Bounds on Codes Derived by Counting Components in Varshamov Graphs

We are interested in improving the Varshamov bound for finite values of length n and minimum distance d. We employ a counting lemma to this end which we find particularly useful in relation to Varshamov graphs. Since a Varshamov graph consists of components corresponding to low weight vectors in the cosets of a code it is a useful tool when trying to improve the estimates involved in the Varshamov bound. We consider how the graph can be iteratively constructed and using our observations are able to achieve a reduction in the over-counting which occurs. This tightens the lower bound for any choice of parameters n, k, d or q and is not dependent on information such as the weight distribution of a code. This work is taken from the author’s thesis [10]     

Molar mass distributions by gradient liquid chromatography: predicting and tailoring selectivity

Interactive liquid chromatography (iLC) for polymer analysis is usually applied to the characterisation of distributions other than molar mass. In particular, its use for the determination of chemical-composition, functionality-type and tacticity distributions has been demonstrated. The application of iLC for the determination of molar mass distributions (MMDs), however, has not yet been fully explored. An expanded version of the reversed-phase liquid chromatography model has been developed to describe and predict how the retention behaviour of polydisperse polystyrene samples changes with molar mass. The relationship between molar mass and the parameters of the model has been investigated in some detail and non-linear correlations were found. From the model and the relationships between the model parameters and molar mass, calibration curves (retention time versus molar mass) were constructed to predict changes in chromatographic selectivity across a given molar mass range. These calibration curves were compared to experimentally obtained curves and, in most cases, excellent agreement was found. The dramatic enhancement in selectivity that can be obtained with iLC in comparison to size-exclusion chromatography (SEC) was illustrated by measuring matrix-assisted laser desorption ionisation (MALDI) MS spectra of fractions collected during a gradient-LC separation. In the low-molar mass range, essentially monodisperse fractions were obtained. Calibration curves, predicted by the model and validated experimentally using narrow-dispersity standards and MALDI-MS spectra of fractions, were used to determine the molar mass distribution of some narrowly distributed polystyrene samples. Molar mass distributions for such standards were found to be somewhat lower than the values reported by the manufacturers. The results also deviated from those obtained by MALDI-MS.     

Geometry optimised AB initio calculations on cyclopropenone and dimethylcyclopropenone adducts with borane and trifluoroborane

Geometry optimised ab initio calculations are reported for R₂C₃O.BY₃ (R = H, CH₃; Y = H, F). The results show that in the above series BH₃ is a stronger Lewis acid than BF₃, and that dimethylation increases the basicity of the cyclopropenone system.