On the connection between harmonic maps and the self-dual Yang—Mills and the sine-Gordon equations

This is an algebraic paper which demonstrates some algebraic connections between the Yang—Mills and the sine-Gordon equation.     

Steric interference modification of the hammerhead ribozyme

Although the structure of the hammerhead ribozyme is well characterized, many questions remain about its catalytic mechanism. Extensive evidence suggests the necessity of a conformational change en route to the transition state. We report a steric interference modification approach for investigating this change. By placing large 2' modifications at residues insensitive to structurally conservative 2'-deoxy modifications, we hoped to discover structural effects distal to the site of modification. Of twenty residues tested, six were identified where the addition of 2' bulk inhibits cleavage, even though these bulky modifications could be accommodated in the crystal structure without steric clash. It is proposed that these 2'-modifications inhibit cleavage by preventing formation of the alternate, active conformation. Since these 2' effects are present in both domain I and domain II of the hammerhead, the entire catalytic core must undergo conformational changes during catalysis.     

The ideal Bose-Einstein gas,revisited

Some questions concerning the ideal Bose-Einstein gas are reviewed and examined further. The bulk behavior including the condensation phenomenon is characterized by the thermodynamical properties, occupations of the states and their fluctuations, and the properties of the density matrices, including the diagonal and off-diagonal long range orders. Particular attention is focused on the difference between the canonical and grand canonical ensembles and a case is made that the latter does not represent any physical system in the condensed region. The properties in a finite region are also examined to study the approach to the bulk limit and secondly to derived the surface properties such as the surface tension (due to the boundary). This is mainly done for the special case of a rectangular parallelopiped (box) for various boundary conditions. The question of the asymptotic behavior of the fluctuations in the occupation of the ground state in the condensed region in the canonical ensemble is examined for these systems. Finally, the local properties near the wall of a half infinite system are calculated and discussed. The surface properties also follow this way and agree with the strictly thermodynamic result. Although it is not intended to be a complete review, it is largely self-contained, with the first section containing the basic formulas and a discussion of some general concepts which will be needed. Especially discussed in detail are the extra considerations that are needed in thermodynamics and statistical mechanics to include the surface properties, and the quantum hierarchy of the density matrices and local conservation laws. In the concluding remarks several problems are mentioned which need further analysis and clarification.     

The Chern classes of Sobolev connections

AssumeF is the curvature (field) of a connection (potential) onR ⁴ with finiteL ² norm . We show the chern number (topological quantum number) is an integer. This generalizes previous results which showed that the integrality holds forF satisfying the Yang-Mills equations. We actually prove the natural general result in all even dimensions larger than 2.