title: Comparison semigroups and algebras of transformations

authors: Stokes, Tim E.

subjects: comparison algebra

abstract: We characterize algebras of transformations on a set under the operations of composition and the pointwise switching function defined as follows: (f,g)[h,k](x)=h(x) if f(x)=g(x), and k(x) otherwise. The resulting algebras are both semigroups and comparison algebras in the sense of Kennison. The same characterization holds for partial transformations under composition and a suitable generalisation of the quaternary operation in which agreement of f,g includes cases where neither is defined. When a zero element is added (modelling the empty function), the resulting signature is rich enough to encompass many operations on semigroups of partial transformations previously considered, including set difference and intersection, restrictive product, and a functional analog of union. When an identity element is also added (modelling the identity function), further domain-related operations can be captured.

text: Comparison semigroups and algebras of transformations We characterize algebras of transformations on a set under the operations of composition and the pointwise switching function defined as follows: (f,g)[h,k](x)=h(x) if f(x)=g(x), and k(x) otherwise. The resulting algebras are both semigroups and comparison algebras in the sense of Kennison. The same characterization holds for partial transformations under composition and a suitable generalisation of the quaternary operation in which agreement of f,g includes cases where neither is defined. When a zero element is added (modelling the empty function), the resulting signature is rich enough to encompass many operations on semigroups of partial transformations previously considered, including set difference and intersection, restrictive product, and a functional analog of union. When an identity element is also added (modelling the identity function), further domain-related operations can be captured.

year: 2010

title: Sequence stratigraphic, paleoenvironmental, and chronological analysis of the late neogene Wanganui River section, Wanganui basin

authors: Hayton, Shaun

abstract: Between Taranaki Basin and the central ranges of the North Island, New Zealand, lies the broadly elliptical, back-arc Wanganui Basin, half of which is onshore. This basin covers an area of about 22,000 km², and contains a Plio-Pleistocene sedimentary succession some 4 km thick. Ongoing south- to southeast-ward migration of the basin depocentre and thermally driven uplift to the north have resulted in the development of broad east-west trending stratal belts that young and dip to the south. The Wanganui River intersects these stratal belts and offers the potential to examine the entire late Miocene to late Pliocene succession in the western half of Wanganui Basin.

For the first time the Wanganui River section has been divided into five predominantly planktic foraminiferal biozones (Globorotalia conomiozea zone, G. punticulata zone, G. inflata zone, combined dextral G. crassaformis and Cibicides molestus zone, and dextral G. crassaformis zone), that are linked to the New Zealand stage classification system. The absolute ages implied by these biostratigraphic datums, combined with a magnetostratigraphy being developed for the section, form an age framework for the sedimentary succession exposed in the Wanganui River valley between Tieke and Parakino. The apparently diachronous nature of the datums traditionally tied to the Mangapanian-Waipipian Stage boundary are highlighted.

The lithostratigraphy of the approximately 3600 m thick sedimentary succession between Tieke and Parakino has been analysed and recorded. Three lithotypes (sandstone, siltstone, shellbed) have been identified, with each containing a number of lithofacies. These lithofacies represent a variety of paleoenvironments from nearshore (0-25 m) to slope type (200-600 m) depths, as determined by analysis of the benthic foraminiferal content and sedimentary structures. This study has resulted in the identification of key unit boundaries and has to some degree simplified the nomenclature assigned to this succession, with five discrete units being recognised.

The Matemateaonga Formation is an at least 1570 m-thick late Miocene (lower Kapitean) to Pliocene (mid Opoitian) succession with 31 discrete cyclothems being identified in the section studied. Each cyclothem displays a coarsening upward trend, with most being related to high-order (6ᵗʰ) glacio-eustatic sea-level fluctuations. Some differences are noted between these cyclothems and those modelled by Naish and Kamp (1997), notably the character of the basal boundary and the architecture of the transgressive systems tract.

The Pliocene (mid Opoitian and Waipipian) aged Tangahoe Formation in the Wanganui River valley is predominantly a deep-water (200-600 m) siltstone, within which occur three distinct sandstone-dominated units (Jerusalem, Matahiwi and Koroniti Sandstone Members). The depocentre, in which this unit was deposited, formed in a shallow continental seaway resulting in a foraminiferal signal that was both deep-water and neritic. The sandstone members are composed of multiple mass-emplaced sandstones interbedded with typical Tangahoe Formation siltstone and are interpreted as being slope and basin floor (in terms of the depocentre, rather than a typical continental margin) fan deposits derived from quasi-steady state grain flows.

The Ahurangi Sandstone overlies the siltstone-dominated Tangahoe Formation, with the basal transition occurring over 15 m. The Ahurangi Sandstone is initially massive but becomes bedded in its upper half. This unit is interpreted as reflecting the rapid infilling of the deep-water basin responsible for the development of the Tangahoe Formation. 

The Waipipian and Mangapanian aged cyclothemic Atene Formation overlies the Ahurangi Sandstone and records the return of high-order glacio-eustatic fluctuations as the dominant control on relative sea-level, and thus sedimentation, within a shelf environment. 

The Mangaweka Mudstone is the uppermost unit within this study. The sedimentary succession as observed in the Wanganui River section is interpreted as being deposited in a “giant foreset” type of environment. Using foraminiferal data, the basal boundary of the Mangaweka Mudstone appears time transgressive across the Wanganui Basin.
 
