title: The holomorphic flow of Riemann’s function ξ(z)

authors: Broughan, Kevin A.

subjects: Riemann’s function Xi(s)

abstract: The holomorphic flow z = ξ(z) of Riemann’s xi function is considered. Phase portraits are plotted and the following results, suggested by the portraits, proved: all separatrices tend to the positive and/or negative real axes. These are an infinite number of crossing separatrices. In the region between each pair of crossing separatrices- a band- there is at most one zero on the critical line. All zeros on the critical line are centres or have all elliptic sectors. The flows for ξ(z) and cosh (z) are linked with a differential equation. Simple zeros on the critical line and Gram points never coincide. The Riemann hypothesis is equivalent to all zeros being centres or multiple together with the non-existence of separatices which enter and leave a band in the same half plane.

text: The holomorphic flow of Riemann’s function ξ(z) The holomorphic flow z = ξ(z) of Riemann’s xi function is considered. Phase portraits are plotted and the following results, suggested by the portraits, proved: all separatrices tend to the positive and/or negative real axes. These are an infinite number of crossing separatrices. In the region between each pair of crossing separatrices- a band- there is at most one zero on the critical line. All zeros on the critical line are centres or have all elliptic sectors. The flows for ξ(z) and cosh (z) are linked with a differential equation. Simple zeros on the critical line and Gram points never coincide. The Riemann hypothesis is equivalent to all zeros being centres or multiple together with the non-existence of separatices which enter and leave a band in the same half plane.

year: 2005

title: Social policy approaches to Hurricane Katrina and the Christchurch Earthquakes

authors: Al-Shamri, Faisal Ali Ahmed

subjects: natural disasters

abstract: Using secondary sources, the purpose of this thesis is to compare the two disasters – Hurricane Katrina in the United States and the two Christchurch Earthquakes in New Zealand and show how the countries managed the aftermath of each of the disasters. The thesis explores Esping-Andersen’s concept of welfare typologies and shows where New Zealand and the United States fit into his framework. The thesis also reviewed some critiques to Esping-Andersen’s typology.  It details the events of the disasters and how the respective governments responded given their social policy approaches.

text: Social policy approaches to Hurricane Katrina and the Christchurch Earthquakes Using secondary sources, the purpose of this thesis is to compare the two disasters – Hurricane Katrina in the United States and the two Christchurch Earthquakes in New Zealand and show how the countries managed the aftermath of each of the disasters. The thesis explores Esping-Andersen’s concept of welfare typologies and shows where New Zealand and the United States fit into his framework. The thesis also reviewed some critiques to Esping-Andersen’s typology.  It details the events of the disasters and how the respective governments responded given their social policy approaches.

year: 2012

title: Microsoft Translator Hub for Māori language

authors: Keegan, Te Taka Adrian Gregory

subjects: computer science

abstract: Recent improvements in Machine Translation (MT) software has opened new possibilities for applications of automatic language translation. But can these opportunities exist for the smaller, minority languages of the world? Training data was collected for the language pair of Māori and English which was used to build an MT system using Microsoft’s Translator Hub software. A comparative analysis was undertaken with this system and Google Translate. Various MT metrics and analysis software was considered before deciding to use the Asiya toolkit to undertake the comparative analysis. Māori language experts were also used to provide a human perspective on the output translations. The overall results showed no significant difference in the translation quality produced by the two systems. Despite some misgivings around the accuracy of the translations these results do show promise for MT usage by minority languages.

text: Microsoft Translator Hub for Māori language Recent improvements in Machine Translation (MT) software has opened new possibilities for applications of automatic language translation. But can these opportunities exist for the smaller, minority languages of the world? Training data was collected for the language pair of Māori and English which was used to build an MT system using Microsoft’s Translator Hub software. A comparative analysis was undertaken with this system and Google Translate. Various MT metrics and analysis software was considered before deciding to use the Asiya toolkit to undertake the comparative analysis. Māori language experts were also used to provide a human perspective on the output translations. The overall results showed no significant difference in the translation quality produced by the two systems. Despite some misgivings around the accuracy of the translations these results do show promise for MT usage by minority languages.

year: 2018