A Comparison of Two Variational Methods

A discussion is given of the relation between the maximum functionaltheorem and Schwinger's variational principle, and it is shownthat the bound given by Schwinger's principle is better thanor the same as that given by the maximum functional theorem.     

Rescue of an abasic hairpin ribozyme by cationic nucleobases: evidence for a novel mechanism of RNA catalysis

The hairpin ribozyme catalyzes a reversible phosphodiester cleavage reaction. We examined the roles of conserved nucleobases in catalysis using an abasic ribozyme rescue strategy. Loss of the active site G8 nucleobase reduced the cleavage rate constant by 350-fold while loss of A9 and A10 nucleobases reduced activity less than 10-fold. Certain heterocyclic amines restored partial activity when provided in solution to the variant lacking G8. Heterocyclic amines that were capable of rescue shared the exocyclic amine and cyclic amide in common with the Watson-Crick hydrogen bonding face of guanine. In contrast to the shallow pH dependence of unmodified ribozyme activity, rescue activity increased sharply with decreasing pH. These results support a novel model for RNA catalysis in which a cationic nucleobase contributes electrostatic stabilization to negative charge developing in the transition state.     

Further Gurtin-type Variational Principles for Linear Initial Value Problems

Following the variational principles for linear initial valueproblems associated with the wave and heat conduction equationsdiscussed by Gurtin and Leitmann and using time convolutionsit is shown that general variational principles exist for theseproblems with sources on the boundaries and within the regionunder consideration.     

Modified Locally One Dimensional Methods for Parabolic Partial Differential Equations in Two Space Variables

In this note we consider the locally one dimensional methodas discussed in Gourlay & Mitchell (1969, 1972) and indicatehow this scheme can be used to solve accurately a parabolicpartial differential equation in two space variables.