Dynamics of homeomorphisms of the torus homotopic to Dehn twists

In this paper we consider torus homeomorphisms $f$ homotopic to Dehn twists. We prove that if the vertical rotation set of $f$ is reduced to zero, then there exists a compact connected essential "horizontal" set K, invariant under $f$. In other words, if we consider the lift $\hat{f}$ of $f$ to the cylinder, which has zero vertical rotation number, then all points have uniformly bounded motion under iterates of $\hat{f}$. Also, we give a simple explicit condition which, when satisfied, implies that the vertical rotation set contains an interval and thus also implies positive topological entropy. As a corollary of the above results, we prove a version of Boyland's conjecture to this setting: If $f$ is area preserving and has a lift $\hat{f}$ to the cylinder with zero Lebesgue measure vertical rotation number, then either the orbits of all points are uniformly bounded under $\hat{f}$, or there are points in the cylinder with positive vertical velocity and others with negative vertical velocity

Personal protective equipment (PPE) in a pandemic: Approaches to PPE preservation for South African healthcare facilities

Personal protective equipment (PPE) is key to protecting healthcare workers from COVID-19 infection, but the pandemic has disrupted supply chains globally and necessitated rapid review of the scientific evidence for PPE re-use. In South Africa, where the COVID-19 epidemic is still developing, healthcare facilities have a short window of opportunity to improve PPE supply chains, train staff on prudent PPE use, and devise plans to track and manage the inevitable increases in PPE demand. This article discusses the available PPE preservation strategies and addresses the issue of decontamination and re-use of N95 respirators as a last-resort strategy for critical shortages during the pandemic

School-visit by pre-service teachers: An insider view on students’ experiences and staff’s perceptions

In this paper we describe and interpret students’ experiences and staff’s perceptions of a school-visit project for pre-service teachers.  Our developmental intention was to ascertain the worth of the intervention with a view to improve practice.  As coordinators of the project, we were well placed to undertake a close-up study by giving a strong role to both fourth-year students and lecturers as evaluators of the teaching and learning context created by the intervention.  Drawing on Paulo Freire’s conception of naïve consciousness, we explore the gap between students’ experiences and staff’s perceptions.  Using illuminative evaluation, we provide support that the students were stimulated to become socially concerned, albeit not critically, by means of a once-off experience of unequal schooling contexts during their first year.  Staff, however, indicated an awareness of what needs to be done to integrate the students’ initial experiences, and there were no real examples that they had drawn on the project to reinforce these experiences through their classroom pedagogies.  We conclude the article by highlighting critical dialogue as a prerequisite for curricular reform

The challenge of quality and relevance in South African education: a philosophical perspective

Within a changing South African socio-political context, quality education and schooling mean radically different things to different people. The call for contextualising education within an African life-world, and the fear of declining quality and standards in education, necessitate a closer look at the role and meaning of quality and relevance in education. This article consequently attempts a philosophical perspective on quality education and the role of educational standards and relevance. (South African Journal of Education: 2001 21(4): 208-212

Using life history to understand the interplay between identity, critical agency and social justice education

Published ArticleIn this article we use the concepts identity, agency and social justice education as a lens to explore the role of life history research in the study of the interconnection between emerging teacher identities, critical agency and social justice education. By exploring the life history of a white woman pre-service teacher, this study foregrounds the use of life history research to help teacher educators to understand the contexts through which student teachers' identities are constructed, and how these identities feed into agency and a stance to bring about social change

Quantifying the spatial implications of future land use policies in South Africa

Land use policies have a definite and lasting impact on the way that cities grow; however, it is difficult for policy- and decision-makers to observe and quantify the implications of their land use policies and strategies. There is thus a need for information and tools that can adequately support policy debates and influence decision-making through scientific evidence. Land use change models provide such a tool and have often been applied and tested in developed countries but lack the ability to simulate many of the multifaceted social problems observed in developing countries. Some more advanced models also require large amounts of data that are normally not available for South African cities. In this research, we adjust the existing Dyna-CLUE model to accommodate the unique multifaceted problems such as informal settlements, backyard shacks, rapid population growth and government interventions with regard to social housing projects and test the model for the city of Johannesburg. Two scenarios (AS-IS and Policy-Led) in combination with an urban development boundary (UDB) were tested and their effect was evaluated based on their influences on the cities spatial inequality, densification of the urban spatial pattern and increase in access to public transport. Results indicated that the Policy-Led scenario can improve the wealth and economic distributions between the north and south of the city. It can also provide more economic opportunities for the households living in the south of the city. Enforcing an UDB has a positive impact on urban sprawl and will result in increased densities across the city. The effect of the policies on the commuter distances indicated that both scenarios will lead to an overall increase in the number of households that have access to public transport, but the Policy-Led scenario will allow a greater number of low-income earners to have access to the public transport systems. We see great possibilities for using the existing model to simulate land use change in South African cities. The model requires less input data compared to some other modelling techniques and with small adjustments and adaptations can prove to be a useful tool for urban planner

