Completions of GBL-algebras: negative results

We provide a simple sufficient criterion to show that a given variety of GBL-algebras does not admit (local) completions. As corollaries, we obtain that no variety of GBL-algebras containing Chang’s chain, no nontrivial variety of ℓ-groups, nor the variety of product algebras admit completions. The first result strengthens a result of Gehrke and Priestley. Received August 10, 2006; accepted in final form March 8, 2007.     

Swelling and contraction of ferrocyanide-containing polyelectrolyte multilayers upon application of an electric potential

We developed a new platform at the interface of polyelectrolyte multilayers (PEMs) and electroactive polymers (EAPs) by combining the easy buildup of PEM thin films and the deformation characteristics of the EAPs. The PEM films were made of poly(L-glutamic acid) (PGA) and poly(allylamine hydrochloride) (PAH). After [Fe(CN)6]4- ions (FCIV) were added, cyclic voltammetry (CV) was performed, resulting in a reversible expansion and contraction of the film. The shape change as well as the film buildup prior to the cycling were monitored in situ using the electrochemical quartz crystal microbalance with dissipation monitoring (EC-QCM-D). Electrochemical atomic force microscopy (EC-AFM) images confirmed the rapid shape deformation. The process takes place in an aqueous environment under mild conditions (maximum potential of 600 mV and no pH change), which makes it a promising tool for biomedical applications. In addition, the electrochemically active films are produced using the layer-by-layer (LbL) method that is already established in biotechnology and biomaterials science; therefore, the presented approach can be readily adapted in these areas, bringing about a new possibility for the nanoscale dynamic control of coating thickness in various applications.     

Donor-functionalized polydentate pyrylium salts and phosphinines: synthesis, structural characterization, and photophysical properties

A series of donor-functionalized pyrylium salts have been prepared by classical condensation reactions which were further converted into the corresponding thienyl- and pyridyl-substituted polydentate lambda(3)-phosphinines by reaction with P(SiMe(3))(3). Further chemical modification of these phosphorus heterocycles with Hg(OAc)(2) in the presence of methanol resulted in the formation of lambda(5)-phosphinines. The photophysical properties of a selected series of thienyl- and pyridyl-functionalized pyrylium salts, lambda(3)- and lambda(5)-phosphinines, were investigated and the results compared and supported by theoretical calculations on the DFT level. Significant fluorescence was observed for the pyrylium salts and lambda(5)-phosphinines. In contrast, the heteroaromatic substituted lambda(3)-phosphinines show very little emission which is consistent with the low oscillator strength predicted by DFT calculations for this pi-->pi* transition. Furthermore, all three classes of compounds show readily observable phosphorescence in solution, which was determined by time-gated detection at low temperature.     

High-performance thin-layer chromatography method for quantitative determination of oenothein B and quercetin glucuronide in aqueous extract of Epilobii angustifolii herba

A method was developed for separation and quantitative determination of oenothein B (OeB) and quercetin glucuronide (QG) in aqueous extract of Epilobii angustifolii herba by HPTLC-densitometry. The analyses were performed on HPTLC RP-18 WF(254) plates with 25% MeCN in water (+50mM H(3)PO(4)) as the mobile phase (distance of 8 cm) for OeB quantification and then with acetonitrile (distance of 4 cm) for QG quantification. OeB and QG were determined by densitometry at 270 and 350 nm, respectively. Their amounts were calculated using the regression equations of the calibration curves which were linear in a range of 1.14-2.28 microg spot(-1) for OeB and of 0.0768-0.6912 microg spot(-1) for QG. The amounts of OeB and QG in aqueous extract of Epilobii angustifolii herba measured by the method developed were 152.46+/-4.92 and 22.07+/-1.38 mg g(-1), respectively. The method was found to be relatively simple, specific, precise and accurate for the quality control of Epilobium angustifolium extracts.     

Controlling interfacial curvature in nanoporous silica films formed by evaporation-induced self-assembly from nonionic surfactants. II. Effect of processing parameters on film structure

