Infinite families of superintegrable systems separable in subgroup coordinates

A method is presented that makes it possible to embed a subgroup separable superintegrable system into an infinite family of systems that are integrable and exactly-solvable. It is shown that in two dimensional Euclidean or pseudo-Euclidean spaces the method also preserves superintegrability. Two infinite families of classical and quantum superintegrable systems are obtained in two-dimensional pseudo-Euclidean space whose classical trajectories and quantum eigenfunctions are investigated. In particular, the wave-functions are expressed in terms of Laguerre and generalized Bessel polynomials.Comment: 19 pages, 6 figure

Energy-momentum conservation in pre-metric electrodynamics with magnetic charges

A necessary and sufficient condition for energy-momentum conservation is proved within a topological, pre-metric approach to classical electrodynamics including magnetic as well as electric charges. The extended Lorentz force, consisting of mutual actions by F=(E, B) on the electric current and G=(H, D) on the magnetic current, can be derived from an energy-momentum "potential" if and only if the constitutive relation G=G(F) satisfies a certain vanishing condition. The electric-magnetic reciprocity introduced by Hehl and Obukhov is seen to define a complex structure on the tensor product of 2-form pairs (F,G) which is independent of but consistent with the Hodge star operator defined by any Lorentzian metric. Contrary to a recent claim in the literature, it does not define a complex structure on the space of 2-forms itself.Comment: 8 pages, 1 fugur

The Settler\u27s Nightmare: A Tract for Farmers

https://commons.und.edu/settler-literature/1101/thumbnail.jp

A generalized photon propagator

A covariant gauge independent derivation of the generalized dispersion relation of electromagnetic waves in a medium with local and linear constitutive law is presented. A generalized photon propagator is derived. For Maxwell constitutive tensor, the standard light cone structure and the standard Feynman propagator are reinstated

An infinite family of superintegrable Hamiltonians with reflection in the plane

We introduce a new infinite class of superintegrable quantum systems in the plane. Their Hamiltonians involve reflection operators. The associated Schr\"odinger equations admit separation of variables in polar coordinates and are exactly solvable. The angular part of the wave function is expressed in terms of little -1 Jacobi polynomials. The spectra exhibit "accidental" degeneracies. The superintegrability of the model is proved using the recurrence relation approach. The (higher-order) constants of motion are constructed and the structure equations of the symmetry algebra obtained.Comment: 19 page

Operator ordering in Two-dimensional N=1 supersymmetry with curved manifold

We investigate an operator ordering problem in two-dimensional N=1 supersymmetric model which consists of n real superfields. There arises an operator ordering problem when the target space is curved. We have to fix the ordering in quantum operator properly to obtain the correct supersymmetry algebra. We demonstrate that the super-Poincar\'{e} algebra fixes the correct operator ordering. We obtain a supercurrent with correct operator ordering and a central extension of supersymmetry algebra.Comment: 7 page

Renal health after long-term exposure to tenofovir disoproxil fumarate (TDF) in HIV/HBV positive adults in Ghana

Objectives: The study assessed markers of renal health in HIV/HBV co-infected patients receiving TDF- containing antiretroviral therapy in Ghana. Methods: Urinary protein-to-creatinine ratio (uPCR) and albumin-to-protein ratio (uAPR) were measured cross-sectionally after a median of four years of TDF. At this time, alongside extensive laboratory testing, patients underwent evaluation of liver stiffness and blood pressure. The estimated glomerular filtration rate (eGFR) was measured longitudinally before and during TDF therapy. Results: Among 101 participants (66% women, median age 44 years, median CD4 count 572 cells/mm 3 ) 21% and 17% had detectable HIV-1 RNA and HBV DNA, respectively. Overall 35% showed hypertension, 6% diabetes, 7% liver stiffness indicative of cirrhosis, and 18% urinary excretion of Schistosoma antigen. Tubular proteinuria occurred in 16% of patients and was independently predicted by female gender and hypertension. The eGFR declined by median 1.8 ml/min/year during TDF exposure (IQR −4.4, −0.0); more pronounced declines ( ≥5 ml/min/year) occurred in 22% of patients and were associated with receiv-ing ritonavir-boosted lopinavir rather than efavirenz. HBV DNA, HBeAg, transaminases, and liver stiffness were not predictive of renal function abnormalities. Conclusions: The findings mandate improved diagnosis and management of hypertension and suggest targeted laboratory monitoring of patients receiving TDF alongside a booster in sub-Saharan Africa