Orbifolds, Sheaves and Groupoids

We characterize orbifolds in terms of their sheaves, and show that orbifolds correspond exactly to a specific class of smooth groupoids. As an application, we construct fibered products of orbifolds and prove a change-of-base formula for sheaf cohomology.     

Selective saturation and inversion of multiple resonances in high-resolution solid-state 13C experiments using slow spinning CP/MAS and tailored DANTE pulse sequences.

Taking advantage of the long 13C T1 values generally encountered in solids, selective saturation and inversion of more than one resonance in 13C CP/MAS experiments can be achieved by sequentially applying several DANTE pulse sequences centered at different transmitter frequency offsets. A new selective saturation pulse sequence is introduced composed of a series of 90 degrees DANTE sequences separated by interrupted decoupling periods during which the selected resonance is destroyed. Applications of this method, including the simplification of the measurement of the principal values of the 13C chemical shift tensor under slow MAS conditions, are described. The determination of the aromaticity of coal using a relatively slow MAS rate is also described.     

Magnetic resonance imaging: a new window into industrial processing.

Although the most important use of nuclear magnetic resonance imaging (MRI) continues to be for diagnostic medicine, recognition is being gained for many nonmedical applications. Examples include the following areas: petrogeology, food, agriculture, polymers and polymer-composites, and pharmaceuticals. These areas all involve studies of species that have short spin-spin relaxation times, and consequently need far fast gradient switching. These technical details are discussed and typical applications given.     

Optical Tunnelling from One-Dimensional Square-Well Potentials

The authors study a one-dimensional model for optical tunnellingwith a refractive index in the shape of a square well. The relevanceof the model and its limiting cases are discussed. The mainresult is the leading behaviour of the exponentially small imaginarypart of the eigenvalue which determines the radiation loss.The leading behaviour of the imaginary part is calculated usingBerry's formula which controls the asymptotic expansion of theAiry function Bi(z) to better-than-exponential accuracy.     

Determination of total ammonium-nitrogen and free ammonia in a fermentation medium by sequential injection analysis

Summary Automated methods for the determination of ammonium and ammonia are reviewed, and techniques based on gas diffusion using a semi-permeable membrane were selected for the determination of both total ammonium-nitrogen and free ammonia in fermentation samples. A simple and robust instrument based on sequential injection analysis (SIA) consisting of a piston pump and two selector valves was used. Two different methods of ammonia detection, the Berthelot method and detection using pH-indicators, have been evaluated and compared. The indicator method showed higher reproducibility and the range of determination could easily be adjusted to match the concentrations of the samples. The range of determination could be adjusted from 0.05 mmol/l to 350 mmol/l, depending on choice of acceptor solution. This method has been evaluated with fermentation medium samples and tested on-line in a yeast fermentation process.Dedicated to Professor Dr. Wilhelm Fresenius on the occasion of his 80th birthday     

Aqueous solution and solid state interactions of lanthanide ions with a methacrylic ester polymer bearing pendant 15‐crown‐5 moieties

The interaction between trivalent lanthanide ions and poly(1,4,7,10,13‐pentaoxacyclopentadecan‐2‐yl‐methyl methacrylate), PCR5, in aqueous solution and in the solid state have been studied. In aqueous solution, evidence of a weak interaction between the lanthanides and PCR5 comes from the small red shift of the Ce(III) emission spectra and the slight broadening of the Gd(III) EPR spectra. From the Tb(III) lifetimes in the presence of H₂O and D₂O the loss of one or two water coordinated molecules is confirmed when Tb(III) is bound to PCR5. An association constant of the order of 200 M^?1 was obtained for a 1:1 (lanthanide:15‐crown‐5) complex from the shift of the polymer NMR signals induced by Tb(III). A similar association constant is obtained from the differences of the molar conductivity of Ce(III) solution at various concentrations in presence and absence of PCR5. When Tb(III) is adsorbed on PCR5 membranes, lifetime experiments in H₂O and D₂O confirm the loss of 5 or 6 water coordinated molecules indicating that in solid state the lanthanide(III)‐PCR5 interaction is stronger than in solution. The adsorption of Ce(III) in PCR5 membranes shows a Langmuir type isotherm, from which an equilibrium constant of 39 M^?1 has been calculated. SEM shows that the membrane morphology is not much affected by lanthanide adsorption. Support for lanthanide ion–crown interactions comes from ab initio calculations on 15‐crown‐5/La(III) complex. © 2007 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 45: 1788–1799, 2007     

Synthesis,dynamic light scattering,and luminescence properties of copolymers containing iridium(III) bisterpyridine in the side chain

Supramolecular block‐random copolymers containing [Ir(terpy)₂]³⁺ in the side chain were synthesized via postfunctionalization of a P(S‐b‐AC_terpy) block copolymer. Absorbance and emission spectra compared to a model compound show that the polymer backbone has a minor effect on the polymer absorbance but produces a larger shift for the phosphorescence signals to higher wavelength. Dynamic light scattering of the metal complex containing copolymer studied in various solvents showed monomodal aggregation with decreasing aggregate size as the solvent dielectric constant increased. The copolymer precursor P(S‐b‐AC_terpy) shows multimodal aggregation in different solvents with the major population consisting of single chains. This difference in behavior between the two polymers is attributed to the electrolytic nature of the complex and the amphiphilicity induced by the charged metal complex. Supramolecular copolymers like these will continue to have interesting self‐organizational properties and may find applications in multicomponent systems for photoinduced charge separation processes. © 2006 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 45: 1109–1121, 2007     

On Critical Stability of Three Quantum Charges Interacting Through Delta Potentials

We consider three one-dimensional quantum, charged and spinless particles interacting through delta potentials. We derive sufficient conditions which guarantee the existence of at least one bound state.     

Butyltins in california river and lake marina waters

Butyltins were analyzed in waters from California river and lake marinas and were detected at the part per trillion (ppt) level in most locations. The tributyltin:dibutyltin (TBT/DBT) ratios in the fresh waters were similar to those in their saline counterparts indicating like rates of degradation in the two salinity regimes.