title: Lie theory and separation of variables. 10. Nonorthogonal R-separable solutions of the wave equation ∂ttψ=∆2ψ

authors: Kalnins, Ernie G.

subjects: Mathematics

abstract: We classify and discuss the possible nonorthogonal coordinate systems which lead to R-separable solutions of the wave equation. Each system is associated with a pair of commuting operators in the symmetry algebra so(3,2) of this equation, one operator first order and the other second order. Several systems appear here for the first time.

text: Lie theory and separation of variables. 10. Nonorthogonal R-separable solutions of the wave equation ∂ttψ=∆2ψ We classify and discuss the possible nonorthogonal coordinate systems which lead to R-separable solutions of the wave equation. Each system is associated with a pair of commuting operators in the symmetry algebra so(3,2) of this equation, one operator first order and the other second order. Several systems appear here for the first time.

year: 1976-03

title: Guest editorial Geography teaching, governance and professional development

authors: Chalmers, Lex

abstract: One of the things that have characterised the activity of secondary teaching in the last two decades has been the increasing impact of ‘governance’, where governance is taken to mean implementation and compliance with new curriculum and assessment frameworks, new teacher/school management and performance criteria andnewways of viewing educational practice. Governance issues affect teaching by consuming time that could more purposefully be directed to professional development, and this matter is the focus of this commentary.

text: Guest editorial Geography teaching, governance and professional development One of the things that have characterised the activity of secondary teaching in the last two decades has been the increasing impact of ‘governance’, where governance is taken to mean implementation and compliance with new curriculum and assessment frameworks, new teacher/school management and performance criteria andnewways of viewing educational practice. Governance issues affect teaching by consuming time that could more purposefully be directed to professional development, and this matter is the focus of this commentary.

year: 2005

title: Te kaumoana Poronīhia: Ngā terenga onamata

authors: Tuaupiki, Jackie Whetumarama

subjects: Kōrero nehe

abstract: Tā tēnei tuhinga e whai ake nei, he wānanga i ngā pūtake o te whanaketanga mai o ngā iwi, nāna ngā motu o Poronīhia i whakakāinga, ka utaina te karangatanga ki runga ki a rātou, he iwi Poronīhia. Ko te pātai matua, i ahu mai ngā iwi Poronīhia i whea? Tēnei, ka hahaina ngā whakaaro Māori me ngā whakaaro Tauiwi e pā ana ki te pūtakenga mai o te iwi tāngata ki te ao. I konei, ka kitea te rerekē o te titiro ā-ao a ēnei iwi tāngata.

Ka ū te titiro ki Hawaiki, e tau ana ngā kōrero tuku iho a te ao Māori, ki te ao Poronīhia hoki. E mea ana te Māori, he tūrangawaewae taurikura a Hawaiki, he pā whakawairua hoki. Ka riariakina e au ngā whakapae mō tēnei karangatanga kāinga i mau roa ai i ōna iwi kōrero.

Ka huri rā ki te āta whakatewhatewha i ngā rangahau mō te horanga haeretanga o te iwi tāngata mai i whirika, ki  hia ki te tonga mā rāwhiti, ā, tau atu rā ki roto i ngā whaitua moana o Poronīhia. I konei, kua āta wānangahia e au ngā whakapae huhua mō ngā take i horapa haere ai ēnei iwi ki roto o Poronīhia, ka tahi. Ka rua, ka tirohia ngā tohe e pā ana ki tō rātou āheinga ki te whakatere i ō rātou waka. Ko ēnei kōrero, he whakatuwhera i te pūtea mātauranga mō runga i ngā mahi whakatere waka a ngā tūpuna Poronīhia.

text: Te kaumoana Poronīhia: Ngā terenga onamata Tā tēnei tuhinga e whai ake nei, he wānanga i ngā pūtake o te whanaketanga mai o ngā iwi, nāna ngā motu o Poronīhia i whakakāinga, ka utaina te karangatanga ki runga ki a rātou, he iwi Poronīhia. Ko te pātai matua, i ahu mai ngā iwi Poronīhia i whea? Tēnei, ka hahaina ngā whakaaro Māori me ngā whakaaro Tauiwi e pā ana ki te pūtakenga mai o te iwi tāngata ki te ao. I konei, ka kitea te rerekē o te titiro ā-ao a ēnei iwi tāngata.

Ka ū te titiro ki Hawaiki, e tau ana ngā kōrero tuku iho a te ao Māori, ki te ao Poronīhia hoki. E mea ana te Māori, he tūrangawaewae taurikura a Hawaiki, he pā whakawairua hoki. Ka riariakina e au ngā whakapae mō tēnei karangatanga kāinga i mau roa ai i ōna iwi kōrero.

Ka huri rā ki te āta whakatewhatewha i ngā rangahau mō te horanga haeretanga o te iwi tāngata mai i whirika, ki  hia ki te tonga mā rāwhiti, ā, tau atu rā ki roto i ngā whaitua moana o Poronīhia. I konei, kua āta wānangahia e au ngā whakapae huhua mō ngā take i horapa haere ai ēnei iwi ki roto o Poronīhia, ka tahi. Ka rua, ka tirohia ngā tohe e pā ana ki tō rātou āheinga ki te whakatere i ō rātou waka. Ko ēnei kōrero, he whakatuwhera i te pūtea mātauranga mō runga i ngā mahi whakatere waka a ngā tūpuna Poronīhia.

year: 2017