title: Models of q-algebra representations: Tensor products of special unitary and oscillator algebras

authors: Kalnins, Ernie G.

subjects: Mathematics

abstract: This paper begins a study of one- and two-variable function space models of irreducible representations of q analogs of Lie enveloping algebras, motivated by recurrence relations satisfied by q-hypergeometric functions. The algebras considered are the quantum algebra Uq(su2) and a q analog of the oscillator algebra (not a quantum algebra). In each case a simple one-variable model of the positive discrete series of finite- and infinite-dimensional irreducible representations is used to compute the Clebsch–Gordan coefficients. It is shown that various q analogs of the exponential function can be used to mimic the exponential mapping from a Lie algebra to its Lie group and the corresponding matrix elements of the ``group operators'' on these representation spaces are computed. It is shown that the matrix elements are polynomials satisfying orthogonality relations analogous to those holding for true irreducible group representations. It is also demonstrated that general q-hypergeometric functions can occur as basis functions in two-variable models, in contrast with the very restricted parameter values for the q-hypergeometric functions arising as matrix elements in the theory of quantum groups.

text: Models of q-algebra representations: Tensor products of special unitary and oscillator algebras This paper begins a study of one- and two-variable function space models of irreducible representations of q analogs of Lie enveloping algebras, motivated by recurrence relations satisfied by q-hypergeometric functions. The algebras considered are the quantum algebra Uq(su2) and a q analog of the oscillator algebra (not a quantum algebra). In each case a simple one-variable model of the positive discrete series of finite- and infinite-dimensional irreducible representations is used to compute the Clebsch–Gordan coefficients. It is shown that various q analogs of the exponential function can be used to mimic the exponential mapping from a Lie algebra to its Lie group and the corresponding matrix elements of the ``group operators'' on these representation spaces are computed. It is shown that the matrix elements are polynomials satisfying orthogonality relations analogous to those holding for true irreducible group representations. It is also demonstrated that general q-hypergeometric functions can occur as basis functions in two-variable models, in contrast with the very restricted parameter values for the q-hypergeometric functions arising as matrix elements in the theory of quantum groups.

year: 1992-07

title: The validity of resting metabolic rate (RMR)-prediction equations and reliability of measured RMR in female athletes

authors: MacKay, Kelsi

subjects: Energy deficiency

abstract: The aim of the current study was to; 1) assess the test-retest reliability of an indirect calorimetry analyzer (Parvo Medics TrueOne), and 2) compare measured RMR with three RMR-predictive (pRMR) equations in female athletes. In part one, 12 recreationally-exercising women (mean ± SD; age 27.5 ± 12.3 y) performed two RMR assessments, on separate days, utilising the Parvo Medics TrueOne analyser. In part two, 25 recreationally-exercising women to sub-elite athletes (mean ± SD; age 30.1 ± 10.2 y) underwent an RMR assessment using the Parvo Medics TrueOne analyser, which was compared to three calculated pRMR equations (Harris-Benedict (H-B) , Mifflin-St Jeor (M), World Health Organisation (WHO)). eTest-retest reliability for the TrueOne analyser was deemed acceptable (CV = 5.3%, ICC = 0.92). The validity of pRMR when compared to measured RMR showed low levels of agreement in all 3 predictive equations (M: CV = 21.4%, TEE = 269 kcal.day⁻¹, r = 0.16, WHO: CV = 21.5%, TEE = 270 kcal.day⁻¹, r = 0.13 H-B: CV = 21.6%, TEE = 270 kcal.day⁻¹, r = 0.13). The Parvo Medics TrueOne analyser is a reliable tool for measuring RMR. Caution should be taken when using pRMR equations in female athletes as they do not take into account the likely differences in fat free mass in these populations.

text: The validity of resting metabolic rate (RMR)-prediction equations and reliability of measured RMR in female athletes The aim of the current study was to; 1) assess the test-retest reliability of an indirect calorimetry analyzer (Parvo Medics TrueOne), and 2) compare measured RMR with three RMR-predictive (pRMR) equations in female athletes. In part one, 12 recreationally-exercising women (mean ± SD; age 27.5 ± 12.3 y) performed two RMR assessments, on separate days, utilising the Parvo Medics TrueOne analyser. In part two, 25 recreationally-exercising women to sub-elite athletes (mean ± SD; age 30.1 ± 10.2 y) underwent an RMR assessment using the Parvo Medics TrueOne analyser, which was compared to three calculated pRMR equations (Harris-Benedict (H-B) , Mifflin-St Jeor (M), World Health Organisation (WHO)). eTest-retest reliability for the TrueOne analyser was deemed acceptable (CV = 5.3%, ICC = 0.92). The validity of pRMR when compared to measured RMR showed low levels of agreement in all 3 predictive equations (M: CV = 21.4%, TEE = 269 kcal.day⁻¹, r = 0.16, WHO: CV = 21.5%, TEE = 270 kcal.day⁻¹, r = 0.13 H-B: CV = 21.6%, TEE = 270 kcal.day⁻¹, r = 0.13). The Parvo Medics TrueOne analyser is a reliable tool for measuring RMR. Caution should be taken when using pRMR equations in female athletes as they do not take into account the likely differences in fat free mass in these populations.

year: 2019

title: Engaging Māori in Biobanking and Genetic Research: Legal, Ethical and Policy Challenges

authors: Beaton, Angela

subjects: Indigenous

abstract: Publically funded biobanking initiatives and genetic research should contribute towards reducing inequalities in health by reducing the prevalence and burden of disease. It is essential that Maori and other Indigenous populations share in health gains derived from these activities. The Health Research Council of New Zealand has funded a research project (2012-2015) to identify Maori perspectives on biobanking and genetic research, and to develop cultural guidelines for ethical biobanking and genetic research involving biospecimens. This review describes relevant values and ethics embedded in Maori indigenous knowledge, and how they may be applied to culturally safe interactions between biobanks, researchers, individual participants, and communities. Key issues of ownership, privacy, and consent are also considered within the legal and policy context that guides biobanking and genetic research practices within New Zealand. Areas of concern are highlighted and recommendations of international relevance are provided. To develop a productive environment for "next-generation" biobanking and genomic research,"‘next-generation" regulatory solutions will be required.

text: Engaging Māori in Biobanking and Genetic Research: Legal, Ethical and Policy Challenges Publically funded biobanking initiatives and genetic research should contribute towards reducing inequalities in health by reducing the prevalence and burden of disease. It is essential that Maori and other Indigenous populations share in health gains derived from these activities. The Health Research Council of New Zealand has funded a research project (2012-2015) to identify Maori perspectives on biobanking and genetic research, and to develop cultural guidelines for ethical biobanking and genetic research involving biospecimens. This review describes relevant values and ethics embedded in Maori indigenous knowledge, and how they may be applied to culturally safe interactions between biobanks, researchers, individual participants, and communities. Key issues of ownership, privacy, and consent are also considered within the legal and policy context that guides biobanking and genetic research practices within New Zealand. Areas of concern are highlighted and recommendations of international relevance are provided. To develop a productive environment for "next-generation" biobanking and genomic research,"‘next-generation" regulatory solutions will be required.

year: 2015