Distances sets that are a shift of the integers and Fourier basis for planar convex sets

The aim of this paper is to prove that if a planar set $A$ has a difference set $\Delta(A)$ satisfying $\Delta(A)\subset \Z^++s$ for suitable $s$ than $A$ has at most 3 elements. This result is motivated by the conjecture that the disk has not more than 3 orthogonal exponentials. Further, we prove that if $A$ is a set of exponentials mutually orthogonal with respect to any symmetric convex set $K$ in the plane with a smooth boundary and everywhere non-vanishing curvature, then # (A \cap {[-q,q]}^2) \leq C(K) q where $C(K)$ is a constant depending only on $K$. This extends and clarifies in the plane the result of Iosevich and Rudnev. As a corollary, we obtain the result from \cite{IKP01} and \cite{IKT01} that if $K$ is a centrally symmetric convex body with a smooth boundary and non-vanishing curvature, then $L^2(K)$ does not possess an orthogonal basis of exponentials

Toxicity and Safety Implications of Herbal Medicines Used in Africa

The use of herbal medicines has seen a great upsurge globally. In developing countries, many patronize them largely due to cultural acceptability, availability and cost. In developed countries, they are used because they are natural and therefore assumed to be safer than allopathic medicines. In recent times, however, there has been a growing concern about their safety. This has created a situation of ambivalence in discussions regarding their use. Some medicinal plants are intrinsically toxic by virtue of their constituents and can cause adverse reactions if inappropriately used. Other factors such as herb-drug interactions, lack of adherence to good manufacturing practice (GMP), poor regulatory measures and adulteration may also lead to adverse events in their use. Many in vivo tests on aqueous extracts largely support the safety of herbal medicines, whereas most in vitro tests on isolated single cells mostly with extracts other than aqueous ones show contrary results and thus continue the debate on herbal medicine safety. It is expected that toxicity studies concerning herbal medicine should reflect their traditional use to allow for rational discussions regarding their safety for their beneficial use. While various attempts continue to establish the safety of various herbal medicines in man, their cautious and responsible use is required

The Australian Early Years Learning Framework: learning what?

Early childhood education and care have assumed importance in many government policy agendas. This attention is often accompanied by calls for greater accountability regarding the anticipated learning outcomes for young children. In Australia, the expected learning outcomes for children aged birth to five years are outlined in the recently published Early Years Learning Framework (EYLF). In this article, the author examines the relationship between the EYLF’s outcomes and subject area or content knowledge. The article draws from post-structural and social constructionist understandings of knowledge as unfinished, contestable and contextual. The author concludes that it is not content knowledge itself that is problematic, but it is the way the child and teacher are often positioned in relation to that knowledge that constrains the potential for effective teaching and learning in the early years. The author suggests that revisiting traditional assumptions about content knowledge extends and develops many of the ideas about teaching and learning that are identified in the EYLF, and opens up new identity positions for both children and early childhood educators

When does the action start and finish? Making the case for an ethnographic action research in educational research

This paper explores how ethnographic and action research methodologies can be justifiably combined to create a new methodological approach in educational research. It draws on existing examples in both educational research and development studies that have discussed the use of ethnography and action research in specific projects. Interpretations of ethnography and action research are developed that aim to minimise the epistemological differences between them. The paper also contextualises an ‘ethnographic action research’ approach with reference to an example of the author’s research into participation in three ‘reception’ (first year of schooling) classes in the United Kingdom. It is argued that research into the theme of participation in early years education, using participative methods, was particularly suitable for this new methodological approach

Theorising interprofessional pedagogic evaluation: framework for evaluating the impact of interprofessional CPD on practice change

This paper outlines the development of a conceptual framework to guide the evaluation of the impact of the pedagogy employed in continuing professional development for professionals in education, health and social care. The work is developed as part of the Centre for Excellence in Teaching and Learning: Interprofessional Learning across the Public Sector (CETL: IPPS) at the University of Southampton. The paper briefly outlines the field for pedagogic research and comments on the underpinning theories that have so far been used to guide research into interprofessional learning (IPL). It maps out the development of interprofessional CPD in its specific context as part of the CETL: IPPS with its links to a local authority undergoing service reorganisation and the role of the continuing professional development (CPD) in effecting change. It then brings together a theoretical framework with the potential toexplore, explain and evaluate the essential features of the model of pedagogy used in interprofessional CPD, in which professionals from education have for the first time been included alongside those from health and social care. The framework draws upon elements of situated learning theory, Activity Theory and Dreier’s work (2002, 1999) on trajectories of participation, particularly Personal Action Potency. By combining the resulting analytic framework with an adapted version of an established evaluation model, a theoretically-driven, practicable evaluation matrix is developed. The matrix has potential use in evaluating the impact of pedagogic input on practice change. The paper models a process for developing a conceptual framework to steer pedagogic evaluation. Such a process and the resulting matrix may be of use to other researchers who are similarly developing pedagogic evaluation

