title: Second-order superintegrable systems in conformally flat spaces. I. Two-dimensional classical structure theory

authors: Kalnins, Ernie G.

subjects: Mathematics

abstract: This paper is the first in a series that lays the groundwork for a structure and classification theory of second-order superintegrable systems, both classical and quantum, in conformally flat spaces. Many examples of such systems are known, and lists of possible systems have been determined for constant curvature spaces in two and three dimensions, as well as few other spaces. Observed features of these systems are multiseparability, closure of the quadratic algebra of second-order symmetries at order 6, use of representation theory of the quadratic algebra to derive spectral properties of the quantum Schrödinger operator, and a close relationship with exactly solvable and quasi-exactly solvable systems. Our approach is, rather than focus on particular spaces and systems, to use a general theoretical method based on integrability conditions to derive structure common to all systems. In this first paper we consider classical superintegrable systems on a general two-dimensional Riemannian manifold and uncover their common structure. We show that for superintegrable systems with nondegenerate potentials there exists a standard structure based on the algebra of 2×2 symmetric matrices, that such systems are necessarily multiseparable and that the quadratic algebra closes at level 6. Superintegrable systems with degenerate potentials are also analyzed. This is all done without making use of lists of systems, so that generalization to higher dimensions, where relatively few examples are known, is much easier.

text: Second-order superintegrable systems in conformally flat spaces. I. Two-dimensional classical structure theory This paper is the first in a series that lays the groundwork for a structure and classification theory of second-order superintegrable systems, both classical and quantum, in conformally flat spaces. Many examples of such systems are known, and lists of possible systems have been determined for constant curvature spaces in two and three dimensions, as well as few other spaces. Observed features of these systems are multiseparability, closure of the quadratic algebra of second-order symmetries at order 6, use of representation theory of the quadratic algebra to derive spectral properties of the quantum Schrödinger operator, and a close relationship with exactly solvable and quasi-exactly solvable systems. Our approach is, rather than focus on particular spaces and systems, to use a general theoretical method based on integrability conditions to derive structure common to all systems. In this first paper we consider classical superintegrable systems on a general two-dimensional Riemannian manifold and uncover their common structure. We show that for superintegrable systems with nondegenerate potentials there exists a standard structure based on the algebra of 2×2 symmetric matrices, that such systems are necessarily multiseparable and that the quadratic algebra closes at level 6. Superintegrable systems with degenerate potentials are also analyzed. This is all done without making use of lists of systems, so that generalization to higher dimensions, where relatively few examples are known, is much easier.

year: 2005-04

title: Emotional labour and well-being for early childhood teachers: The role of psychological capital and perceived organisational support

authors: Carey, Samantha

subjects: early childhood

abstract: Early childhood teachers play an integral role in the development of children enrolled in early childhood services, yet teachers often face stressful and challenging conditions that impact their well-being and consequently the quality of care and education they provide. Emotional labour, the requirement to suppress and express emotions as determined by the organisation, is considered a prominent component of early childhood teachers’ roles. Emotional labour is comprised of two display-rule strategies: Surface Acting where employees suppress their feelings and feign their emotions, and Deep Acting where feelings are modified to create a genuine performance of emotion. Both negatively relate to employee well-being, but we don’t know what personal or organisational resources might help protect early childhood teachers’ well-being. The present study sought to explore this, examining if Psychological Capital (PsyCap: hope, optimism, efficacy, resilience) and perceived organisational support could mitigate any negative consequences of emotional labour. The cross-sectional, non-experimental design surveyed 320 early childhood teachers currently working in New Zealand who completed measures assessing emotional labour, well-being, PsyCap, and perceived organisational support. Structural Equation Modeling examined the relationships between the constructs under investigation. The findings indicated that early childhood teachers who engaged in surface acting, but not deep acting, were likely to experience a decrease in well-being. The PsyCap resources of hope and optimism, but not efficacy and resilience, were found to be viable avenues to increase or protect early childhood teachers’ well-being, as was perceived organisational support. These results present a valuable contribution to our understanding of early childhood teachers’ well-being and highlight the importance of personal and organisational resources in supporting teachers.

