Maxwell's Theory of Solid Angle and the Construction of Knotted Fields

We provide a systematic description of the solid angle function as a means of constructing a knotted field for any curve or link in $\mathbb{R}^3$. This is a purely geometric construction in which all of the properties of the entire knotted field derive from the geometry of the curve, and from projective and spherical geometry. We emphasise a fundamental homotopy formula as unifying different formulae for computing the solid angle. The solid angle induces a natural framing of the curve, which we show is related to its writhe and use to characterise the local structure in a neighborhood of the knot. Finally, we discuss computational implementation of the formulae derived, with C code provided, and give illustrations for how the solid angle may be used to give explicit constructions of knotted scroll waves in excitable media and knotted director fields around disclination lines in nematic liquid crystals.Comment: 20 pages, 9 figure

Open Access eXchange (OAeX): an economic model and platform for fundraising open scholarship services

This article describes the Open Access eXchange (OAeX) project, a pragmatic and comprehensive economic model and fundraising platform for open scholarship initiatives. OAeX connects bidders with funders at scale and right across the open scholarship spectrum through crowdfunding: financial expenditure is regulated by a market of freely competing providers and financial transactions and transparency are assured by a clearing-house entity. Specifically, OAeX seeks to facilitate open access publishing without the barrier of article processing charges (APCs), as well as contribute to solving challenges of transparency and economic sustainability in open scholarship projects in the broader sense

"Busybodies, Cranks and Mischief-Makers": Revisiting Finnigan v New Zealand Rugby Football Union and the Pro Bono Ethos

Finnigan v New Zealand Rugby Football Union has assumed a prominent position in New Zealand's relatively short legal history. This is in part due to the legal principles established by the case – it is recognised as a leading case in both administrative law and sports law. The case is perhaps more notable for its social and historical significance – it is fondly remembered as "the case that stopped the tour". This article argues that the case is significant on two further levels. It is a little-known fact that the case was taken on an entirely pro bono basis. The premise of this article is that, without the pro bono ethos of the lawyers involved, one of New Zealand's most famous cases would never have eventuated. The second little-known element of the case is how the plaintiffs' lawyers tactfully avoided the common law doctrine of maintenance. The true significance of Finnigan v New Zealand Rugby Football Union is only realised when the case is examined from a wider perspective than has been done previously.&nbsp

Concerns of middle and high school teachers toward inclusion of students with exceptional education needs

Includes bibliographical references

C*-algebras associated to graphs of groups

To a large class of graphs of groups we associate a C*-algebra universal for generators and relations. We show that this C*-algebra is stably isomorphic to the crossed product induced from the action of the fundamental group of the graph of groups on the boundary of its Bass-Serre tree. We characterise when this action is minimal, and find a sufficient condition under which it is locally contractive. In the case of generalised Baumslag-Solitar graphs of groups (graphs of groups in which every group is infinite cyclic) we also characterise topological freeness of this action. We are then able to establish a dichotomy for simple C*-algebras associated to generalised Baumslag-Solitar graphs of groups: they are either a Kirchberg algebra, or a stable Bunce-Deddens algebra.Comment: 59 page