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.     

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).

     

Conservative methods for the Toda lattice equations

We are concerned with the numerical integration of the Todalattice equations by using different conservative methods. Numericalexperiments suggest that the global error for isospectral schemesdecreases exponentially with time but it is almost constantfor either symplectic or more general integrators. We providea theoretical explanation for these experimental findings.     

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.     

Quantitative comparison of selectivities in the polymerization of cyclic esters

Chain transfer processes (k_tr) taking place in the polymerization (anionic and pseudoanionic) of cyclic esters (lactones) are reviewed. These reactions are mostly responsible for the departure of these systems from the fully controlled (living) polymerizations. The ratios of k_p/k_tr have been determined for a number of initiating systems and the structures of the growing species are related to their selectivity, expressed by k_p/k_tr. It has been shown that the less reactive and more sterically crowded active species polymerize more selectively.     

Four-Body Bound-States Systems in Relativistic Scalar Quantum Field Theory: Variational Basis-State Approach

The variational method within the Hamiltonian formalism of quantum field theory has been used in order to investigate the effect of virtual pairs for four-body scalar systems consisting of two particles and two antiparticles of the same mass. The scalar particles and antiparticles interact via a massive or massless mediating scalar field. The ground state energy solutions of Fock-space variational trial states (\(|N{\bar {N}}N{\bar {N}}{ \rangle }+|N{\bar {N}}N{\bar {N}}N{\bar {N}\rangle }\)) of the relativistic wave equations have been studied. We have compared these results with the previous work of four-body system (variational trial states of the form \(|N{ \bar {N}}N{\bar {N}}{\rangle }\)) and we have shown that the inclusion of virtual pairs has a noticeable effect at low coupling and at high coupling the energy of the system is changed by an important amount. In other words, the calculations show that the inclusion of virtual pairs augments the binding energy of the four-body system by a substantial amount at strong coupling. This study can pave the way for some new ideas in order to investigate the effect of virtual pairs, for example, for a bound-states quark-antiquark or tetraquark systems in future.