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: Development of a map service

authors: Huang, Xiaotie (Anthony)

subjects: map

abstract: Geographic Information Systems (GIS) a computerized mapping system for capturing, storing, retrieving, analysing, and displaying spatial data (the type of data that has a geographic location). It is one of the fastest growing high tech fields and has been widely used in my areas where analysis of spatial referenced data is needed. In this paper we developed and implemented a GIS-based personalized Travel Planning application. Our goal is to provide a map based information system that gives recommendation information (e.g. closeby sights, must-see sights) to travellers according to their destinations, locations and preferences. Furthermore, the TP application was developed as a client-side service under the Tourist Information Provider System. It runs on client machines and uses the spatial referenced data stored at the TIP server-side database.

text: Development of a map service Geographic Information Systems (GIS) a computerized mapping system for capturing, storing, retrieving, analysing, and displaying spatial data (the type of data that has a geographic location). It is one of the fastest growing high tech fields and has been widely used in my areas where analysis of spatial referenced data is needed. In this paper we developed and implemented a GIS-based personalized Travel Planning application. Our goal is to provide a map based information system that gives recommendation information (e.g. closeby sights, must-see sights) to travellers according to their destinations, locations and preferences. Furthermore, the TP application was developed as a client-side service under the Tourist Information Provider System. It runs on client machines and uses the spatial referenced data stored at the TIP server-side database.

year: 2007

title: Student belonging: critical relationships and responsibilities

authors: Berryman, Mere

subjects: Belonging

abstract: In this paper, we consider New Zealand’s education system to understand what can happen when we focus only on excellence and students reaching their potential, without simultaneously investing in their sense of belonging and wellbeing. National statistics suggest we are alienating and shortchanging an increasing number of students and, for disproportionate numbers of Indigenous students, these statistics are part of a world trend. The literature, and the students themselves, highlight the need to overturn the underlying racism that persistently disadvantages clearly identifiable groups of students over others. Until we do, using equity and excellence as the most powerful drivers for reform, will continue to promote conditions where our students’ sense of belonging and wellbeing are undermined throughout their education and we will risk, failing to address the ensuing negative statistics. We conclude with a response that we have learned from working with these same students.

text: Student belonging: critical relationships and responsibilities In this paper, we consider New Zealand’s education system to understand what can happen when we focus only on excellence and students reaching their potential, without simultaneously investing in their sense of belonging and wellbeing. National statistics suggest we are alienating and shortchanging an increasing number of students and, for disproportionate numbers of Indigenous students, these statistics are part of a world trend. The literature, and the students themselves, highlight the need to overturn the underlying racism that persistently disadvantages clearly identifiable groups of students over others. Until we do, using equity and excellence as the most powerful drivers for reform, will continue to promote conditions where our students’ sense of belonging and wellbeing are undermined throughout their education and we will risk, failing to address the ensuing negative statistics. We conclude with a response that we have learned from working with these same students.

year: 2019