On the boundedness of periodic pseudo-differential operators

In this paper we investigate the $L^p$-boundedness of certain classes of periodic pseudo-differential operators. The operators considered arise from the study of symbols on $\mathbb{T}^n\times\mathbb{Z}^n$ with limited regularity.Comment: Pseudo-differential operator

Some Remarks about Duality, Analytic Torsion and Gaussian Integration in Antisymmetric Field Theories

From a path integral point of view (e.g. \cite{Q98}) physicists have shown how {\it duality} in antisymmetric quantum field theories on a closed space-time manifold $M$ relies in a fundamental way on Fourier Transformations of formal infinite-dimensional volume measures. We first review these facts from a measure theoretical point of view, setting the importance of the Hodge decomposition theorem in the underlying geometric picture, ignoring the local symmetry which lead to degeneracies of the action. To handle these degeneracies we then apply Schwarz's Ansatz showing how duality leads to a factorization of the analytic torsion of $M$ in terms of the partition functions associated to degenerate "dual" actions, which in the even dimensional case corresponds to the identification of these partition functions.Comment: 15 pages, LaTe

Extended Symmetries and Poisson Algebras Associated to Twisted Dirac Structures

In this paper we study the relationship between the extended symmetries of exact Courant algebroids over a manifold $M$, defined by Bursztyn, Cavalcanti and Gualtieri, and the Poisson algebras of admissible functions associated to twisted Dirac structures when acted by Lie groups. We show that the usual homomorphisms of Lie algebras between the algebras of infinitesimal symmetries of the action, vector fields on the manifold and the Poisson algebra of observables, appearing in symplectic geometry, generalize to natural maps of Leibniz algebras induced both by the extended action and compatible moment maps associated to it in the context of twisted Dirac structures.Comment: 11 pages, no figure

The known unknown : identification, provenancing, and relocation of pieces of decorative architecture from Roman public buildings and other private structures in Malta

In archaeology a narrative or story is usually reconstructed on the basis of a meticulous study of material. In normal circumstances, the physical material constitutes the known, while the actual story remains the unknown until the material is deciphered and put in context. When it comes to certain aspects of Roman architecture in Malta, and especially the architecture of public buildings, the story is somewhat reversed. This is because we know of the presence of public buildings but the actual physical evidence of such structures has for long remained unknown. This study seeks to provide a story, one that gives a provenance to some of the most important architectural elements found in various local collections, thereby bringing to the attention of researchers a corpus of data that has hitherto been little known.peer-reviewe