title: On EQ-monoids

authors: Stokes, Tim E.

subjects: mathematics

abstract: An EQ-monoid A is a monoid with distinguished subsemilattice L with 1 2 L and such that any a, b 2 A have a largest right equalizer in L. The class of all such monoids equipped with a binary operation that identifies this largest right equalizer is a variety. Examples include Heyting algebras, Cartesian products of monoids with zero, as well as monoids of relations and partial maps on sets. The variety is 0-regular (though not ideal determined and hence congruences do not permute), and we describe the normal subobjects in terms of a global semilattice structure. We give representation theorems for several natural subvarieties in terms of Boolean algebras, Cartesian products and partial maps. The case in which the EQmonoid is assumed to be an inverse semigroup with zero is given particular attention. Finally, we define the derived category associated with a monoid having a distinguished subsemilattice containing the identity (a construction generalising the idea of a monoid category), and show that those monoids for which this derived category has equalizers in the semilattice constitute a variety of EQ-monoids.

text: On EQ-monoids An EQ-monoid A is a monoid with distinguished subsemilattice L with 1 2 L and such that any a, b 2 A have a largest right equalizer in L. The class of all such monoids equipped with a binary operation that identifies this largest right equalizer is a variety. Examples include Heyting algebras, Cartesian products of monoids with zero, as well as monoids of relations and partial maps on sets. The variety is 0-regular (though not ideal determined and hence congruences do not permute), and we describe the normal subobjects in terms of a global semilattice structure. We give representation theorems for several natural subvarieties in terms of Boolean algebras, Cartesian products and partial maps. The case in which the EQmonoid is assumed to be an inverse semigroup with zero is given particular attention. Finally, we define the derived category associated with a monoid having a distinguished subsemilattice containing the identity (a construction generalising the idea of a monoid category), and show that those monoids for which this derived category has equalizers in the semilattice constitute a variety of EQ-monoids.

year: 2006

title: Compact nonlinear model of an implantable electrode array for spinal cord stimulation (SCS)

authors: Scott, Jonathan B.

subjects: electrical stimulation

abstract: We describe the construction of a model of the electrode-electrolyte interface and surrounding electrolyte in the case of a platinum-electrode array intended for spinal-cord stimulation (SCS) application. We show that a finite, two dimensional, resistor array provides a satisfactory model of the bulk electrolyte, and we identify the complexity required of that resistor array. The electrode-electrolyte interface is modelled in a fashion suitable for commonly-available, compact simulators using a nonlinear extension of the model of Franks et al. that incorporates diodes and a memristor. The electrode-electrolyte interface model accounts for the nonlinear current-overpotential characteristic and diffusion-limiting effects. We characterise a commercial, implantable, electrode array, fit the model to it, and show that the model successfully predicts subtle operational characteristics.

text: Compact nonlinear model of an implantable electrode array for spinal cord stimulation (SCS) We describe the construction of a model of the electrode-electrolyte interface and surrounding electrolyte in the case of a platinum-electrode array intended for spinal-cord stimulation (SCS) application. We show that a finite, two dimensional, resistor array provides a satisfactory model of the bulk electrolyte, and we identify the complexity required of that resistor array. The electrode-electrolyte interface is modelled in a fashion suitable for commonly-available, compact simulators using a nonlinear extension of the model of Franks et al. that incorporates diodes and a memristor. The electrode-electrolyte interface model accounts for the nonlinear current-overpotential characteristic and diffusion-limiting effects. We characterise a commercial, implantable, electrode array, fit the model to it, and show that the model successfully predicts subtle operational characteristics.

year: 2013

title: Te manemanerau a te kāwanatanga: A history of the confiscation of Tūhoe lands in the Bay of Plenty

