Constrained Dynamics of Universally Coupled Massive Spin 2-spin 0 Gravities

The 2-parameter family of massive variants of Einstein's gravity (on a Minkowski background) found by Ogievetsky and Polubarinov by excluding lower spins can also be derived using universal coupling. A Dirac-Bergmann constrained dynamics analysis seems not to have been presented for these theories, the Freund-Maheshwari-Schonberg special case, or any other massive gravity beyond the linear level treated by Marzban, Whiting and van Dam. Here the Dirac-Bergmann apparatus is applied to these theories. A few remarks are made on the question of positive energy. Being bimetric, massive gravities have a causality puzzle, but it appears soluble by the introduction and judicious use of gauge freedom.Comment: 6 pages; Talk given at QG05, Cala Gonone (Italy), September 200

Global Existence and Non-existence Theorems for Nonlinear Wave Equations

In this article we focus on the global well-posedness of an initial-boundary value problem for a nonlinear wave equation in all space dimensions. The nonlinearity in the equation features the damping term |u|k |ut|m sgn(ut) and a source term of the form |u|p-1u, where k, p ≥ 1 and 0 \u3c m \u3c 1. In addition, if the space dimension n ≥ 3, then the parameters k, m and p satisfy p, k/(1-m) ≤ n/(n - 2). We show that whenever k + m ≥ p, then local weak solutions are global. On the other hand, we prove that whenever p \u3e k + m and the initial energy is negative, then local weak solutions blow-up in finite time, regardless of the size of the initial data

The Anglo-Norman Bible's Book of Judges: A Critical Edition (BL Royal 1 C III)

A silver-tongued assassin, a motherly prophetess, a consecrated strongman unable to resist the charms of foreign women: the Anglo-Norman Bible’s Book of Judges features a roll-call of unlikely heroes. At the book’s core is a cycle of saviour stories. Twelve times the Israelites embrace foreign gods, succumb to neighbouring enemies, repent and are delivered by a ‘judge’. As Israel itself descends into ever-greater religious, moral and political decay, the narrative pattern also unravels. The book ends bleakly, with stories of rape, murder and civil war. The stage is set for a king. Gideon-a doubting Thomas who repeatedly ‘tests’ God-and Samson-lion-killer and lover of Delilah-were firm medieval favourites. Their tales and those of other flawed judges inspired heroic deeds on the battlefield and provided lessons on how to behave (and indeed how not to behave). With its remarkable heroines, moreover-from cut-throat Jael, who wields a tent-peg to devastating effect, to Jephthah’s dignified daughter, sacrificed because of her father’s rash vow-this is a book that prompted much reflection in the Middle Ages on the place of women in society. The Anglo-Norman Bible’s Book of Judges survives in two fourteenth-century manuscripts: British Library Royal MS 1 C III (L), noted for its multilingual glosses, and the richly illustrated Paris, Bibliothèque nationale de France, fonds français 1 (P). The critical text, based on L, has been prepared by Pitts. An introduction and notes by Grange aim to elucidate and interpret the Anglo-Norman Bible’s Book of Judges for the modern reader

A dependent nominal type theory

Nominal abstract syntax is an approach to representing names and binding pioneered by Gabbay and Pitts. So far nominal techniques have mostly been studied using classical logic or model theory, not type theory. Nominal extensions to simple, dependent and ML-like polymorphic languages have been studied, but decidability and normalization results have only been established for simple nominal type theories. We present a LF-style dependent type theory extended with name-abstraction types, prove soundness and decidability of beta-eta-equivalence checking, discuss adequacy and canonical forms via an example, and discuss extensions such as dependently-typed recursion and induction principles

Infusing disability sport into the sport management curriculum

Disability sport is growing around the world with momentum and is described as a “movement” (Bailey, 2008; De- Pauw & Gavron, 2005). While there are more similarities than differences with sport management for able-bodied athletes and those with disabilities, there are additional needs and considerations for persons with disabilities (DePauw & Gavron, 2005). The noticeable visibility of individuals with disabilities in society, including sport, raises concerns about the degree to which sport management academic programs have modified their curricula to ensure that individuals working in the sport management field are prepared to deal with the uniqueness of disability sport. This paper (a) discusses theoretical perspectives toward understanding and thinking about disability, (b) explores ways to enhance sport management curricula through infusion of disability sport, (c) reflects upon current social practices for curriculum integration of athletes with disabilities in sport, and (d) acknowledges infusion of disability sport businesses, organizations and events

Universally Coupled Massive Gravity

We derive Einstein's equations from a linear theory in flat space-time using free-field gauge invariance and universal coupling. The gravitational potential can be either covariant or contravariant and of almost any density weight. We adapt these results to yield universally coupled massive variants of Einstein's equations, yielding two one-parameter families of distinct theories with spin 2 and spin 0. The Freund-Maheshwari-Schonberg theory is therefore not the unique universally coupled massive generalization of Einstein's theory, although it is privileged in some respects. The theories we derive are a subset of those found by Ogievetsky and Polubarinov by other means. The question of positive energy, which continues to be discussed, might be addressed numerically in spherical symmetry. We briefly comment on the issue of causality with two observable metrics and the need for gauge freedom and address some criticisms by Padmanabhan of field derivations of Einstein-like equations along the way.Comment: Introduction notes resemblance between Einstein's discovery process and later field/spin 2 project; matches journal versio

A principled approach to programming with nested types in Haskell

Initial algebra semantics is one of the cornerstones of the theory of modern functional programming languages. For each inductive data type, it provides a Church encoding for that type, a build combinator which constructs data of that type, a fold combinator which encapsulates structured recursion over data of that type, and a fold/build rule which optimises modular programs by eliminating from them data constructed using the buildcombinator, and immediately consumed using the foldcombinator, for that type. It has long been thought that initial algebra semantics is not expressive enough to provide a similar foundation for programming with nested types in Haskell. Specifically, the standard folds derived from initial algebra semantics have been considered too weak to capture commonly occurring patterns of recursion over data of nested types in Haskell, and no build combinators or fold/build rules have until now been defined for nested types. This paper shows that standard folds are, in fact, sufficiently expressive for programming with nested types in Haskell. It also defines buildcombinators and fold/build fusion rules for nested types. It thus shows how initial algebra semantics provides a principled, expressive, and elegant foundation for programming with nested types in Haskell