title: Coverpage and Contents

authors: Waikato Geological Society

abstract: Coverpage and Contents from Volume 2, Number 1, 1968 of Earth Science Journal.

text: Coverpage and Contents Coverpage and Contents from Volume 2, Number 1, 1968 of Earth Science Journal.

year: 1968

title: Infinite order symmetries for two-dimensional separable Schrödinger equations

authors: Kalnins, Ernie G.

subjects: mathematics

abstract: Consider a non-relativistic Hamiltonian operator H in 2 dimensions consisting of a kinetic energy term plus a potential. We show that if the associated Schrödinger eigenvalue equation admits an orthogonal separation of variables, there is a calculus to describe the (in general) infinite-order differential operator symmetries of the Schrödinger equation. The calculus is formal but can be made rigorous when all functions in the eigenvaue equation are analytic. The infinite-order calculus exhibits structure that is not apparent when one studies only finite-order symmetries. The search for finite-order symmetries can then be reposed as one of looking for solutions of a coupled system of PDEs that are polynomial in certain parameters. We go further and extend the calculus to the situation where the Schrödinger equation admits a second-order symmetry operator, not necessarily associated with orthogonal separable coordinates.

text: Infinite order symmetries for two-dimensional separable Schrödinger equations Consider a non-relativistic Hamiltonian operator H in 2 dimensions consisting of a kinetic energy term plus a potential. We show that if the associated Schrödinger eigenvalue equation admits an orthogonal separation of variables, there is a calculus to describe the (in general) infinite-order differential operator symmetries of the Schrödinger equation. The calculus is formal but can be made rigorous when all functions in the eigenvaue equation are analytic. The infinite-order calculus exhibits structure that is not apparent when one studies only finite-order symmetries. The search for finite-order symmetries can then be reposed as one of looking for solutions of a coupled system of PDEs that are polynomial in certain parameters. We go further and extend the calculus to the situation where the Schrödinger equation admits a second-order symmetry operator, not necessarily associated with orthogonal separable coordinates.

year: 2004

title: Fragmentation and Restoration: Generational Legacies of 21st Century Māori

authors: Malcolm-Buchanan, Vincent Alan

subjects: Maori

abstract: The content of this thesis is premised on a reflexive examination of some historical juxtapositions culminating in critical aspects of being Māori in the twenty first century and how such aspects have informed contemporary indigenous identity. That is, the continuing acknowledgement and exponential public recognition of critical concepts which inextricably link indigenous and civic identity. 

The theoretical sources for this research are, in the main, derived from anthropological and religious studies, particularly on the significance of mythologies and oral histories, as well as from the oral theorising of elders in Aotearoa New Zealand. A very significant contribution from one such elder, a senior Māori woman academic, has been included in the form of the transcript of an interview. She herself had collected the views of a number of elders on myth, creating a rare and valuable resource.  In the interview she married her reflections on these with her own experiences and her cogent analyses. 

From the outset, it was necessary to be discerning so as to ensure the thesis workload was manageable and realistic.  For this reason the selected critical aspects that have been used to frame this research are (1) a developing Western validation (that is, acknowledgement and respect) of Māori, Māori culture and their mythology; (2) oral history (genealogy) and traditions that have remained constant despite the influences of modernity; and (3) notions of fluidity, negotiation and pragmatism regarding kinship legacies and cultural heritage. The thesis is comprised of six chapters starting from a subjective narrative leading through increasingly objective discourses that culminate in a conclusion which supports a belief that modern Māori require a balancing of critical aspects of cultural heritage, with a broad understanding of the world of the 'other', in order to realise and develop their contemporary indigenous identity.

Ultimately, indigenous ideologies, practices and knowledge recorded and examined in the world of academia today, become potential resources for tomorrow. The intention of this research is to aggregate and discuss intrinsic aspects of the Māori past as well as developing aspects of the present, in order to better understand the significance of the future, and to add to the growing corpus of indigenous worldviews.

text: Fragmentation and Restoration: Generational Legacies of 21st Century Māori The content of this thesis is premised on a reflexive examination of some historical juxtapositions culminating in critical aspects of being Māori in the twenty first century and how such aspects have informed contemporary indigenous identity. That is, the continuing acknowledgement and exponential public recognition of critical concepts which inextricably link indigenous and civic identity. 

The theoretical sources for this research are, in the main, derived from anthropological and religious studies, particularly on the significance of mythologies and oral histories, as well as from the oral theorising of elders in Aotearoa New Zealand. A very significant contribution from one such elder, a senior Māori woman academic, has been included in the form of the transcript of an interview. She herself had collected the views of a number of elders on myth, creating a rare and valuable resource.  In the interview she married her reflections on these with her own experiences and her cogent analyses. 

From the outset, it was necessary to be discerning so as to ensure the thesis workload was manageable and realistic.  For this reason the selected critical aspects that have been used to frame this research are (1) a developing Western validation (that is, acknowledgement and respect) of Māori, Māori culture and their mythology; (2) oral history (genealogy) and traditions that have remained constant despite the influences of modernity; and (3) notions of fluidity, negotiation and pragmatism regarding kinship legacies and cultural heritage. The thesis is comprised of six chapters starting from a subjective narrative leading through increasingly objective discourses that culminate in a conclusion which supports a belief that modern Māori require a balancing of critical aspects of cultural heritage, with a broad understanding of the world of the 'other', in order to realise and develop their contemporary indigenous identity.

Ultimately, indigenous ideologies, practices and knowledge recorded and examined in the world of academia today, become potential resources for tomorrow. The intention of this research is to aggregate and discuss intrinsic aspects of the Māori past as well as developing aspects of the present, in order to better understand the significance of the future, and to add to the growing corpus of indigenous worldviews.

year: 2009