Two-Dimensional Supersymmetric Quantum Mechanics: Two Fixed Centers of Force

The problem of building supersymmetry in the quantum mechanics of two Coulombian centers of force is analyzed. It is shown that there are essentially two ways of proceeding. The spectral problems of the SUSY (scalar) Hamiltonians are quite similar and become tantamount to solving entangled families of Razavy and Whittaker-Hill equations in the first approach. When the two centers have the same strength, the Whittaker-Hill equations reduce to Mathieu equations. In the second approach, the spectral problems are much more difficult to solve but one can still find the zero-energy ground states.Comment: This is a contribution to the Proc. of the Seventh International Conference ''Symmetry in Nonlinear Mathematical Physics'' (June 24-30, 2007, Kyiv, Ukraine), published in SIGMA (Symmetry, Integrability and Geometry: Methods and Applications) at http://www.emis.de/journals/SIGMA

Building research capacity for indigenous health : a case study of the National Health and Medical Research Council : the evolution and impact of policy and capacity building strategies for indigenous health research over a decade from 1996 to 2006

As Australia’s leading agency for funding health research (expending over $400 million in 2006), the National Health and Medical Research Council (NHMRC) has a major responsibility to improve the evidence base for health policy and practice. There is an urgent need for better evidence to guide policy and programs that improve the health of Indigenous peoples. In 2002, NHMRC endorsed a series of landmark policy changes to acknowledge its ongoing role and responsibilities in Indigenous health research—adopting a strategic Road Map for research, improving Indigenous representation across NHMRC Council and Principal Committees, and committing 5% of its annual budget to Indigenous health research. This thesis examines how these policies evolved, the extent to which they have been implemented, and their impact on agency expenditure in relation to People Support. Additionally, this thesis describes the impact of NHMRC policies in reshaping research practices among Indigenous populations

Spectroscopic and dynamical properties of comet C/2018 F4, likely a true average former member of the Oort cloud

The population of comets hosted by the Oort cloud is heterogeneous. Most studies in this area focused on highly active objects, those with small perihelion distances or examples of objects with peculiar physical properties and/or unusual chemical compositions. This may have produced a biased sample of Oort cloud comets in which the most common objects may be rare, particularly those with perihelia well beyond the orbit of the Earth. Within this context, the known Oort cloud comets may not be representative of the full sample. Here, we study the spectral properties in the visible region and the cometary activity of Comet C/2018 F4 (PANSTARRS). We also explore its orbital evolution with the aim of understanding its origin within the context of known minor bodies moving along nearly parabolic or hyperbolic paths. We present observations obtained with the 10.4 m Gran Telescopio Canarias (GTC), derive the spectral class and visible slope of C/2018 F4 and characterise its level of cometary activity. Direct N-body simulations are carried out to explore its orbital evolution. The absolute magnitude of C/2018 F4 is Hr=13.62+/-0.04. Assuming a pV=0.04 its diameter is D<10.4 km. The object presents a conspicuous coma, with a level of activity comparable to those of other comets observed at similar heliocentric distances. Comet C/2018 F4 has a visible spectrum consistent with that of an X-type asteroid, and has a spectral slope S'=4.0+/-1.0 %/1000\AA and no evidence of hydration. The spectrum matches those of well-studied primitive asteroids and comets. The analysis of its dynamical evolution prior to discovery suggests that C/2018 F4 is not of extrasolar origin. Although the present-day heliocentric orbit of C/2018 F4 is slightly hyperbolic, its observational properties and past orbital evolution are consistent with those of a dynamically old comet with an origin in the Oort cloud.Comment: 6 pages, 5 figures. In pres

Implementation and Effects of LDC and MDC in Kentucky Districts

This brief summarizes early evidence on the success of two tools Kentucky districts have used to support their teachers' transition to these more demanding goals: Literacy Design Collaborative (LDC) and Math Design Collaborative (MDC). With support from the Bill and Melinda Gates Foundation, LDC and MDC tools have been designed and implemented to embody the key shifts in teaching and learning that the new standards demand. By implementing the tools, teachers then engage in new pedagogy and address relevant learning goals of the Kentucky Core Academic Standards

Factorization of supersymmetric Hamiltonians in curvilinear coordinates

Planar supersymmetric quantum mechanical systems with separable spectral problem in curvilinear coordinates are analyzed in full generality. We explicitly construct the supersymmetric extension of the Euler/Pauli Hamiltonian describing the motion of a light particle in the field of two heavy fixed Coulombian centers. We shall also show how the SUSY Kepler/Coulomb problem arises in two different limits of this problem: either, the two centers collapse in one center - a problem separable in polar coordinates -, or, one of the two centers flies to infinity - to meet the Coulomb problem separable in parabolic coordinates.Comment: 13 pages. Based on the talk presented by M.A. Gonzalez Leon at the 7th International Conference on Quantum Theory and Symmetries (QTS7), August 07-13, 2011, Prague, Czech Republi