Teaching for social justice education: the intersection between identity, critical agency, and social justice education

In line with national policy requirements, educators are increasingly addressing forms of social justice education by focusing on classroom pedagogies and educational practices to combat different forms of oppression such as racism and sexism. As all educators have a role to play in dismantling oppression and generating a vision for a more socially just future, teacher education has the responsibility to capacitate pre-service teachers to work in areas of social justice education. It is, however, difficult to conceptualise programmes for social justice education without considering the interconnection between various social identities and how such identities can feed into critical agency and education for social justice. Working with the assumption that white women teachers must be part of the solution to bring about social change in South African education, we used in-depth interviewing to explore pre-service teachers’ emerging identities as teachers, and how these identities are connected to notions of critical agency and a stance towards social justice.Keywords: agency; anti-oppressive education; identity; social justice education; teacher education; white women pre-service teacher

Evolution of the Great Tehuelche Paleolake in the Torres del Paine National Park of Chilean Patagonia during the Last Glacial Maximum and Holocene

Indexación: Web of Science; ScieloRESUMEN. Una serie de morrenas glaciares se distribuyen desde el margen oriental de la cuenca de drenaje Torres del Paine a cerca del actual margen de los Campos de Hielo Patagónico, junto con una serie de terrazas lacustres regional continuos relacionados con las fluctuaciones glaciales. La geomorfología, apoyada por la evidencia de sedimentos del lago, indica la existencia de un único paleolago proglacial en esta zona, aquí denominado el Gran Tehuelche paleolago. Este concepto ayuda a aclarar la cronología de eventos glaciales y conduce a una mejor comprensión de la evolución del sistema hidrológico de la zona de Torres del Paine. Avances glaciales referidos anteriormente como ocurrieron A, B y C durante el Último Máximo Glacial y alimentados con la Gran Tehuelche paleolago con agua de deshielo, que le permite alcanzar su máxima extensión. El descubrimiento de trombolitos en Laguna Amarga sugiere que el drenaje de la paleolago hacia el fiordo de Última Esperanza tuvo lugar en 7113 Cal. años AP, después de la fusión de una barrera de hielo que existía durante el avance glacial antes. Esto dio lugar al desarrollo de un sistema hidrológico fluvio-lacustre complejo que persiste hasta nuestros días. Palabras clave: Patagonia, último máximo glacial, Younger Dryas, trombolitos. RESUMEN. Un grupo de morrenas glaciales estan Distribuidas desde el margen Este de la cuenca de drenaje de Torres del Paine Hacia el margen real de los Campos de Hielo Patagónicos. Las morrenas se observan en conjunto con las Naciones Unidas Grupo de terrazas Lacustres Regionales, las Cuales estan vinculadas y una las fluctuaciones glaciales. La geomorfología y Evidencias de sedimentos Lacustres indicano la existence De unico ONU lago proglacial, referido En Este Estudio de Como Gran Paleolago Tehuelche. Este Concepto ayuda a clarificar la cronología de los eventos glaciales y permite Una mejor Comprensión de la Evolución del Sistema hidrológico del sector de Torres del Paine. Los eventos glaciales, previamente Referidos Como Avance A, B y C, ocurrieron Durante el Último Máximo Glacial y alimentaron con Aguas de fusión al Gran Paleolago Tehuelche, permitiéndole Alcanzar su alcalde extensión. El Descubrimiento de trombolitos en Laguna Amarga sugiere Que El desagüe del paleolago Ocurrió Hace 7.113 Cal. Por años AP el Seno de Última Esperanza, producto de la fusión De Una barrera glaciar existente Durante los Avances glaciales Anteriores. LUEGO del drenaje sí Desarrollo en Un complejo Sistema hidrológico Que Persiste Hasta el presente. Palabras clave: Patagonia, Último Máximo Glacial, Dryas Temprano, Trombolitos.http://ref.scielo.org/wgc2q