Quadratic Algebra Approach to Relativistic Quantum Smorodinsky-Winternitz Systems

There exist a relation between the Klein-Gordon and the Dirac equations with scalar and vector potentials of equal magnitude (SVPEM) and the Schrodinger equation. We obtain the relativistic energy spectrum for the four Smorodinsky-Winternitz systems from the quasi-Hamiltonian and the quadratic algebras obtained by Daskaloyannis in the non-relativistic context. We point out how results obtained in context of quantum superintegrable systems and their polynomial algebras may be applied to the quantum relativistic case. We also present the symmetry algebra of the Dirac equation for these four systems and show that the quadratic algebra obtained is equivalent to the one obtained from the quasi-Hamiltonian.Comment: 19 page

Reproduction of the Lyman α irradiance variability from analysis of full-disk images in the CaII K-line

We have compared three years of daily CaII K-line images from the Big Bear Solar Observatory (BBSO) with HI Lymanα irradiance data from the Upper Atmosphere Research Satellite (UARS). The daily full-disk CaII K-line images are reduced to a new index of integrated excess emission, which reproduces both the 27 day rotational modulation and the solar cycle decrease in Lyα irradiance. Our analysis shows that while plages reproduce the 27-day variation quite well, the total K-line emission excess above the quiet background is needed to reproduce the secular solar cycle trend in the Lyα irradiance. The resulting K-line index exhibits a high degree of correlation (0.9) with the time series of measured Lyα flux

New RR Lyrae variables in binary systems

Despite their importance, very few RR Lyrae (RRL) stars have been known to reside in binary systems. We report on a search for binary RRL in the OGLE-III Galactic bulge data. Our approach consists in the search for evidence of the light-travel time effect in so-called observed minus calculated ($O-C$) diagrams. Analysis of 1952 well-observed fundamental-mode RRL in the OGLE-III data revealed an initial sample of 29 candidates. We used the recently released OGLE-IV data to extend the baselines up to 17 years, leading to a final sample of 12 firm binary candidates. We provide $O-C$ diagrams and binary parameters for this final sample, and also discuss the properties of 8 additional candidate binaries whose parameters cannot be firmly determined at present. We also estimate that $\gtrsim 4$ per cent of the RRL reside in binary systems.Comment: MNRAS Letters, in pres

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

High-Density Spot Seeding for Tissue Model Formation

A method for making a tissue includes seeding cells at a selected concentration on a support to form a cell spot, incubating the cells to allow the cells to partially attach, rinsing the cells to remove any unattached cells, adding culture medium to enable the cells to proliferate at a periphery of the cell spot and to differentiate toward a center of the cell spot, and further incubating the cells to form the tissue. The cells may be C2C12 cells or other subclones of the C2 cell line, H9c2(2-1) cells, L6 cells, L8 cells, QM7 cells, Sol8 cells, G-7 cells, G-8 cells, other myoblast cells, cells from other tissues, or stem cells. The selected concentration is in a range from about 1 x 10(exp 5) cells/ml to about 1 x 10(exp 6) cells/ml. The tissue formed may be a skeletal muscle tissue, a cardiac muscle tissue, nerve tissue, or a bone tissue

Addition theorems and the Drach superintegrable systems

We propose new construction of the polynomial integrals of motion related to the addition theorems. As an example we reconstruct Drach systems and get some new two-dimensional superintegrable Stackel systems with third, fifth and seventh order integrals of motion.Comment: 18 pages, the talk given on the conference "Superintegrable Systems in Classical and Quantum Mechanics", Prague 200

High-Density Spot Seeding for Tissue Model Formation

A model of tissue is produced by steps comprising seeding cells at a selected concentration on a support to form a cell spot, incubating the cells to allow the cells to partially attach, rinsing the cells to remove any cells that have not partially attached, adding culture medium to enable the cells to proliferate at a periphery of the cell spot and to differentiate toward a center of the cell spot, and further incubating the cells to form the tissue. The cells may be C2C12 cells or other subclones of the C2 cell line, H9c2(2-1) cells, L6 cells, L8 cells, QM7 cells, Sol8 cells, G-7 cells, G-8 cells, other myoblast cells, cells from other tissues, or stem cells. The selected concentration is in a range from about 1 x 10(exp 5) cells/ml to about 1 x 10(exp 6) cells/ml. The tissue formed may be a muscle tissue or other tissue depending on the cells seeded

The Star Blended with the MOA-2008-BLG-310 Source Is Not the Exoplanet Host Star

High resolution Hubble Space Telescope (HST) image analysis of the MOA-2008-BLG-310 microlens system indicates that the excess flux at the location of the source found in the discovery paper cannot primarily be due to the lens star because it does not match the lens-source relative proper motion, $\mu_{\rm rel}$, predicted by the microlens models. This excess flux is most likely to be due to an unrelated star that happens to be located in close proximity to the source star. Two epochs of HST observations indicate proper motion for this blend star that is typical of a random bulge star, but is not consistent with a companion to the source or lens stars if the flux is dominated by only one star, aside from the lens. We consider models in which the excess flux is due to a combination of an unrelated star and the lens star, and this yields 95\% confidence level upper limit on the lens star brightness of $I_L > 22.44$ and $V_L >23.62$. A Bayesian analysis using a standard Galactic model and these magnitude limits yields a host star mass $M_h = 0.21 ^{+0.21}_{-0.09}~ M_\odot$, a planet mass of $m_p = 23.4 ^{+23.9}_{-9.9}~M_\oplus$ at a projected separation of $a_\perp = 1.12^{+0.16}_{-0.17},$AU. This result illustrates excess flux in a high resolution image of a microlens-source system need not be due to the lens. It is important to check that the lens-source relative proper motion is consistent with the microlensing prediction. The high resolution image analysis techniques developed in this paper can be used to verify the WFIRST exoplanet microlensing survey mass measurements.Comment: Submitted to AJ on March 18, 201

Third order superintegrable systems separating in polar coordinates

A complete classification is presented of quantum and classical superintegrable systems in $E_2$ that allow the separation of variables in polar coordinates and admit an additional integral of motion of order three in the momentum. New quantum superintegrable systems are discovered for which the potential is expressed in terms of the sixth Painlev\'e transcendent or in terms of the Weierstrass elliptic function

Improved Cell Culture Method for Growing Contracting Skeletal Muscle Models

An improved method for culturing immature muscle cells (myoblasts) into a mature skeletal muscle overcomes some of the notable limitations of prior culture methods. The development of the method is a major advance in tissue engineering in that, for the first time, a cell-based model spontaneously fuses and differentiates into masses of highly aligned, contracting myotubes. This method enables (1) the construction of improved two-dimensional (monolayer) skeletal muscle test beds; (2) development of contracting three-dimensional tissue models; and (3) improved transplantable tissues for biomedical and regenerative medicine applications. With adaptation, this method also offers potential application for production of other tissue types (i.e., bone and cardiac) from corresponding precursor cells