Mahler measure under variations of the base group

We study properties of a generalization of the Mahler measure to elements in group rings, in terms of the Lueck-Fuglede-Kadison determinant. Our main focus is the variation of the Mahler measure when the base group is changed. In particular, we study how to obtain the Mahler measure over an infinite group as limit of Mahler measures over finite groups, for example, in the classical case of the free abelian group or the infinite dihedral group, and others.Comment: 21 page

A global protocol for monitoring of coral bleaching

Coral bleaching and subsequent mortality represent a major threat to the future health and productivity of coral reefs. However a lack of reliable data on occurrence, severity and other characteristics of bleaching events hampers research on the causes and consequences of this important phenomenon. This article describes a global protocol for monitoring coral bleaching events, which addresses this problem and can be used by people with different levels of expertise and resources

Excited-state contribution to the axial-vector and pseudo-scalar correlators with two extra pions

We study multi-particle state contributions to the QCD two-point functions of the axial-vector and pseudo-scalar quark bilinears in a finite spatial volume. For sufficiently small quark masses one expects three-meson states with two additional pions at rest to have the lowest total energy after the ground state. We calculate this three-meson state contribution using chiral perturbation theory. We find it to be strongly suppressed and too small to be seen in present-day lattice simulations.Comment: 17 pages, 5 figure

On the Consistent Effect Histories Approach to Quantum Mechanics

A formulation of the consistent histories approach to quantum mechanics in terms of generalized observables (POV measures) and effect operators is provided. The usual notion of `history' is generalized to the notion of `effect history'. The space of effect histories carries the structure of a D-poset. Recent results of J.D. Maitland Wright imply that every decoherence functional defined for ordinary histories can be uniquely extended to a bi-additive decoherence functional on the space of effect histories. Omnes' logical interpretation is generalized to the present context. The result of this work considerably generalizes and simplifies the earlier formulation of the consistent effect histories approach to quantum mechanics communicated in a previous work of this author.Comment: LaTeX 2.09 version replaced by LaTeX2e version, minor change