Bethe Ansatz and the Spectral Theory of Affine Lie Algebra-Valued Connections I. The simply-laced Case

We study the ODE/IM correspondence for ODE associated to \({\widehat{\mathfrak{g}}}\)-valued connections, for a simply-laced Lie algebra \({\mathfrak{g}}\). We prove that subdominant solutions to the ODE defined in different fundamental representations satisfy a set of quadratic equations called \({\Psi}\)-system. This allows us to show that the generalized spectral determinants satisfy the Bethe Ansatz equations.     

On the structure of 3‐acetylamino‐5‐methyl‐1,2,4‐oxadiazole and on the fully degenerate rearrangements (FDR) of its anion: a stimulating comparison between the results of ‘in‐silicon chemistry’ and ‘laboratory chemistry’

An accurate crystal structure determination has provided evidence for a planar conformation for 3‐acetylamino‐5‐methyl‐1,2,4‐oxadiazole ( 5 ), in agreement with quantum‐mechanical calculations in the gas phase. In the crystal, a series of strong intermolecular N7H7^….O9 hydrogen bonds link the amido groups of different molecules, causing the formation of infinite parallel ordered chains. The effect of the DMSO solvent on the energy and charge distribution of compound 5 and on its relevant 5 ^? anion, involved in a fully degenerate rearrangement (FDR), has been deepened by quantum‐mechanical DFT calculations. The calculated energy barrier for the FDR increases in going from in vacuo to DMSO, in agreement with previsions based on the Hughes and Ingold rules concerning the nucleophilic substitution of an anionic reagent (the deprotonated amido group in the side chain) on a neutral substrate (the 1,2,4‐oxadiazole ring). Copyright © 2009 John Wiley & Sons, Ltd.     

Size-fractionated characterization and quantification of nanoparticle release rates from a consumer spray product containing engineered nanoparticles

This study describes methods developed for reliable quantification of size- and element-specific release of engineered nanoparticles (ENP) from consumer spray products. A modified glove box setup was designed to allow controlled spray experiments in a particle-minimized environment. Time dependence of the particle size distribution in a size range of 10–500 nm and ENP release rates were studied using a scanning mobility particle sizer (SMPS). In parallel, the aerosol was transferred to a size-calibrated electrostatic TEM sampler. The deposited particles were investigated using electron microscopy techniques in combination with image processing software. This approach enables the chemical and morphological characterization as well as quantification of released nanoparticles from a spray product. The differentiation of solid ENP from the released nano-sized droplets was achieved by applying a thermo-desorbing unit. After optimization, the setup was applied to investigate different spray situations using both pump and gas propellant spray dispensers for a commercially available water-based nano-silver spray. The pump spray situation showed no measurable nanoparticle release, whereas in the case of the gas spray, a significant release was observed. From the results it can be assumed that the homogeneously distributed ENP from the original dispersion grow in size and change morphology during and after the spray process but still exist as nanometer particles of size <100 nm. Furthermore, it seems that the release of ENP correlates with the generated aerosol droplet size distribution produced by the spray vessel type used. This is the first study presenting results concerning the release of ENP from spray products.