title: Quadratic algebra contractions and second-order superintegrable systems

authors: Kalnins, Ernie G.

abstract: Quadratic algebras are generalizations of Lie algebras; they include the symmetry algebras of second-order superintegrable systems in two dimensions as special cases. The superintegrable systems are exactly solvable physical systems in classical and quantum mechanics. For constant curvature spaces, we show that the free quadratic algebras generated by the first- and second-order elements in the enveloping algebras of their Euclidean and orthogonal symmetry algebras correspond one-to-one with the possible superintegrable systems with potential defined on these spaces. We describe a contraction theory for quadratic algebras and show that for constant curvature superintegrable systems, ordinary Lie algebra contractions induce contractions of the quadratic algebras of the superintegrable systems that correspond to geometrical pointwise limits of the physical systems. One consequence is that by contracting function space realizations of representations of the generic superintegrable quantum system on the 2-sphere (which give the structure equations for Racah/Wilson polynomials) to the other superintegrable systems one obtains the full Askey scheme of orthogonal hypergeometric polynomials. © 2014 World Scientific Publishing Company.

text: Quadratic algebra contractions and second-order superintegrable systems Quadratic algebras are generalizations of Lie algebras; they include the symmetry algebras of second-order superintegrable systems in two dimensions as special cases. The superintegrable systems are exactly solvable physical systems in classical and quantum mechanics. For constant curvature spaces, we show that the free quadratic algebras generated by the first- and second-order elements in the enveloping algebras of their Euclidean and orthogonal symmetry algebras correspond one-to-one with the possible superintegrable systems with potential defined on these spaces. We describe a contraction theory for quadratic algebras and show that for constant curvature superintegrable systems, ordinary Lie algebra contractions induce contractions of the quadratic algebras of the superintegrable systems that correspond to geometrical pointwise limits of the physical systems. One consequence is that by contracting function space realizations of representations of the generic superintegrable quantum system on the 2-sphere (which give the structure equations for Racah/Wilson polynomials) to the other superintegrable systems one obtains the full Askey scheme of orthogonal hypergeometric polynomials. © 2014 World Scientific Publishing Company.

year: 2014

title: Shifting Selves: Home beyond the House - A Study of Ageing, Housing and Wellbeing of Older Chinese Migrants to New Zealand

authors: Li, Wendy Wen

subjects: Self

abstract: Older Chinese immigrants are one of the largest ethnic ageing groups in New Zealand. However, people‘s everyday experiences of settling in a new and unfamiliar environment have been largely overlooked, particularly for older adults. This research explores the biographies, identities and everyday experiences of filial piety among older Chinese immigrants. Particular consideration is given to the role of filial piety in participants‘ housing and ageing experiences. This research is one of the first explorations of Chinese immigrant ageing in place, which also considers changing enactments of filial piety. The research is informed by a hybrid narrative approach that draws on episodic, go-along and fangtan interview techniques used with 32 older Chinese immigrants in Auckland and Hamilton. Findings support the importance of exploring positive experiences of migration and ageing. Older Chinese immigrants do often experience biographical disruptions and status-discrepancies when they move from China to New Zealand. However, in response, the participants engage in positive activities such as gardening and art as a means of cultivating a new sense of self and place in a new land that is compatible with their existing identities as older Chinese adults. The analysis explores the material-mediated basis for participant adjustment and acculturation. Through adaptive acculturation, older Chinese immigrants‘ abilities for both integrating into the host culture and maintaining their ethnic identities are realised. The analysis also demonstrates that traditional Chinese aged care models of family support with high level of intergenerational co-residence are evolving to encompass practices of filial piety at a distance and to encompass more pluralistic familial living arrangements. The analysis also demonstrates the importance of considering how ageing occurs beyond physical spaces and within cultural, social, relational and imagined landscapes. The analysis shifts away from the focus in existing literature on how older Chinese immigrants are passively transformed into minority subjects to how they are transforming themselves through migration and their efforts to age well in New Zealand.

text: Shifting Selves: Home beyond the House - A Study of Ageing, Housing and Wellbeing of Older Chinese Migrants to New Zealand Older Chinese immigrants are one of the largest ethnic ageing groups in New Zealand. However, people‘s everyday experiences of settling in a new and unfamiliar environment have been largely overlooked, particularly for older adults. This research explores the biographies, identities and everyday experiences of filial piety among older Chinese immigrants. Particular consideration is given to the role of filial piety in participants‘ housing and ageing experiences. This research is one of the first explorations of Chinese immigrant ageing in place, which also considers changing enactments of filial piety. The research is informed by a hybrid narrative approach that draws on episodic, go-along and fangtan interview techniques used with 32 older Chinese immigrants in Auckland and Hamilton. Findings support the importance of exploring positive experiences of migration and ageing. Older Chinese immigrants do often experience biographical disruptions and status-discrepancies when they move from China to New Zealand. However, in response, the participants engage in positive activities such as gardening and art as a means of cultivating a new sense of self and place in a new land that is compatible with their existing identities as older Chinese adults. The analysis explores the material-mediated basis for participant adjustment and acculturation. Through adaptive acculturation, older Chinese immigrants‘ abilities for both integrating into the host culture and maintaining their ethnic identities are realised. The analysis also demonstrates that traditional Chinese aged care models of family support with high level of intergenerational co-residence are evolving to encompass practices of filial piety at a distance and to encompass more pluralistic familial living arrangements. The analysis also demonstrates the importance of considering how ageing occurs beyond physical spaces and within cultural, social, relational and imagined landscapes. The analysis shifts away from the focus in existing literature on how older Chinese immigrants are passively transformed into minority subjects to how they are transforming themselves through migration and their efforts to age well in New Zealand.

year: 2011

title: Hoea a mai tōu waka – Claiming spaces for Māori tamariki and rangatahi in cognitive behaviour therapy

authors: Cargo, Tania

subjects: Maori

abstract: Cognitive Behaviour Therapy (CBT) has been shown to be an effective therapeutic intervention for a variety of psychological difficulties for children and youth (Barrett, Healey-Farrell, March, 2004; Stulemeijer, de Jong, Fiselier, Hoogveld, Bleijenberg, 2005; Butler, Chapman, Forman & Beck, 2006). However there is very little literature on its utility with indigenous children or youth, most of the literature has tended to look at “minority” populations and has focused on psychological outcomes (Weersing & Weisz, 2002; McNeil, Capage, Bennett, 2002).

text: Hoea a mai tōu waka – Claiming spaces for Māori tamariki and rangatahi in cognitive behaviour therapy Cognitive Behaviour Therapy (CBT) has been shown to be an effective therapeutic intervention for a variety of psychological difficulties for children and youth (Barrett, Healey-Farrell, March, 2004; Stulemeijer, de Jong, Fiselier, Hoogveld, Bleijenberg, 2005; Butler, Chapman, Forman & Beck, 2006). However there is very little literature on its utility with indigenous children or youth, most of the literature has tended to look at “minority” populations and has focused on psychological outcomes (Weersing & Weisz, 2002; McNeil, Capage, Bennett, 2002).

year: 2008