Constructing quality childcare: Perspectives of quality and their connection to Belonging, Being and Becoming

Discourse on quality, within the context of childcare, has moved beyond the level of licensing to consider children’s right to belong. Within Western Australia (WA), there has been a paradigm shift as international research literature on quality childcare has advocated the long- term benefits for individuals and the community when children experience high quality early education and care. This paradigm shift has resulted in new legislation in WA that articulates the components of quality across childcare, as well as the criteria on which centres are assessed. This paper reports the findings of an investigation into the constructs of quality from two stakeholder groups; parents and educators. Findings from this study indicated that, when it comes to quality, what matters most to both parents and educators are the types of interactions children have with others and their environment; the ways in which children’s needs are met; and children’s experiences for development and learning. These findings align with the themes of the nationally mandated early years’ document – the Early Years Learning Framework (Department of Education, Employment and Workplace Relations [DEEWR], 2009) Belonging, Being and Becoming

The Navier-Stokes regularity problem

There is currently no proof guaranteeing that, given a smooth initial condition, the three-dimensional Navier–Stokes equations have a unique solution that exists for all positive times. This paper reviews the key rigorous results concerning the existence and uniqueness of solutions for this model. In particular, the link between the regularity of solutions and their uniqueness is highlighted

Latin Square Thue-Morse Sequences are Overlap-Free

We define a morphism based upon a Latin square that generalizes the Thue-Morse morphism. We prove that fixed points of this morphism are overlap-free sequences generalizing results of Allouche - Shallit and Frid.Comment: 5 pages, 1 figur

Global Environmental Justice

The term “environmental justice” carries with it a sort of ambiguity. On the one hand, it refers to a movement of social activism in which those involved fight and argue for fairer, more equitable distribution of environmental goods and equal treatment of environmental duties. This movement is related to, and ideally informed by, the second use of the term, which refers to the academic discipline associated with legal regulations and theories of justice and ethics with regard to sustainability, the environment, and ecology. It is this latter, more academic—though vast and interdisciplinary—use of the term that is the subject of this essay. However, activists who pay careful attention to the arguments offered with regard to the political, legal, social, and philosophical treatments of these issues are potentially in a stronger position with regard to their own social movement. In that way, the two uses of the term may progress hand in hand. More broadly, however, the foundational claim about which both grassroots activists and legal, ethical, and policy advocates can agree is that environmental burdens—climate change, pollution, and their associated health risks—are borne disproportionately by the poorest and most vulnerable populations, and tend to have the greatest impact on racial and ethnic minorities, no matter where they are in the world. This is what makes the empirical questions about the environment a normative question about justice

Parametrization of global attractors experimental observations and turbulence

This paper is concerned with rigorous results in the theory of turbulence and fluid flow. While derived from the abstract theory of attractors in infinite-dimensional dynamical systems, they shed some light on the conventional heuristic theories of turbulence, and can be used to justify a well-known experimental method. Two results are discussed here in detail, both based on parametrization of the attractor. The first shows that any two fluid flows can be distinguished by a sufficient number of point observations of the velocity. This allows one to connect rigorously the dimension of the attractor with the Landau–Lifschitz ‘number of degrees of freedom’, and hence to obtain estimates on the ‘minimum length scale of the flow’ using bounds on this dimension. While for two-dimensional flows the rigorous estimate agrees with the heuristic approach, there is still a gap between rigorous results in the three-dimensional case and the Kolmogorov theory. Secondly, the problem of using experiments to reconstruct the dynamics of a flow is considered. The standard way of doing this is to take a number of repeated observations, and appeal to the Takens time-delay embedding theorem to guarantee that one can indeed follow the dynamics ‘faithfully’. However, this result relies on restrictive conditions that do not hold for spatially extended systems: an extension is given here that validates this important experimental technique for use in the study of turbulence. Although the abstract results underlying this paper have been presented elsewhere, making them specific to the Navier–Stokes equations provides answers to problems particular to fluid dynamics, and motivates further questions that would not arise from within the abstract theory itself

Representation theory of C-algebras for a higher order class of spheres and tori

We construct C-algebras for a class of surfaces that are inverse images of certain polynomials of arbitrary degree. By using the directed graph associated to a matrix, the representation theory can be understood in terms of ``loop'' and ``string'' representations, which are closely related to the dynamics of an iterated map in the plane. As a particular class of algebras we introduce the ``Henon algebras'', for which the dynamical map is a generalized Henon map, and give an example where irreducible representations of all dimensions exist.Comment: 14 page

Well-posedness for the diffusive 3D Burgers equations with initial data in H1/2H^{1/2}

In this note we discuss the diffusive, vector-valued Burgers equations in a three-dimensional domain with periodic boundary conditions. We prove that given initial data in $H^{1/2}$ these equations admit a unique global solution that becomes classical immediately after the initial time. To prove local existence, we follow as closely as possible an argument giving local existence for the Navier--Stokes equations. The existence of global classical solutions is then a consequence of the maximum principle for the Burgers equations due to Kiselev and Ladyzhenskaya (1957). In several places we encounter difficulties that are not present in the corresponding analysis of the Navier--Stokes equations. These are essentially due to the absence of any of the cancellations afforded by incompressibility, and the lack of conservation of mass. Indeed, standard means of obtaining estimates in $L^2$ fail and we are forced to start with more regular data. Furthermore, we must control the total momentum and carefully check how it impacts on various standard estimates.Comment: 15 pages, to appear in "Recent Progress in the Theory of the Euler and Navier--Stokes Equations", eds. J.C. Robinson, J.L. Rodrigo, W. Sadowski and A. Vidal-L\'opez, Cambridge University Press, 201