Factorization of holomorphic mappings on -spaces

We prove a universal mapping theorem for a large class of holomorphic mappings on a -space, stating that can be locally written in the form where and are bounded linear operators on certain Banach spaces consisting of functions on , and the division is taken pointwise.

     

Solid-phase synthesis of 1,2,3-triazoles via 1,3-dipolar cycloaddition

The solid-phase synthesis of 1,2,3-triazoles via 1,3-dipolar cycloaddition of polymer-bound azides to various alkynes is reported. Polymer-bound azides were synthesized from polymer-bound halides and sodium azide and reacted with alkynes to produce polymer-bound 1,2,3-triazoles. Cleavage of the triazoles was performed with trifluoroacetic acid. A traceless synthesis of 1,2,3-triazoles was developed using 2-methoxy-substituted resin (polymer-bound 4-hydroxy-2-methoxybenzyl alcohol). In addition, a synthesis of 4-hydroxybenzyl-substituted 1,2,3-triazoles from the bromo-Wang resin (4-(bromomethyl)phenoxymethyl polystyrene) was achieved.     

Anionic liposomes in capillary electrophoresis: Effect of calcium on 1-palmitoyl-2-oleyl-<Emphasis Type="Italic">sn</Emphasis>-glycero-3-phosphatidylcholine / phosphatidylserine-coating in silica capillaries

The effect of calcium on phospholipid coatings in fused silica capillaries used in capillary electrophoresis was studied. The anionic liposomes used for the coating consisted of 3 mM 1-palmitoyl-2-oleyl-sn-glycero-3-phosphatidylcholine and phosphatidylserine in the ratio 80/20 mol%. Coating was performed as part of the preconditioning, and the capillaries could be used for several runs without the need for liposomes in the background electrolyte solution or for liposome rinses between runs. Phospholipids could easily be flushed away by rinsing with a chloroform-methanol (2:1 v/v) mixture, which made it possible to recoat and reuse the capillaries. A calcium:phospholipid ratio of approximately 3 gave the most stable coating. The stability of the coating and success of the coating procedure were studied by measuring the electroosmotic flow and by separating uncharged steroids, which were used as model compounds. Many parameters that affect the coating, such as preconditioning (with different acids and bases), buffer, temperature during coating, and the physical structures of liposomes, were studied, with and without calcium in the liposome solution. The separation of steroids was improved and was less dependent on coating conditions when calcium was present during the coating. Capillaries optimally coated with anionic phospholipids were applied in the separation of phenols.     

Exploring the scope of the 29G12 antibody catalyzed 1,3-dipolar cycloaddition reaction

[Chemical reaction: See text] 29G12 is a murine monoclonal antibody programmed to catalyze the regio- and enantioselective 1,3-dipolar cycloaddition reaction between 4-acetamidobenzonitrile N-oxide 1a and N,N-dimethylacrylamide 2a (Toker, J. D.; Wentworth, P., Jr.; Hu, Y.; Houk, K. N.; Janda, K. D. J. Am. Chem. Soc. 2000, 122, 3244). Given the unique nature of 29G12 as a protein biocatalyst for this chemical reaction, we have investigated both the substrate specificity and mechanistic parameters of the 29G12-catalyzed process. These studies have shown that while 29G12 is specific for its dipole substrate 1a, the antibody is highly promiscuous with respect to the dipolarophiles it can process. 29G12 accepts a bulky hydrophobic dipolarophile cosubstrate, with rates of product formation up to 70-fold faster than with the original substrate 2a. In all cases, the respective isoxazoline products are produced with exquisite regio- and stereochemical control (78-98% ee). Comparison between the steady-state kinetic parameters from the 29G12-catalyzed reaction of 1a with the most efficient versus the original dipolarophile cosubstrate (2m and 2a, respectively), reveals that while the effective molarities (EM)s are almost identical (EM(2m)) 26 M; EM((2a)) 23 M), the affinity of 29G12 for the larger dipolarophile 2m is more than 1 order of magnitude higher than for 2a [Km(2m) 0.44 +/- 0.04 mM; Km(2a) 5.8 +/- 0.4 mM]. Furthermore, when 2m is the cosubstrate, the affinity of 29G12 for its dipole 1a is also greatly improved [Km(1a) 0.82 +/- 0.1 mM compared to Km(1a) 3.4 +/- 0.4 mM when 2a is the cosubstrate]. An analysis of the temperature dependence of the 29G12-catalyzed reaction between 1a and 2m reveals that catalysis is achieved via a decrease in enthalpy of activation (DeltaDeltaH 4.4 kcal mol(-1)) and involves a large increase in the entropy of activation (DeltaDeltaS 10.4 eu). The improved affinity of 29G12 for the nitrile oxide 1a in the presence of 2m, coupled with the increase in DeltaDeltaS during the 29G12-catalyzed reaction between 1a and 2m supports the notion of a structural reorganization of the active site to facilitate this antibody-catalyzed reaction.     

Immobilization of phospholipid-avidin on fused-silica capillaries for chiral separation in open-tubular capillary electrochromatography

Phospholipid-coated fused-silica capillaries with immobilized avidin were applied in the chiral separation of D,L-tryptophan, D,L-PTH-serine, and D,L-PTH-threonine at pH 7.4 by open-tubular CEC. Liposomes prepared from 1,2-dipalmitoyl-sn-glycero-3-phosphocholine, 1,2-dipalmitoyl-sn-glycero-3-phosphoethanolamine-N-(Cap biotinyl), or 1,2-dipalmitoyl-sn-glycero-3-phosphoethanolamine-N-(Biotinyl) with different amounts of phosphatidylserine were assessed as phospholipid coating materials. The stability of the coating and the success of the coating procedure were evaluated in terms of the repeatability of the enantiomer migration times and the resolution of enantiomers. The coating procedure itself significantly affected the migration times and resolution of the enantiomers. Reliable chiral separations with high separation efficiencies were achieved through careful choice of the coating method.     

On generalized Toeplitz and little Hankel operators on Bergman spaces

We find a concrete integral formula for the class of generalized Toeplitz operators \(T_a\) in Bergman spaces \(A^p\), \(1<p<\infty \), studied in an earlier work by the authors. The result is extended to little Hankel operators. We give an example of an \(L^2\)-symbol a such that \(T_{|a|} \) fails to be bounded in \(A^2\), although \(T_a : A^2 \rightarrow A^2\) is seen to be bounded by using the generalized definition. We also confirm that the generalized definition coincides with the classical one whenever the latter makes sense.     

Solid-phase synthesis of pyrazolopyridines from polymer-bound alkyne and azomethine imines

Study was made of the 1,3-dipolar cycloaddition of polymer-bound alkynes to azomethine imines generated in situ from N-aminopyridine iodides. Aromatization of the cycloadducts gives polymer-bound pyrazolopyridines that can be released from the resin as carboxylic acids with trifluoroacetic acid or as methyl esters with sodium methoxide.