Analysis of a three-component model phase diagram by Catastrophe Theory: Potentials with two Order Parameters

In this work we classify the singularities obtained from the Gibbs potential of a lattice gas model with three components, two order parameters and five control parameters applying the general theorems provided by Catastrophe Theory. In particular, we clearly establish the existence of Landau potentials in two variables or, in other words, corank 2 canonical forms that are associated to the hyperbolic umbilic, D_{+4}, its dual the elliptic umbilic, D_{-4}, and the parabolic umbilic, D_5, catastrophes. The transversality of the potential with two order parameters is explicitely shown for each case. Thus we complete the Catastrophe Theory analysis of the three-component lattice model, initiated in a previous paper.Comment: 17 pages, 3 EPS figures, Latex file, continuation of Phys. Rev. B57, 13527 (1998) (cond-mat/9707015), submitted to Phys. Rev.

Children’s and parents’ involvement in care order proceedings: a cross-national comparison of judicial decision-makers’ views and experiences

This paper presents the views of judicial decision-makers (n= 1794) in four child protection jurisdictions (England, Finland, Norway, and the USA (California)), about whether parents and children are provided with appropriate opportunities to participate in proceedings in their countries. Overall, the study found a high degree of agreement within and between the countries as regards the important conditions for parents and children´s involvement, although the four systems themselves are very different. There was less agreement about children’s involvement than parents’, and the court decision-makers from Norway and Finland were more likely to express doubts about this. Nevertheless, the main message from the judicial decision-makers is that they are relatively satisfied as to how parents and children´s involvement is handled in their countries. Whether or not this confidence is justified, the emphasis on achieving effective involvement of children and parents in court proceedings is likely to grow, with major implications for the workers, decision-makers and agencies involved

Improved gadolinium-enhanced subtraction MR angiography of the femoropopli-teal arteries: reintroduction of osseous anatomic landmarks.

To describe and detail the clinical relevance of a simple post-processing MR technique that preserves the benefit of subtracted images while reintroducing bony landmark