We show that the enveloping space \ of a partial action of a Polish group G on a Polish space \ is a standard Borel space, that is to say, there is a topology \ on \ such that \\) is Polish and the quotient Borel structure on \ is equal to \\). To prove this result we show a generalization of a theorem of Burgess about Borel selectors for the orbit equivalence relation induced by a group action and also (...) show that some properties of the Vaught’s transform are valid for partial actions of groups. (shrink)

Deinde qui minus grauis esset iis senectus, si octingentesimum annum agerent quam [si] octogesimum ? This sentence has to do with people who complain that the evils of old age have come upon them all too soon. Cicero rejoins that they would be of exactly the same mind, even though they had a life ten times as long to look back upon.

It is traditionally believed that cerebral activation (the presence of low voltage fast electrical activity in the neocortex and rhythmical slow activity in the hippocampus) is correlated with arousal, while deactivation (the presence of large amplitude irregular slow waves or spindles in both the neocortex and the hippocampus) is correlated with sleep or coma. However, since there are many exceptions, these generalizations have only limited validity. Activated patterns occur in normal sleep (active or paradoxical sleep) and during states of anesthesia (...) and coma. Deactivated patterns occur, at times, during normal waking, or during behavior in awake animals treated with atropinic drugs. Also, the fact that patterns characteristic of sleep, arousal, and waking behavior continue in decorticate animals indicates that reticulo-cortical mechanisms are not essential for these aspects of behavior. (shrink)

By considering the irreducible representations of the Lorentz group, an analysis of the different spin-2 waves is presented. In particular, the question of the helicity is discussed. It is concluded that, although from the point of view of representation theory there are no compelling reasons to choose between spin-2 waves with helicity σ=±1 or σ=±2, consistency arguments of the ensuing field theories favor waves with helicity σ=±1.