title: Symmetry and separation of variables for the Hamilton–Jacobi equation W2t −W2x  −W2y  =0

authors: Boyer, C.P.

subjects: Mathematics

abstract: We present a detailed group theoretical study of the problem of separation of variables for the characteristic equation of the wave equation in one time and two space dimensions. Using the well-known Lie algebra isomorphism between canonical vector fields under the Lie bracket operation and functions (modulo constants) under Poisson brackets, we associate, with each R-separable coordinate system of the equation, an orbit of commuting constants of the motion which are quadratic members of the universal enveloping algebra of the symmetry algebra o (3,2). In this, the first of two papers, we essentially restrict ourselves to those orbits where one of the constants of the motion can be split off, giving rise to a reduced equation with a nontrivial symmetry algebra. Our analysis includes several of the better known two-body problems, including the harmonic oscillator and Kepler problems, as special cases.

text: Symmetry and separation of variables for the Hamilton–Jacobi equation W2t −W2x  −W2y  =0 We present a detailed group theoretical study of the problem of separation of variables for the characteristic equation of the wave equation in one time and two space dimensions. Using the well-known Lie algebra isomorphism between canonical vector fields under the Lie bracket operation and functions (modulo constants) under Poisson brackets, we associate, with each R-separable coordinate system of the equation, an orbit of commuting constants of the motion which are quadratic members of the universal enveloping algebra of the symmetry algebra o (3,2). In this, the first of two papers, we essentially restrict ourselves to those orbits where one of the constants of the motion can be split off, giving rise to a reduced equation with a nontrivial symmetry algebra. Our analysis includes several of the better known two-body problems, including the harmonic oscillator and Kepler problems, as special cases.

year: 1978-01

title: How cost elastic are remittances? Estimates from Tongan migrants in New Zealand

authors: Gibson, John

subjects: remittances

abstract: Pacific Island economies are some of the most remittance- dependent in the world. Proposals to lower the costs of sending money across borders are a core recommendation of recent international studies that aim to enhance the development impact of remittances. The potential increase in remittances that recipient countries can expect from such policies depends critically on the sensitivity of remittance transfers to the costs of remitting. This paper provides the first estimates of the cost-elasticity of remittances, using data from a survey of Tongan migrants in New Zealand. The costs of remitting to Tonga are high by international standards and remittances are found to have a negative cost-elasticity with respect to the fixed fee component of money transfer costs. These findings suggest that Pacific Island countries can expect a more than proportionate increase in remittances from a reduction in costs.

text: How cost elastic are remittances? Estimates from Tongan migrants in New Zealand Pacific Island economies are some of the most remittance- dependent in the world. Proposals to lower the costs of sending money across borders are a core recommendation of recent international studies that aim to enhance the development impact of remittances. The potential increase in remittances that recipient countries can expect from such policies depends critically on the sensitivity of remittance transfers to the costs of remitting. This paper provides the first estimates of the cost-elasticity of remittances, using data from a survey of Tongan migrants in New Zealand. The costs of remitting to Tonga are high by international standards and remittances are found to have a negative cost-elasticity with respect to the fixed fee component of money transfer costs. These findings suggest that Pacific Island countries can expect a more than proportionate increase in remittances from a reduction in costs.

year: 2006-03

title: Bilingual/immersion education in Aotearoa/New Zealand: Setting the context.

authors: May, Stephen

subjects: bilingual education

abstract: Introduction to a special issue of IJBEB, focusing on recent developments in bilingual/
immersion education in Aotearoa/New Zealand, particularly, but not solely,
Maori-medium education.

text: Bilingual/immersion education in Aotearoa/New Zealand: Setting the context. Introduction to a special issue of IJBEB, focusing on recent developments in bilingual/
immersion education in Aotearoa/New Zealand, particularly, but not solely,
Maori-medium education.

year: 2005-01-01