title: Quadratic algebra contractions and second-order superintegrable systems

authors: Kalnins, Ernie G.

abstract: Quadratic algebras are generalizations of Lie algebras; they include the symmetry algebras of second-order superintegrable systems in two dimensions as special cases. The superintegrable systems are exactly solvable physical systems in classical and quantum mechanics. For constant curvature spaces, we show that the free quadratic algebras generated by the first- and second-order elements in the enveloping algebras of their Euclidean and orthogonal symmetry algebras correspond one-to-one with the possible superintegrable systems with potential defined on these spaces. We describe a contraction theory for quadratic algebras and show that for constant curvature superintegrable systems, ordinary Lie algebra contractions induce contractions of the quadratic algebras of the superintegrable systems that correspond to geometrical pointwise limits of the physical systems. One consequence is that by contracting function space realizations of representations of the generic superintegrable quantum system on the 2-sphere (which give the structure equations for Racah/Wilson polynomials) to the other superintegrable systems one obtains the full Askey scheme of orthogonal hypergeometric polynomials. © 2014 World Scientific Publishing Company.

text: Quadratic algebra contractions and second-order superintegrable systems Quadratic algebras are generalizations of Lie algebras; they include the symmetry algebras of second-order superintegrable systems in two dimensions as special cases. The superintegrable systems are exactly solvable physical systems in classical and quantum mechanics. For constant curvature spaces, we show that the free quadratic algebras generated by the first- and second-order elements in the enveloping algebras of their Euclidean and orthogonal symmetry algebras correspond one-to-one with the possible superintegrable systems with potential defined on these spaces. We describe a contraction theory for quadratic algebras and show that for constant curvature superintegrable systems, ordinary Lie algebra contractions induce contractions of the quadratic algebras of the superintegrable systems that correspond to geometrical pointwise limits of the physical systems. One consequence is that by contracting function space realizations of representations of the generic superintegrable quantum system on the 2-sphere (which give the structure equations for Racah/Wilson polynomials) to the other superintegrable systems one obtains the full Askey scheme of orthogonal hypergeometric polynomials. © 2014 World Scientific Publishing Company.

year: 2014

title: Syntheses and structural studies of several diynyl-ruthenium complexes and their adducts with cyano-alkenes

authors: Bruce, Michael I.

subjects: ruthenium

abstract: Herein are described some continuing investigations into the reactions of cyano-alkenes with diynyl-ruthenium complexes which have resulted in the preparation and characterisation of diynyl-ruthenium compounds Ru(C≡CC≡CR)(PP)Cp [R = Ph, PP = dppe; R = Fc, PP = dppf; R = CPh=CBr₂, PP = (PPh₃)₂], together with the polycyanobutadienyls Ru{C≡CC[=C(CN) ₂]CR=CR′(CN)}(PP)Cp′ [R = Fc, (PP)Cp′ = (dppf)Cp; R = H, SiMe₃, (PP)Cp′ = (dppe)Cp*] formed by [2 + 2]-cycloaddition of the cyano-alkenes to the outer C≡C triple bonds and subsequent ring-opening reactions. Single-crystal XRD molecular structure determinations of six complexes are reported.

text: Syntheses and structural studies of several diynyl-ruthenium complexes and their adducts with cyano-alkenes Herein are described some continuing investigations into the reactions of cyano-alkenes with diynyl-ruthenium complexes which have resulted in the preparation and characterisation of diynyl-ruthenium compounds Ru(C≡CC≡CR)(PP)Cp [R = Ph, PP = dppe; R = Fc, PP = dppf; R = CPh=CBr₂, PP = (PPh₃)₂], together with the polycyanobutadienyls Ru{C≡CC[=C(CN) ₂]CR=CR′(CN)}(PP)Cp′ [R = Fc, (PP)Cp′ = (dppf)Cp; R = H, SiMe₃, (PP)Cp′ = (dppe)Cp*] formed by [2 + 2]-cycloaddition of the cyano-alkenes to the outer C≡C triple bonds and subsequent ring-opening reactions. Single-crystal XRD molecular structure determinations of six complexes are reported.

year: 2011

title: Ngā kanohi hou – identifying and exploring the issues: Experiences of an intern

authors: Masters-Awatere, Bridgette

subjects: Maori

abstract: The current paper reflects upon the discovery of an intern from the post graduate diploma in community psychology programme (PGDipPsych (Com). The PGDipPsych (Com) is currently facilitated through the University of Waikato School of Arts and Social Sciences, Psychology Department. This journey of discovery is presented from the perspective of a Māori student who is employed in a mainstream public health organisation. The perspective of a person who is new to the workforce, and the “real world,” who views the surrounding environment with a pair of fresh eyes.

This paper highlights the importance of the internship period as it supports the student who moves from a structured environment with a strong emphasis on theory, towards a competitive, semi structured environment that is driven by deadlines, budgets and contracts.

Factors identified are the demands of Māori communities on Māori health researchers, supportive versus competitive environments, the benefits and drawbacks of being based in a mainstream health organisation, and the future direction of Māori health research. It is hoped that the current paper will encourage further discussion about the future direction of a diploma programme such as the PGDipPsychCom for Māori graduates of a New Zealand tertiary institution.

text: Ngā kanohi hou – identifying and exploring the issues: Experiences of an intern The current paper reflects upon the discovery of an intern from the post graduate diploma in community psychology programme (PGDipPsych (Com). The PGDipPsych (Com) is currently facilitated through the University of Waikato School of Arts and Social Sciences, Psychology Department. This journey of discovery is presented from the perspective of a Māori student who is employed in a mainstream public health organisation. The perspective of a person who is new to the workforce, and the “real world,” who views the surrounding environment with a pair of fresh eyes.

This paper highlights the importance of the internship period as it supports the student who moves from a structured environment with a strong emphasis on theory, towards a competitive, semi structured environment that is driven by deadlines, budgets and contracts.

Factors identified are the demands of Māori communities on Māori health researchers, supportive versus competitive environments, the benefits and drawbacks of being based in a mainstream health organisation, and the future direction of Māori health research. It is hoped that the current paper will encourage further discussion about the future direction of a diploma programme such as the PGDipPsychCom for Māori graduates of a New Zealand tertiary institution.

year: 1999