It is shown that the analytical stellar model of Duorah and Ray (1987) does not satisfy Einstein's field equations. All possible solutions derivable from the generalised density distribution are exhibited; these include a solution due to Durgapal and Bannerji. The correct solution following from the ansatz of Duorah and Ray is given. The equation of state for the model is obtained in terms of elementary functions, and the solution is shown to be both regular and physically realistic for a range of masses and radii. A comparison between the model and numerical integrations of neutron stars described by Walecka's relativistic mean-field theory description of neutron matter shows good overall agreement.

An extension of the ideas of the Prelle-Singer procedure to second order differential equations is proposed. As in the original PS procedure, this version of our method deals with differential equations of the form y ′′ = M (x, y, y ′ )/N (x, y, y ′ ), where M and N are polynomials with coefficients in the field of complex numbers C . The key to our approach is to focus not on the final solution but on the first-order invariants of the equation. Our method is an attempt to address algorithmically the solution of SOODEs whose first integrals are elementary functions of x, y and y ′ .

We study conformally flat pure radiation spacetimes by means of their invariant classifications and show that no such spacetime requires higher than the fourth covariant derivative of the Riemann tensor in its invariant classification. Additional side results that we obtain are as follows. The Edgar - Ludwig metric for conformally flat pure radiation is shown to be a true generalization of the Wils metric; the subclass of the Edgar - Ludwig spacetimes which admit exactly one Killing vector is identified, generalizing Koutras's G1 subclass of the Wils metric; it is shown that the Edgar - Ludwig spacetimes with no Killing vectors can further be split into three discrete subsets, depending on the Cartan invariant where the fourth essential coordinate is found.

This is the first in a series of papers concerning a project to set up a computer database of exact solutions in general relativity which can be accessed and updated by the user community. In this paper, we briefly discuss the Cartan-Karlhede invariant classification of geometries and the significance of the standard form of a spinor. We then present algorithms for putting the Weyl spinor, Ricci spinor and general spinors into standard form.

Across Europe, there is considerable interest in establishing stronger links between environmental regulation and standards for environmental management systems (EMSs) such as ISO 14001. If it can be demonstrated that possession of an EMS results in improved environmental or regulatory performance, then there is a case for granting ‘regulatory relief’ in the form of, for example, reduced inspection frequencies. This paper describes the analysis of information on almost 800 sites regulated under the UK's Integrated Pollution Control regime. It demonstrates that having an EMS improves certain procedural aspects of environmental management but does not appear to reduce the likelihood of breaching permit conditions. Interviews with certification bodies revealed the factors, such as differentiation of services in the market for certification, that underlie this finding. It is concluded that some limited recognition of EMS in regulation is warranted, because there is overlap between some regulatory and certification procedures, and because having an EMS facilitates the supply of information necessary for regulation. The broader implications for regulated industry, certification bodies, regulators and wider environmental policymaking are considered. Copyright © 2003 John Wiley & Sons, Ltd and ERP Environment.