Lesotho: Will the Enclave Empty?

This is a brief and largely descriptive summary of migration flows in and out of Lesotho, and trends therein over tha last forty years. It includes some explanatory discussion and some speculation about likely future trends.Lesotho, Migration, South Africa, Brain Drain

An explicit candidate for the set of Steinitz classes of tame Galois extensions with fixed Galois group of odd order

Given a finite group G and a number field k, a well-known conjecture asserts that the set R_t(k,G) of Steinitz classes of tame G-Galois extensions of k is a subgroup of the ideal class group of k. In this paper we investigate an explicit candidate for R_t(k,G), when G is of odd order. More precisely, we define a subgroup W(k,G) of the class group of k and we prove that R_t(k,G) is contained in W(k,G). We show that equality holds for all groups of odd order for which a description of R_t(k,G) is known so far. Furthermore, by refining techniques introduced in arXiv:0910.5080v1, we use the Shafarevich-Weil Theorem in cohomological class field theory, to construct some tame Galois extensions with given Steinitz class. In particular, this allows us to prove the equality R_t(k,G)=W(k,G) when G is a group of order dividing l^4, where l is an odd prime.Comment: 25 page

The equivariant local ϵ\epsilon-constant conjecture for unramified twists of Zp(1)\mathbb{Z}_p(1)

We study the equivariant local epsilon constant conjecture, denoted by $C_{EP}^{na}(N/K,V)$, as formulated in various forms by Kato, Benois and Berger, Fukaya and Kato and others, for certain 1-dimensional twists $T=\mathbb{Z}_p(\chi^{nr})(1)$ of $\mathbb{Z}_p(1)$. Following ideas of recent work of Izychev and Venjakob we prove that for $T=\mathbb{Z}_p(1)$ a conjecture of Breuning is equivalent to $C_{EP}^{na}(N/K,V)$. As our main result we show the validity of $C_{EP}^{na}(N/K,V)$ for certain wildly and weakly ramified abelian extensions $N/K$. A crucial step in the proof is the construction of an explicit representative of $R\Gamma(N,T)$.Comment: 63 page

Answer to a question on AA-groups, arisen from the study of Steinitz classes

In this short note we answer to a question of group theory from arXiv:0910.5080. In that paper the author describes the set of realizable Steinitz classes for so-called $A'$-groups of odd order, obtained iterating some direct and semidirect products. It is clear from the definition that $A'$-groups are solvable $A$-groups, but the author left as an open question whether the converse is true. In this note we prove the converse when only two prime numbers divide the order of the group, but we show it to be false in general, producing a family of counterexamples which are metabelian and with exactly three primes dividing the order. Steinitz classes which are realizable for such groups in the family are computed and verified to form a group.Comment: 5 page

Blood rheology, cardiovascular risk factors, and cardiovascular disease: The West of Scotland Coronary Prevention Study

The West of Scotland Coronary Prevention Study (WOSCOPS) showed that pravastatin reduced the risk of coronary heart disease (CHD) events in 6,595 middle-aged hypercholesterolaemic men aged 45-64 years without prior myocardial infarction followed for an average of 4.9 years. We hypothesised prospectively (a) that baseline levels of haemorheological variables were related to baseline and incident CHD and to mortality; and (b) that reduction in lipoproteins by pravastatin would lower plasma and blood viscosity, a potential contributory mechanism to CHD events. We therefore studied plasma and blood viscosity, fibrinogen, haematocrit, and blood cell counts at baseline and 1 year. At baseline, plasma and blood viscosity were related to risk factors, CHD measures, and claudication. On univariate analysis, baseline levels of all rheological variables (except platelet count) were related to incident CHD; CHD mortality; and total mortality. On multivariate analysis including baseline CHD and risk factors, plasma and blood viscosity, haematocrit and white cell count each remained significantly associated with incident CHD; while fibrinogen remained an independent predictor of mortality (all p<0.03). After one year, lipoprotein reduction by pravastatin was associated with significant reductions (about one quarter of a standard deviation) in plasma viscosity (mean difference 0.02 mPa.s, p<0.001) and in blood viscosity (mean difference 0.06 mPa.s, p<0.001), but was not associated with significant changes in other rheological variables. We therefore suggest that pravastatin therapy, which reduces elevated lipoproteins in hypercholesterolaemic men, may lower risks of CHD and mortality partly by lowering plasma and blood viscosity. Further studies are required to test this hypothesis

DNA-controlled assembly of protein-modified gold nanocrystals

The controlled assembly in solution of gold nanocrystals modified by attachment of complementary protein-DNA conjugates is described. The size of the aggregates formed can be controlled by the addition of single-stranded DNA, which quickly terminates the assembly process. The rate of formation of the aggregates can also be controlled by varying the salt concentration. Consequently, two distinct regimes of aggregation kinetics are observed. At low salt concentrations, aggregation is shown to be dependent on the rate of duplex formation between the modified gold nanocrystals, i.e., reaction-limited. At higher salt concentrations, aggregation is shown to be dependent only on the rate of diffusion of the nanocrystals, i.e., diffusion-limited. The results presented provide important insights into the rates of formation of nanocrystal assemblies. Moreover, the approach adopted is modular, requiring only the relevant biotin linker chemistry to be developed for a given nanoparticle, while also precluding unfavorable interactions between the DNA and the streptavidin-coated nanoparticle. The ability to control the rate of formation and size of nanocrystal aggregates assembled is important new knowledge. Application of this knowledge will inform future studies of nanocrystal assembly in solution involving different types of nanocrystals, which is of increasing technological significance.This research was supported by a grant from the Petroleum Research Fund (Grant No. PRF# 32879-ACS). The Authors also thank Dr. Hakan Rensmo for helpful discussions and express their gratitude for the services provided by D. Cottell and the staff at the Electron Microscopy Centre, National University of Ireland, Dublin.Peer reviewe