title: Second order superintegrable systems in conformally flat spaces. IV. The classical 3D Stäckel transform and 3D classification theory

authors: Kalnins, Ernie G.

subjects: Mathematics

abstract: This article is one of 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. In the first part of the article we study the Stäckel transform (or coupling constant metamorphosis) as an invertible mapping between classical superintegrable systems on different three-dimensional spaces. We show first that all superintegrable systems with nondegenerate potentials are multiseparable and then that each such system on any conformally flat space is Stäckel equivalent to a system on a constant curvature space. In the second part of the article we classify all the superintegrable systems that admit separation in generic coordinates. We find that there are eight families of these systems.

text: Second order superintegrable systems in conformally flat spaces. IV. The classical 3D Stäckel transform and 3D classification theory This article is one of 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. In the first part of the article we study the Stäckel transform (or coupling constant metamorphosis) as an invertible mapping between classical superintegrable systems on different three-dimensional spaces. We show first that all superintegrable systems with nondegenerate potentials are multiseparable and then that each such system on any conformally flat space is Stäckel equivalent to a system on a constant curvature space. In the second part of the article we classify all the superintegrable systems that admit separation in generic coordinates. We find that there are eight families of these systems.

year: 2006-04

title: Hardy’s Mines Ltd, of Waiorongomai

authors: Hart, Philip

abstract: Hardy’s Mines Ltd was formed on 30 April l904 to acquire all Edwin Henry Hardy’s mining properties. Because of his experience, Hardy was to supervise the work for the first three years of the company’s existence. Details are provided of the directors and shareholders, who included experienced businessmen from many places in New Zealand. Immediately upon its formation, the company had to undertake a considerable amount of dead work and to improve the battery before it could extract and process the ore. Much prospecting and testing was done, but only a small amount of gold was treated. Nevertheless, hopes were high during 1904 and 1905, and concentrates were tested in Australia.
Being, as was the norm, under-capitalized, increasingly the company faced financial difficulties, and in 1906 most work ceased and the mines were protected because the payable ore had run out. In that year, Hardy ceased to be the supervisor. Exploration had proved that the lode below where he had extracted good ore was unpayable, being increasingly refractory and therefore expensive to treat.
Once the capital was exhausted, further capital was sought, including in England. The company was reconstructed in 1907, but continued to be under-capitalized. It was hoped that a new low-level drive, known as McLean’s level, would strike good ore below the existing Colonist workings, but driving this took several years and the hoped-for valuable ore did not exist. 
A new company was formed in 1910, which continued to extend McLean’s level and to test any ore struck, all the while hoping to sell its property. Although mining had ceased, some income was received through treating the tailings using cyanide. When it was discovered that the mine manager had extended McLean’s level in the wrong direction, this work was abandoned, especially because assays revealed that earlier ones had been ‘misleading’. The company abandoned its property in 1924.

text: Hardy’s Mines Ltd, of Waiorongomai Hardy’s Mines Ltd was formed on 30 April l904 to acquire all Edwin Henry Hardy’s mining properties. Because of his experience, Hardy was to supervise the work for the first three years of the company’s existence. Details are provided of the directors and shareholders, who included experienced businessmen from many places in New Zealand. Immediately upon its formation, the company had to undertake a considerable amount of dead work and to improve the battery before it could extract and process the ore. Much prospecting and testing was done, but only a small amount of gold was treated. Nevertheless, hopes were high during 1904 and 1905, and concentrates were tested in Australia.
Being, as was the norm, under-capitalized, increasingly the company faced financial difficulties, and in 1906 most work ceased and the mines were protected because the payable ore had run out. In that year, Hardy ceased to be the supervisor. Exploration had proved that the lode below where he had extracted good ore was unpayable, being increasingly refractory and therefore expensive to treat.
Once the capital was exhausted, further capital was sought, including in England. The company was reconstructed in 1907, but continued to be under-capitalized. It was hoped that a new low-level drive, known as McLean’s level, would strike good ore below the existing Colonist workings, but driving this took several years and the hoped-for valuable ore did not exist. 
A new company was formed in 1910, which continued to extend McLean’s level and to test any ore struck, all the while hoping to sell its property. Although mining had ceased, some income was received through treating the tailings using cyanide. When it was discovered that the mine manager had extended McLean’s level in the wrong direction, this work was abandoned, especially because assays revealed that earlier ones had been ‘misleading’. The company abandoned its property in 1924.

year: 2016

title: Talking together: The effects of traditional Māori Pedagogy on children’s early literacy development

authors: Derby, Melissa

abstract: This article presents findings from a project that sought to determine the effects of a home-based literacy intervention on bilingual (English and Te Reo Māori) preschool children’s early literacy skills. The culturally responsive intervention, which was adapted from Tender Shoots, incorporated traditional Māori teaching and learning approaches, such as the use of storytelling, songs, games, and reminiscing about the past, as practices for supporting key cognitive skills crucial to foundational literacy, specifically phonological awareness and vocabulary knowledge. Over a 12-week period, during which the intervention was conducted, data were gathered from eight Māori preschool children and their families. The study utilised a crossover design. Four children and their families participated in the Rich Reading and Reminiscing (RRR) component of the intervention, which ran for six weeks, followed by the Strengthening Sound Sensitivity (SSS) portion of the intervention. The remaining four children completed the intervention in the reverse order of delivery. The crossover approach established a control in the study and allowed the effects of each part of the intervention on the aforementioned cognitive skills to be more clearly revealed. Overall, the data indicate that traditional Māori pedagogical practices helped to strengthen the early literacy skills of the children participating in the study.

text: Talking together: The effects of traditional Māori Pedagogy on children’s early literacy development This article presents findings from a project that sought to determine the effects of a home-based literacy intervention on bilingual (English and Te Reo Māori) preschool children’s early literacy skills. The culturally responsive intervention, which was adapted from Tender Shoots, incorporated traditional Māori teaching and learning approaches, such as the use of storytelling, songs, games, and reminiscing about the past, as practices for supporting key cognitive skills crucial to foundational literacy, specifically phonological awareness and vocabulary knowledge. Over a 12-week period, during which the intervention was conducted, data were gathered from eight Māori preschool children and their families. The study utilised a crossover design. Four children and their families participated in the Rich Reading and Reminiscing (RRR) component of the intervention, which ran for six weeks, followed by the Strengthening Sound Sensitivity (SSS) portion of the intervention. The remaining four children completed the intervention in the reverse order of delivery. The crossover approach established a control in the study and allowed the effects of each part of the intervention on the aforementioned cognitive skills to be more clearly revealed. Overall, the data indicate that traditional Māori pedagogical practices helped to strengthen the early literacy skills of the children participating in the study.

year: 2023-02