title: Subcubic trades in Steiner triple systems

authors: Cavenagh, Nicholas J.

subjects: Science & Technology

abstract: We consider the problem of classifying trades in Steiner triple systems such that each block of the trade contains one of three fixed elements. We show that the fundamental building blocks for such trades are 3-regular graphs that are 1-factorisable. In the process we also generate all possible 2- and 3-way simultaneous edge colourings of graphs with maximum degree 3 using at most 3 colours, where multiple edges but not loops are allowed. Moreover, we generate all possible Latin trades within three rows.

text: Subcubic trades in Steiner triple systems We consider the problem of classifying trades in Steiner triple systems such that each block of the trade contains one of three fixed elements. We show that the fundamental building blocks for such trades are 3-regular graphs that are 1-factorisable. In the process we also generate all possible 2- and 3-way simultaneous edge colourings of graphs with maximum degree 3 using at most 3 colours, where multiple edges but not loops are allowed. Moreover, we generate all possible Latin trades within three rows.

year: 2017

title: Shedding the shackles of Bowman: A critical review of the political purpose doctrine and charity law in New Zealand

authors: Chevalier-Watts, Juliet

abstract: The shackles that bound New Zealand to the political purpose doctrine, the notorious doctrine found within charity law, have now, at last, been shed, with the delivery of the long awaited Supreme Court judgment of Re Greenpeace of New Zealand Incorporated. This article explores whether the shedding of the shackles that bound New Zealand jurisprudence to this doctrine was inevitable, in light of national and international judicial influences and commentary.

text: Shedding the shackles of Bowman: A critical review of the political purpose doctrine and charity law in New Zealand The shackles that bound New Zealand to the political purpose doctrine, the notorious doctrine found within charity law, have now, at last, been shed, with the delivery of the long awaited Supreme Court judgment of Re Greenpeace of New Zealand Incorporated. This article explores whether the shedding of the shackles that bound New Zealand jurisprudence to this doctrine was inevitable, in light of national and international judicial influences and commentary.

year: 2015

title: “Papatuanuku/papa:” Some thoughts on the oppositional grounds of the doctoral experience

authors: Mika, Carl Te Hira

subjects: Kaupapa

abstract: There are significant challenges that face Māori students and supervisors as a “doctoral team.” Perhaps the most fundamental of these is that there is a metaphysics at work in writing and talking that Māori are encouraged to speculate on and reclaim. One term for this metaphysics, “Papatūānuku” (often abbreviated to “Papa”), signifies an active entity that rejects strict definition but influences both doctoral text and team. This article proposes that student and supervisor must simultaneously glance towards the conventions of academic writing and recollect Papatūānuku as potential being in the doctoral process.

text: “Papatuanuku/papa:” Some thoughts on the oppositional grounds of the doctoral experience There are significant challenges that face Māori students and supervisors as a “doctoral team.” Perhaps the most fundamental of these is that there is a metaphysics at work in writing and talking that Māori are encouraged to speculate on and reclaim. One term for this metaphysics, “Papatūānuku” (often abbreviated to “Papa”), signifies an active entity that rejects strict definition but influences both doctoral text and team. This article proposes that student and supervisor must simultaneously glance towards the conventions of academic writing and recollect Papatūānuku as potential being in the doctoral process.

year: 2016