title: Lie theory and separation of variables. 9. Orthogonal R-separable coordinate systems for the wave equation ψtt-∆2ψ=0

authors: Kalnins, Ernie G.

subjects: Mathematics

abstract: A list of orthogonal coordinate systems which permit R-separation of the wave equation ψtt-∆2ψ=0 is presented. All such coordinate systems whose coordinate curves are cyclides or their degenerate forms are given. In each case the coordinates and separation equations are computed. The two basis operators associated with each coordinate system are also presented as symmetric second order operators in the enveloping algebra of the conformal group O(3,2).

text: Lie theory and separation of variables. 9. Orthogonal R-separable coordinate systems for the wave equation ψtt-∆2ψ=0 A list of orthogonal coordinate systems which permit R-separation of the wave equation ψtt-∆2ψ=0 is presented. All such coordinate systems whose coordinate curves are cyclides or their degenerate forms are given. In each case the coordinates and separation equations are computed. The two basis operators associated with each coordinate system are also presented as symmetric second order operators in the enveloping algebra of the conformal group O(3,2).

year: 1976-03

title: Re-embodying (preservice middle years) teachers? An attempt to reposition the body and its presence in teaching and learning

authors: lisahunter

subjects: body

abstract: This four-part story is about one teacher educator’s attempt to embody praxis as a form of academic work, emphasizing the importance of the corporeal in learning and teaching. I describe the inter-related context (1) of my embodied self, the teacher education course I constructed, and theory employed in mediating course practices. Evidence of praxis in emergence (2) is illustrated through written text and visual artefacts of the operationalized assessment. I discuss (3) using embodied subjectivities, the importance of practice/praxis, and how we operationalize discourse in education to then pose questions (4) as flows for teacher educators, preservice teachers and teachers in their classpaces.

text: Re-embodying (preservice middle years) teachers? An attempt to reposition the body and its presence in teaching and learning This four-part story is about one teacher educator’s attempt to embody praxis as a form of academic work, emphasizing the importance of the corporeal in learning and teaching. I describe the inter-related context (1) of my embodied self, the teacher education course I constructed, and theory employed in mediating course practices. Evidence of praxis in emergence (2) is illustrated through written text and visual artefacts of the operationalized assessment. I discuss (3) using embodied subjectivities, the importance of practice/praxis, and how we operationalize discourse in education to then pose questions (4) as flows for teacher educators, preservice teachers and teachers in their classpaces.

year: 2010

title: Hoera Te Mimiha

authors: Hart, Philip

abstract: Hoera Te Mimiha was a rangatira of Ngati Koi, an inferior hapu to Ngati Tamatera, and had affiliations to other hapu. Although to Pakeha he was a mere labourer, in Maori society in Ohinemuri in the 1870s and 1880s he was a leading figure. Details have been traced of his whakapapa, his wider family, and especially his children, one of whom married Hone Werahiko. 
Mimiha spent much time in the Maori Land Court trying to prove his entitlement to be included as an owner of several blocks of land, not always successfully, for he could not prove some of his cases either through ancestry or occupation. Other rangatira with superior whakapapa were able to show the weaknesses of some of his claims, forcing him into giving evasive answers to cross-examination. His evidence did reveal what land he had occupied and farmed.
Mimiha willingly sold land, including his interest in the Ohinemuri goldfield (the boundaries of which he had pointed out to surveyors), and obtained a good income, for a time. Being interested in mining from the early 1870s onwards, he was one of the few Maori willing to descend a shaft at Thames, an experience that encouraged him to push for opening Ohinemuri to mining, even, it seemed, if that endangered Maori control of their land. Having prospected at Karangahake before it was opened to mining in 1875, he participated in this rush and subsequently in the Te Aroha one of 1880, having interests in claims at all three portions of the latter field. When his daughter’s partner was murdered at Te Aroha, he calmed Maori anger, once again winning the gratitude of Pakeha.
Because of selling much of his land, he struggled financially, although unlike some Maori he did not drink his money away. Cutting off part of the ear of a Pakeha accused of raping his wife resulted in several court cases marked by dubious evidence presented by both sides. After being imprisoned for perjury, efforts by Pakeha to have his conviction reviewed resulted in his being judged to have been the only witness not to have lied to the court, but this sordid affair blackened his character.

text: Hoera Te Mimiha Hoera Te Mimiha was a rangatira of Ngati Koi, an inferior hapu to Ngati Tamatera, and had affiliations to other hapu. Although to Pakeha he was a mere labourer, in Maori society in Ohinemuri in the 1870s and 1880s he was a leading figure. Details have been traced of his whakapapa, his wider family, and especially his children, one of whom married Hone Werahiko. 
Mimiha spent much time in the Maori Land Court trying to prove his entitlement to be included as an owner of several blocks of land, not always successfully, for he could not prove some of his cases either through ancestry or occupation. Other rangatira with superior whakapapa were able to show the weaknesses of some of his claims, forcing him into giving evasive answers to cross-examination. His evidence did reveal what land he had occupied and farmed.
Mimiha willingly sold land, including his interest in the Ohinemuri goldfield (the boundaries of which he had pointed out to surveyors), and obtained a good income, for a time. Being interested in mining from the early 1870s onwards, he was one of the few Maori willing to descend a shaft at Thames, an experience that encouraged him to push for opening Ohinemuri to mining, even, it seemed, if that endangered Maori control of their land. Having prospected at Karangahake before it was opened to mining in 1875, he participated in this rush and subsequently in the Te Aroha one of 1880, having interests in claims at all three portions of the latter field. When his daughter’s partner was murdered at Te Aroha, he calmed Maori anger, once again winning the gratitude of Pakeha.
Because of selling much of his land, he struggled financially, although unlike some Maori he did not drink his money away. Cutting off part of the ear of a Pakeha accused of raping his wife resulted in several court cases marked by dubious evidence presented by both sides. After being imprisoned for perjury, efforts by Pakeha to have his conviction reviewed resulted in his being judged to have been the only witness not to have lied to the court, but this sordid affair blackened his character.

year: 2016