Abstract Argumentation is a simple yet powerful formalism for modeling the human reasoning and argumentation process. Various semantics have been suggested with a view of arriving at coherent outcomes of the argumentation process. Two categories of semantics are well-known, extension-based semantics and labeling-based semantics. Translations between semantics are an important area of interest t...

The Great Artesian Basin (GAB) underlies about one fifth of mainland Australia. Much of this area is arid or semiarid and often artesian water is the only reliable source of potable water, historically via springs. Prior to the 1870s, there were around 3,000 flowing springs ringing the GAB. The springs were a vital source of water for Aborigines as well as early explorers, workers and pastorali...

Transverse–tracefree (TT–) tensors on (R, gab), with gab an asymptotically flat metric of fast decay at infinity, are studied. When the source tensor from which these TT tensors are constructed has fast fall–off at infinity, TT tensors allow a multipole–type expansion. When gab has no conformal Killing vectors (CKV’s) it is proven that any finite but otherwise arbitrary set of moments can be re...

Perturbation analysis provides the framework for an understanding of the effects of a small mass moving through a “background” spacetime. The analysis begins with a background spacetime metric gab which is usually a vacuum solution of the Einstein equations Gab(g) = 0. An object of small mass μ then disturbs the geometry by an amount hab = O(μ) which is governed by the perturbed Einstein equati...

At a fixed point in spacetime (say, x0), gravitational phase space consists of the space of symmetric matrices {F ab} [corresponding to the canonical momentum π(x0)] and of symmetric matrices {Gab} [corresponding to the canonical metric gab(x0)], where 1 ≤ a, b ≤ n, and, crucially, the matrix {Gab} is necessarily positive definite, i.e. ∑ uGabu b > 0 whenever ∑ (ua)2 > 0. In an alternative quan...

At a fixed point in spacetime (say, x0), gravitational phase space consists of the space of symmetric matrices {F ab} [corresponding to the canonical momentum π(x0)] and of symmetric matrices {Gab} [corresponding to the canonical metric gab(x0)], where 1 ≤ a, b ≤ n, and, crucially, the matrix {Gab} is necessarily positive definite, i.e. ∑ uGabu b > 0 whenever ∑ (ua)2 > 0. In an alternative quan...