Pairs of oblique duals in spaces of periodic functions

We construct non-tight frames in finite-dimensional spaces consisting of periodic functions. In order for these frames to be useful in practice one needs to calculate a dual frame; while the canonical dual frame might be cumbersome to work with, the setup presented here enables us to obtain explicit constructions of some particularly convenient oblique duals. We also provide explicit oblique duals belonging to prescribed spaces different from the space where we obtain the expansion. In particular this leads to oblique duals that are trigonometric polynomials.     

Highly enantioselective alkynylzinc addition to aromatic aldehydes catalyzed by self-assembled titanium catalysts

A highly enantioselective catalyst generated by a combination of BINOL and another ligand with Ti(OiPr)4 was found to be highly effective for the alkynylzinc addition to aromatic aldehydes with enantioselectivities as high as >99%.     

Catalytic hydrogenation of arenes with rhodium nanoparticles in a water-in-supercritical CO2 microemulsion

Rhodium nanoparticles dispersed by a CO2 microemulsion are effective catalysts for rapid hydrogenation of arenes in supercritical CO2.     

High-throughput approaches for the discovery and optimization of new olefin polymerization catalysts

The discovery of new olefin polymerization catalysts is currently a time-intensive trial-and-error process with no guarantee of success. A fully integrated high-throughput screening workflow for the discovery of new catalysts for polyolefin production has been implemented at Symyx Technologies. The workflow includes the design of the metal-ligand libraries using custom-made computer software, automated delivery of metal precursors and ligands into the reactors using a liquid-handling robot, and a rapid primary screen that serves to assess the potential of each metalligand-activator combination as an olefin polymerization catalyst. "Hits" from the primary screen are subjected to secondary screens using a 48-cell parallel polymerization reactor. Individual polymerization reactions are monitored in real time under conditions that provide meaningful information about the performance capabilities of each catalyst. Rapid polymer characterization techniques support the primary and secondary screens. We have discovered many new and interesting catalyst classes using this technology.     

Analysis of High-Resolution FTIR Spectrum of the nu6 Band of H13COOH

The FTIR spectrum of the nu6 band of H13COOH has been collected at a resolution of 0.004 cm-1 in the frequency range of 1030-1160 cm-1. The nu6 band was analyzed to be an A-B hybrid band and perturbed by the nearby nu8 band through a-, and b-Coriolis coupling terms. Using a Watson's A-reduced Hamiltonian in the Ir representation, with the inclusion of a- and b-Coriolis resonances, a total of 3004 IR transitions of nu6 have been analyzed to provide rovibrational constants for the v6 = 1 state with a standard deviation of 0.00047 cm-1. The nu6 band was found to be centered at 1095.40365 +/- 0.00003 cm-1. Copyright 1999 Academic Press.     

Dimers from α-alkoxybenzyl radicals. An NMR study

meso and dl Dimers (ArCHOR)₂ where R is Me, Et, ⁱPr, ^tBu, cyclohexyl and 1-adamantyl may readily be differentiated by their NMR spectra; the benzylic protons of the meso isomer always absorb at a slightly higher field than those of the dl isomer in each of the solvents used. Differences in chemical shift are discussed in terms of preferences in conformer distribution. The formation of equal amounts of both dimers from the corresponding radical ArCHOR shows that steric and polar factors are not important in influencing the dimerization. Magnetic non-equivalence due to the presence of asymmetric centres was found in some of the compounds discussed above.