Quadratic estimates for perturbed Dirac type operators on doubling measure metric spaces

We consider perturbations of Dirac type operators on complete, connected metric spaces equipped with a doubling measure. Under a suitable set of assumptions, we prove quadratic estimates for such operators and hence deduce that these operators have a bounded functional calculus. In particular, we deduce a Kato square root type estimate.Comment: To appear in Proceedings of the AMSI International Conference on Harmonic Analysis and Applications, Proc. Centre Math. Appl. Austral. Nat. Uni

Modernist expert to postmodernist innovative cultural hermaneutist : a journey in adult education : a thesis submitted to Massey University (Wellington) in partial fulfillment of the requirements for the degree of Master of Education (Adult Education)

The repercussions of the turbulent years of the greater part of the twentieth century have been responsible for the demise of both the Enlightenment project and the modern period which was its bearer. This modern period was characterised by legitimising grand metanarratives (récits) that were built on the foundations of rationality, optimism and progress in which reality was represented, understood and lived. Human emancipation was expected to be the ultimate goal. An impressive modernist representative of these metanarratives in the field of my own academic expertise, theology, is the German philosophical theologian, Paul Tillich (1886-1965). His "theology of culture" was a significant theological adult educational project in which he had attempted to represent and convey reality (and meaning) to a generation of adults in the postwar era of the 20 th century. Postmodernism has come to be characteristic of our experience of the world and our present worldview. It questions the legitimacy of the modernist project and along with it the modernist approach to education. In the context of discussing self-directed learning and its application in my own role as an educator, in this thesis I use Paul Tillich's "theology of culture" as an example of a collapsed modern metanarrative to examine how the educator as an "innovative cultural hermeneutist" would better reposition his/her role as an adult educator in the present

Geographic determinants of Australian foreign direct investments

The volume of investment that has flowed from Australia into the outside world, and its implications for economic policy, has attracted substantial policy debate among Australian policy makers, particularly in the context of regionalisation of the world economy. Using hypotheses from investment demand model and new trade theory we investigate if market size, its growth rate, openness, regional economic integration, language and cultural similarity and the availability of knowledge capital have any impact in attracting Australian investments offshore. Our results suggest that countries which are open, have a large domestic market and stable macro-economic environment tend to attract most Australian FDI. Regional integration, and the similarity in language and culture do not have any effect in attracting FDI from Australia. This result has a significant policy implications not only for Australia, but also for other countries who are increasingly engaged in forming trading blocs like Australia-US free trade agreements (AUSFTA)

Analysing and improving a recruitment process: A teaching case for developing business process improvement capabilities

The demand for Business Process Management (BPM) is rapidly rising and with that, the need for capable BPM professionals is also rising. Yet, only a very few structured BPM training/ education programs are available, across universities and professional trainers globally. The ‘lack of appropriate teaching resources’ has been identified as a critical issue for BPM educators in prior studies. Case-based teaching can be an effective means of educating future BPM professionals. A main reason is that cases create an authentic learning environment where the complexities and challenges of the ‘real world’ can be presented in a narrative enabling the students to develop crucial skills such as problem solving, analysis and creativity-within-constraints, and to apply the tools and techniques within a richer and real (or proxy to real) context. However, so far well documented BPM teaching cases are scarce. This article aims to contribute to address this gap by providing a comprehensive teaching case and teaching notes that facilitates the education of selected process improvement phases, namely identification, modelling, analysis, and improvement. The article is divided into three main parts: (i) Introductory teaching notes, (ii) The case narrative, and (iii) Student activities from the case and teaching notes

Riesz continuity of the Atiyah-Singer Dirac operator under perturbations of local boundary conditions

On a smooth complete Riemannian spin manifold with smooth compact boundary, we demonstrate that the Atiyah-Singer Dirac operator $\mathrm{D}_{\mathcal B}$ in $\mathrm{L}^{2}$ depends Riesz continuously on $\mathrm{L}^{\infty}$ perturbations of local boundary conditions ${\mathcal B}$. The Lipschitz bound for the map ${\mathcal B} \to {\mathrm{D}}_{\mathcal B}(1 + {\mathrm{D}}_{\mathcal B}^2)^{-\frac{1}{2}}$ depends on Lipschitz smoothness and ellipticity of ${\mathcal B}$ and bounds on Ricci curvature and its first derivatives as well as a lower bound on injectivity radius. More generally, we prove perturbation estimates for functional calculi of elliptic operators on manifolds with local boundary conditions.Comment: Final versio