Computing Galois groups over the rationals

Practical computational techniques are described to determine the Galois group of a polynomial over the rationals, and each transitive permutation group of degree 3 to 7 is realised as a Galois group over the rationals. The exact computations furnish a proof of the result.     

Theoretical model of the transition between C1 and C2 chevron structures in smectic liquid crystals

We present a study of the effect of weak anchoring on the transition between C1 and C2 chevron structures in smectic-C liquid crystals. The coexistence of C1 and C2 chevron structures within a single cell causes zigzag defects to occur and may affect the optical characteristics of the cell. By standard Euler-Lagrange minimisation of the total energy of the system, we obtain analytical expressions for the equilibrium director cone angle in the two chevron states. These in turn allow us to compare the total energies of the states and determine the globally stable chevron profile. We show that analytical predictions for the critical transition temperature, which depends on anchoring strength and pretilt angle, are in good agreement with those obtained numerically.     

Pitch ranking ability of cochlear implant recipients: a comparison of sound-processing strategies

Pitch ranking of sung vowel stimuli, separated in fundamental frequency (F0) by half an octave, was measured with a group of eleven Nucleus 24 cochlear implant recipients using different sound coding strategies. In three consecutive studies, either two or three different sound coding strategies were compared to the Advanced Combinational Encoder (ACE) strategy. These strategies included Continuous Interleaved Sampling (CIS), Peak Derived Timing (PDT), Modulation Depth Enhancement (MDE), F0 Synchronized ACE (FOSync), and Multi-channel Envelope Modulation (MEM), the last four being experimental strategies. While pitch ranking results on average were poor compared to those expected for most normal hearing listeners, significantly higher scores were obtained using the MEM, MDE, and FOSync strategies compared to ACE. These strategies enhanced coding of temporal F0 cues by providing deeper modulation cues to F0 coincidentally in time across all activated electrodes. In the final study, speech recognition tests were also conducted using ACE, CIS, MDE, and MEM. Similar results among all strategies were obtained for word tests in quiet and between ACE and MEM for sentence tests in noise. These findings demonstrate that strategies such as MEM may aid perception of pitch and still adequately code segmental speech features as per existing coding strategies.     

Film and intraparticle mass transfer during the adsorption of metal ions onto bone char

The sorption of three metal ions, namely, copper, cadmium, and zinc, onto bone char has been studied in terms of equilibrium and rate studies. Equilibrium studies have been analyzed using the Langmuir isotherm equation and the maximum sorption capacities for the metals were 0.477, 0.709, and 0.505 mmolg(-1) bone char for cadmium, copper, and zinc ions, respectively. The kinetic experimental data were used to analyze the effect of external film boundary layer and intraparticle mass transfer resistance on the sorption process and its significance. Four methods of determining the external film transport coefficient were developed and tested; three utilized experimental data to obtain the coefficient and the fourth method was completely empirical. The three experimentally based models give very similar results and consequently similar values of the deviation error values, whereas the error values for the empirical correlation were greater than these three values. The results also demonstrated that the methods for determining the film coefficient could be integrated into more complex diffusion-transport models such as film-intraparticle diffusion processes.     

Enantioselective gas chromatographic assays with electron-capture detection for methoxyphenamine and its three primary metabolites in human urine

Sensitive and enantioselective gas chromatographic assays have been developed and applied to the quantitation in human urine of the enantiomers of methoxyphenamine and its three primary oxidative metabolites, namely, N-desmethylmethoxyphenamine, O-desmethylmethoxyphenamine and 5-hydroxymethoxyphenamine. The separation of the various analytes was achieved through the combined use of high-resolution gas chromatography coupled with electron-capture detection and employing a capillary OV-225 column. The formation of diastereometric derivatives involved the chiral acylating reagent N-heptafluorobutyryl-L-prolyl chloride. The assays for methoxyphenamine and O-desmethylmethoxyphenamine were linear over the range 0.25-2.0 micrograms/ml for each analytes' enantiomers, while in the case of the enantiomers for N-desmethylmethoxyphenamine and 5-hydroxymethoxyphenamine linearity was shown over the ranges 0.094-0.75 and 0.188-1.5 micrograms/ml, respectively. The mean coefficients of variation in all cases were less than 4%.     

RuII and IrIII Complexes Containing ADA and DAD Triple Hydrogen Bonding Motifs: Potential Tectons for the Assembly of Functional Materials

The synthesis and characterisation of a series of [Ru^II(bpy)₂L] and [Ir(ppy)₂L] complexes containing ligands L with the potential to engage in triple hydrogen bonding interactions is described. L1 and L2 comprise pyridyl triazole chelating units with pendant diaminotriazine units, capable of donor‐acceptor‐donor (DAD) hydrogen bonding, while L3 and L4 contain ADA hydrogen bonding units proximal to N^N and N^O cleating sites, respectively. X‐ray crystallography shows the L1 and L2 containing Ru^II complexes to assemble via hydrogen bonding dimers, while [Ru^II(bpy)₂L 4 ] assembles via extended hydrogen bonding motifs to form one dimensional chains. By contrast, the expected hydrogen bonding patterns are not observed for the Ru^II and Ir^III complexes of L3 . Spectroscopic studies show that the absorption spectra of the complexes result from combinations of MLCT and LLCT transitions. The L1 and L2 complexes of Ir^III and Ru^II complexes are emissive in the solid state and it seems likely that hydrogen bonding to complementary species may facilitate tuning of their ³ILCT emission. Low frequency Raman spectra provide further evidence for ordered interactions in the solid state for the L4 complexes, consistent with the results from X‐ray crystallography.