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.     

The role of additional solvents in transition metal complex catalyzed asymmetric reductions in ionic liquid containing systems

When ionic liquids (ILs) are employed as solvents for transition metal complex (TMC) catalyzed reductions, a second solvent can be added to increase the efficiency of the catalytic cycle and the solubility of the reactant in the IL phase. Two industrially relevant asymmetric hydrogenations, the enantioselective reductions of methyl 2-acetamidoacrylate with Rh-EtDuPHOS and methyl acetoacetate with Ru-BINAP, were performed in different catalytic systems including 1-butyl-3-methylimidazolium hexafluorophosphate/ tetrafluoroborate as ILs. Product separation and TMC recycling was performed by extracting the product from the reaction mixture. This can be accomplished by cooling the system, by adding an excess of the second solvent or by adding a third solvent. A high solubility of the second solvent in the IL catalytic phase favors the reaction activity, but can induce leaching of the IL and TMC.     

Immobilized Glucose Oxidase in the Potentiometric Detection of Glucose

Previous work has shown that glucose oxidase can be immobilized on platinum to give an electrode that responds potentiometrically to glucose over the clinically useful range of about 10-250 mg glucose/100 mL. The present studies were carried out with electrochemically pretreated platinum and with gold or porous graphite substituted for the platinum support. The presence of the enzyme gave a significantly enhanced potentiometric response over that obtained with the bare support for both the pretreated platinum and the porous graphite, but not with gold. However, with platinum the potentiometric response became more negative with increasing glucose concentration. With porous graphite, the potential changed in the positive direction as the glucose concentration was increased. Hysteresis was demonstrated for the platinum-enzyme electrode. Mass transfer measurements with a rotating ring-disc electrode (RRDE) showed measurable diffusional resistances to the transport of a model electroactive compound (potassium ferrocyanide) through a matrix of immobilized enzyme attached to the disc of the RRDE. These results are part of a larger study to define the source of the potentiometric response by examining the roles of the support and the mass transfer resistances through the immobilized enzyme matrix.