title: Contractions of 2D 2nd order quantum superintegrable systems and the Askey scheme for hypergeometric orthogonal polynomials

authors: Kalnins, Ernie G.

subjects: Askey scheme

abstract: We show explicitly that all 2nd order superintegrable systems in 2 dimensions are limiting cases of a single system: the generic 3-parameter potential on the 2-sphere, S9 in our listing. We extend the Wigner-Inönü method of Lie algebra contractions to contractions of quadratic algebras and show that all of the quadratic symmetry algebras of these systems are contractions of that of S9. Amazingly, all of the relevant contractions of these superintegrable systems on flat space and the sphere are uniquely induced by the well known Lie algebra contractions of e(2) and so(3). By contracting function space realizations of irreducible representations of the S9 algebra (which give the structure equations for Racah/Wilson polynomials) to the other superintegrable systems, and using Wigner's idea of ''saving'' a representation, we obtain the full Askey scheme of hypergeometric orthogonal polynomials. This relationship directly ties the polynomials and their structure equations to physical phenomena. It is more general because it applies to all special functions that arise from these systems via separation of variables, not just those of hypergeometric type, and it extends to higher dimensions.

text: Contractions of 2D 2nd order quantum superintegrable systems and the Askey scheme for hypergeometric orthogonal polynomials We show explicitly that all 2nd order superintegrable systems in 2 dimensions are limiting cases of a single system: the generic 3-parameter potential on the 2-sphere, S9 in our listing. We extend the Wigner-Inönü method of Lie algebra contractions to contractions of quadratic algebras and show that all of the quadratic symmetry algebras of these systems are contractions of that of S9. Amazingly, all of the relevant contractions of these superintegrable systems on flat space and the sphere are uniquely induced by the well known Lie algebra contractions of e(2) and so(3). By contracting function space realizations of irreducible representations of the S9 algebra (which give the structure equations for Racah/Wilson polynomials) to the other superintegrable systems, and using Wigner's idea of ''saving'' a representation, we obtain the full Askey scheme of hypergeometric orthogonal polynomials. This relationship directly ties the polynomials and their structure equations to physical phenomena. It is more general because it applies to all special functions that arise from these systems via separation of variables, not just those of hypergeometric type, and it extends to higher dimensions.

year: 2013

title: Foraging on café sugar packets by the house sparrow (Passer domesticus): Learning mechanisms, distribution, and human perception

authors: Davy, Michael Ambrose

subjects: urban ecology

abstract: People in cities interact with house sparrows (Passer domesticus) on a daily basis. Sparrows have previously been observed foraging on sugar packets at a single café in Hamilton City, New Zealand. The aim of this thesis was to explore aspects of this novel foraging innovation by sparrows and to investigate people’s perceptions of sparrows being present at cafés. 

Sparrows’ preferences for different grain sizes of raw sugar and artificial sweetener were assessed at a single café, which demonstrated that sparrows have a strong preference for raw sugar over artificial sweetener, but no clear preference between granulated raw sugar and powdered raw sugar. Sparrows’ responses to novel sugar packet colours were also investigated at the same café. The sparrows did not start foraging on the novel-coloured sugar packets within 10 experimental sessions, but did interact with the novel sugar packets, which demonstrated neophilia in the sparrows and is an important step in the process of learning.

The distribution of sugar packet foraging by sparrows across 174 cafés in Hamilton City was determined, and staff from 15 cafés had observed sparrows taking sugar packets. A short survey was also used to assess the attitudes of café staff members towards the presence of sparrows at their cafés, which showed that café staff had mixed views on the local sparrows. A different survey was used to investigate the attitudes of 249 members of the general public towards sparrows being at cafés. These participants tended to like sparrows being present as part of their café experience. 

This thesis demonstrates the value of sparrows being present in the urban environment, and is the first study to comprehensively describe sugar packet foraging in sparrows: a fascinating behavioural innovation.

text: Foraging on café sugar packets by the house sparrow (Passer domesticus): Learning mechanisms, distribution, and human perception People in cities interact with house sparrows (Passer domesticus) on a daily basis. Sparrows have previously been observed foraging on sugar packets at a single café in Hamilton City, New Zealand. The aim of this thesis was to explore aspects of this novel foraging innovation by sparrows and to investigate people’s perceptions of sparrows being present at cafés. 

Sparrows’ preferences for different grain sizes of raw sugar and artificial sweetener were assessed at a single café, which demonstrated that sparrows have a strong preference for raw sugar over artificial sweetener, but no clear preference between granulated raw sugar and powdered raw sugar. Sparrows’ responses to novel sugar packet colours were also investigated at the same café. The sparrows did not start foraging on the novel-coloured sugar packets within 10 experimental sessions, but did interact with the novel sugar packets, which demonstrated neophilia in the sparrows and is an important step in the process of learning.

The distribution of sugar packet foraging by sparrows across 174 cafés in Hamilton City was determined, and staff from 15 cafés had observed sparrows taking sugar packets. A short survey was also used to assess the attitudes of café staff members towards the presence of sparrows at their cafés, which showed that café staff had mixed views on the local sparrows. A different survey was used to investigate the attitudes of 249 members of the general public towards sparrows being at cafés. These participants tended to like sparrows being present as part of their café experience. 

This thesis demonstrates the value of sparrows being present in the urban environment, and is the first study to comprehensively describe sugar packet foraging in sparrows: a fascinating behavioural innovation.

year: 2019

title: Culture – the foundation of Maori Governance

authors: Toki, Valmaine

abstract: The structure of a governance system specifies the distribution of rights and responsibilities among different participants dictating the mutually agreed rules and procedures for making decisions on business affairs. For Maori, an indigenous people, the unique and pivotal factor that provides the point of difference, for governance, is the importance of their culture. Notwithstanding this point of difference, there exists a paucity of governance structures that adequately cater and provide for culture.

text: Culture – the foundation of Maori Governance The structure of a governance system specifies the distribution of rights and responsibilities among different participants dictating the mutually agreed rules and procedures for making decisions on business affairs. For Maori, an indigenous people, the unique and pivotal factor that provides the point of difference, for governance, is the importance of their culture. Notwithstanding this point of difference, there exists a paucity of governance structures that adequately cater and provide for culture.

year: 2013