A funds of knowledge approach to examining play interests: listening to children’s and parents’ perspectives.

Children’s interests are widely recognised as pivotal to meaningful learning and play in the early years. However, less is known about how children’s diverse interests may contribute to relationships within peer cultures. This article builds upon previous studies to argue that participation in sociocultural activity generates interests informed by funds of knowledge that children reconstruct in their play. It reports findings from an interpretive study that used filmed footage of children’s play as a provocation to explore the perspectives of children, parents and teachers. The article presents original insights regarding some ways in which mutually constituted funds of knowledge afford opportunities for children to co-construct meaning within peer cultures. The findings also indicate that interests arising from diverse funds of knowledge may contribute to the interplay of power, agency and status during play. This raises some issues regarding how matters of inclusion and exclusion are understood and responded to within early years settings. The article recommends that teachers and researchers engage critically with children’s individual and collective funds of knowledge in order to better understand the complexities of play cultures

A Voltage-Gated H+ Channel Underlying pH Homeostasis in Calcifying Coccolithophores

Marine coccolithophorid phytoplankton are major producers of biogenic calcite, playing a significant role in the global carbon cycle. Predicting the impacts of ocean acidification on coccolithophore calcification has received much recent attention and requires improved knowledge of cellular calcification mechanisms. Uniquely amongst calcifying organisms, coccolithophores produce calcified scales (coccoliths) in an intracellular compartment and secrete them to the cell surface, requiring large transcellular ionic fluxes to support calcification. In particular, intracellular calcite precipitation using HCO3− as the substrate generates equimolar quantities of H+ that must be rapidly removed to prevent cytoplasmic acidification. We have used electrophysiological approaches to identify a plasma membrane voltage-gated H+ conductance in Coccolithus pelagicus ssp braarudii with remarkably similar biophysical and functional properties to those found in metazoans. We show that both C. pelagicus and Emiliania huxleyi possess homologues of metazoan Hv1 H+ channels, which function as voltage-gated H+ channels when expressed in heterologous systems. Homologues of the coccolithophore H+ channels were also identified in a diversity of eukaryotes, suggesting a wide range of cellular roles for the Hv1 class of proteins. Using single cell imaging, we demonstrate that the coccolithophore H+ conductance mediates rapid H+ efflux and plays an important role in pH homeostasis in calcifying cells. The results demonstrate a novel cellular role for voltage gated H+ channels and provide mechanistic insight into biomineralisation by establishing a direct link between pH homeostasis and calcification. As the coccolithophore H+ conductance is dependent on the trans-membrane H+ electrochemical gradient, this mechanism will be directly impacted by, and may underlie adaptation to, ocean acidification. The presence of this H+ efflux pathway suggests that there is no obligate use of H+ derived from calcification for intracellular CO2 generation. Furthermore, the presence of Hv1 class ion channels in a wide range of extant eukaryote groups indicates they evolved in an early common ancestor

Long-term outcomes of early childhood science education: insight from a cross-national comparative case study on conceptual understanding of science

The purpose of this research was to explore the long term outcomes of either participating or not participating in early childhood science education on Grade 6 students’ conceptual understanding of science. The research is situated in a conceptual framework that evokes Piagetian developmental levels as both potential curriculum constraints and potential models of efficacy. The research design was a multiple case study of Grade 6 children from three schools in China (n=140) who started formal science education in the third grade, and Grade 6 children from three matched schools in Australia (n=105) who started learning science in kindergarten. The students’ understanding was assessed by a science quiz and in-depth interview. The data showed that participating children from the high socio-economic schools in China and Australia had similar understandings of science. Divergence between the medium and low socio-economic schools, however, indicated that the grounding in early childhood science education in Australia may have placed these children at an advantage. Alternative explanations for the divergence including the nature of classroom instruction in the two countries are discussed