the geometries of isolated adenine, guanine, cytosine, and thyminehave been optimized using 6-31+g(d,p) basis function sets. these geometries then will be used inthe monte carlo calculation o...