Chris Miller

The derivation of a category of ‘environmental rights’ (as argued in this journal by Margaret DeMerieux) from certain cases heard in the European Court of Human Rights is examined. Opposing the majority judicial opinion of that court, there is emerging a dissenting view which is reluctant to extend a rights perspective to those nuisances which can, in theory, be avoided by relocation of the family home. This critique is then extended to Marcic v Thames Water Utilities in which the claimant used the Human Rights Act 1998 (as well as common law) to secure damages for an environmental threat (flooding) to his home. It is further argued that any ‘rights’ dimension currently attached to environmental intrusion on private life will give way to policy imperatives once the effects of climate change come to be recognized

In this paper, we continue investigations into the asymptotic behavior of solutions of differential equations over o-minimal structures.Let ℜ be an expansion of the real field (ℝ, +, ·).A differentiable mapF= (F1,…,F1): (a, b) → ℝiisℜ-Pfaffianif there existsG: ℝ1+l→ ℝldefinable in ℜ such thatF′(t) =G(t, F(t)) for allt∈ (a, b) and each component functionGi: ℝ1+l→ ℝ is independent of the lastl−ivariables (i= 1, …,l). If ℜ is o-minimal andF: (a, b) → ℝlis ℜ-Pfaffian, then (ℜ,F) is o-minimal (Proposition 7). We say thatF: ℝ → ℝlis ultimately ℜ-Pfaffian if there existsr∈ ℝ such that the restrictionF↾(r, ∞) is ℜ-Pfaffian. (In general,ultimatelyabbreviates “for all sufficiently large positive arguments”.)The structure ℜ isclosed under asymptotic integrationif for each ultimately non-zero unary (that is, ℝ → ℝ) functionfdefinable in ℜ there is an ultimately differentiable unary functiongdefinable in ℜ such that limt→+∞[g′(t)/f(t)] = 1- If ℜ is closed under asymptotic integration, then ℜ is o-minimal and definesex: ℝ → ℝ (Proposition 2).Note that the above definitions make sense for expansions of arbitrary ordered fields.

An open U ⊆ ℝ is produced such that (ℝ, +, ·, U) defines a Borel isomorph of (ℝ, +, ·, ℕ) but does not define ℕ. It follows that (ℝ, +, ·, U) defines sets in every level of the projective hierarchy but does not define all projective sets. This result is elaborated in various ways that involve geometric measure theory and working over o-minimal expansions of (ℝ, +, ·). In particular, there is a Cantor set E ⊆ ℝ such that (ℝ, +, ·, E) defines a Borel isomorph of (ℝ, +, ·, ℕ) and, for every exponentially bounded o-minimal expansion $\germ{R}$ of (ℝ, +, ·), every subset of ℝ definable in ( $\germ{R}$ , E) either has interior or is Hausdorff null

© 2016. The American Astronomical Society. All rights reserved.We present DES14X3taz, a new hydrogen-poor superluminous supernova discovered by the Dark Energy Survey supernova program, with additional photometric data provided by the Survey Using DECam for Superluminous Supernovae. Spectra obtained using Optical System for Imaging and low-Intermediate-Resolution Integrated Spectroscopy on the Gran Telescopio CANARIAS show DES14X3taz is an SLSN-I at z = 0.608. Multi-color photometry reveals a double-peaked light curve: a blue and relatively bright initial peak that fades rapidly prior to the slower rise of the main light curve. Our multi-color photometry allows us, for the first time, to show that the initial peak cools from 22,000 to 8000 K over 15 rest-frame days, and is faster and brighter than any published core-collapse supernova, reaching 30% of the bolometric luminosity of the main peak. No physical 56Ni-powered model can fit this initial peak. We show that a shock-cooling model followed by a magnetar driving the second phase of the light curve can adequately explain the entire light curve of DES14X3taz. Models involving the shock-cooling of extended circumstellar material at a distance of ≃400 R⊙ are preferred over the cooling of shock-heated surface layers of a stellar envelope. We compare DES14X3taz to the few double-peaked SLSN-I events in the literature. Although the rise times and characteristics of these initial peaks differ, there exists the tantalizing possibility that they can be explained by one physical interpretation.