Stark's conjecture over complex cubic number fields

Systematic computation of Stark units over nontotally real base fields is carried out for the first time. Since the information provided by Stark's conjecture is significantly less in this situation than the information provided over totally real base fields, new techniques are required. Precomputing Stark units in relative quadratic extensions (where the conjecture is already known to hold) and coupling this information with the Fincke-Pohst algorithm applied to certain quadratic forms leads to a significant reduction in search time for finding Stark units in larger extensions (where the conjecture is still unproven). Stark's conjecture is verified in each case for these Stark units in larger extensions and explicit generating polynomials for abelian extensions over complex cubic base fields, including Hilbert class fields, are obtained from the minimal polynomials of these new Stark units.

     

Constructing orthogonal pandiagonal Latin squares and panmagic squares from modular n‐queens solutions

In this article, we show how to construct pairs of orthogonal pandiagonal Latin squares and panmagic squares from certain types of modular n‐queens solutions. We prove that when these modular n‐queens solutions are symmetric, the panmagic squares thus constructed will be associative, where for an n × n associative magic square A = (a_ij), for all i and j it holds that a_ij + an?i?1,n?j?1 = c for a fixed c. We further show how to construct orthogonal Latin squares whose modular difference diagonals are Latin from any modular n‐queens solution. As well, we analyze constructing orthogonal pandiagonal Latin squares from particular classes of non‐linear modular n‐queens solutions. These pandiagonal Latin squares are not row cyclic, giving a partial solution to a problem of Hedayat. © 2007 Wiley Periodicals, Inc. J Combin Designs 15: 221–234, 2007     

Immobilization of catalase on membranes of poly(ethylene)-g-co-acrylic acid and poly(tetrafluoroethylene)-g-co-acrylic acid and their application in hydrogen peroxide electrochemical sensors

The immobilization of catalase on grafted membranes of poly(ethylene)-g-co-acrylic acid and poly(tetrafluoroethylene)-g-co-acrylic acid and their application in hydrogen peroxide electrochemical sensors is described. The introduction of carboxylic acid groups onto a hydrophobic support provides a good environment for subsequent enzyme immobilization. This single membrane, hydrogen peroxide sensor showed significant improvement with respect to the double membrane versions. The response is very rapid, the linear range being from 10 μM up to 6 mM, with a detection limit of 4.7 μM, and a lifetime of more than 4 months.     

Enolization of acetone in superheated water detected via radical formation

Muoniated free radicals have been detected in muon-irradiated aqueous solutions of acetone at high temperatures and pressures. At temperatures below 250 degrees C, the radical product is consistent with muonium addition to the keto form of acetone. However, at higher temperatures, a different radical was detected, which is attributed to muonium addition to the enol form. Muon hyperfine coupling constants have been determined for both radicals over a wide range of temperatures, significantly extending the range of conditions under which these radicals and the keto-enol equilibrium have been studied.     

A study of the formation of silica-supported mixed magnesium-manganese spinel oxides from multicomponent gels

The effects of thermal treatment on composite materials prepared by the gelation of sols comprising large concentrations of metal oxide precursor salts have been investigated, in order to determine the compositional and thermal requirements for forming spinel magnesium manganates in such systems. The preparative technique has been found to give rise to derived gel materials in which the metal oxide phase, in the form of regular spherical particles, is dispersed throughout a continuous silica matrix. Silica-supported mixed magnesium and manganese spinel oxide phases were obtained for systems comprising at least 30 wt% metal nitrate after heating to temperatures between 700 and 850°C, but not without concomitant formation of Mn₂O₃ and modification of the silica network by magnesium.     

Double gradient ion chromatography on a short carboxybetaine coated monolithic anion exchanger

An ultra-short 1.0 x 0.46 cm carboxybetaine coated monolithic anion exchanger has been used with a new double gradient ion chromatography (DG-IC) technique. The novel monolithic column can be used with flow rate gradients giving excellent peak efficiencies, and retention times can be simultaneously reduced through combining flow gradients with an eluent pH gradient.     

Comparative properties of siloxane vs phosphonate monolayers on a key titanium alloy

A direct comparison of surface loading, interface shear strength, and interface hydrolytic stability was made between a phosphonate and two siloxane monolayers formed on the native oxide surface of Ti-6Al-4V. Surface loading for the phosphonate was ca. four times greater (on a nanomole/area basis) than for the siloxanes; mechanical strengths per surface-bound molecule were comparable, but the hydrolytic stability (pH 7.5) of the siloxanes was poor. These results suggest that phosphonate monolayer interfaces are more desirable than comparable siloxane ones for applications where such interfaces contact even slightly alkaline water.     

Stereoselective association of binuclear metallacycles in coordination polymers

A series of structurally related binuclear metallacycles [Cd(NO(3))(2)L](2), where L is an angular exo-bidentate ligand, have been synthesized. Each metallacycle contains two coordinatively unsaturated, chiral metal centers within a single molecule, and the assembly of these metallacycles into polymeric framework structures has been studied systematically for the first time. Stereoselective homochiral association of [Cd(NO(3))(2)L](2) leads to the formation of helical coordination polymers, whereas meso type association results in nonhelical chain structures. The type of stereoselective aggregation depends on the conditions of self-assembly as well as on ligand functionality. Both helical and nonhelical polymeric complexes have been isolated for the metallacycle [Cd(NO(3))(2)(2,4'-pyacph)](2) (2,4'-pyacph = 2,4'-(4-ethynylphenyl)bipyridyl). Homochiral association results in the formation of helical [Cd(NO(3))]( infinity ) chains which link the binuclear [Cd(NO(3))(2)(2,4'-pyacph)](2) metallacycles into racemic two-dimensional sheets which contain both P and M [Cd(NO(3))]( infinity ) helices. In contrast, meso-association leads to the formation of nonhelical one-dimensional chains. It is shown that the product of homochiral association is predominately formed at room temperature and that of meso-association is generated at elevated temperatures. Thus, it may be concluded that the homochiral association appears to be energetically less favorable than the meso-association, a conclusion that has been confirmed by theoretical calculations of the crystal lattice energy. Several high-yield syntheses of bipyridyl-type ligands used for metallacyclic assembly are also reported.     

Iminodiacetic acid functionalised monolithic silica chelating ion exchanger for rapid determination of alkaline earth metal ions in high ionic strength samples

Iminodiacetic acid has been covalently bonded to a bare silica monolith to produce the first reported high-performance monolithic chelating ion exchange column. Using the new column, separation and determination of traces of alkaline earth metal ions (low ppm) in high ionic strength samples (up to 2 M NaCl and KCl brines), could be achieved in under 40 s. At an eluent flow rate of 4 mL min(-1) retention time precision was < 1.2% (n = 9) for Mg(II) and Ca(II), with detector linearity (n = 5) over the range 2-10 mg L(-1) of between R2 = 0.985 and R2 = 0.995. In 1 M KCl and NaCl brine samples, detection limits of 0.2 mg L(-1) were possible.     

A deuterium nuclear quadrupole double resonance study of the ferroelectric phase transition in potassium dihydrogen phosphate

A study has been made of the nuclear quadrupole double resonance (NQDR) spectrum of deuterium in a powdered sample of potassium dihydrogen phosphate, KH₂PO₄ or KDP for short, both as a function of temperature and of percentage deuteration. Double transitions have also been observed and these enable the orientation of the ferroelectric electric field gradient (EFG) tensor to be determined.