The omega-limit sets of quadratic Julia sets

In this paper we characterize \w-limit sets of dendritic Julia sets for quadratic maps. We use Baldwin's symbolic representation of these spaces as a non-Hausdorff itinerary space and prove that quadratic maps with dendritic Julia sets have shadowing, and also that for all such maps, a closed invariant set is an \w-limit set of a point if, and only if, it is internally chain transitive.Comment: 24 page

On the omega-limit sets of tent maps

For a continuous map f on a compact metric space (X,d), a subset D of X is internally chain transitive if for every x and y in D and every delta > 0 there is a sequence of points {x=x_0,x_1, ...,x_n=y} such that d(f(x_i),x_{i+1}) < delta for i=0,1, ...,n-1. It is known that every omega-limit set is internally chain transitive; in earlier work it was shown that for X a shift of finite type, a closed subset D of X is internally chain transitive if and only if D is an omega-limit set for some point in X, and that the same is also true for the tent map with slope equal to 2. In this paper, we prove that for tent maps whose critical point c=1/2 is periodic, every closed, internally chain transitive set is necessarily an omega-limit set. Furthermore, we show that there are at least countably many tent maps with non-recurrent critical point for which there is a closed, internally chain transitive set which is not an omega-limit set. Together, these results lead us to conjecture that for those tent maps with shadowing (or pseudo-orbit tracing), the omega-limit sets are precisely those sets having internal chain transitivity.Comment: 17 page

Applied linguistics and mathematics education: More than words and numbers

The preceding set of papers has explored various aspects of the role of language in mathematics education. The papers reflect the work of individual contributors. An important part of our collaboration, however, has been the conversation between us. This paper reflects aspects of that conversation, as we draw together some of the themes that have emerged during our work. In particular, we discuss some of the implications of our analyses for theory, policy, practice and inter-disciplinarity in mathematics education and applied linguistics

The incidence of nominal and real wage rigidities in Great Britain: 1978–1998

This paper analyzes the extent of rigidities in wage setting in Great Britain over the 1980s and 1990s. Our estimation strategy, which generalizes the work of Altonji and Devereux (2000), models the notional wage growth distribution--the distribution of nominal wage growth that would occur in the absence of rigidities in pay--while allowing for the presence of measurement error in the data. The model then allows for the possibility that the nominal wage growth of a fraction of the workforce may be subject to a nominal or real downward rigidity. Our model suggests that real rigidities in wage setting are more prevalent than nominal rigidities, although the incidence of these real wage rigidities has fallen gradually over time. If firms cannot cut real wages in response to negative demand shocks they may resort to laying off workers. Our results support this microfoundation of the wage-unemployment Phillips curve: Workers who are more likely to be protected from wage cuts are also more likely to lose their jobs.Wages - Great Britain

Shadowing and Expansivity in Sub-Spaces

We address various notions of shadowing and expansivity for continuous maps restricted to a proper subset of their domain. We prove new equivalences of shadowing and expansive properties, we demonstrate under what conditions certain expanding maps have shadowing, and generalize some known results in this area. We also investigate the impact of our theory on maps of the interval, in which context some of our results can be extended.Comment: 18 page

Albatross

Albatross looks at the place of these iconic birds in a wide variety of human cultures, from early responses by north Atlantic mariners to modern encounters, examining in detail the role the bird plays in the lives of different peoples and societies. The albatross s remarkable ease in the air and its huge wingspan strikes all those who observe them, and the huge journeys they undertake across the oceans inspires awe. The bird has been celebrated through proverbs, folk stories, art, and ceremony. For many, the bird\u27s cultural significance is still determined by Coleridge\u27s The Rime of the Ancient Mariner. People have engaged with the bird over the last two centuries, from those who sought to exploit them to those who devoted their lives to them. Writers, artists and documentary makers have all focused on the albatross and its place in the human imagination has been demonstrated throughout history. The book concludes with a consideration of the bird s changing significance in the modern world, as well as threats to its continued existence and its prospects for the future

Coleridge’s albatross and the impulse to seabird conservation

oleridge was a regular companion. Emigrants’ diaries and journals rarely failed to describe one particular landmark experience: the first sighting of the albatross, followed by attempts to kill or capture a specimen, in the style of the Ancient Mariner. ‘Who could doubt their supernatural attributes? Certainly not a spirit-chilled landswoman, with Coleridge’s magic legend perpetually repeating itself to her’, wrote 27-year-old Luisa [sic] Meredith, arriving in Sydney in 1839. (Lyons 13)

Reports of Three Cases Illustrative of the Good Effects of Pressure in Strumous Synovitis.

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