title: Lie theory and separation of variables. 7. The harmonic oscillator in elliptic coordinates and Ince polynomials

authors: Boyer, C.P.

subjects: Mathematics

abstract: As a continuation of Paper 6 we study the separable basis eigenfunctions and their relationships for the harmonic oscillator Hamiltonian in two space variables with special emphasis on products of Ince polynomials, the eigenfunctions obtained when one separates variables in elliptic coordinates. The overlaps connecting this basis to the polar and Cartesian coordinate bases are obtained by computing in a simpler Bargmann Hilbert space model of the problem. We also show that Ince polynomials are intimately connected with the representation theory of SU (2), the group responsible for the eigenvalue degeneracy of the oscillator Hamiltonian.

text: Lie theory and separation of variables. 7. The harmonic oscillator in elliptic coordinates and Ince polynomials As a continuation of Paper 6 we study the separable basis eigenfunctions and their relationships for the harmonic oscillator Hamiltonian in two space variables with special emphasis on products of Ince polynomials, the eigenfunctions obtained when one separates variables in elliptic coordinates. The overlaps connecting this basis to the polar and Cartesian coordinate bases are obtained by computing in a simpler Bargmann Hilbert space model of the problem. We also show that Ince polynomials are intimately connected with the representation theory of SU (2), the group responsible for the eigenvalue degeneracy of the oscillator Hamiltonian.

year: 1975-03

title: Analysis of environmental and economic efficiency using a farm population micro-simulation model

authors: Ramilan, Thiagarajah

subjects: Data Envelopment Analysis

abstract: New Zealand's success in raising agricultural productivity has been accompanied by higher input use, leading to adverse effects on the environment. Until recently, analysis of farm performance has tended to ignore such negative externalities. The current emphasis on environmental issues has led dairy farmers to target improvements in both environmental performance and productivity. Therefore, measuring the environmental performance of farms and integrating this information into farm productivity calculations should assist in making informed policy decisions which promote sustainable development. However, this is a challenging process since conventional environmental efficiency measures are usually based on simple input and output flows but nitrogen discharge is a complex process affected by climate, pasture composition, cow physiology and geophysical variability. Furthermore, the outdoor pastoral nature of New Zealand farming means that it is difficult to control input and output flows, particularly of nitrogen. We present a novel approach to measure the environmental and economic efficiency of farms, using the Overseer nutrient budget model and spatially micro-simulated virtual population data. The empirical analysis is based on dairy farms in the Karapiro catchment, where nitrogen discharge from dairy farming is a major source of nonpoint pollution.

text: Analysis of environmental and economic efficiency using a farm population micro-simulation model New Zealand's success in raising agricultural productivity has been accompanied by higher input use, leading to adverse effects on the environment. Until recently, analysis of farm performance has tended to ignore such negative externalities. The current emphasis on environmental issues has led dairy farmers to target improvements in both environmental performance and productivity. Therefore, measuring the environmental performance of farms and integrating this information into farm productivity calculations should assist in making informed policy decisions which promote sustainable development. However, this is a challenging process since conventional environmental efficiency measures are usually based on simple input and output flows but nitrogen discharge is a complex process affected by climate, pasture composition, cow physiology and geophysical variability. Furthermore, the outdoor pastoral nature of New Zealand farming means that it is difficult to control input and output flows, particularly of nitrogen. We present a novel approach to measure the environmental and economic efficiency of farms, using the Overseer nutrient budget model and spatially micro-simulated virtual population data. The empirical analysis is based on dairy farms in the Karapiro catchment, where nitrogen discharge from dairy farming is a major source of nonpoint pollution.