authors: Melbourne, Sydney

subjects: Ngāi Tūhoe

abstract: This thesis endeavours to show that Tūhoe lands should never have been confiscated and that Tūhoe efforts to gain compensation have been totally unsuccessful to date. When certain lands within the confiscated district of the Bay of Plenty were returned to the tribes there, Tūhoe were not granted any. Furthermore, lands which actually belonged to Tūhoe were granted to other tribes.
Although the major focus is on issues specific to Tūhoe, these are viewed within the wider context of nineteenth century land acquisition in New Zealand. This study looks at Tūhoe historical claims to disputed lands included in the confiscation district of the Bay of Plenty. Chapter One traces the extent of Tūhoe territories within the confiscation district and describes how Tūhoe came to occupy them and the duration of their occupation. Information about these claims came from tribal oral sources and original manuscripts, as well as from more generally accessible sources.
The development of colonial expansion patterns is discussed in Chapter Two. The contention is that they were based on materialistic considerations and legal pretexts to justify the acquisition of Māori lands. Hostilities between Māori and Government in the Bay of Plenty are dealt with in Chapter Three. Particular attention is paid to the causes of the hostilities and the complex racial and political misunderstandings which contributed to the inevitability of war. As a result of these encounters, the New Zealand Settlements Act was imposed.
Chapter Four covers the implementation of its provisions through the Compensation Court. The failings of this Court and its commissioners and field officials are exposed.
Chapter Five examines the settlement of Tūhoe lands in Ōpouriao and Waimana, as well as the changing fortunes of some of the settlers who took advantage of the settlement scheme. After placing the experiences of Tūhoe people within the wider context of what had taken place in New Zealand, Chapter Six focuses on Tūhoe attempts to bring the wrongs they had suffered to the attention of Government. In retrospect these early Tūhoe attempts at redress show that much has to be learnt about presenting substantial submissions. It was obvious that much of what was known by the elders then, though recorded, was never used in evidence to support their petitions. Nonetheless, without the existence of these manuscripts, present attempts would not be possible.
Chapter Seven gives a basis for a proposed just settlement for the confiscation of Tūhoe lands. In order to provide a guide for monetary compensation, details of values of Tūhoe confiscated land have been sought from official records. Compensation for the denial of justice, the loss of human life, land and property, remain open for negotiation.
Finally, while certain conclusions can be and are drawn from these investigations, the end of the story remains unwritten. It will depend on the outcome of new Tūhoe attempts to gain redress from the appropriate statutory body.

text: Te manemanerau a te kāwanatanga: A history of the confiscation of Tūhoe lands in the Bay of Plenty This thesis endeavours to show that Tūhoe lands should never have been confiscated and that Tūhoe efforts to gain compensation have been totally unsuccessful to date. When certain lands within the confiscated district of the Bay of Plenty were returned to the tribes there, Tūhoe were not granted any. Furthermore, lands which actually belonged to Tūhoe were granted to other tribes.
Although the major focus is on issues specific to Tūhoe, these are viewed within the wider context of nineteenth century land acquisition in New Zealand. This study looks at Tūhoe historical claims to disputed lands included in the confiscation district of the Bay of Plenty. Chapter One traces the extent of Tūhoe territories within the confiscation district and describes how Tūhoe came to occupy them and the duration of their occupation. Information about these claims came from tribal oral sources and original manuscripts, as well as from more generally accessible sources.
The development of colonial expansion patterns is discussed in Chapter Two. The contention is that they were based on materialistic considerations and legal pretexts to justify the acquisition of Māori lands. Hostilities between Māori and Government in the Bay of Plenty are dealt with in Chapter Three. Particular attention is paid to the causes of the hostilities and the complex racial and political misunderstandings which contributed to the inevitability of war. As a result of these encounters, the New Zealand Settlements Act was imposed.
Chapter Four covers the implementation of its provisions through the Compensation Court. The failings of this Court and its commissioners and field officials are exposed.
Chapter Five examines the settlement of Tūhoe lands in Ōpouriao and Waimana, as well as the changing fortunes of some of the settlers who took advantage of the settlement scheme. After placing the experiences of Tūhoe people within the wider context of what had taken place in New Zealand, Chapter Six focuses on Tūhoe attempts to bring the wrongs they had suffered to the attention of Government. In retrospect these early Tūhoe attempts at redress show that much has to be learnt about presenting substantial submissions. It was obvious that much of what was known by the elders then, though recorded, was never used in evidence to support their petitions. Nonetheless, without the existence of these manuscripts, present attempts would not be possible.
Chapter Seven gives a basis for a proposed just settlement for the confiscation of Tūhoe lands. In order to provide a guide for monetary compensation, details of values of Tūhoe confiscated land have been sought from official records. Compensation for the denial of justice, the loss of human life, land and property, remain open for negotiation.
Finally, while certain conclusions can be and are drawn from these investigations, the end of the story remains unwritten. It will depend on the outcome of new Tūhoe attempts to gain redress from the appropriate statutory body.

year: 1987