title: Superintegrability in a two-dimensional space of nonconstant curvature

authors: Kalnins, Ernie G.

subjects: Mathematics

abstract: A Hamiltonian with two degrees of freedom is said to be superintegrable if it admits three functionally independent integrals of the motion. This property has been extensively studied in the case of two-dimensional spaces of constant (possibly zero) curvature when all the independent integrals are either quadratic or linear in the canonical momenta. In this article the first steps are taken to solve the problem of superintegrability of this type on an arbitrary curved manifold in two dimensions. This is done by examining in detail one of the spaces of revolution found by G. Koenigs. We determine that there are essentially three distinct potentials which when added to the free Hamiltonian of this space have this type of superintegrability. Separation of variables for the associated Hamilton–Jacobi and Schrödinger equations is discussed. The classical and quantum quadratic algebras associated with each of these potentials are determined.

text: Superintegrability in a two-dimensional space of nonconstant curvature A Hamiltonian with two degrees of freedom is said to be superintegrable if it admits three functionally independent integrals of the motion. This property has been extensively studied in the case of two-dimensional spaces of constant (possibly zero) curvature when all the independent integrals are either quadratic or linear in the canonical momenta. In this article the first steps are taken to solve the problem of superintegrability of this type on an arbitrary curved manifold in two dimensions. This is done by examining in detail one of the spaces of revolution found by G. Koenigs. We determine that there are essentially three distinct potentials which when added to the free Hamiltonian of this space have this type of superintegrability. Separation of variables for the associated Hamilton–Jacobi and Schrödinger equations is discussed. The classical and quantum quadratic algebras associated with each of these potentials are determined.

year: 2002-02

title: Optimising the zoospore release, germination, development of gametophytes and formation of sporophytes of Ecklonia radiata

authors: Praeger, Christina

subjects: Cultivation

abstract: The kelp Ecklonia radiata has become a target for controlled cultivation. However, to date there are no standardised protocols for the hatchery stage of this species that result in high rates of germination, gametophyte development and transition to sporophytes. Therefore, the objective of this study was to quantify the effect of photoperiod, light intensity, temperature, nutrient media and use of  GeO2 on the key hatchery processes of germination, gametophyte development and transition to sporophytes in controlled laboratory experiments. Germination of E. radiata was high (≥ 85%) throughout the study, regardless of treatments. Temperature had a major effect on the length of gametophytes, which increased with increasing temperature. The formation of sporophytes was favoured when individuals were maintained under 17 °C continuously, while reduced by approximately 30% when using F/2 compared to PES nutrient media. Overall, the recommended conditions for the hatchery stage of E. radiata are to maintain cultures under a 12 h L:12 h D photoperiod at 17 °C as this resulted in higher germination rates, good gametophyte development and higher transition to sporophytes compared to other treatments. Moreover, the use of  GeO2 has to be limited to no more than 2 days as extended use has detrimental effects on the development of sporophytes. Finally, storage of sorus-bearing fronds of sporophytes up to 4 days after the collection from the field generally increased the number of released zoospores and is a simple mechanism to increase the fertility of brood stock.

text: Optimising the zoospore release, germination, development of gametophytes and formation of sporophytes of Ecklonia radiata The kelp Ecklonia radiata has become a target for controlled cultivation. However, to date there are no standardised protocols for the hatchery stage of this species that result in high rates of germination, gametophyte development and transition to sporophytes. Therefore, the objective of this study was to quantify the effect of photoperiod, light intensity, temperature, nutrient media and use of  GeO2 on the key hatchery processes of germination, gametophyte development and transition to sporophytes in controlled laboratory experiments. Germination of E. radiata was high (≥ 85%) throughout the study, regardless of treatments. Temperature had a major effect on the length of gametophytes, which increased with increasing temperature. The formation of sporophytes was favoured when individuals were maintained under 17 °C continuously, while reduced by approximately 30% when using F/2 compared to PES nutrient media. Overall, the recommended conditions for the hatchery stage of E. radiata are to maintain cultures under a 12 h L:12 h D photoperiod at 17 °C as this resulted in higher germination rates, good gametophyte development and higher transition to sporophytes compared to other treatments. Moreover, the use of  GeO2 has to be limited to no more than 2 days as extended use has detrimental effects on the development of sporophytes. Finally, storage of sorus-bearing fronds of sporophytes up to 4 days after the collection from the field generally increased the number of released zoospores and is a simple mechanism to increase the fertility of brood stock.

