Superintegrability in three-dimensional Euclidean space

Potentials for which the corresponding Schrödinger equation is maximally superintegrable in three-dimensional Euclidean space are studied. The quadratic algebra which is associated with each of these potentials is constructed and the bound state wave functions are computed in the separable coordinates

Symmetry operators and separation of variables for spin-wave equations in oblate spheroidal coordinates

A family of second-order differential operators that characterize the solution of the massless spin s field equations, obtained via separation of variables in oblate spheroidal coordinates and using a null tetrad is found. The first two members of the family also characterize the separable solutions in the Kerr space-time. It is also shown that these operators are symmetry operators of the field equations in empty space-times whenever the space-time admits a second-order Killing–Yano tensor

Teukolsky–Starobinsky identities for arbitrary spin

The Teukolsky–Starobinsky identities are proven for arbitrary spin s. A pair of covariant equations are given that admit solutions in terms of Teukolsky functions for general s. The method of proof is shown to extend to the general class of space-times considered by Torres del Castillo [J. Math. Phys. 29, 2078 (1988)]

Matrix operator symmetries of the Dirac equation and separation of variables

The set of all matrix-valued first-order differential operators that commute with the Dirac equation in n-dimensional complex Euclidean space is computed. In four dimensions it is shown that all matrix-valued second-order differential operators that commute with the Dirac operator in four dimensions are obtained as products of first-order operators that commute with the Dirac operator. Finally some additional coordinate systems for which the Dirac equation in Minkowski space can be solved by separation of variables are presented. These new systems are comparable to the separation in oblate spheroidal coordinates discussed by Chandrasekhar [S. Chandrasekhar, The Mathematical Theory of Black Holes (Oxford U.P., Oxford, 1983)]

Killing–Yano tensors and variable separation in Kerr geometry

A complete analysis of the free-field massless spin-s equations (s=0, (1)/(2) ,1) in Kerr geometry is given. It is shown that in each case the separation constants occurring in the solutions obtained from a potential function can be characterized in an invariant way. This invariant characterization is given in terms of the Killing–Yano tensor admitted by Kerr geometry

Electron transport in gated InGaAs and InAsP quantum well wires in selectively-grown InP ridge structures

The purpose of this work is to fabricate ribbon-like InGaAs and InAsP wires embedded in InP ridge structures and investigate their transport properties. The InP ridge structures that contain the wires are selectively grown by chemical beam epitaxy (CBE) on pre-patterned InP substrates. To optimize the growth and micro-fabrication processes for electronic transport, we explore the Ohmic contact resistance, the electron density, and the mobility as a function of the wire width using standard transport and Shubnikov-de Haas measurements. At low temperatures the ridge structures reveal reproducible mesoscopic conductance fluctuations. We also fabricate ridge structures with submicron gate electrodes that exhibit non-leaky gating and good pinch-off characteristics acceptable for device operation. Using such wrap gate electrodes, we demonstrate that the wires can be split to form quantum dots evidenced by Coulomb blockade oscillations in transport measurements.Comment: 5 pages, 4 figures, additional references and improved Fig. 4c, MSS-14 conference, submitted to Physica

Smartphone apps for the self-management of low back pain: A systematic review

Guidelines for low back pain (LBP) often recommend the use of self-management such as unsupervised exercise, booklets, and online education. Another potentially useful way for patients to self-manage LBP is by using smartphone applications (apps). However, to date, there has been no rigorous evaluation of LBP apps and no guidance for consumers on how to select high-quality, evidence-based apps. This chapter reviews smartphone apps for the self-management of LBP and evaluates their content quality and whether they recommend evidence-based interventions. This chapter shows that generally app developers are selecting interventions that are endorsed by guidelines, although their quality is low. There are many apps available for the self-management of LBP, but their effectiveness in improving patient outcomes has not been rigorously assessed. App developers need to work closely with healthcare professionals, researchers, and patients to ensure app content is accurate, evidence based, and engaging

Self-employed workers and the achievement of the 2030 agenda for sustainable development: an overview of their social benefit entitlements across 31 European countries

One of the Sustainable Development Goals of the United Nations’ 2030 Agenda for Sustainable Development is Decent Work and Economic Growth (SDG 8). While the actions suggested to reach this goal target numerous actors in the labor market, such as entrepreneurs running small and medium-sized enterprises, unemployed people, students and young people, persons with disabilities, children and adults forced to work, and migrant workers, these are not the only important groups to focus on. This paper discusses a group receiving less attention: self-employed workers. Through a review of literature and the legislative framework on the social benefits of self-employment across 31 European countries, challenges to the self-employed achieving decent work are identified. The most prominent challenges are that, in many countries, these workers lack social protection against unemployment or accidents at work and that the conditions for their entitlement to social benefits are more demanding than for employees. These constitute impediments to achieving SDG 8‘s goal of “decent work for all”, and SDG 10′s aim to “reduce inequalities”

COSMOGRAIL: XVII. Time delays for the quadruply imaged quasar PG 1115+080

Indexación: Scopus.Acknowledgements. The authors would like to thank R. Gredel for his help in setting up the program at the ESO MPIA 2.2 m telescope, and the anonymous referee for his or her comments on this work. This work is supported by the Swiss National Fundation. This research made use of Astropy, a community-developed core Python package for Astronomy (Astropy Collaboration et al. 2013, 2018) and the 2D graphics environment Matplotlib (Hunter 2007). K.R. acknowledge support from PhD fellowship FIB-UV 2015/2016 and Becas de Doctorado Nacional CONICYT 2017 and thanks the LSSTC Data Science Fellowship Program, her time as a Fellow has benefited this work. M.T. acknowledges support by the DFG grant Hi 1495/2-1. G. C.-F. C. acknowledges support from the Ministry of Education in Taiwan via Government Scholarship to Study Abroad (GSSA). D. C.-Y. Chao and S. H. Suyu gratefully acknowledge the support from the Max Planck Society through the Max Planck Research Group for S. H. Suyu. T. A. acknowledges support by the Ministry for the Economy, Development, and Tourism’s Programa Inicativa Científica Milenio through grant IC 12009, awarded to The Millennium Institute of Astrophysics (MAS).We present time-delay estimates for the quadruply imaged quasar PG 1115+080. Our results are based on almost daily observations for seven months at the ESO MPIA 2.2 m telescope at La Silla Observatory, reaching a signal-to-noise ratio of about 1000 per quasar image. In addition, we re-analyze existing light curves from the literature that we complete with an additional three seasons of monitoring with the Mercator telescope at La Palma Observatory. When exploring the possible source of bias we considered the so-called microlensing time delay, a potential source of systematic error so far never directly accounted for in previous time-delay publications. In 15 yr of data on PG 1115+080, we find no strong evidence of microlensing time delay. Therefore not accounting for this effect, our time-delay estimates on the individual data sets are in good agreement with each other and with the literature. Combining the data sets, we obtain the most precise time-delay estimates to date on PG 1115+080, with Δt(AB) = 8.3+1.5 -1.6 days (18.7% precision), Δt(AC) = 9.9+1.1 -1.1 days (11.1%) and Δt(BC) = 18.8+1.6 -1.6 days (8.5%). Turning these time delays into cosmological constraints is done in a companion paper that makes use of ground-based Adaptive Optics (AO) with the Keck telescope. © ESO 2018.https://www.aanda.org/articles/aa/abs/2018/08/aa33287-18/aa33287-18.htm