title: Exact and quasiexact solvability of second-order superintegrable quantum systems: I. Euclidean space preliminaries

authors: Kalnins, Ernie G.

subjects: Mathematics

abstract: We show that second-order superintegrable systems in two-dimensional and three-dimensional Euclidean space generate both exactly solvable (ES) and quasiexactly solvable (QES) problems in quantum mechanics via separation of variables, and demonstrate the increased insight into the structure of such problems provided by superintegrability. A principal advantage of our analysis using nondegenerate superintegrable systems is that they are multiseparable. Most past separation of variables treatments of QES problems via partial differential equations have only incorporated separability, not multiseparability. Also, we propose another definition of ES and QES. The quantum mechanical problem is called ES if the solution of Schrödinger equation can be expressed in terms of hypergeometric functions mFn and is QES if the Schrödinger equation admits polynomial solutions with coefficients necessarily satisfying a three-term or higher order of recurrence relations. In three dimensions we give an example of a system that is QES in one set of separable coordinates, but is not ES in any other separable coordinates. This example encompasses Ushveridze's tenth-order polynomial QES problem in one set of separable coordinates and also leads to a fourth-order polynomial QES problem in another separable coordinate set.

text: Exact and quasiexact solvability of second-order superintegrable quantum systems: I. Euclidean space preliminaries We show that second-order superintegrable systems in two-dimensional and three-dimensional Euclidean space generate both exactly solvable (ES) and quasiexactly solvable (QES) problems in quantum mechanics via separation of variables, and demonstrate the increased insight into the structure of such problems provided by superintegrability. A principal advantage of our analysis using nondegenerate superintegrable systems is that they are multiseparable. Most past separation of variables treatments of QES problems via partial differential equations have only incorporated separability, not multiseparability. Also, we propose another definition of ES and QES. The quantum mechanical problem is called ES if the solution of Schrödinger equation can be expressed in terms of hypergeometric functions mFn and is QES if the Schrödinger equation admits polynomial solutions with coefficients necessarily satisfying a three-term or higher order of recurrence relations. In three dimensions we give an example of a system that is QES in one set of separable coordinates, but is not ES in any other separable coordinates. This example encompasses Ushveridze's tenth-order polynomial QES problem in one set of separable coordinates and also leads to a fourth-order polynomial QES problem in another separable coordinate set.

year: 2006-03

title: Importing documents and metadata into digital libraries: requirements analysis and an extensible architecture

authors: Witten, Ian H.

subjects: computer science

abstract: Flexible digital library systems need to be able to accept, or “import,” documents and metadata in a variety of forms, and associate metadata with the appropriate documents. This paper analyzes the requirements of the import process for general digital libraries. The requirements include (a) format conversion for source documents, (b) the ability to incorporate existing conversion utilities, (c) provision for metadata to be specified in the document files themselves and/or in separate metadata files, (d) format conversion for metadata files, (e) provision for metadata to be computed from the document content, and (f) flexible ways of associating metadata with documents or sets of documents. We argue that these requirements are so open-ended that they are best met by an extensible architecture that facilitates the addition of new document formats and metadata facilities to existing digital library systems. An implementation of this architecture is briefly described.

text: Importing documents and metadata into digital libraries: requirements analysis and an extensible architecture Flexible digital library systems need to be able to accept, or “import,” documents and metadata in a variety of forms, and associate metadata with the appropriate documents. This paper analyzes the requirements of the import process for general digital libraries. The requirements include (a) format conversion for source documents, (b) the ability to incorporate existing conversion utilities, (c) provision for metadata to be specified in the document files themselves and/or in separate metadata files, (d) format conversion for metadata files, (e) provision for metadata to be computed from the document content, and (f) flexible ways of associating metadata with documents or sets of documents. We argue that these requirements are so open-ended that they are best met by an extensible architecture that facilitates the addition of new document formats and metadata facilities to existing digital library systems. An implementation of this architecture is briefly described.