year: 2022-10

title: Kūkupa, koro, and kai: The use of Māori vocabulary items in New Zealand English children's picture books

authors: Daly, Nicola

subjects: New Zealand

abstract: When a linguistic form from one language is used in another language, such words are known as borrowings or loan words (Crystal 2003: 56). The English language is renowned for its large capacity for borrowing and it has been suggested that the growth in internationalism in recent times has led to people seeking new words to indicate their local identity (Crystal 1995; Crystal 2003). Certainly this is the case of New Zealand English, the most distinctive aspect of which is borrowings from te reo Maori (Deverson 1991). In 1984 Deverson estimated that most New Zealanders have a passive knowledge of at least 40-50 borrowed Maori loan words (Deverson 1984). This figure has been recently revised by Macalister to 70-80 such words (20,-,63.). A study of the frequency of Maori loan words in New Zealand English in New Zealand School Journals of the 1960s and 1990s showed an incidence of around 6 words per 1,000 (Macalister 1999). Kennedy and Yamazaki (1999) also found borrowed Maori words at a rate of 6 per thousand words. Macalister (2006b) has examined the use of Maori loan words in New Zealand English across a 150 year period from 1850-2000. He examined a corpus of a little under five and a half million words from three sources: Newspapers, parliamentary debates and School Journals. Across the three sources there was an increase from 3.29 words per 1,000 in 1850 to 8.8 per thousand in 2000. Macalister lists the reasons for this change as including urbanisation of the Maori population between 1945 and 1975, which created more contact; the changing status of the Maori language with the kOhanga reo movement; the establishment of the Maori Language Commission (Te Taura Whiri i te Reo Maori) and legislation of Maori as an official language of New Zealand in 1987.

text: Kūkupa, koro, and kai: The use of Māori vocabulary items in New Zealand English children's picture books When a linguistic form from one language is used in another language, such words are known as borrowings or loan words (Crystal 2003: 56). The English language is renowned for its large capacity for borrowing and it has been suggested that the growth in internationalism in recent times has led to people seeking new words to indicate their local identity (Crystal 1995; Crystal 2003). Certainly this is the case of New Zealand English, the most distinctive aspect of which is borrowings from te reo Maori (Deverson 1991). In 1984 Deverson estimated that most New Zealanders have a passive knowledge of at least 40-50 borrowed Maori loan words (Deverson 1984). This figure has been recently revised by Macalister to 70-80 such words (20,-,63.). A study of the frequency of Maori loan words in New Zealand English in New Zealand School Journals of the 1960s and 1990s showed an incidence of around 6 words per 1,000 (Macalister 1999). Kennedy and Yamazaki (1999) also found borrowed Maori words at a rate of 6 per thousand words. Macalister (2006b) has examined the use of Maori loan words in New Zealand English across a 150 year period from 1850-2000. He examined a corpus of a little under five and a half million words from three sources: Newspapers, parliamentary debates and School Journals. Across the three sources there was an increase from 3.29 words per 1,000 in 1850 to 8.8 per thousand in 2000. Macalister lists the reasons for this change as including urbanisation of the Maori population between 1945 and 1975, which created more contact; the changing status of the Maori language with the kOhanga reo movement; the establishment of the Maori Language Commission (Te Taura Whiri i te Reo Maori) and legislation of Maori as an official language of New Zealand in 1987.

year: 2007