A Lie theoretic galois theory for the spectral curves of an integrable system: I

In the study of integrable systems of ODE's arising from a Lax pair with a parameter, the constants of the motion occur as spectral curves. The specific curves depend upon the representation of the Lie algebra. In this paper a Galois theory of spectral curves is given that classifies the spectral curves from an integrable system. The spectral curves correspond to conjugacy classes of certain subgroups of the Weyl group for the Lie algebra. The theory is illustrated with the periodic Toda lattice.Partially supported by a Louisiana Education Quality Support Fund grant LEQSF (87-89)-RD-A-8     

Traceability issues in measurement

This paper reviews the current state of play of the Mutual Recognition Arrangement created by the International Committee for Weights and Measures in 1999. The aim of the MRA is to provide a framework within which National Metrology Institutes can demonstrate the equivalence of their realisations of the units and quantities of the SI system to which accredited laboratories are traceable. The article offers some views on the need for traceable measurements, their relevance to technical barriers to trade, and the use that is being made of the MRA framework by national and international bodies.     

Europium-151 Mössbauer spectroscopic and XANES investigation of europium-exchanged Y-zeolite

Eu³⁺ in ca. 10 wt% europium-exchanged Y-zeolite is partially reduced by treatment in hydrogen at 600°C to Eu²⁺. The reduction of Eu³⁺ is more readily achieved in Y-zeolite than in europium(III) oxide. The discrepancy in the extent of reduction as revealed by¹⁵¹Eu Mössbauer spectroscopy and near edge X-ray absorption fine structure (XANES) is associated with any difference in the recoil free fractions of Eu²⁺ and Eu³⁺ which may exist at 298 K and the enhanced sensitivity of the XANES to changes in the europium oxidation state.     

The Möbius distribution on the disc

A simple new family of distributions is proposed which has support the unit disc in two dimensions. The density functions of the family are unimodal, monotonic or uniantimodal. The bivariate symmetric beta distributions, which include the uniform distribution, are special cases, but many members of the family are skew. The distributions have three parameters, one controlling orientation, one controlling degree of concentration and the third controlling skewness, or more precisely off-centredness. Importantly, these parameters are globally orthogonal. An illustrative example of fitting the model to data is given. Conditional and marginal distributions are considered. The new distributions are compared favourably with an earlier suggestion of the same author.     

Sulfur adsorption on Fe(1 1 0): a DFT study

The adsorption of atomic S on the Fe(1 1 0) surface is examined using density functional theory (DFT). Three different adsorption sites are considered, including the atop, hollow and bridge sites and the S is adsorbed at a quarter monolayer coverage in a p(2 × 2) arrangement. The hollow site is found to be the most stable, followed by the bridge and atop sites. At all three sites, S adsorption results in relatively minor surface reconstruction, with the most significant being that for the hollow site, with lateral displacements of 0.09 Å. Comparisons between S-adsorbed and pure Fe surfaces revealed reductions in the magnetic moments of surface-layer Fe atoms in the vicinity of the S. At the hollow site, the presence of S causes an increase in the surface Fe d-orbital density of states between 4 and 5 eV. However, S adsorption has no significant effect on the structure and magnetic properties of the lower substrate layers.     

Regularity, partial elimination ideals and the canonical bundle

We present partial elimination ideals, which set-theoretically cut out the multiple point loci of a generic projection of a projective variety, as a way to bound the regularity of a variety in projective space. To do this, we utilize a combination of initial ideal methods and geometric methods. We first define partial elimination ideals and establish through initial ideal methods the way in which, for a given ideal, the regularity of the partial elimination ideals bounds the regularity of the given ideal. Then we explore the partial elimination ideals as a way to compute the canonical bundle of the generic projection of a variety and the canonical bundles of the multiple point loci of the projection, and we use Kodaira Vanishing to bound the regularity of the partial elimination ideals.