title: A New Way to Look at Homomorphisms

authors: Guo, Yue

subjects: Distributors

abstract: This thesis is about arbitrary functions between groups. We look at two way to measure how close an arbitrary function is to being a homomorphism. We first look at an action of the group on functions in which homomorphisms are invariant. We also look at distributors, structures which are similar to commutators and which are trivial for a homomorphism. This leads to a rich and interesting theory and gives us a new way to look at homomorphisms and new tools to try to build homomorphisms from arbitrary functions. We demonstrate the applicability of these tools by constructing several alternate proofs of the Schur-Zassenhaus theorem.

text: A New Way to Look at Homomorphisms This thesis is about arbitrary functions between groups. We look at two way to measure how close an arbitrary function is to being a homomorphism. We first look at an action of the group on functions in which homomorphisms are invariant. We also look at distributors, structures which are similar to commutators and which are trivial for a homomorphism. This leads to a rich and interesting theory and gives us a new way to look at homomorphisms and new tools to try to build homomorphisms from arbitrary functions. We demonstrate the applicability of these tools by constructing several alternate proofs of the Schur-Zassenhaus theorem.

year: 2013

title: Immigration futures: New Zealand in a global context

authors: Bedford, Richard

abstract: At no other time in the past century has there been such focused and intense global interest in international migration. Never before has there been such interest, internationally, in how Australia, Canada and New Zealand manage their international migration. These countries have become models for governments elsewhere who are seeking to develop policy that has a more direct impact on the quality of the population flows into their countries.

New Zealand is unusual by OECD standards in that it has a high level of emigration of citizens at the same time that it has a very high per capita rate of immigration. New Zealand’s contemporary migration flows are examined briefly and it is demonstrated that the system is not nearly as dominated by migration from countries in northeast Asia as it was a decade ago.

A more flexible approach to the attainment of permits to reside in a country is being adopted in most countries now. The prospective migrants take the opportunity to assess employment opportunities and the quality of life in a prospective new home (perhaps not their only home either), while working or studying on temporary permits and gaining the sort of local experience that is valued in the points-based immigrant selection systems. The paper concludes with a brief analysis of data relating to transition to residence in New Zealand.

text: Immigration futures: New Zealand in a global context At no other time in the past century has there been such focused and intense global interest in international migration. Never before has there been such interest, internationally, in how Australia, Canada and New Zealand manage their international migration. These countries have become models for governments elsewhere who are seeking to develop policy that has a more direct impact on the quality of the population flows into their countries.

New Zealand is unusual by OECD standards in that it has a high level of emigration of citizens at the same time that it has a very high per capita rate of immigration. New Zealand’s contemporary migration flows are examined briefly and it is demonstrated that the system is not nearly as dominated by migration from countries in northeast Asia as it was a decade ago.

A more flexible approach to the attainment of permits to reside in a country is being adopted in most countries now. The prospective migrants take the opportunity to assess employment opportunities and the quality of life in a prospective new home (perhaps not their only home either), while working or studying on temporary permits and gaining the sort of local experience that is valued in the points-based immigrant selection systems. The paper concludes with a brief analysis of data relating to transition to residence in New Zealand.

year: 2006

title: Ko te reo i Te Rarawa: Pēhea rainī te tūāhua reo o ngā mātua tūpuna i Pukepoto

authors: McGrath, Daniel

abstract: Ko te reo Māori, ko te reo ā-iwi, ko te mita o te reo; ko tēhea te mea nui? Mai anō tēnei tohe, ko tēhea ko runga, ko tēhea ko raro. He tinitini nei anō ngā rangahau mō te reo Māori, mō ngā rautaki whakaora i te reo Māori. Erangi pēhea mai ana te reo ā-iwi? I te mahi nui whakaharahara ki te whakaora i te reo Māori e noho ana tērā kaupapa hei aronga matua. E kite mārika ana i ngā hua o aua mahi, hoi anō te reo ā-iwi, te hanga nei, i paria ki rāhaki. Nā, i ngā tau tata nei anō, kua kitea rawatia te wheinu o ngā uri whakaheke, o ngā mokopuna o ngā iwi ki te ako i ō rātou mita, otirā i te reo ā-iwi.
Hoi anō tēnei kaupapa rangahau he mea whakapiripiri ki ngā rangahau mō te reo Māori, waihoki mō te reo ā-iwi. E āta mātai atu ana te titiro ki te reo ake anō o Te Rarawa, otirā ki te reo o ngā kaumātua i noho ai i Pukepoto. Ko ngā whāinga matua o te rangahau kia kitea pēnā rainī he patanga wō te reo i te kāinga ki te mana, ki te ahurea o te tangata, ka tahi. Ka rua, kia huraina mai ai ngā āhuatanga motuhake o te reo o Te Rarawa, otirā, o te reo i Pukepoto. I runga i tērā, ko te pātai matua o te rangahau nei, ko tēnei;
Pēhea hoki nei te tūāhua reo Māori i kōrerohia ai e ngā mātua tūpuna, e ngā wheinga i Pukepoto?
Nā, e tutuki ngā whāinga rangahau, i arohia wētahi rīpene kei te pātaka kōrero o Te Reo Irirangi Māori o Te Hiku o Te Ika e mau nei ngā reo o ngā kaumātua o te kāinga e kōrero ana mō ngā tini āhuatanga e hāngai ana ki ō rātou nā ao. E tāwharautia ana tēnei kaupapa e te Rangahau Kaupapa Māori, ā, ko ngā tikanga, ko ngā kōrero i ahua mai i Te Rarawa i Pukepoto e noho mai ana hei tāhuhu tikanga mōku. Ko ngā taupānga hou kua oti kē nei i a Te Reo Irirangi Māori o Te Hiku o Te Ika hei taputapu e nanao atu ai a hau ki te pātaka kōrero o Te Hiku o Te Ika, e pai ai taku āta wānanga i ngā kupu, i ngā kōrero kei ngā rīpene e mau ana.
Tokowhitu katoa ngā kaumātua i āta arohia e ahau i tēnei rangahau nei, katoa i noho ai i Pukepoto. Ko tāku, he āta whakataringa atu ki wā rātou kōrero, ka āta arotake ai i wētahi kupu, i wētahi kīwaha, i wētahi whakatakotoranga rerenga kōrero i kaha whakahuangia e rātou mā. Kei te puke tuaono te roanga o ngā kōrero mō ngā kitenga o te rangahau; i mārama te kite atu he tini ngā momo kupu, ngā kīwaha me ngā rerenga kōrero he tikanga kē atu wō rātou, he whakamahinga kē anō, ka mutu, arā wētahi kāhore e tino rangona ana i wēnei wā nei. Nō reira, ko tā tēnei rangahau e whai ana kia whakahokia wēnei āhuatanga o te reo ki ngā arero o ngā uri whakaheke o Pukepoto, o Te Rarawa, otirā o Te Hiku o te Ika.

