Deviations of Fischer-Tropsch products from an Anderson-Schulz-Flory distribution

Negative deviations from an Anderson-Schulz-Flory distribution have been observed for the product of the Fischer-Tropsch synthesis. The catalyst was a complex-derived iron-calcium catalyst promoted with cesium sulphate, therefore, neither carrier acidity nor shape selectivity can explain the deviations. This is the first time that chemical modifications of the catalyst are observed to result in negative ASF deviations

Bivariate Hermite subdivision

A subdivision scheme for constructing smooth surfaces interpolating scattered data in $\mathbb{R}^3$ is proposed. It is also possible to impose derivative constraints in these points. In the case of functional data, i.e., data are given in a properly triangulated set of points $\{(x_i, y_i)\}_{i=1}^N$ from which none of the pairs $(x_i,y_i)$ and $(x_j,y_j)$ with $i\neq j$ coincide, it is proved that the resulting surface (function) is $C^1$. The method is based on the construction of a sequence of continuous splines of degree 3. Another subdivision method, based on constructing a sequence of splines of degree 5 which are once differentiable, yields a function which is $C^2$ if the data are not 'too irregular'. Finally the approximation properties of the methods are investigated

The harmonic map and Killing fields for self-dual SU(3) Yang-Mills equations

Using symbolic computations, the unique metric in the space of fields, required to describe self-dual SU(3) Yang-Mills equations by a harmonic map, is determined. Moreover the complete Lie algebra of Killing fields for this metric is established

Fine-tuning and the doublet-triplet splitting problem in the minimal SU(5)SU(5) GUT

In this paper we analyse the doublet-triplet splitting problem in the minimal non-super-symmetric $SU(5)$ GUT. We take into account the full symmetry breaking pattern with both high scale $SU(5)$ breaking and electroweak symmetry breaking. Our analysis shows that the only phenomenologically acceptable model has three vevs, with a strong hierarchy determined by the minimization conditions. The amount of fine-tuning in the model is then numerically evaluated by looking at the effect of variation of input parameters on both the minimization conditions and the bosonic masses. Regarding the vevs as output parameters, a large amount of fine-tuning is required in this scenario, which is an expression of the doublet-triplet splitting problem. We show that this problem is more general, since a model with coupled scalar sectors will in general never realise a hierarchy in vevs. To avoid these problems we advocate imposing the desired hierarchy in vevs as part of the theory. We argue for this viewpoint because the $SU(5)$ breaking and electroweak symmetry breaking need to be adjusted to each other anyway and cannot be regarded as independent mechanisms. We suggest that not only the symmetry breaking pattern needs to be imposed, but also the scales at which the breakings happen. We show quantitatively that the generic theory with hierarchy imposed does not require any fine-tuning of the free parameters which can all be natural and perturbative as desired.Comment: 14 pages, 3 figure

Prolongation structure of the Krichever-Novikov equation

We completely describe Wahlquist-Estabrook prolongation structures (coverings) dependent on u, u_x, u_{xx}, u_{xxx} for the Krichever-Novikov equation u_t=u_{xxx}-3u_{xx}^2/(2u_x)+p(u)/u_x+au_x in the case when the polynomial p(u)=4u^3-g_2u-g_3 has distinct roots. We prove that there is a universal prolongation algebra isomorphic to the direct sum of a commutative 2-dimensional algebra and a certain subalgebra of the tensor product of sl_2(C) with the algebra of regular functions on an affine elliptic curve. This is achieved by identifying this prolongation algebra with the one for the anisotropic Landau-Lifshitz equation. Using these results, we find for the Krichever-Novikov equation a new zero-curvature representation, which is polynomial in the spectral parameter in contrast to the known elliptic ones.Comment: 13 pages, revised version with minor change

Social Europe. ENEPRI Occasional Paper No. 5, November 2003

[From the Introduction and Summary]. Building a Social Europe has received due attention since the founding of the European Community in Rome. The European summit in Lisbon in 2000 was an important milestone in this process. European leaders committed themselves to working together through the 'open coordination' method to develop a policy to combat poverty and social exclusion. The open coordination approach means that countries exchange information and encourage each other to pursue policies geared to their social objectives. The European Union does not itself play an active role in the way in which individual member states set about achieving those objectives. It has however been agreed that member states will draw up a National Action Plan every two years setting out the way in which they plan to realise their objectives