Duality for Finite Hopf Algebras Explained by Corings

We give a coring version for the duality theorem for actions and coactions of a finitely generated projective Hopf algebra. We also provide a coring analogue for a theorem of H.-J. Schneider, which generalizes and unifies the duality theorem for finite Hopf algebras and its refinements. This paper was written while the first author visited the Mathematics Departments of Syracuse University and California State University Dominguez Hills. He would like to thank both departments for their hospitality.     

The effect of a magnetic field on the singlet/triplet ratio in geminate ion recombination

Excited state formation by ion recombination in solutions of fluorene in squalene has been studied by pulse radiolysis at the center of a large electromagnet. The products of the slower part of the ion recombination are affected by an applied magnetic field. The fluorescence yield increases by a factor of about 1.5 whereas the triplet yield decreases.     

Asymmetric total synthesis of rollicosin

[structure: see text] The first total synthesis of rollicosin, a member of a rare subgroup of Annonaceous acetogenins containing two terminal gamma-lactones, is reported. The approach features a highly regio- and stereoselective tandem ring-closing/cross-metathesis reaction for construction of the east-wing lactone and incorporation of the alkyl spacer. Establishment of the C4 stereocenter and addition of the west-wing lactone were achieved by Sharpless asymmetric dihydroxylation and enolate alkylation.     

Understanding the factors controlling the photo-oxidation of natural DNA by enantiomerically pure intercalating ruthenium polypyridyl complexes through TA/TRIR studies with polydeoxynucleotides and mixed sequence oligodeoxynucleotides

Ruthenium polypyridyl complexes which can sensitise the photo-oxidation of nucleic acids and other biological molecules show potential for photo-therapeutic applications. In this article a combination of transient visible absorption (TrA) and time-resolved infra-red (TRIR) spectroscopy are used to compare the photo-oxidation of guanine by the enantiomers of [Ru(TAP)₂(dppz)]²⁺ in both polymeric {poly(dG-dC), poly(dA-dT) and natural DNA} and small mixed-sequence duplex-forming oligodeoxynucleotides. The products of electron transfer are readily monitored by the appearance of a characteristic TRIR band centred at ca. 1700 cm⁻¹ for the guanine radical cation and a band centered at ca. 515 nm in the TrA for the reduced ruthenium complex. It is found that efficient electron transfer requires that the complex be intercalated at a G-C base-pair containing site. Significantly, changes in the nucleobase vibrations of the TRIR spectra induced by the bound excited state before electron transfer takes place are used to identify preferred intercalation sites in mixed-sequence oligodeoxynucleotides and natural DNA. Interestingly, with natural DNA, while it is found that quenching is inefficient in the picosecond range, a slower electron transfer process occurs, which is not found with the mixed-sequence duplex-forming oligodeoxynucleotides studied.

Efficient electron transfer requires the complex to be intercalated at a G-C base-pair. Identification of preferred intercalation sites is achieved by TRIR monitoring of the nucleobase vibrations before electron transfer.     

Rapid method for the determination of alachlor, atrazine and metolachlor in groundwater by solid-phase extraction

A solid-phase extraction method is described for the separation of alachlor, atrazine and metolachlor from groundwater using solid-phase disposable columns. The method is rapid, reproducible and uses considerably fewer reagents than classical liquid-liquid methods. The average recoveries were greater than 90% for all three compounds.     

Chern-Simons theory with finite gauge group

We construct in detail a 2+1 dimensional gauge field theory with finite gauge group. In this case the path integral reduces to a finite sum, so there are no analytic problems with the quantization. The theory was originally introduced by Dijkgraaf and Witten without details. The point of working it out carefully is to focus on the algebraic structure, and particularly the construction of quantum Hilbert spaces on closed surfaces by cutting and pasting. This includes the Verlinde formula. The careful development may serve as a model for dealing with similar issues in more complicated cases.The first author is supported by NSF grant DMS-8805684, an Alfred P. Sloan Research Fellowship, a Presidential Young Investigators award, and by the O'Donnell Foundation. The second author is supported by NSF grant DMS-9207973     

Detailed analysis of α,ω-bis(4-hydroxybutyl) poly(dimethylsiloxane) using GPC-MALDI TOF mass spectrometry

In this study the prepolymer alpha,omega-bis(4-hydroxybutyl) poly(dimethylsiloxane), used in the formulation of oxygen permeable films, is evaluated by gel permeation chromatography (GPC) combined with matrix assisted laser desorption ionization (MALDI) time of flight (TOF) mass spectrometry (MS). Two unexpected mass distributions are observed in the mass spectra. Reaction schemes for the formation of these distributions are proposed. A solution phase trimethylsilane end group modification was performed on the prepolymer to determine whether the unexpected mass distributions occur as impurities from synthesis or as artifacts from the MS process. Evaluation of the TMS modified prepolymer indicates the unexpected mass distributions indeed occur as impurities from the synthetic procedure. Average molecular weight values are determined by traditional GPC, direct MALDI-TOF MS, and GPC-MALDI-TOF MS methods and the results are compared.