year: 2011

title: Maori at Te Aroha after the opening of the goldfield in 1880 (mostly through Pakeha eyes)

authors: Hart, Philip

abstract: As the Maori population continued to decline, the aged rangatira admired by Pakeha (even including those who had fought against the Crown) gradually died off, to be replaced by Maori more noted for their drinking and occasional violence than their prestige. Although concerts and haka were popular with many Pakeha, much Maori behaviour was mocked, including by children. Many Maori were seen as being unsophisticated, unable to express themselves properly in English, and prone to drunkenness and laziness, whereas those who adopted Pakeha ways were praised.
Some Pakeha sympathized with poverty-stricken Maori and regretted the decline of their language. There were many examples of close and friendly relations and of Maori assisting Pakeha in trouble, but in general they lived geographically separate lives. To earn money, Maori were forced to work at road making, timber cutting, gum digging, and farming what land remained in their possession. Most Maori struggled financially, their limited resources being stretched by holding expensive tangi and entertaining visitors – resulting in more land sales. They used the court system to defend their economic interests.
Ngati Rahiri (including supporters of the Kingitanga) were seen as ‘loyal’ to the Crown, and visiting Maori kings received kindly treatment from Pakeha as well as from Maori. 
Poor health prompted some government assistance, but poor housing remained, although some attempts were made to improve it (partly to protect Pakeha from diseases). Before the twentieth century only a few children, mostly ‘half-castes’, were educated. Most Ngati Rahiri were members of the Church of England before being attracted by the new Mormon faith.
Ngati Rahiri participated with Pakeha in horse races, sporting contests, and, especially, rugby, and a few joined the Volunteers. Much less desirable to most residents was their heavy drinking (encouraged by some publicans and their Pakeha drinking buddies), and occasional fights, very occasionally with Pakeha. Overall, Pakeha ways, both good and bad, of necessity were adopted, and Ngati Rahiri became inextricably a subordinate part of the Pakeha community, although still retaining some distinctive features. 

 (Note: Unless otherwise indicated, all those named in this paper, both Maori and Pakeha, were shareholders in claims in the Te Aroha district.)

text: Maori at Te Aroha after the opening of the goldfield in 1880 (mostly through Pakeha eyes) As the Maori population continued to decline, the aged rangatira admired by Pakeha (even including those who had fought against the Crown) gradually died off, to be replaced by Maori more noted for their drinking and occasional violence than their prestige. Although concerts and haka were popular with many Pakeha, much Maori behaviour was mocked, including by children. Many Maori were seen as being unsophisticated, unable to express themselves properly in English, and prone to drunkenness and laziness, whereas those who adopted Pakeha ways were praised.
Some Pakeha sympathized with poverty-stricken Maori and regretted the decline of their language. There were many examples of close and friendly relations and of Maori assisting Pakeha in trouble, but in general they lived geographically separate lives. To earn money, Maori were forced to work at road making, timber cutting, gum digging, and farming what land remained in their possession. Most Maori struggled financially, their limited resources being stretched by holding expensive tangi and entertaining visitors – resulting in more land sales. They used the court system to defend their economic interests.
Ngati Rahiri (including supporters of the Kingitanga) were seen as ‘loyal’ to the Crown, and visiting Maori kings received kindly treatment from Pakeha as well as from Maori. 
Poor health prompted some government assistance, but poor housing remained, although some attempts were made to improve it (partly to protect Pakeha from diseases). Before the twentieth century only a few children, mostly ‘half-castes’, were educated. Most Ngati Rahiri were members of the Church of England before being attracted by the new Mormon faith.
Ngati Rahiri participated with Pakeha in horse races, sporting contests, and, especially, rugby, and a few joined the Volunteers. Much less desirable to most residents was their heavy drinking (encouraged by some publicans and their Pakeha drinking buddies), and occasional fights, very occasionally with Pakeha. Overall, Pakeha ways, both good and bad, of necessity were adopted, and Ngati Rahiri became inextricably a subordinate part of the Pakeha community, although still retaining some distinctive features. 

 (Note: Unless otherwise indicated, all those named in this paper, both Maori and Pakeha, were shareholders in claims in the Te Aroha district.)

year: 2016