title: Tools for verifying classical and quantum superintegrability

authors: Kalnins, Ernie G.

subjects: superintegrability

abstract: Recently many new classes of integrable systems in n dimensions occurring in classical and quantum mechanics have been shown to admit a functionally independent set of 2n−1 symmetries polynomial in the canonical momenta, so that they are in fact superintegrable. These newly discovered systems are all separable in some coordinate system and, typically, they depend on one or more parameters in such a way that the system is superintegrable exactly when some of the parameters are rational numbers. Most of the constructions to date are for n=2 but cases where n>2 are multiplying rapidly. In this article we organize a large class of such systems, many new, and emphasize the underlying mechanisms which enable this phenomena to occur and to prove superintegrability. In addition to proofs of classical superintegrability we show that the 2D caged anisotropic oscillator and a Stäckel transformed version on the 2-sheet hyperboloid are quantum superintegrable for all rational relative frequencies, and that a deformed 2D Kepler-Coulomb system is quantum superintegrable for all rational values of a parameter k in the potential.

text: Tools for verifying classical and quantum superintegrability Recently many new classes of integrable systems in n dimensions occurring in classical and quantum mechanics have been shown to admit a functionally independent set of 2n−1 symmetries polynomial in the canonical momenta, so that they are in fact superintegrable. These newly discovered systems are all separable in some coordinate system and, typically, they depend on one or more parameters in such a way that the system is superintegrable exactly when some of the parameters are rational numbers. Most of the constructions to date are for n=2 but cases where n>2 are multiplying rapidly. In this article we organize a large class of such systems, many new, and emphasize the underlying mechanisms which enable this phenomena to occur and to prove superintegrability. In addition to proofs of classical superintegrability we show that the 2D caged anisotropic oscillator and a Stäckel transformed version on the 2-sheet hyperboloid are quantum superintegrable for all rational relative frequencies, and that a deformed 2D Kepler-Coulomb system is quantum superintegrable for all rational values of a parameter k in the potential.

year: 2010

title: Factors influencing women in engineering in New Zealand

authors: Fox-Turnbull, Wendy

subjects: attitudes

abstract: There is a significant underrepresentation of women in engineering disciplines at the tertiary level in New Zealand, posing both economic and equity challenges. Innovation and creativity, which are crucial to engineering and the New Zealand economy, benefit from diverse perspectives. However, various factors such as parental and teacher influence, self-perception, and societal stereotypes impact girls' career choices. This study uniquely investigates the factors influencing women’s interest in engineering in New Zealand, drawing insights from current engineering students and high school students. Key barriers identified include insufficient career guidance, lack of promotion of the engineering profession, and the perception of engineering as a masculine field. Additionally, life experiences play a crucial role in deterring girls from pursuing engineering careers.

text: Factors influencing women in engineering in New Zealand There is a significant underrepresentation of women in engineering disciplines at the tertiary level in New Zealand, posing both economic and equity challenges. Innovation and creativity, which are crucial to engineering and the New Zealand economy, benefit from diverse perspectives. However, various factors such as parental and teacher influence, self-perception, and societal stereotypes impact girls' career choices. This study uniquely investigates the factors influencing women’s interest in engineering in New Zealand, drawing insights from current engineering students and high school students. Key barriers identified include insufficient career guidance, lack of promotion of the engineering profession, and the perception of engineering as a masculine field. Additionally, life experiences play a crucial role in deterring girls from pursuing engineering careers.

year: 2024

title: Kaitiakitanga - Active guardianship, responsibilities and relationships with the world: Towards a bio-cultural future In early childhood education

authors: Paul-Burke, Kura

abstract: The world is a vast family, and humans are children of the earth and sky, and cousins to all living things. Such unity means that nature is the ultimate teacher about life (Royal 2010, p. 9).
For Māori (indigenous peoples of Aotearoa New Zealand) the term kaitiakitanga (pronounced, kye-tee-ah-key-tar-ngah) is often used to refer to the active guardianship and management of natural organisms and their environments. Mātauranga Māori or Māori knowledge positions humans within nature and focuses on ways in which cultural understandings and intergenerational connections between people and their biophysical contexts assist in the retention and protection of biodiversity and ecologically sustainable ecosystems. This entry critically reflects notions of kaitiakitanga and bio-cultural connectivity as important and meaningful contributors for young children and their relationships with and for the world.

text: Kaitiakitanga - Active guardianship, responsibilities and relationships with the world: Towards a bio-cultural future In early childhood education The world is a vast family, and humans are children of the earth and sky, and cousins to all living things. Such unity means that nature is the ultimate teacher about life (Royal 2010, p. 9).
For Māori (indigenous peoples of Aotearoa New Zealand) the term kaitiakitanga (pronounced, kye-tee-ah-key-tar-ngah) is often used to refer to the active guardianship and management of natural organisms and their environments. Mātauranga Māori or Māori knowledge positions humans within nature and focuses on ways in which cultural understandings and intergenerational connections between people and their biophysical contexts assist in the retention and protection of biodiversity and ecologically sustainable ecosystems. This entry critically reflects notions of kaitiakitanga and bio-cultural connectivity as important and meaningful contributors for young children and their relationships with and for the world.

year: 2015