title: Superintegrability and associated polynomial solutions: Euclidean space and the sphere in two dimensions

authors: Kalnins, Ernie G.

subjects: Mathematics

abstract: In this work we examine the basis functions for those classical and quantum mechanical systems in two dimensions which admit separation of variables in at least two coordinate systems. We do this for the corresponding systems defined in Euclidean space and on the two-dimensional sphere. We present all of these cases from a unified point of view. In particular, all of the special functions that arise via variable separation have their essential features expressed in terms of their zeros. The principal new results are the details of the polynomial bases for each of the nonsubgroup bases, not just the subgroup Cartesian and polar coordinate cases, and the details of the structure of the quadratic algebras. We also study the polynomial eigenfunctions in elliptic coordinates of the n-dimensional isotropic quantum oscillator.

text: Superintegrability and associated polynomial solutions: Euclidean space and the sphere in two dimensions In this work we examine the basis functions for those classical and quantum mechanical systems in two dimensions which admit separation of variables in at least two coordinate systems. We do this for the corresponding systems defined in Euclidean space and on the two-dimensional sphere. We present all of these cases from a unified point of view. In particular, all of the special functions that arise via variable separation have their essential features expressed in terms of their zeros. The principal new results are the details of the polynomial bases for each of the nonsubgroup bases, not just the subgroup Cartesian and polar coordinate cases, and the details of the structure of the quadratic algebras. We also study the polynomial eigenfunctions in elliptic coordinates of the n-dimensional isotropic quantum oscillator.

year: 1996-12

title: Using Engel curves to measure CPI bias for Indonesia

authors: Olivia, Susan

subjects: CPI bias

abstract: To measure real income growth over time, a price index is needed to adjust for changes in the cost of living. The consumer price index (CPI) is often used for this task; but several country studies show that it is a biased measure of such changes, leading to potentially inaccurate estimates of the rate of real income growth. This paper calculates CPI bias for urban Indonesia by estimating food Engel curves for households with the same level of CPI-deflated incomes at four different points in time between 1993 and 2008. The results suggest that CPI bias was negative during the 1997–98 crisis but has been positive since 2000. From 1993 to 2008, CPI bias averaged 4% annually, equivalent to almost one-third of the measured inflation rate.

text: Using Engel curves to measure CPI bias for Indonesia To measure real income growth over time, a price index is needed to adjust for changes in the cost of living. The consumer price index (CPI) is often used for this task; but several country studies show that it is a biased measure of such changes, leading to potentially inaccurate estimates of the rate of real income growth. This paper calculates CPI bias for urban Indonesia by estimating food Engel curves for households with the same level of CPI-deflated incomes at four different points in time between 1993 and 2008. The results suggest that CPI bias was negative during the 1997–98 crisis but has been positive since 2000. From 1993 to 2008, CPI bias averaged 4% annually, equivalent to almost one-third of the measured inflation rate.

year: 2013

title: William Grey Nicholls and Rihitoto Mataia

authors: Hart, Philip

abstract: The son of a Pakeha Maori, Nicholls had an illustrious ancestry on his mother’s side, and his wife Rihitoto Mataia also had a distinguished whakapapa. From the 1870s Nicholls farmed in Ohinemuri, and as a licensed interpreter played an important role in land transactions at the same time as he was becoming prominent in the Pakeha community. For over 30 years he invested in mining, starting at Te Aroha in 1880. He also invested in a variety of other enterprises, becoming prosperous through these investments, his farming, and in particular by acquiring and selling land. Over a 40-year period, Nicholls conducted many cases in the land court, and assisted Pakeha to acquire Maori land, and also acquired a considerable amount of land for himself and Rihitoto, who inherited many blocks from her father (but had to pay off his massive debts).
         Whereas Rihitoto was a prominent leader in the Maori community of Hauraki, Nicholls had the same role in Pakeha society. Active in a variety of initiatives to benefit the Ohinemuri community, he was a popular member and chairman of the Ohinemuri County Council, and late in life was elevated to the Legislative Council. Reputedly he assisted Maori in various ways, but clearly he identified rather more with his Pakeha ancestry. His career was a remarkably successful one, and his wife was also successful in maximizing the benefits that could be derived from her ancestry.

text: William Grey Nicholls and Rihitoto Mataia The son of a Pakeha Maori, Nicholls had an illustrious ancestry on his mother’s side, and his wife Rihitoto Mataia also had a distinguished whakapapa. From the 1870s Nicholls farmed in Ohinemuri, and as a licensed interpreter played an important role in land transactions at the same time as he was becoming prominent in the Pakeha community. For over 30 years he invested in mining, starting at Te Aroha in 1880. He also invested in a variety of other enterprises, becoming prosperous through these investments, his farming, and in particular by acquiring and selling land. Over a 40-year period, Nicholls conducted many cases in the land court, and assisted Pakeha to acquire Maori land, and also acquired a considerable amount of land for himself and Rihitoto, who inherited many blocks from her father (but had to pay off his massive debts).
         Whereas Rihitoto was a prominent leader in the Maori community of Hauraki, Nicholls had the same role in Pakeha society. Active in a variety of initiatives to benefit the Ohinemuri community, he was a popular member and chairman of the Ohinemuri County Council, and late in life was elevated to the Legislative Council. Reputedly he assisted Maori in various ways, but clearly he identified rather more with his Pakeha ancestry. His career was a remarkably successful one, and his wife was also successful in maximizing the benefits that could be derived from her ancestry.

year: 2016