On finite action solutions of the nonlinear σ-model

The instanton and anti-instanton solutions of the two-dimensional O(3) σ-model are special examples of harmonic maps, which have been studied extensively in the mathematical literature. We give an elementary and self-contained proof that these solutions are the only continuous maps for which the action is finite and stationary under variations, without assuming any additional boundary conditions at infinity. An element of the proof is the vanishing of the stress tensor for a finite action solution, which actually holds true for the general O(N) σ-model. For the two-dimensional O(2l + 1) σ-model we exhibit explicit finite action solutions that do not lie in any lower dimensional sphere; the existence of such solutions has been pointed out in the mathematical literature. We also present a rigorous proof, based on Derrick's scaling argument, that there are no nonconstant finite action solutions in more than two dimensions.     

Über die Äquivalenz von diskreten und kontinuierlichen Cesàro-Verfahren bei Funktionen vom Exponentialtyp

Ohne Zusammenfassung     

Novel penicillins synthesized by biotransformation using laccase from Trametes spec

Eight novel penicillins were synthesized by heteromolecular reaction of ampicillin or amoxicillin with 2,5-dihydroxybenzoic acid derivatives using a laccase from Trametes spec. All products inhibited the growth of several gram positive bacterial strains in the agar diffusion assay, among them methicillin-resistant Staphylococcus aureus and vancomycin-resistant Enterococci. The products protected mice against an infection with Staphylococcus aureus lethal to the untreated animals. Cytotoxicity and acute toxicity of the new compounds were neglectable. The results show the usefulness of laccase for the synthesis of potential new antibiotics. The biological activity of the new compounds stimulates intensified pharmacological tests.     

Creation of an atomic superlattice by immersing metallic adatoms in a two-dimensional electron sea

Cerium adatoms, deposited on a Ag(111) surface, are found by low-temperature scanning tunneling microscopy to self-assemble into large ordered hexagonal arrays covering macroscopically the entire surface. We show that the 32 A periodicity of the superlattice is caused by the interaction of surface-state electrons with Ce adatoms and that the large-scale formation of the superlattice is governed by a subtle balance between the sample temperature, the surface diffusion barrier, and the concentration-dependent adatom interaction potential.