Caustics of plane curves, their birationality and matrix projections

After recalling the notion of caustics of plane curves and basic equations, we first show the birationality of the caustic map for a general source point S in the plane. Then we prove more generally a theorem for curves D in the projective space of 3x3 symmetric matrices B. For a general 3x1 vector S the projection to the plane given by B --- BS is birational on D, unless D is not a line and D is contained in a plane of the form Delta_v = {B | Bv = 0}.Comment: 10 pages, to appear in a Springer Verlag volume dedicated to Klaus Hulek on the occasion of his 60-th birthday. Final version, added some remarks by the refere

University Students Promoting Science in the Community

Project SEARCH (Science Education and Research for Children) has brought these undergraduate students here today. It is an outreach program designed to bring the science resources of a large research university to classrooms and community centers. For the past 9 years, SEARCH students have spent 4 hours each week doing hands-on-science experiments, dissecting frogs, demonstrating microscopes, lecturing about the planets, playing computer games, exploring the World Wide Web, and creating Web pages.published or submitted for publicationis peer reviewe

Can the goldfish see the water? A critical analysis of ‘good intentions’ in cross-cultural practice

We claim to hold values that our students are responsible and autonomous adults whose success in our courses is best facilitated by our understanding of and respect for their specific backgrounds. We wish to be judged on these values by feedback provided by our students and those with whom we work. However, how well, if ever, are we able to ‘see the water,’ the cultural conditioning that leads us to act in ways that seem supportive of our students to us, but may be perceived differently by them? In this paper, we present conflicting evidence around perceptions of our practice. We discuss where things have gone well, and where interventions have possibly been traumatic for the recipients. We question whether, and how, our practice cross-culturally can be safe. We challenge ourselves and others to think carefully about our responsibilities to our students, whether our privileged positioning obliges us to share and if so, how that sharing can occur in ways that validate and equally respect the values of those with whom we work

Minding our ps and qs: Issues of property, provenance, quantity and quality in institutional repositories

The development of institutional repositories has opened the path to the mass availability of peer-reviewed scholarly information and the extension of information democracy to the academic domain. A secondary space of free-to-all documents has begun to parallel the hitherto-closed world of journal publishing and many publishers have consented to the inclusion of copyrighted documents in digital repositories, although frequently specifying that a version other than the formally-published one be used. This paper will conceptually examine the complex interplay of rights, permissions and versions between publishers and repositories, focussing on the New Zealand situation and the challenges faced by university repositories in recruiting high-quality peer-reviewed documents for the open access domain. A brief statistical snapshot of the appearance of material from significant publishers in repositories will be used to gauge the progress that has been made towards broadening information availability. The paper will also look at the importance of harvesting and dissemination, in particular the role of Google Scholar in bringing research information within reach of ordinary internet users. The importance of accuracy, authority, provenance and transparency in the presentation of research-based information and the important role that librarians can and should play in optimising the open research discovery experience will be emphasised

Modelling Socially Intelligent Agents

The perspective of modelling agents rather than using them for a specificed purpose entails a difference in approach. In particular an emphasis on veracity as opposed to efficiency. An approach using evolving populations of mental models is described that goes some way to meet these concerns. It is then argued that social intelligence is not merely intelligence plus interaction but should allow for individual relationships to develop between agents. This means that, at least, agents must be able to distinguish, identify, model and address other agents, either individually or in groups. In other words that purely homogeneous interaction is insufficient. Two example models are described that illustrate these concerns, the second in detail where agents act and communicate socially, where this is determined by the evolution of their mental models. Finally some problems that arise in the interpretation of such simulations is discussed

On the geometry of Pr\"ufer intersections of valuation rings

Let $F$ be a field, let $D$ be a subring of $F$ and let $Z$ be an irreducible subspace of the space of all valuation rings between $D$ and $F$ that have quotient field $F$. Then $Z$ is a locally ringed space whose ring of global sections is $A = \bigcap_{V \in Z}V$. All rings between $D$ and $F$ that are integrally closed in $F$ arise in such a way. Motivated by applications in areas such as multiplicative ideal theory and real algebraic geometry, a number of authors have formulated criteria for when $A$ is a Pr\"ufer domain. We give geometric criteria for when $A$ is a Pr\"ufer domain that reduce this issue to questions of prime avoidance. These criteria, which unify and extend a variety of different results in the literature, are framed in terms of morphisms of $Z$ into the projective line ${\mathbb{P}}^1_D$Comment: 13 pages, to appear in Pacific Journal of Mathematic