title: Superintegrable systems in Darboux spaces

authors: Kalnins, Ernie G.

subjects: Mathematics

abstract: Almost all research on superintegrable potentials concerns spaces of constant curvature. In this paper we find by exhaustive calculation, all superintegrable potentials in the four Darboux spaces of revolution that have at least two integrals of motion quadratic in the momenta, in addition to the Hamiltonian. These are two-dimensional spaces of nonconstant curvature. It turns out that all of these potentials are equivalent to superintegrable potentials in complex Euclidean 2-space or on the complex 2-sphere, via "coupling constant metamorphosis" (or equivalently, via Stäckel multiplier transformations). We present a table of the results.

text: Superintegrable systems in Darboux spaces Almost all research on superintegrable potentials concerns spaces of constant curvature. In this paper we find by exhaustive calculation, all superintegrable potentials in the four Darboux spaces of revolution that have at least two integrals of motion quadratic in the momenta, in addition to the Hamiltonian. These are two-dimensional spaces of nonconstant curvature. It turns out that all of these potentials are equivalent to superintegrable potentials in complex Euclidean 2-space or on the complex 2-sphere, via "coupling constant metamorphosis" (or equivalently, via Stäckel multiplier transformations). We present a table of the results.

year: 2003-12

title: Theoretical study of the structures of 4-(2,3,5,6-tetrafluoropyridyl)diphenylphosphine oxide and tris(pentafluorophenyl)phosphine oxide: Why does the crystal structure of (tetrafluoropyridyl)diphenylphosphine oxide have two different P=O bond lengths?

authors: Lane, Joseph R.

subjects: Science & Technology

abstract: The crystal structure of 4-(2,3,5,6-tetrafluoropyridyl)diphenylphosphine oxide (1) contains two independent molecules in the asymmetric unit. Although the molecules are virtually identical in all other aspects, the P=O bond distances differ by ca. 0.02 Å. In contrast, although tris(pentafluorophenyl)phosphine oxide (2) has a similar crystal structure, the P=O bond distances of the two independent molecules are identical. To investigate the reason for the difference, a density functional theory study was undertaken. Both structures comprise chains of molecules. The attraction between molecules of 1, which comprises lone pair–π, weak hydrogen bonding and C–H···arene interactions, has energies of 70 and 71 kJ mol⁻¹. The attraction between molecules of 2 comprises two lone pair–π interactions, and has energies of 99 and 100 kJ mol−1. There is weak hydrogen bonding between molecules of adjacent chains involving the oxygen atom of 1. For one molecule, this interaction is with a symmetry independent molecule, whereas for the other, it also occurs with a symmetry related molecule. This provides a reason for the difference in P=O distance. This interaction is not possible for 2, and so there is no difference between the P=O distances of 2.

text: Theoretical study of the structures of 4-(2,3,5,6-tetrafluoropyridyl)diphenylphosphine oxide and tris(pentafluorophenyl)phosphine oxide: Why does the crystal structure of (tetrafluoropyridyl)diphenylphosphine oxide have two different P=O bond lengths? The crystal structure of 4-(2,3,5,6-tetrafluoropyridyl)diphenylphosphine oxide (1) contains two independent molecules in the asymmetric unit. Although the molecules are virtually identical in all other aspects, the P=O bond distances differ by ca. 0.02 Å. In contrast, although tris(pentafluorophenyl)phosphine oxide (2) has a similar crystal structure, the P=O bond distances of the two independent molecules are identical. To investigate the reason for the difference, a density functional theory study was undertaken. Both structures comprise chains of molecules. The attraction between molecules of 1, which comprises lone pair–π, weak hydrogen bonding and C–H···arene interactions, has energies of 70 and 71 kJ mol⁻¹. The attraction between molecules of 2 comprises two lone pair–π interactions, and has energies of 99 and 100 kJ mol−1. There is weak hydrogen bonding between molecules of adjacent chains involving the oxygen atom of 1. For one molecule, this interaction is with a symmetry independent molecule, whereas for the other, it also occurs with a symmetry related molecule. This provides a reason for the difference in P=O distance. This interaction is not possible for 2, and so there is no difference between the P=O distances of 2.

year: 2020

title: Drawing on linguistic concepts to teach te reo Māori; Drawing on te reo Māori to teach linguistic concepts

authors: Wessels, Kanauhea Janion

subjects: linguistic pedagogy

abstract: In this paper, we explore the intersections in our teaching practice between the discipline of linguistics and te reo Māori. From the perspective of language teaching, in pedagogic materials for te reo Māori, we have observed that linguistic concepts are not typically highlighted (cf. Moorfield 2001, Jacobs 2012). From the perspective of teaching linguistics, te reo Māori is seldom employed to illustrate or assess linguistic concepts, although it commonly features in accounts of language revitalization. Content that does occur is limited (cf. Burridge & Stebbins, 2016). 
As a tertiary lecturer of the Māori language, I (Kanauhea) consider how, in my teaching practice, I draw on my technical knowledge of linguistics to enhance my explanations of language structures and their functions, where these are unfamiliar to language learners. As a tertiary linguistics lecturer, I (Julie) consider ways in which I draw on my beginner knowledge of te reo Māori to enhance my teaching of linguistic concepts, reflecting on materials I have developed to teach and assess students. 
We argue that students of te reo can benefit from linguistic understandings on their language learning journeys. Equally, as Aotearoa New Zealand's indigenous language, te reo Māori should have a strong presence in linguistic teaching materials, and our linguistics students should graduate with an indepth knowledge of te reo Māori structures.

text: Drawing on linguistic concepts to teach te reo Māori; Drawing on te reo Māori to teach linguistic concepts In this paper, we explore the intersections in our teaching practice between the discipline of linguistics and te reo Māori. From the perspective of language teaching, in pedagogic materials for te reo Māori, we have observed that linguistic concepts are not typically highlighted (cf. Moorfield 2001, Jacobs 2012). From the perspective of teaching linguistics, te reo Māori is seldom employed to illustrate or assess linguistic concepts, although it commonly features in accounts of language revitalization. Content that does occur is limited (cf. Burridge & Stebbins, 2016). 
As a tertiary lecturer of the Māori language, I (Kanauhea) consider how, in my teaching practice, I draw on my technical knowledge of linguistics to enhance my explanations of language structures and their functions, where these are unfamiliar to language learners. As a tertiary linguistics lecturer, I (Julie) consider ways in which I draw on my beginner knowledge of te reo Māori to enhance my teaching of linguistic concepts, reflecting on materials I have developed to teach and assess students. 
We argue that students of te reo can benefit from linguistic understandings on their language learning journeys. Equally, as Aotearoa New Zealand's indigenous language, te reo Māori should have a strong presence in linguistic teaching materials, and our linguistics students should graduate with an indepth knowledge of te reo Māori structures.

year: 2023