AbslracL An invariant characterization of warped spacetimes is given and a clauillcalion scheme for them is proposed. Some resuits on the cuvature StNCtUre (Petrov and Segre types of the Weyl and Ricci lensom) are given and a thomugh study of the hometry group that each class of warped spacetime may admit is carried out.

Matter collineations, as a symmetry property of the energy-momentum tensor Tab, are studied from the point of view of the Lie algebra of vector fields generating them. Most attention is given to space-times with a degenerate energy-momentum tensor. Some examples of matter collineations are found for dust fluids (including Szekeres's space-times), and null fluid space-times.

Although curvature collineations (curvature preserving transformations) have been studied within the context of general relativity for 20 years, there has been little attempt to study them systematically and there does not appear to have been a detailed mathematical investigation of their properties. This is the first of two papers that are intended as a contribution to this deficiency. This paper presents a discussion of the more general mathematical aspects of curvature collineations and suggests a program for studying them. The implementation of this program and the analysis of specific examples will be carried out in the second paper.

The existence of affine collineations in space-time is discussed and the types of space-time admitting proper affine collineations is displayed. The close connection between such space-times and their holonomy structure and local decomposability is established. Affine collineations with fixed points are also considered as is the problem of extending local affine collineations to the whole of space-time.

This paper is the second of a set of two papers on curvature collineations in general relativity. The first paper presented the mathematical basis of curvature collineations and a possible approach to their study. This paper continues from the first one by investigating in detail many of the cases where curvature collineations can occur in space-time. It is based on a classification of the curvature tensor which is discussed in the first paper and reviewed briefly here. This, together with the geometrical approach favored in this paper, leads to a rather general discussion of the problem which, it is hoped, does not obscure those physical aspects of the situation that are important in Einstein’s theory.

The partial replacement of fossil fuels by biofuels contributes to a reduction of CO2 emissions, alleviating the greenhouse effect and climate changes. Furthermore, fuels produced from waste biomass materials have no impact on agricultural land use and reduce deposition of such wastes in landfills. In this paper we evaluate the addition of pyrolysis biogasoline (pyrogasoline) as an additive for fossil gasoline. Pyrogasoline was produced from used cooking oils unfit to produce biodiesel. This study was based on a set of engine tests using binary and ternary mixtures of gasoline with 0, 2.5, and 5% pyrogasoline and ethanol. The use of ternary blends of gasoline and two different biofuels was tested with the purpose of achieving optimal combustion conditions and lower emissions, taking advantage of synergistic effects due to the different properties and chemical compositions of those biofuels. The tests were performed on a spark-ignition engine, operated at full load (100% throttle, or WOT—wide open throttle) between 2000 and 6000 rpm, while recording engine performance and exhaust gases pollutants data. Binary mixtures with pyrogasoline did not improve or worsen the engine’s performance, but the ternary mixtures (gasoline + pyrogasoline + ethanol) positively improved the engine’s performance with torque gains between 0.8 and 3.1% compared to gasoline. All fuels presented CO and unburned hydrocarbons emissions below those produced by this type of engine operated under normal (fossil) gasoline. On the other hand, NOx emissions from oxygenated fuels had contradictory behaviour compared to gasoline. If we consider the gains achieved by the torque with the ternary mixtures and reductions in polluting emissions obtained by mixtures with pyrogasoline, a future for this fuel can be foreseen as a partial replacement of fossil gasoline.

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ResumoÉ corrente ouvir-se dizer que a religião desapareceu do espaço público nas nossas sociedades secularizadas. Logo se acrescenta, porém, que a religião não desapareceu das nossas vidas privadas. Este artigo trata, precisamente, das relações entre a coisa desaparecida e o espaço de onde desapareceu -um espaço mediatizado e reflexivizado que acaba por ser palco de um supermercado de fés. Palavras-chave: media, novos movimentos religiosos, reflexividade, religião, secularizaçãoSe encararmos a secularização ocidental como uma forma de retirada da religião do espaço público, e se constatarmos que a religião não desapareceu, então teremos de pensar nas relações entre a religião e esse espaço público -um espaço reflexivizado e mediatizado.Tomo a palavra secularização nos termos de Marcel Gauchet: "Eis o mistério do mundo em que vivemos: por mais religiosos que sejam os indivíduos, a sociedade que eles formam permanece ateia nos seus princípios e nos seus mecanismos" (1985b): 12). Continuando: "Pode-se conceber, no limite, uma sociedade [organizada] para além do religioso" (1997:133), "onde a fé se torna uma opção sem influência nem alcance na definição da organização colectiva"(1997: 235). É isto o "fim da religião", quer dizer, o fim do mundo organizado segundo preceitos religiosos ou "a saída da organização religiosa do mundo" -não o fim da crença religiosa e da sua importância para os indivíduos.J. Bauberot (ref. Hervieu-Léger e Champion, 1986: 279, 280) fala-nos, a propósito, de cultura de pluralismo religioso: a religião torna-se opção da vida privada, porventura intensa, vivida no seio dum ateísmo social que rege a vida colectiva sem obedecer a critérios religiosos.