title: Lie theory and separation of variables. 6. The equation iUt + ∆2U = 0

authors: Boyer, C.P.

subjects: Mathematics

abstract: This paper constitutes a detailed study of the nine−parameter symmetry group of the time−dependent free particle Schrödinger equation in two space dimensions. It is shown that this equation separates in exactly 26 coordinate systems and that each system corresponds to an orbit consisting of a commuting pair of first− and second−order symmetry operators. The study yields a unified treatment of the (attractive and repulsive) harmonic oscillator, linear potential and free particle Hamiltonians in a time−dependent formalism. Use of representation theory for the symmetry group permits simple derivations of addition and expansion theorems relating various solutions of the Schrödinger equation, many of which are new.

text: Lie theory and separation of variables. 6. The equation iUt + ∆2U = 0 This paper constitutes a detailed study of the nine−parameter symmetry group of the time−dependent free particle Schrödinger equation in two space dimensions. It is shown that this equation separates in exactly 26 coordinate systems and that each system corresponds to an orbit consisting of a commuting pair of first− and second−order symmetry operators. The study yields a unified treatment of the (attractive and repulsive) harmonic oscillator, linear potential and free particle Hamiltonians in a time−dependent formalism. Use of representation theory for the symmetry group permits simple derivations of addition and expansion theorems relating various solutions of the Schrödinger equation, many of which are new.

year: 1975-03

title: Isolated learners from diverse language backgrounds in the mainstream primary classroom: A sociocultural perspective

authors: Barnard, Roger

subjects: language culture

abstract: This paper focuses on the linguistic and cultural (‘languaculture’, Agar, 1994) challenges faced by learners from diverse language backgrounds (DLB) in New Zealand schools. It describes the typical learning context in primary classrooms terms of interactional, instructional, and cognitive dimensions. It then presents vignettes of four DLB learners and explains their relative competence in terms of Cummin’s (1981) distinction between BICS and CALP (Basic Interactional Communication Skills and Cognitive-Academic Language Proficiency). It goes on to discuss the extent to which such proficiency is the result of linguistic and cultural distance, and how that distance might be bridged by applying key constructs from sociocultural theory, and the implementation of Individual Languaculture Plans for DLB learners. The paper concludes with discussing the issue of where responsibility lies for coping with the challenges face by DLB learners.

text: Isolated learners from diverse language backgrounds in the mainstream primary classroom: A sociocultural perspective This paper focuses on the linguistic and cultural (‘languaculture’, Agar, 1994) challenges faced by learners from diverse language backgrounds (DLB) in New Zealand schools. It describes the typical learning context in primary classrooms terms of interactional, instructional, and cognitive dimensions. It then presents vignettes of four DLB learners and explains their relative competence in terms of Cummin’s (1981) distinction between BICS and CALP (Basic Interactional Communication Skills and Cognitive-Academic Language Proficiency). It goes on to discuss the extent to which such proficiency is the result of linguistic and cultural distance, and how that distance might be bridged by applying key constructs from sociocultural theory, and the implementation of Individual Languaculture Plans for DLB learners. The paper concludes with discussing the issue of where responsibility lies for coping with the challenges face by DLB learners.

year: 2005

title: What a difference a default setting makes

authors: Keegan, Te Taka Adrian Gregory

subjects: computer science

abstract: This paper examines the effect of the default interface language on the usage of a bilingual digital library. In 2005 the default interface language of a bilingual digital library was alternated on a monthly basis between Māori and English. A comprehensive transaction log analysis over this period reveals that not only did usage in a particular language increase when the default interface language was set to that language but that the way the interface was used, in both languages, was quite different depending on the default language.

text: What a difference a default setting makes This paper examines the effect of the default interface language on the usage of a bilingual digital library. In 2005 the default interface language of a bilingual digital library was alternated on a monthly basis between Māori and English. A comprehensive transaction log analysis over this period reveals that not only did usage in a particular language increase when the default interface language was set to that language but that the way the interface was used, in both languages, was quite different depending on the default language.

year: 2008