Long‐chain‐branched polyethene by the copolymerization of ethene and nonconjugated α,ω‐dienes

Ethene was copolymerized (1) with 1,5‐hexadiene with rac‐ethylenebis(indenyl)zirconium dichloride/methylaluminoxane (MAO) used as a catalyst and (2) with 1,7‐octadiene with bis(n‐butylcyclopentadienyl)zirconium dichloride/MAO and rac‐ethylenebis(indenyl)hafnium dichloride (Et[Ind]₂HfCl₂)/MAO used as catalysts at 80 °C in toluene. The copolymer microstructure and the influence of diene incorporation on the rheological properties were examined. Ethene and 1,5‐hexadiene formed a copolymer in which a major fraction of the 1,5‐hexadiene was incorporated into rings and a small fraction formed 1‐butenyl branches. The copolymerization of ethene with 1,7‐octadiene resulted in a higher selectivity toward branch formation. Some of the branches formed long‐chain‐branching (LCB) structures. The ring formation selectivity increased with decreasing ethene concentration in the polymerization reactor. Melt rheological properties of the diene copolymers resembled those of metallocene‐catalyzed LCB homopolyethenes and depended on the vinyl content, the catalyst, and the polymerization conditions. At high diene contents, all three catalysts produced crosslinked polyethene. This was especially pronounced with Et[Ind]₂HfCl₂, where only 0.2 mol % 1,7‐octadiene in the copolymer was required to achieve significantly modified rheological properties. © 2001 John Wiley & Sons, Inc. J Polym Sci Part A: Polym Chem 39: 3805–3817, 2001     

Numerical valuation of options under Kou's model

Numerical methods are developed for pricing European and American options under Kou's jump-diffusion model which assumes the price of the underlying asset to behave like a geometrical Brownian motion with a drift and jumps whose size is log-double-exponentially distributed. The price of a European option is given by a partial integro-differential equation (PIDE) while American options lead to a linear complementarity problem (LCP) with the same operator. Spatial differential operators are discretized using finite differences on nonuniform grids and time stepping is performed using the implicit Rannacher scheme. For the evaluation of the integral term easy to implement recursion formulas are derived which have optimal computational cost. When pricing European options the resulting dense linear systems are solved using a stationary iteration. Also for pricing American options similar iterations can be employed. A numerical experiment demonstrates that the described method is very efficient as accurate option prices can be computed in a few milliseconds on a PC. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

bb̄-fragmentation and Bπ correlations

We show that experimental data are in very good agreement with predictions from the string fragmentation model by Bowler and Morris. We present a physical interpretation and discuss the relation to results obtained from Perturbative QCD and Local Hadron Parton Duality (LPHD). We also present implications for Bar correlations and the possibility to use these as a tag to study CP violation in B decays.     

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.     

Estimation of the Relative Stabilities of the E,Z-Isomers of α,β-Dialkylsubstituted Methyl Vinyl Ethers by Various Computational Methods

The relative thermodynamic stabilities (relative enthalpies) of the E,Z-isomers of ,-dialkylsubstituted methyl vinyl ethers MeOC(R₁)=CHR₂ have been estimated by various computational methods including molecular mechanics, semiempirical, ab initio, and DFT calculations. The best performance, approaching the accuracy of the experimental method of chemical equilibration, is shown by the DFT calculations. Ab initio methods, provided that electron correlation is taken into account, are also satisfactory, but clearly less successful than the DFT calculations. The reliability of the semiempirical methods AM1 and PM3 is considerably less good, and varies in an unpredictable manner from case to case. The poorest general performance is shown by the MM2 and MM3 calculations, which may overestimate the relative stability of the Z isomer by as much as 18 kJ mol^–1.     

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.     

CoMFA modeling of human catechol O-methyltransferase enzyme kinetics

Three-dimensional QSAR models with different charge calculation methods (MOPAC-AM1-ESP, MOPAC-AM1-Coulson and Gasteiger-Hückel) were developed for predicting all three enzyme kinetic parameters Km, Vmax and Vmax/Km for catecholic substrates of human soluble catechol O-methyltransferase (S-COMT). The empirical parameters of 45 substrates were correlated to the steric and electronic molecular fields of the substrates utilizing Comparative Molecular Field Analysis (CoMFA). Alignment rules for CoMFA were developed based on the catalytic mechanism and crystal structure of S-COMT, and the analysis was optimized using an all-space search technique. Leave-one-out and leave-n-out cross-validation (with 5 and 10 cross-validation groups) was carried out, and all developed models proved to be statistically significant with q2 values up to 0.84. The models based on MOPAC charge calculations predicted the empirical values clearly better than the Gasteiger-Hückel method. The derived CoMFA coefficient contour maps of steric and electrostatic interactions correlated clearly with the S-COMT crystallographic structures.