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.     

Identification of 4-amino-4-deoxychorismate synthase as the molecular target for the antimicrobial action of (6s)-6-fluoroshikimate

(6S)-6-Fluoroshikimate has antimicrobial activity. The molecular basis of this effect had not been identified, but there was speculation that (6S)-6-fluoroshikimate is first converted in vivo into 2-fluorochorismate, which then could inhibit 4-amino-4-deoxychorismate synthase (ADCS). 2-Fluorochorismate was prepared from E-fluorophosphoenolpyruvate and erythose-4-phosphate by the sequential reactions of DAHP synthase, dehydroquinate synthase, dehydroquinase, shikimate dehydrogenase, EPSP synthase, and chorismate synthase. Inhibition studies on ADCS showed that it was inhibited rapidly and irreversibly by 2-fluorochorismate. Electrospray mass spectrometry of the inactivated enzyme showed an additional mass of 198 +/- 10 Da. A novel peptide of 1087.6 Da was identified in the HPLC trace for the tryptic digest of 2-fluorochorismate-inactivated ADCS. Sequencing of this peptide by MS/MS showed that the peptide corresponded to residues 272-279 with a modification of 206.1 Da on Lys-274. This observation is particularly exciting in the context of a recent proposal for the catalytic mechanism of ADCS.     

The different steric environments of the 5-exo- and 5-endo- substituent for a pair of isomeric tricarbonyl(methoxycyclohexa-1,-diene)irons

A shift reagent has been employed to demonstrate the sterically-hindered environment of the methoxy group in tricarbonyl(5-endo-methoxycyclohexa-1,-diene)iron relative to that of the methoxy group in the 5-exo analogue.     

Resolution of the non-steady-state kinetics of the two-step mechanism for the Diels-Alder reaction between anthracene and tetracyanoethylene in acetonitrile

The Diels-Alder reaction between anthracene and tetracyanoethylene in acetonitrile does not reach a steady-state during the first half-life. The reaction follows the reversible consecutive second-order mechanism accompanied by the formation of a kinetically significant intermediate. The experimental observations consistent with this mechanism include extent of reaction-time profiles which deviate markedly from those expected for the irreversible second-order mechanism and initial pseudo first-order rate constants which differ significantly from those measured at longer times. It is concluded that the reaction intermediate giving rise to these deviations cannot be the charge-transfer (CT) complex, which is formed during the time of mixing, but rather a more intimate complex with a geometry favorable to the formation of the Diels-Alder adduct. The kinetics of the reaction were resolved into the microscopic rate constants for the individual steps. The rate constants, as shown in equation 1, at 293 K were observed to be 5.46 M(-)(1) s(-)(1) (k(f)), 14.8 s(-)(1) (k(b)), and 12.4 s(-)(1) (k(p)). Concentration profiles calculated under all conditions show that intermediate concentrations increase to maximum values early in the reaction and then continually decay during the first half-life. It is concluded that the charge-transfer complex may be an intermediate preceding the formation of the reactant complex, but due to its rapid formation and dissociation it is not detected by the kinetic measurements.     

Free energy of adsorption of water and calcium on the [10 1 4] calcite surface

Molecular dynamics simulations of the calcite-water interface have shown that the free energy of adsorption of water is relatively small compared to the previously calculated enthalpy of adsorption implying a large entropy change and that the free energy profile of a calcium adsorbing on the surface correlates with the solvent density; these calculations allow us to begin to address the rates of adsorption and desorption which are essential for studying growth and dissolution.     

PHOTOREACTION OF BENZ(A)PYRENE IN SOLUTIONS CONTAINING POLYMER

Abstract— An unusual photo-reaction of benz(a)pyrene has been investigated by measuring prompt and delayed fluorescence spectra. The proposed mechanism involves adsorption of triplet benz(a)pyrene by the polymer and its reaction to give substitution products. Further work is in progress with pyrene, which also undergoes photo-reaction in the presence of polymer.