An infinite family of superintegrable systems from higher order ladder operators and supersymmetry

We will discuss how we can obtain new quantum superintegrable Hamiltonians allowing the separation of variables in Cartesian coordinates with higher order integrals of motion from ladder operators. We will discuss also how higher order supersymmetric quantum mechanics can be used to obtain systems with higher order ladder operators and their polynomial Heisenberg algebra. We will present a new family of superintegrable systems involving the fifth Painleve transcendent which possess fourth order ladder operators constructed from second order supersymmetric quantum mechanics. We present the polynomial algebra of this family of superintegrable systems.Comment: 8 pages, presented at ICGTMP 28, accepted for j.conf.serie

Superintegrability and higher order polynomial algebras II

In an earlier article, we presented a method to obtain integrals of motion and polynomial algebras for a class of two-dimensional superintegrable systems from creation and annihilation operators. We discuss the general case and present its polynomial algebra. We will show how this polynomial algebra can be directly realized as a deformed oscillator algebra. This particular algebraic structure allows to find the unitary representations and the corresponding energy spectrum. We apply this construction to a family of caged anisotropic oscillators. The method can be used to generate new superintegrable systems with higher order integrals. We obtain new superintegrable systems involving the fourth Painleve transcendent and present their integrals of motion and polynomial algebras.Comment: 11 page

Effects of High Functional Resistance Training on Parameters of Arterial Stiffness- Pilot Study

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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

Minimum Time Effect of Fish Oil on Arterial Stiffness - A Pilot Study

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Eclipsing binary stars in the Large Magellanic Cloud : results from the EROS-2, OGLE and VMC surveys

We present a catalogue of 1768 eclipsing binary stars (EBs) detected in the Large Magellanic Cloud (LMC) by the second generation of the EROS survey (hereinafter EROS-2); 493 of them are new discoveries located in outer regions (out of the central bar) of the LMC. These sources were originally included in a list of candidate classical Cepheids (CCs) extracted from the EROS-2 catalogue on the basis of the period (0.89 < 17.82 mag] diagram. After visual inspection of the light curves we reclassified them as eclipsing binaries. They have blue colours (B_EROS - R_EROS < 0.2 mag) hence we classed them as hot eclipsing binaries (HEBs) containing hot massive components: main sequence (MS) stars or blue giants. We present Ks-band light curves for 999 binaries from our sample that have a counterpart in the VISTA near-infrared ESO public survey of the Magellanic Clouds system (VMC). We provide spectral classifications of 13 HEBs with existing spectroscopy. We divided our sample into contact-like binaries and detached/semi-detached systems based on both visual inspection and the parameters of the Fourier decomposition of the light curves and analysed the period-luminosity (PL) relations of the contact-like systems using the R_EROS and Ks magnitudes at maximum light. The contact-like binaries in our sample do not follow PL relations. We analysed the sample of contact binaries from the OGLE III catalogue and confirmed that PL_I and PL_Ks sequences are defined only by eclipsing binaries containing a red giant component.Peer reviewe

Gas phase production of NHD2 in L134N

We show analytically that large abundances of NH2D and NHD2 can be produced by gas phase chemistry in the interiors of cold dense clouds. The calculated fractionation ratios are in good agreement with the values that have been previously determined in L134N and suggest that triply-deuterated ammonia could be detectable in dark clouds. Grain surface reactions may lead to similar NH2D and NHD2 enhancements but, we argue, are unlikely to contribute to the deuteration observed in L134N.Comment: 6 pages, 2 figures, uses psfig.sty and emulateapj.sty, to appear in Astrophysical Journal, vol 55

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