year: 2002

title: E hoki ki to maunga: The quintessential elements of home

authors: Emery, Debra Joy Tepora

subjects: hau kainga

abstract: He kopu puta tahi, he taura whiri tātou;
whiringa a nuku, whiringa a rangi, te whatia e
Issue of one womb, we are a rope woven of many strands; woven on earth, woven in heaven, it will not break (Rev Māori Marsden, 1992)
Ngati Te Takinga is a hapū (sub-tribe) belonging to the Iwi (tribe) Ngati Pikiao. An affiliated member of the Te Arawa confederation of tribes, Ngati Pikiao occupies the Okere and Rotoiti Lakes district of Rotorua in the central North Island of Aotearoa New Zealand.
This thesis seeks to acknowledge and address the concerns that Ngati Te Takinga has regarding impending cultural discontinuity. The concerns arise due to the hapū's limited human capability and capacity being the result of three things. Firstly, the ongoing demise of tribal elders (and leaders) and the subsequent loss to the hapū of cultural knowledge, skills, leadership and expertise. Secondly, the low numbers of adept,
culturally proficient successors 'coming through' (to replace the elders) and finally, the detribalised and diasporic (dispersed) nature of our people. The hapū and the marae Te Takinga (a last outwardly discernible bastion of Ngati Te Takinga cultural identity and distinction) are jeopardised as a result of these phenomenon.
This thesis is part of a hapū strategy that attempts to address these problems. Positing the
reconnection of our dispersed Ngati Te Takinga 'away-dwellers' as a beginning
solution, the central questions raised by this thesis are  how [does] Ngati Te Takinga
'home-dweller' discourse impact on the 'coming home' experiences and 'reconnection'
of Ngati Te Takinga away-dwellers?  and  what are the [are there] implications for Ngati
Te Takinga cultural continuity? 
The maintenance of Ngati Te Takinga cultural continuity forms the aho mātua or main thread of this work. Using narrative enquiry as a broad methodological framework,stories were gathered from four different groups of Ngati Te Takinga peoples. The groups were home-dwellers (mana whenua or ahi kaa), te ahi tere (away-dwellers who
have returned home to live); te ahi tere (away-dwellers who intend returning in the future) and te ahi tere (away-dwellers who have no intention of returning home to live). The stories (narratives) investigated notions of home, belongingness and Māori identity in relation to the trichotomy of the connection, disconnection and the reconnection of Ngati Te Takinga peoples; the stories were analysed and co-constructed with participants for meaning.
The stories showed that while the hapū aspires to gather up the strengths of a dispersed people to reinvigorate our culture and the marae, existing and competing discourses around authenticity, authority and Ngati Te Takinga identity create a tension between the home (mana whenua/ahi kaa) and away-dwelling Ngati Te Takinga people; including those away-dwellers who have returned. As a basic requirement, this tension must be
diminished in order to build the relationships necessary to improve hapū allegiance
(whānaungatanga), to build hapū strength and to maintain hapū culture and identity. As a priority, decolonising strategies that facilitate an understanding of diversity, promote
participation, maintain tikanga and include our away-dwellers, our 'returnees' and/or our
disconnected people in our hapū-marae interactions, must be considered, developed,
promoted and practiced.

text: E hoki ki to maunga: The quintessential elements of home He kopu puta tahi, he taura whiri tātou;
whiringa a nuku, whiringa a rangi, te whatia e
Issue of one womb, we are a rope woven of many strands; woven on earth, woven in heaven, it will not break (Rev Māori Marsden, 1992)
Ngati Te Takinga is a hapū (sub-tribe) belonging to the Iwi (tribe) Ngati Pikiao. An affiliated member of the Te Arawa confederation of tribes, Ngati Pikiao occupies the Okere and Rotoiti Lakes district of Rotorua in the central North Island of Aotearoa New Zealand.
This thesis seeks to acknowledge and address the concerns that Ngati Te Takinga has regarding impending cultural discontinuity. The concerns arise due to the hapū's limited human capability and capacity being the result of three things. Firstly, the ongoing demise of tribal elders (and leaders) and the subsequent loss to the hapū of cultural knowledge, skills, leadership and expertise. Secondly, the low numbers of adept,
culturally proficient successors 'coming through' (to replace the elders) and finally, the detribalised and diasporic (dispersed) nature of our people. The hapū and the marae Te Takinga (a last outwardly discernible bastion of Ngati Te Takinga cultural identity and distinction) are jeopardised as a result of these phenomenon.
This thesis is part of a hapū strategy that attempts to address these problems. Positing the
reconnection of our dispersed Ngati Te Takinga 'away-dwellers' as a beginning
solution, the central questions raised by this thesis are  how [does] Ngati Te Takinga
'home-dweller' discourse impact on the 'coming home' experiences and 'reconnection'
of Ngati Te Takinga away-dwellers?  and  what are the [are there] implications for Ngati
Te Takinga cultural continuity? 
The maintenance of Ngati Te Takinga cultural continuity forms the aho mātua or main thread of this work. Using narrative enquiry as a broad methodological framework,stories were gathered from four different groups of Ngati Te Takinga peoples. The groups were home-dwellers (mana whenua or ahi kaa), te ahi tere (away-dwellers who
have returned home to live); te ahi tere (away-dwellers who intend returning in the future) and te ahi tere (away-dwellers who have no intention of returning home to live). The stories (narratives) investigated notions of home, belongingness and Māori identity in relation to the trichotomy of the connection, disconnection and the reconnection of Ngati Te Takinga peoples; the stories were analysed and co-constructed with participants for meaning.
The stories showed that while the hapū aspires to gather up the strengths of a dispersed people to reinvigorate our culture and the marae, existing and competing discourses around authenticity, authority and Ngati Te Takinga identity create a tension between the home (mana whenua/ahi kaa) and away-dwelling Ngati Te Takinga people; including those away-dwellers who have returned. As a basic requirement, this tension must be
diminished in order to build the relationships necessary to improve hapū allegiance
(whānaungatanga), to build hapū strength and to maintain hapū culture and identity. As a priority, decolonising strategies that facilitate an understanding of diversity, promote
participation, maintain tikanga and include our away-dwellers, our 'returnees' and/or our
disconnected people in our hapū-marae interactions, must be considered, developed,
promoted and practiced.

year: 2008