Experimental results on spectra and wave functions of a ray-splitting microwave billiard are presented. The billiard is formed by a flat rectangular microwave cavity with a quarter-circle insert made of teflon in one of the corners. Using the Gutzwiller trace formula, the contribution of the periodic orbits of the billiard to the density of states are determined. The wave functions, many of them showing scars associated with periodic orbits, are interpreted in terms of the semiclassical Green function.

"We prove that any variety of relation algebras which contains an algebra with infinitely many elements below the identity, or which contains the full group relation algebra on some infinite group (or on arbitrarily large finite groups), must have an undecidable equational theory. Then we construct an embedding of the lattice of all subsets of the natural numbers into the lattice of varieties of relation algebras such that the variety correlated with a set [italic capital]X of natural numbers has a (...) decidable equational theory if and only if [italic capital]X is a decidable (i.e., recursive) set. Finally, we construct an example of an infinite, finitely generated, simple, representable relation algebra that has a decidable equational theory.'' -- Abstract. (shrink)

Diogenes Laertius relates the tale that Aristotle, upon being reproached for giving alms to a debased fellow, replied, ‘It was not his character, but the man, that I pitied.’ Some such reply is equally apt in apology for a paper paying homage to an idea long discredited in the philosophical world, Aristotle's theory of Place. I have been moved, not indeed by the apparent character of Aristotle's theory, for that is easily reproached, but by what has proved for the philosophical (...) tradition of infinite worth, what we may call the theory's ‘latent virtue’. There is a danger, of course, as hard-headed philologists and commentators are always reminding us, that in attending to this latent virtue we may be paying sentimental homage to the dead. Thus it will be important that we first carefully and coldly examine the overt character of the Aristotelian doctrine before attempting to justify any philosophical compassion felt in its presence. More than likely in such a disinterested inquiry it will be found that our ‘debased fellow’ is a good deal more of a man than the modern reformers have allowed. (shrink)

Summary One aim of this paper is to provide an assessment of the recent attempts to interpret the development of Galileo's theory of motion in the late Paduan period 1604?1610. In addition to this a new interpretation of this process of development is advanced. This interpretation is the first that proves able to provide a full account of all the features on folio 152r of volume 72 of the Galilean manuscripts which has been claimed to be of crucial significance. The (...) major feature of the interpretation is that it is the first to account for the relationship between Galileo's theoretical and experimental work in the period 1604?1610. (shrink)