title: Characterizing the sum of two cubes

authors: Broughan, Kevin A.

subjects: sum of two cubes

abstract: An intrinsic characterization of positive integers which can be represented as the sum or difference of two cubes is given. Every integer has a smallest multiple with is a sum of two cubes and such that the multiple, in the form of an iterated function of the integer, is eventually periodic with period one or two. The representation of any integer as the sum of two cubes to a fixed modulus is always possible if and only if the modulus is not divisible by 7 or 9.

text: Characterizing the sum of two cubes An intrinsic characterization of positive integers which can be represented as the sum or difference of two cubes is given. Every integer has a smallest multiple with is a sum of two cubes and such that the multiple, in the form of an iterated function of the integer, is eventually periodic with period one or two. The representation of any integer as the sum of two cubes to a fixed modulus is always possible if and only if the modulus is not divisible by 7 or 9.

year: 2003

title: Considerations for sustainable tourism development in developing countries: Perspectives from the South Pacific

authors: Panakera, Charlie

subjects: Pacific

abstract: Nations of the South Pacific face a number of major challenges with respect to sustainable tourism development. Much of the literature presents overtly pessimistic conceptualisations of South Pacific nations as environmentally vulnerable and economically dependent. This paper argues that the narrative concerning sustainable tourism development in the South Pacific is incomplete and the predominant narrative viewing the South Pacific nations as economically and environmentally vulnerable is too simplistic. Additionally, this paper challenges the narrative that high or mass levels of tourism within the South Pacific cannot be sustainable. Based on experience derived from operational experience and consultancy, this paper provides insights into the challenges and possibilities for sustainable tourism development in the South Pacific.

text: Considerations for sustainable tourism development in developing countries: Perspectives from the South Pacific Nations of the South Pacific face a number of major challenges with respect to sustainable tourism development. Much of the literature presents overtly pessimistic conceptualisations of South Pacific nations as environmentally vulnerable and economically dependent. This paper argues that the narrative concerning sustainable tourism development in the South Pacific is incomplete and the predominant narrative viewing the South Pacific nations as economically and environmentally vulnerable is too simplistic. Additionally, this paper challenges the narrative that high or mass levels of tourism within the South Pacific cannot be sustainable. Based on experience derived from operational experience and consultancy, this paper provides insights into the challenges and possibilities for sustainable tourism development in the South Pacific.

year: 2011

title: Reclaiming Kaitiakitanga : An intergenerational perspective of Kaitiakitanga within Te Parawhau

authors: Walker, Erana

subjects: Kaitiakitanga

abstract: Kaitiakitanga is a concept that is utilised widely throughout the Māori world for the protection and preservation of cultural aspects to Māori. Through years of application by westernised mainstream processes the value has largely been restricted to the realms of environmental protection. This restriction has often been the result of misinterpretation of Kaitiakitanga and its relevance as a concept to Māori. The purpose of the thesis is to question how the perspective of Kaitiakitanga is constructed in the minds of representatives from the hapū of Te Parawhau. To test for variance, the research spans across two generations of hapū members. Using Whakawhiti Kōrero for data collection as well as Kaupapa Māori methodology as guidance, the thesis explores perspectives of two generations of Te Parawhau descendants around Kaitiakitanga and how it can be developed to aid in the growth and prosperity of the hapū. Key themes highlighted by the analysis encompass ideas of connectedness as well as spiritual, physical, environmental and human elements of responsibility and obligation. The thesis introduces a distinct Te Parawhau analytical framework for its analysis of rich kōrero by hapū members in relation to Kaitiakitanga. Through this framework the value of Kaitiakitanga is tested for relevance to Te Parawhau and its future development. The world view of Te Parawhau has formed the basis of participant perspectives around Kaitiakitanga and leads the researcher to consider that such knowledge is important to the future functionality of Māori value’s. The thesis concludes to show that there are indeed differences in application and perspectives of Kaitiakitanga within the hapū of Te Parawhau.

text: Reclaiming Kaitiakitanga : An intergenerational perspective of Kaitiakitanga within Te Parawhau Kaitiakitanga is a concept that is utilised widely throughout the Māori world for the protection and preservation of cultural aspects to Māori. Through years of application by westernised mainstream processes the value has largely been restricted to the realms of environmental protection. This restriction has often been the result of misinterpretation of Kaitiakitanga and its relevance as a concept to Māori. The purpose of the thesis is to question how the perspective of Kaitiakitanga is constructed in the minds of representatives from the hapū of Te Parawhau. To test for variance, the research spans across two generations of hapū members. Using Whakawhiti Kōrero for data collection as well as Kaupapa Māori methodology as guidance, the thesis explores perspectives of two generations of Te Parawhau descendants around Kaitiakitanga and how it can be developed to aid in the growth and prosperity of the hapū. Key themes highlighted by the analysis encompass ideas of connectedness as well as spiritual, physical, environmental and human elements of responsibility and obligation. The thesis introduces a distinct Te Parawhau analytical framework for its analysis of rich kōrero by hapū members in relation to Kaitiakitanga. Through this framework the value of Kaitiakitanga is tested for relevance to Te Parawhau and its future development. The world view of Te Parawhau has formed the basis of participant perspectives around Kaitiakitanga and leads the researcher to consider that such knowledge is important to the future functionality of Māori value’s. The thesis concludes to show that there are indeed differences in application and perspectives of Kaitiakitanga within the hapū of Te Parawhau.

year: 2016