The double-gyroid phase of nanoporous silica films has been shown to possess facile mass-transport properties and may be used as a mold to fabricate a variety of highly ordered inverse double-gyroid metal and semiconductor films. This phase exists only over a very small region of the binary phase diagram for most surfactants, and it has been very difficult to synthesize metal oxide films with this structure by evaporation-induced self-assembly (EISA). Here, we show the interplay of the key parameters needed to synthesize these structures reproducibly and show that the interfacial curvature may be systematically controlled. Grazing angle of incidence small-angle X-ray scattering (GISAXS) is used to determine the structure and orientation of nanostructured silica films formed by EISA from dilute silica/(poly(ethylene oxide)-b-poly(propylene oxide)-b-alkyl) surfactant solutions. Four different highly ordered film structures are observed by changing only the concentration of the surfactant, the relative humidity during dip-coating, and the aging time of the solution prior to coating. The highly ordered films progress from rhombohedral (Rm) to 2D rectangular (c2m) to double-gyroid (distorted Iad) to lamellar systematically as interfacial curvature decreases. Under all experimental conditions investigated, increasing the aging time of the coating solution was found to decrease the interfacial curvature. In particular, this parameter was critical to being able to synthesize highly ordered, pure-phase double-gyroid films. The key role of the aging time is shown via processing diagrams that map out the interplay between the aging time, composition, and relative humidity. 29Si nuclear magnetic resonance (NMR) spectroscopy and solution-phase small-angle X-ray scattering (SAXS) of the aged coating solutions presented in part I of this series are then used to interpret the effects of aging prior to dip-coating. Specifically, it was found that a predictive model based on volume fractions and the silica cluster stoichiometry obtained from 29Si NMR qualitatively explains the trends observed with composition and aging. However, apart from the effects of relative humidity, a quantitative comparison of the predicted phase with the experimental processing diagram suggests that less-condensed silica clusters are more effective at swelling the EO blocks at early aging times. This enhanced swelling decreases with aging time and results in lower-curvature nanostructures such as the double-gyroid. The decrease in swelling is attributed to the decreased thermodynamic driving force for the more-condensed silica clusters to mix with the EO block of the surfactant.     

On algebraic -groups

We introduce the categories of algebraic -varieties and -groups over a difference field . Under a ``linearly -closed" assumption on we prove an isotriviality theorem for -groups. This theorem immediately yields the key lemma in a proof of the Manin-Mumford conjecture. The present paper crucially uses ideas of Pilay and Ziegler (2003) but in a model theory free manner. The applications to Manin-Mumford are inspired by Hrushovski's work (2001) and are also closely related to papers of Pink and Roessler (2002 and 2004).

     

Approximating Band- and Energy-Limited Signals in the Presence of Jitter

This paper deals with recovering band- and energy-limited signals from a finite set of their perturbed samples taken at slightly wrong points. The perturbations in sample points reading (called jitter) and in the measurements of the corresponding samples are assumed to be bounded byγandδ, respectively. The goal is to analyze how the minimal worst-case recovery error depends onγandδ. This is accomplished by proving tight upper and lower bounds on the diameter of information. The main conclusion is that the jitter causes the error of orderγΔ^3/2+δ, whereΔis the bandwidth.     

Three‐Dimensional Information on the Phase Domain Structure of Thin Films of Polymer Blends Revealed by Secondary Ion Mass Spectrometry

We describe the technique of dynamic secondary ion mass spectrometry developed to determine three‐dimensional phase domain structures of films of polymer blends. The polymers are composed of light elements or are labeled with deuterium or heavy elements. The applicability of this method to various polymer blends forming thin and ultrathin films with flat and undulated air/film interface is discussed.     

Luminescent and Photoredox-Active Molybdenum(0) Complexes Competitive with Isoelectronic Ruthenium(II) Polypyridines

Ruthenium(II) complexes with chelating polypyridine ligands are among the most frequently investigated compounds in photophysics and photochemistry, owing to their favorable luminescence and photoredox properties. Equally good photoluminescence performance and attractive photocatalytic behavior is now achievable with isoelectronic molybdenum(0) complexes. The zero-valent oxidation state of molybdenum is stabilized by carbonyl or isocyanide ligands, and metal-to-ligand charge transfer (MLCT) excited states analogous to those in ruthenium(II) complexes can be established. Microsecond MLCT excited-state lifetimes and photoluminescence quantum yields up to 0.2 have been achieved in solution at room temperature, and the emission wavelength has become tunable over a large range. The molybdenum(0) complexes are stronger photoreductants than ruthenium(II) polypyridines and can therefore perform more challenging chemical reductions. The triplet nature of their luminescent MLCT states allows sensitization of photon upconversion via triplet-triplet annihilation, to convert low-energy input radiation into higher-energy output fluorescence. This review summarizes the current state of the art concerning luminescent molybdenum(0) complexes and highlights their application potential. Molybdenum is roughly 140 times more abundant and far cheaper than ruthenium, hence this research is relevant in the greater context of finding more sustainable alternatives to using precious and rare transition metals in photophysics and photochemistry.