Pseudo-holomorphic maps and bubble trees

This paper proves a strong convergence theorem for sequences of pseudo-holomorphic maps from a Riemann surface to a symplectic manifoldN with tamed almost complex structure. (These are the objects used by Gromov to define his symplectic invariants.) The paper begins by developing some analytic facts about such maps, including a simple new isoperimetric inequality and a new removable singularity theorem. The main technique is a general procedure for renormalizing sequences of maps to obtain “bubbles on bubbles.” This is a significant step beyond the standard renormalization procedure of Sacks and Uhlenbeck. The renormalized maps give rise to a sequence of maps from a “bubble tree”—a map from a wedge Σ V S² V S² V ... →N. The main result is that the images of these renormalized maps converge in L^1,2 ∪C° to the image of a limiting pseudo-holomorphic map from the bubble tree. This implies several important properties of the bubble tree. In particular, the images of consecutive bubbles in the bubble tree intersect, and if a sequence of maps represents a homology class then the limiting map represents this class.     

Synthesis of ansamycins: An approach to the naphthoquinone portion of the rifamycins and streptovaricins

Naphthoquinone $\text{1}$, a fully functionalized model for intermediates in ansamycin synthesis, was prepared by the intramolecular Claisen condensation of benzofuran $\text{9}$ followed by oxidation of the novel tricyclic compound $\text{10}$.     

Self-assembly of flexible supramolecular metallacyclic ensembles: structures and adsorption properties of their nanoporous crystalline frameworks

The syntheses, structures, and N2 adsorption properties of six new supramolecular metallacycles are reported. Flexible ditopic linkers, 1-4, with systematically varied lengths and conformational degrees of freedom were synthesized utilizing ester linkages. They were used in combination with (dppp)M(OTf)2, where M = Pt(II) and Pd(II), and cis-(Me3P)2Pt(OTf)2 to form flexible supramolecular metallacycles 5-10 in 88-98% isolated yields. Their structures were characterized via multinuclear NMR and X-ray crystallography. The metallacycles stack to form porous structures in the crystalline state. The pore dimensions depend on both the phosphorus ligands attached to the metals and the flexible linkers. Adsorption studies on the porous materials show that 5a, 6, 8, and 9 held 11.7, 16.5, 5.7, and 6.8 cm3/g STP of N2 at 77 K, respectively. A guest-exchange study with nitromethane and toluene reveals that the nanopore in 5 is flexible, a property which was transferred from the linker to the supramolecular structure in the solid state.     

Syntheses and degradations of fluorinated heterocyclics III. Perfluoroalkyl and perfluoroalkylether-1,3,4-oxadiazoles

2,5-Bis(perfluoro-n-heptyl)-, 2-perfluoroalkylether-5-perfluoro-n-heptyl-, and 2,5-bisperfluoroalkylether-1,3,4-oxadiazoles were synthesized and characterized. 2,5-Bis(perfluoro-n-heptyl)-1,3,4-oxadiazole was thermally and hydrolytically stable at 325°C; however, in the presence of air, degradation took place at 235°C. The perfluoroalkylether analogue exhibited thermal and hydrolytic stability at 325°C; it was found to be unaffected by Jet-A fuel and air at 235°C. At 325°C in air some degradation occured as evidenced by volatiles production, oxygen consumption, and 96% starting material recovery.