title: On trivial p-adic zeroes for elliptic curves over Kummer extensions

authors: Delbourgo, Daniel

abstract: We prove the exceptional zero conjecture is true for semistable elliptic curves E/Q over number fields of the form F(e²ⁿⁱ⁄ｑⁿ, ∆₁¹⁄ｑⁿ , . . . , ∆₁¹⁄ⁿd) where F is a totally real field, and the split multiplicative prime p ≠ 2 is inert in F(e²ⁿⁱ⁄ｑⁿ) ∩ R.

text: On trivial p-adic zeroes for elliptic curves over Kummer extensions We prove the exceptional zero conjecture is true for semistable elliptic curves E/Q over number fields of the form F(e²ⁿⁱ⁄ｑⁿ, ∆₁¹⁄ｑⁿ , . . . , ∆₁¹⁄ⁿd) where F is a totally real field, and the split multiplicative prime p ≠ 2 is inert in F(e²ⁿⁱ⁄ｑⁿ) ∩ R.

year: 2015

title: Modelling Energy Balance and Storage in the Design of Smart Microgrids

authors: Apperley, Mark

subjects: Science & Technology

abstract: This paper introduces and demonstrates appropriate and realistic modelling approaches for smart microgrids, with a focus on local energy balance. There is an increasing interest in microgrids, as the nature of large-scale electricity generation and distribution changes, with a conscious shift to more sustainable and renewable energy sources. However, the modelling and design techniques traditionally used have tended to be based on economics and design criteria more suited to the top-down planning for power generation and distribution typical of legacy grids, than to bottom-up energy balance incorporating localised distributed generation and storage, significant characteristics of these new systems. Several aspects of microgrid design and specification are modelled using an example based on an installation incorporating solar photovoltaic panels and battery storage. Important features of each of the models shown are the associated visualisations, which lead to improved understanding of design implications, compromises, and consequences, and the true context of a renewable-energy based microgrid.

text: Modelling Energy Balance and Storage in the Design of Smart Microgrids This paper introduces and demonstrates appropriate and realistic modelling approaches for smart microgrids, with a focus on local energy balance. There is an increasing interest in microgrids, as the nature of large-scale electricity generation and distribution changes, with a conscious shift to more sustainable and renewable energy sources. However, the modelling and design techniques traditionally used have tended to be based on economics and design criteria more suited to the top-down planning for power generation and distribution typical of legacy grids, than to bottom-up energy balance incorporating localised distributed generation and storage, significant characteristics of these new systems. Several aspects of microgrid design and specification are modelled using an example based on an installation incorporating solar photovoltaic panels and battery storage. Important features of each of the models shown are the associated visualisations, which lead to improved understanding of design implications, compromises, and consequences, and the true context of a renewable-energy based microgrid.

year: 2017

title: Kua Hiri Mai Te Rā - A journey of self identification for the descendants of Ngāti Rāhiri ki Taranaki

authors: Marsh, Melissa Sue-ann

subjects: Ngāti Rāhiri

abstract: Prior to the arrival of Pakehā to the shores of Aotearoa, Māori retained and transmitted their histories, genealogies and protocols orally through such mediums as song and chant. The intracacies of the information held was such that every aspect of the Māori culture had its assigned expert whose job was to both retain and pass on their area of expertise. The settlement of Pakehā saw a change in how information was stored and disseminated, with a number of ethnographers, surveyors and historians recording accounts given to them from various Māori sources in written form. The main motivation for this at the time was to secure the information and cultural practises of a people who were deemed to be a dying race.

The implication that Māori were close to extinction was in vain, as many resisted against the gradual assimilation of Aotearoa (New Zealand) by the new foreign immigrants. The subsequent annexation of Aotearoa under British colonial rule eventually led to war against Māori, as Māori attempted to protect and retain both their lands and their identity. The result of the war led to a great loss of Māori lands, lives, and most importantly – identity.

Within Taranaki the Ngāti Rāhiri Hapū fought many generations for the right to stand unified as a people. Although they can be regarded as a small coastal hapū entity, they are at the forefront of maintaining and asserting their rangatiratanga status within today’s society. At the centre of the proclamation of rights and entitlement within their ancestral lands, questions have been raised that, for a number of generations, had baffled the likes of Elsdon Best and S. Percy Smith, as many sought to find answers regarding the true origins of Ngāti Rāhiri.

The impetus in undertaking this research is to ascertain who this prominent ancestor Rāhiri is from both a Ngā Puhi and Taranaki perspective, and investigate how these combined histories assist in the assertion of self by the Ngāti Rāhiri ki Taranaki people. By undertaking a critical review and analysis of literature, court minute records, hapū documents, proverbs, histories and knowledge from tribal elders pertaining to Rāhiri, this researcher will endeavour to provide and present relevant information and evidence, in a cohesive format, to show the close ancestral ties and affiliations between the two peoples. Furthermore, it is hoped that the research findings presented within this body of work may provide a significant contribution to the descendants of the Ngāti Rāhiri ki Taranaki Hapū, as they continue to assert their mana and rangatiratanga through the knowledge and understanding of self, when posed with the question - Ko wai a Ngāti Rāhiri?

text: Kua Hiri Mai Te Rā - A journey of self identification for the descendants of Ngāti Rāhiri ki Taranaki Prior to the arrival of Pakehā to the shores of Aotearoa, Māori retained and transmitted their histories, genealogies and protocols orally through such mediums as song and chant. The intracacies of the information held was such that every aspect of the Māori culture had its assigned expert whose job was to both retain and pass on their area of expertise. The settlement of Pakehā saw a change in how information was stored and disseminated, with a number of ethnographers, surveyors and historians recording accounts given to them from various Māori sources in written form. The main motivation for this at the time was to secure the information and cultural practises of a people who were deemed to be a dying race.

The implication that Māori were close to extinction was in vain, as many resisted against the gradual assimilation of Aotearoa (New Zealand) by the new foreign immigrants. The subsequent annexation of Aotearoa under British colonial rule eventually led to war against Māori, as Māori attempted to protect and retain both their lands and their identity. The result of the war led to a great loss of Māori lands, lives, and most importantly – identity.

Within Taranaki the Ngāti Rāhiri Hapū fought many generations for the right to stand unified as a people. Although they can be regarded as a small coastal hapū entity, they are at the forefront of maintaining and asserting their rangatiratanga status within today’s society. At the centre of the proclamation of rights and entitlement within their ancestral lands, questions have been raised that, for a number of generations, had baffled the likes of Elsdon Best and S. Percy Smith, as many sought to find answers regarding the true origins of Ngāti Rāhiri.

The impetus in undertaking this research is to ascertain who this prominent ancestor Rāhiri is from both a Ngā Puhi and Taranaki perspective, and investigate how these combined histories assist in the assertion of self by the Ngāti Rāhiri ki Taranaki people. By undertaking a critical review and analysis of literature, court minute records, hapū documents, proverbs, histories and knowledge from tribal elders pertaining to Rāhiri, this researcher will endeavour to provide and present relevant information and evidence, in a cohesive format, to show the close ancestral ties and affiliations between the two peoples. Furthermore, it is hoped that the research findings presented within this body of work may provide a significant contribution to the descendants of the Ngāti Rāhiri ki Taranaki Hapū, as they continue to assert their mana and rangatiratanga through the knowledge and understanding of self, when posed with the question - Ko wai a Ngāti Rāhiri?

year: 2011