We characterize those Einstein four manifolds which are locally symmetric spaces of noncompact type. Namely they are four manifolds which admit solutions to the (non-Abelian) Seiberg Witten equations and satisfy certain characteristic number equality.

Proof systems for logics with recursive definitions typically impose a strict syntactic stratification on the body of a definition to ensure cut elimination and consistency of the logics, i.e., by forbidding any negative occurrences of the predicate being defined. Often such a restriction is too strong, as there are cases where such negative occurrences do not lead to inconsistency. Several log...

It is known that six Painlevé equations are in general irreducible, namely, their solutions cannot be expressed by “classical functions” in the sense of Umemura [18]. However, it is also known that they admit classical solutions for special values of parameters except for PI. Much effort have been made for the investigation of classical solutions. As a result, it has been recognized that there ...

Sleep scientists admit that they neither know, nor do they really understand what the fundamental purpose or function of sleep is. Such an extraordinary admission seems to indicate that problems may exist both at the conceptual and the methodological levels. This paper attempts to offer reasoned and logical arguments, explaining the purpose of sleep at the conceptual level. It also draws attent...

Walter Block’s (2003) supposedly “entirely critical” (p. 48) reply greatly narrows the gap between our positions (Caplan 2001, 1999, 1997; Block 1999). It is a major concession for Block to admit that synthetic a priori propositions can have a low probability and empirical propositions can have a high probability. The implication, though he does not admit it, is that his initial claims most con...

We extend the earlier results on the equivalence between the Boolean and the multivalued dependencies in relational databases and fragments of the Boolean propositional logic. It is shown that these equivalences are still valid for the databases that store complex data elements obtained from the recursive nesting of record, list, set and multiset constructors. The major proof argument utilises ...

We consider N=2 supersymmetric extensions of the Camassa-Holm and HunterSaxton equations. We show that they admit geometric interpretations as Euler equations on the superconformal algebra of contact vector fields on the 1|2dimensional supercircle. We use the bi-Hamiltonian formulation to derive Lax pairs. Moreover, we present some simple examples of explicit solutions. As a byproduct of our an...