text: Ko te reo i Te Rarawa: Pēhea rainī te tūāhua reo o ngā mātua tūpuna i Pukepoto Ko te reo Māori, ko te reo ā-iwi, ko te mita o te reo; ko tēhea te mea nui? Mai anō tēnei tohe, ko tēhea ko runga, ko tēhea ko raro. He tinitini nei anō ngā rangahau mō te reo Māori, mō ngā rautaki whakaora i te reo Māori. Erangi pēhea mai ana te reo ā-iwi? I te mahi nui whakaharahara ki te whakaora i te reo Māori e noho ana tērā kaupapa hei aronga matua. E kite mārika ana i ngā hua o aua mahi, hoi anō te reo ā-iwi, te hanga nei, i paria ki rāhaki. Nā, i ngā tau tata nei anō, kua kitea rawatia te wheinu o ngā uri whakaheke, o ngā mokopuna o ngā iwi ki te ako i ō rātou mita, otirā i te reo ā-iwi.
Hoi anō tēnei kaupapa rangahau he mea whakapiripiri ki ngā rangahau mō te reo Māori, waihoki mō te reo ā-iwi. E āta mātai atu ana te titiro ki te reo ake anō o Te Rarawa, otirā ki te reo o ngā kaumātua i noho ai i Pukepoto. Ko ngā whāinga matua o te rangahau kia kitea pēnā rainī he patanga wō te reo i te kāinga ki te mana, ki te ahurea o te tangata, ka tahi. Ka rua, kia huraina mai ai ngā āhuatanga motuhake o te reo o Te Rarawa, otirā, o te reo i Pukepoto. I runga i tērā, ko te pātai matua o te rangahau nei, ko tēnei;
Pēhea hoki nei te tūāhua reo Māori i kōrerohia ai e ngā mātua tūpuna, e ngā wheinga i Pukepoto?
Nā, e tutuki ngā whāinga rangahau, i arohia wētahi rīpene kei te pātaka kōrero o Te Reo Irirangi Māori o Te Hiku o Te Ika e mau nei ngā reo o ngā kaumātua o te kāinga e kōrero ana mō ngā tini āhuatanga e hāngai ana ki ō rātou nā ao. E tāwharautia ana tēnei kaupapa e te Rangahau Kaupapa Māori, ā, ko ngā tikanga, ko ngā kōrero i ahua mai i Te Rarawa i Pukepoto e noho mai ana hei tāhuhu tikanga mōku. Ko ngā taupānga hou kua oti kē nei i a Te Reo Irirangi Māori o Te Hiku o Te Ika hei taputapu e nanao atu ai a hau ki te pātaka kōrero o Te Hiku o Te Ika, e pai ai taku āta wānanga i ngā kupu, i ngā kōrero kei ngā rīpene e mau ana.
Tokowhitu katoa ngā kaumātua i āta arohia e ahau i tēnei rangahau nei, katoa i noho ai i Pukepoto. Ko tāku, he āta whakataringa atu ki wā rātou kōrero, ka āta arotake ai i wētahi kupu, i wētahi kīwaha, i wētahi whakatakotoranga rerenga kōrero i kaha whakahuangia e rātou mā. Kei te puke tuaono te roanga o ngā kōrero mō ngā kitenga o te rangahau; i mārama te kite atu he tini ngā momo kupu, ngā kīwaha me ngā rerenga kōrero he tikanga kē atu wō rātou, he whakamahinga kē anō, ka mutu, arā wētahi kāhore e tino rangona ana i wēnei wā nei. Nō reira, ko tā tēnei rangahau e whai ana kia whakahokia wēnei āhuatanga o te reo ki ngā arero o ngā uri whakaheke o Pukepoto, o Te Rarawa, otirā o Te Hiku o te Ika.

year: 2021