Embeddings and immersions of tropical curves

We construct immersions of trivalent abstract tropical curves in the Euclidean plane and embeddings of all abstract tropical curves in higher dimensional Euclidean space. Since not all curves have an embedding in the plane, we define the tropical crossing number of an abstract tropical curve to be the minimum number of self-intersections, counted with multiplicity, over all its immersions in the plane. We show that the tropical crossing number is at most quadratic in the number of edges and this bound is sharp. For curves of genus up to two, we systematically compute the crossing number. Finally, we use our immersed tropical curves to construct totally faithful nodal algebraic curves via lifting results of Mikhalkin and Shustin.Comment: 23 pages, 14 figures, final submitted versio

Egyptian stelae from Malta

In 1829, four Egyptian stelae of Twelfth and Eighteenth Dynasty date were found, surprisingly, on Malta. Based on their far-flung findspot, some have suggested that the stelae were locally made by Egyptian colonists who had settled on the island during the second millennium BC. This contribution argues that the stelae offer no basis for such historical reconstructions. Style, content and petrology demonstrate that all four stelae were made in Egypt and that they originally stood in the necropolis of Abydos in Upper Egypt. Microfossils show that these stelae are made of Egyptian limestones, which are of a different geological age to limestones available on Malta. The examination of polished thin sections of samples from the stelae using scanning electron microscopy suggests that the limestones employed were quarried from four geological formations of different ages in the Nile Valley.peer-reviewe

ANALYSIS OF PHARMACEUTICALS AND BIOMOLECULES USING HPLC COUPLED TO ICP-MS AND ESI-MS

The work described within this thesis explores the use of HPLC coupled with ICPMS and ESI-MS in order to develop novel methods which overcome specific analytical challenges in the pharmaceutical industry. A membrane desolvation interface has been evaluated for coupling high performance liquid chromatography (HPLC) with inductively coupled plasma mass spectrometry (ICP-MS). Desolvation of the sample prior to reaching the plasma was shown to facilitate a versatile coupling of the two instrumental techniques, enabling chromatographic eluents containing up to 100 % organic to be used. This interface also allowed gradient elution to be used with ICP-MS. Tris(2,4,6-trimethoxyphenyl)phosphonium propylamine bromide (TMPP) was used for the derivatisation of maleic, fumaric, sorbic and salicylic acids to facilitate determination by HPLC-electrospray ionisation tandem mass spectrometry (ESIMS/ MS) in positive ion mode. Improvements in detection limits post-derivatisation were achieved, and this method was successfully used for the determination of sorbic acid in a sample of Panadol™. HPLC coupled with sector field inductively coupled plasma mass spectrometry (SF-ICP-MS) has been used for the determination of maleic, sorbic and fumaric acids after derivatisation with TMPP. This allowed 31P+ selective detection to be performed for these compounds, which are normally undetectable by ICP-MS. Optimal reagent conditions for the derivatisation of 0.1 mM maleic acid were: 1 mM TMPP; 10 mM 2-chloro-1-methylpyridinium iodide (CMPI); 11 mM triethylamine. The efficiency of the derivatisation reaction was estimated to be between 10-20%. Detection limits, estimated as 3 times baseline noise, were 0.046 nmol for TMPP and 0.25 nmol for derivatised maleic acid, for a 5 f.JL injection. Following on from this, a novel derivatising reagent, tris(3,5-dibromo-2,4,6- trimethoxyphenyl) phosphonium propylamine bromide (BrTMPP), was synthesised and subsequently characterised by proton NMR spectroscopy and ESI-MS. This was utilised to derivatise maleic acid, with a 9-fold increase in sensitivity gained when analysed by bromine selective detection as apposed to phosphorus selective ICP-MS. This derivatising reagent (BrTMPP) was also utilised to determine the degree of phosphorylation on phosphorylated peptides. A phosphorus containing carboxylic acid was successfully derivatised and the correct Br:P ratio was determined for this compound by ICP-MS. However, phosphorylated peptides were not successfully derivatised by BrTMPP. A combination of UV and phosphorus selective ICP-MS was also used to distinguish between phosphorylated and un-phosphorylated peptides after HPLC separation.GlaxoSmithKiin

Implementing land reform in post-Communist Romania

This thesis examines the implementation of ownership reforms following the collapse of Communist rule in Romania in 1989. It concentrates upon the rural sector and, in particular, the question of what to do with the collective farms. The aim has been to provide a critical account of the roots of the post-Communist land question, going back as far as the agrarian situation in the last century. To this end, regard is had to the land question in the pre-Communist era, concentrating on the efforts made by the state to create a sustainable system of land tenure. The second part of the work investigates how the Communist regime reformed land use and agricultural production, in particular, the methods by which the private control of land was transformed during collectivisation. In this way, the recent land reforms are linked to a much longer history of struggle over land. The objective has been to examine the legal process of implementing post-Communist land reforms as a means whereby history is rewritten, both nationally and locally. The land reforms are, partly, the official recognition of abuses committed by the former regime and yet, they are also a means of restructuring the country's agricultural sector. As in other countries in eastern Europe, Communist rule in Romania transformed a predominantly agrarian society into an industrial one. Before the Communists almost three-quarters of the population lived and worked on the land. By the time President Nicolae Ceausescu fell, the proportion was less than a third. The land question in post-Communist Romania centred on the extent to which the need to compensate former landowners could direct the content of reform