text: Emotional labour and well-being for early childhood teachers: The role of psychological capital and perceived organisational support Early childhood teachers play an integral role in the development of children enrolled in early childhood services, yet teachers often face stressful and challenging conditions that impact their well-being and consequently the quality of care and education they provide. Emotional labour, the requirement to suppress and express emotions as determined by the organisation, is considered a prominent component of early childhood teachers’ roles. Emotional labour is comprised of two display-rule strategies: Surface Acting where employees suppress their feelings and feign their emotions, and Deep Acting where feelings are modified to create a genuine performance of emotion. Both negatively relate to employee well-being, but we don’t know what personal or organisational resources might help protect early childhood teachers’ well-being. The present study sought to explore this, examining if Psychological Capital (PsyCap: hope, optimism, efficacy, resilience) and perceived organisational support could mitigate any negative consequences of emotional labour. The cross-sectional, non-experimental design surveyed 320 early childhood teachers currently working in New Zealand who completed measures assessing emotional labour, well-being, PsyCap, and perceived organisational support. Structural Equation Modeling examined the relationships between the constructs under investigation. The findings indicated that early childhood teachers who engaged in surface acting, but not deep acting, were likely to experience a decrease in well-being. The PsyCap resources of hope and optimism, but not efficacy and resilience, were found to be viable avenues to increase or protect early childhood teachers’ well-being, as was perceived organisational support. These results present a valuable contribution to our understanding of early childhood teachers’ well-being and highlight the importance of personal and organisational resources in supporting teachers.

year: 2023

title: A Critical Tiriti Analysis of the Treaty Statement From a University in Aotearoa New Zealand

authors: Hamley, Logan

abstract: Universities in Aotearoa New Zealand have been placed under the spotlight for claims of systemic racism. Following the claims made in relation to the University of Waikato in 2020 and University of Otago in 2022, universities have the responsibility to create an inclusive environment where systemic racism is dismantled, to meaningfully partner with Māori to construct a model for decolonisation, and to enhance the academic experience of Māori staff and students by weaving in mātauranga Māori into existing teaching and research practices. The University of Waikato progresses ahead of other universities in its attempt to fulfil Te Tiriti o Waitangi commitment through the introduction of the Treaty Statement. In this paper, the Treaty Statement is used as a case study to identify how universities articulate bicultural commitments. To do so, our team (consisting of Māori and tauiwi scholars) performed a critical Tiriti analysis comprising five phases to investigate the degree of alignment of the statement with Te Tiriti. The desktop analysis showed poor engagement with most Te Tiriti elements. The analysis evaluation of “good” (more than satisfactory) was measured for the consideration of “Māori exercising equitable citizenship”. This article concludes with recommendations of how universities can strengthen their practices to live up to Te Tiriti aspirations.

text: A Critical Tiriti Analysis of the Treaty Statement From a University in Aotearoa New Zealand Universities in Aotearoa New Zealand have been placed under the spotlight for claims of systemic racism. Following the claims made in relation to the University of Waikato in 2020 and University of Otago in 2022, universities have the responsibility to create an inclusive environment where systemic racism is dismantled, to meaningfully partner with Māori to construct a model for decolonisation, and to enhance the academic experience of Māori staff and students by weaving in mātauranga Māori into existing teaching and research practices. The University of Waikato progresses ahead of other universities in its attempt to fulfil Te Tiriti o Waitangi commitment through the introduction of the Treaty Statement. In this paper, the Treaty Statement is used as a case study to identify how universities articulate bicultural commitments. To do so, our team (consisting of Māori and tauiwi scholars) performed a critical Tiriti analysis comprising five phases to investigate the degree of alignment of the statement with Te Tiriti. The desktop analysis showed poor engagement with most Te Tiriti elements. The analysis evaluation of “good” (more than satisfactory) was measured for the consideration of “Māori exercising equitable citizenship”. This article concludes with recommendations of how universities can strengthen their practices to live up to Te Tiriti aspirations.

year: 2024-02-21