Path Integral Approach for Superintegrable Potentials on Spaces of Non-constant Curvature: II. Darboux Spaces DIII and DIV

This is the second paper on the path integral approach of superintegrable systems on Darboux spaces, spaces of non-constant curvature. We analyze in the spaces \DIII and \DIV five respectively four superintegrable potentials, which were first given by Kalnins et al. We are able to evaluate the path integral in most of the separating coordinate systems, leading to expressions for the Green functions, the discrete and continuous wave-functions, and the discrete energy-spectra. In some cases, however, the discrete spectrum cannot be stated explicitly, because it is determined by a higher order polynomial equation. We show that also the free motion in Darboux space of type III can contain bound states, provided the boundary conditions are appropriate. We state the energy spectrum and the wave-functions, respectively

Families of superintegrable Hamiltonians constructed from exceptional polynomials

We introduce a family of exactly-solvable two-dimensional Hamiltonians whose wave functions are given in terms of Laguerre and exceptional Jacobi polynomials. The Hamiltonians contain purely quantum terms which vanish in the classical limit leaving only a previously known family of superintegrable systems. Additional, higher-order integrals of motion are constructed from ladder operators for the considered orthogonal polynomials proving the quantum system to be superintegrable

Deformed oscillator algebras for two dimensional quantum superintegrable systems

Quantum superintegrable systems in two dimensions are obtained from their classical counterparts, the quantum integrals of motion being obtained from the corresponding classical integrals by a symmetrization procedure. For each quantum superintegrable systema deformed oscillator algebra, characterized by a structure function specific for each system, is constructed, the generators of the algebra being functions of the quantum integrals of motion. The energy eigenvalues corresponding to a state with finite dimensional degeneracy can then be obtained in an economical way from solving a system of two equations satisfied by the structure function, the results being in agreement to the ones obtained from the solution of the relevant Schrodinger equation. The method shows how quantum algebraic techniques can simplify the study of quantum superintegrable systems, especially in two dimensions.Comment: 22 pages, THES-TP 10/93, hep-the/yymmnn

Is complexity leadership theory complex enough? A critical appraisal, some modifications and suggestions for further research

Scholars are increasingly seeking to develop theories that explain the underlying processes whereby leadership is enacted. This shifts attention away from the actions of ‘heroic’ individuals and towards the social contexts in which people with greater or lesser power influence each other. A number of researchers have embraced complexity theory, with its emphasis on non-linearity and unpredictability. However, some complexity scholars still depict the theory and practice of leadership in relatively non-complex terms. They continue to assume that leaders can exercise rational, extensive and purposeful influence on other actors to a greater extent than is possible. In effect, they offer a theory of complex organizations led by non-complex leaders who establish themselves by relatively non-complex means. This testifies to the enduring power of ‘heroic’ images of leader agency. Without greater care, the terminology offered by complexity leadership theory could become little more than a new mask for old theories that legitimize imbalanced power relationships in the workplace. This paper explores how these problems are evident in complexity leadership theory, suggests that communication and process perspectives help to overcome them, and outlines an agenda for further research on these issues

Massless geodesics in AdS5×Y(p,q)AdS_5\times Y(p,q) as a superintegrable system

A Carter like constant for the geodesic motion in the $Y(p,q)$ Einstein-Sasaki geometries is presented. This constant is functionally independent with respect to the five known constants for the geometry. Since the geometry is five dimensional and the number of independent constants of motion is at least six, the geodesic equations are superintegrable. We point out that this result applies to the configuration of massless geodesic in $AdS_5\times Y(p,q)$ studied by Benvenuti and Kruczenski, which are matched to long BPS operators in the dual N=1 supersymmetric gauge theory.Comment: 20 pages, no figures. Small misprint is corrected in the Killing-Yano tensor. No change in any result or conclusion

Do herbivorous minnows have “plug-flow reactor” guts? Evidence from digestive enzyme activities, gastrointestinal fermentation, and luminal nutrient concentrations

Few investigations have empirically analyzed fish gut function in the context of chemical reactor models. In this study, digestive enzyme activities, levels of gastrointestinal fermentation products [short chain fatty acids (SCFA)], luminal nutrient concentrations, and the mass of gut contents were measured along the digestive tract in herbivorous and carnivorous minnows to ascertain whether their guts function as “plug-flow reactors” (PFRs). Four of the species, Campostoma anomalum, C. ornatum, C. oligolepis, and C. pauciradii, are members of a monophyletic herbivorous clade, whereas the fifth species, Nocomis micropogon, is a carnivore from an adjacent carnivorous clade. In the context of a PFR model, the activities of amylase, trypsin and lipase, and the concentrations of glucose, protein, and lipid were predicted to decrease moving from the proximal to the distal intestine. I found support for this as these enzyme activities and nutrient concentrations generally decreased moving distally along the intestine of the four Campostoma species. Furthermore, gut content mass and the low SCFA concentrations did not change (increase or decrease) along the gut of any species. Combined with a previous investigation suggesting that species of Campostoma have rapid gut throughput rates, the data presented here generally support Campostoma as having guts that function as PFRs. The carnivorous N. micropogon showed some differences in the measured parameters, which were interpreted in the contexts of intake and retention time to suggest that PFR function breaks down in this carnivorous species

Different experimental approaches in modelling cataractogenesis: An overview of selenite-induced nuclear cataract in rats

Cataract, the opacification of eye lens, is the leading cause of blindness worldwide. At present, the only remedy is surgical removal of the cataractous lens and substitution with a lens made of synthetic polymers. However, besides significant costs of operation and possible complications, an artificial lens just does not have the overall optical qualities of a normal one. Hence it remains a significant public health problem, and biochemical solutions or pharmacological interventions that will maintain the transparency of the lens are highly required. Naturally, there is a persistent demand for suitable biological models. The ocular lens would appear to be an ideal organ for maintaining culture conditions because of lacking blood vessels and nerves. The lens in vivo obtains its nutrients and eliminates waste products via diffusion with the surrounding fluids. Lens opacification observed in vivo can be mimicked in vitro by addition of the cataractogenic agent sodium selenite (Na2SeO3) to the culture medium. Moreover, since an overdose of sodium selenite induces also cataract in young rats, it became an extremely rapid and convenient model of nuclear cataract in vivo. The main focus of this review will be on selenium (Se) and its salt sodium selenite, their toxicological characteristics and safety data in relevance of modelling cataractogenesis, either under in vivo or in vitro conditions. The studies revealing the mechanisms of lens opacification induced by selenite are highlighted, the representatives from screening for potential anti-cataract agents are listed

The Efficacy of Energy-Restricted Diets in Achieving Preoperative Weight Loss for bariatric Pateints: A Systematic Review

The final publication is available at Springer via https://doi.org/10.1007/s11695-018-3451-1In bariatric practice, a preoperative weight loss of at least 5% is recommended. However, the hypocaloric diets prescribed vary and no consensus exists. This study examined the efficacy of preoperative diets in achieving 5% weight loss. From a systematic literature search, eight randomised controlled trials (n = 862) were identified. Half of the trials used a Bvery-low-calorie diet^ whilst the rest employed a Blow-calorie diet^. Only five diets achieved ≥ 5% weight loss over varying durations and energy intakes. By inference, compliance with a 700–1050 kcal (2929–4393 kJ) diet, consisting of moderate carbohydrate, high protein and low/moderate fat, for 3 weeks is likely to achieve 5% weight loss. A low-carbohydrate diet (< 20 g/day) may achieve this target within a shorter duration. Additional research is required to validate these conclusions