The development of the Wanganui River valley succession between Tieke and Parakino can be subdivided into a series of six phases within an overall subsiding basin. The four complete phases (Ngaporo, Puraroto Caves, Pipiriki and Ranana) show a period of major deepening followed by shallowing before re-establishment of high-order glacio-eustatic sea-level fluctuations as the primary control on relative sea-level. These deepening events have been interpreted as representing stages of tectonically controlled depocentre development. The variability (lithological, architecture and size) in the phases is related to the proximity of the Wanganui River section to the loci of depocentre development. The Ranana phase is regarded as being centrally located, while the Ngaporo and Puraroto Caves phases represent more distal locations relative to their contemporary depocentre(s).

text: Sequence stratigraphic, paleoenvironmental, and chronological analysis of the late neogene Wanganui River section, Wanganui basin Between Taranaki Basin and the central ranges of the North Island, New Zealand, lies the broadly elliptical, back-arc Wanganui Basin, half of which is onshore. This basin covers an area of about 22,000 km², and contains a Plio-Pleistocene sedimentary succession some 4 km thick. Ongoing south- to southeast-ward migration of the basin depocentre and thermally driven uplift to the north have resulted in the development of broad east-west trending stratal belts that young and dip to the south. The Wanganui River intersects these stratal belts and offers the potential to examine the entire late Miocene to late Pliocene succession in the western half of Wanganui Basin.

For the first time the Wanganui River section has been divided into five predominantly planktic foraminiferal biozones (Globorotalia conomiozea zone, G. punticulata zone, G. inflata zone, combined dextral G. crassaformis and Cibicides molestus zone, and dextral G. crassaformis zone), that are linked to the New Zealand stage classification system. The absolute ages implied by these biostratigraphic datums, combined with a magnetostratigraphy being developed for the section, form an age framework for the sedimentary succession exposed in the Wanganui River valley between Tieke and Parakino. The apparently diachronous nature of the datums traditionally tied to the Mangapanian-Waipipian Stage boundary are highlighted.

The lithostratigraphy of the approximately 3600 m thick sedimentary succession between Tieke and Parakino has been analysed and recorded. Three lithotypes (sandstone, siltstone, shellbed) have been identified, with each containing a number of lithofacies. These lithofacies represent a variety of paleoenvironments from nearshore (0-25 m) to slope type (200-600 m) depths, as determined by analysis of the benthic foraminiferal content and sedimentary structures. This study has resulted in the identification of key unit boundaries and has to some degree simplified the nomenclature assigned to this succession, with five discrete units being recognised.

The Matemateaonga Formation is an at least 1570 m-thick late Miocene (lower Kapitean) to Pliocene (mid Opoitian) succession with 31 discrete cyclothems being identified in the section studied. Each cyclothem displays a coarsening upward trend, with most being related to high-order (6ᵗʰ) glacio-eustatic sea-level fluctuations. Some differences are noted between these cyclothems and those modelled by Naish and Kamp (1997), notably the character of the basal boundary and the architecture of the transgressive systems tract.

The Pliocene (mid Opoitian and Waipipian) aged Tangahoe Formation in the Wanganui River valley is predominantly a deep-water (200-600 m) siltstone, within which occur three distinct sandstone-dominated units (Jerusalem, Matahiwi and Koroniti Sandstone Members). The depocentre, in which this unit was deposited, formed in a shallow continental seaway resulting in a foraminiferal signal that was both deep-water and neritic. The sandstone members are composed of multiple mass-emplaced sandstones interbedded with typical Tangahoe Formation siltstone and are interpreted as being slope and basin floor (in terms of the depocentre, rather than a typical continental margin) fan deposits derived from quasi-steady state grain flows.

The Ahurangi Sandstone overlies the siltstone-dominated Tangahoe Formation, with the basal transition occurring over 15 m. The Ahurangi Sandstone is initially massive but becomes bedded in its upper half. This unit is interpreted as reflecting the rapid infilling of the deep-water basin responsible for the development of the Tangahoe Formation. 

The Waipipian and Mangapanian aged cyclothemic Atene Formation overlies the Ahurangi Sandstone and records the return of high-order glacio-eustatic fluctuations as the dominant control on relative sea-level, and thus sedimentation, within a shelf environment. 

The Mangaweka Mudstone is the uppermost unit within this study. The sedimentary succession as observed in the Wanganui River section is interpreted as being deposited in a “giant foreset” type of environment. Using foraminiferal data, the basal boundary of the Mangaweka Mudstone appears time transgressive across the Wanganui Basin.
 
The development of the Wanganui River valley succession between Tieke and Parakino can be subdivided into a series of six phases within an overall subsiding basin. The four complete phases (Ngaporo, Puraroto Caves, Pipiriki and Ranana) show a period of major deepening followed by shallowing before re-establishment of high-order glacio-eustatic sea-level fluctuations as the primary control on relative sea-level. These deepening events have been interpreted as representing stages of tectonically controlled depocentre development. The variability (lithological, architecture and size) in the phases is related to the proximity of the Wanganui River section to the loci of depocentre development. The Ranana phase is regarded as being centrally located, while the Ngaporo and Puraroto Caves phases represent more distal locations relative to their contemporary depocentre(s).

year: 1998

title: Engaging and working with Maori? Effective practice for psychologists in education

authors: Glynn, Ted

subjects: New Zealand

abstract: I believe this whakatauki captures the reflective processes I am now engaged in, as I assess where I have come from and where I am going, as a second-generation pakeha of Irish descent, who completed postgraduate degrees in Psychology and Education in New Zealand and Canada, and who has been engaging and working with Māori in the field of education for many years.

text: Engaging and working with Maori? Effective practice for psychologists in education I believe this whakatauki captures the reflective processes I am now engaged in, as I assess where I have come from and where I am going, as a second-generation pakeha of Irish descent, who completed postgraduate degrees in Psychology and Education in New Zealand and Canada, and who has been engaging and working with Māori in the field of education for many years.

year: 2008