Scalar fields non-minimally coupled to (2 + 1)-gravity, in the presence of cosmological constant term, are considered. Non-minimal couplings are described by the term ζ R Ψ 2 in the Lagrangian. Within a class of static circularly symmetric space-times, it is shown that the only existing physically relevant solutions are the anti-de Sitter space-time for ζ = 0, and the Martínez-Zanelli black hole for ζ = 1/8. We obtain also two new solutions with non-trivial scalar field, for ζ = 1/6 and ζ = 1/8 respectively, nevertheless, the corresponding space-times can be reduced, via coordinate transformations, to the standard anti-de Sitter space.

The results show that the asymmetric logit improves the predictive capacity of conventional logistic regressions.

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Modelling automobile insurance claims is a crucial component in the ratemaking procedure. This paper focuses on the probability that a policyholder reports a claim, where the classical logit link does not provide a right model. This is so because databases related with automobile claims are often unbalanced, containing more non-claims than the presence of claims. In this work an asymmetric logit model, which takes into account the large number of non-claims in the portfolio, is considered. Both, logit and asymmetric logit models from a Bayesian point of view, are used to a sample that was collected from a major automobile insurance company in Spain in 2009, resulting in a dataset of 2,000 passenger vehicle. We establish the validity of the asymmetric model in front of the conventional logit link. The use of a garage, the age of the vehicle and the duration of the client's relation with the company are all shown to be significant explanatory variables by the logit model. The asymmetric model includes, in addition, the length of time the policyholder has held a driving licence and the type of use made of the vehicle. The asymmetric model provides a better fit to the data examined.