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

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

A Theory Of Bust-Up Corporate Takeovers

Quite often, the market value of a firm in parts exceeds its value as a single entity.  The maximum value can be attained in such instances, by splitting the firm up.  We observe several instances where a firm’s management breaks up the firm to achieve maximum value.  In other cases, firms require a change in management to initiate divestiture. Lastly, takeover by outsiders is sometimes required to split the firm up and sell it in parts to achieve full value.  This study provides an economic analysis of the payoffs to all parties involved in a corporate breakup.  Models of the costs and benefits to shareholders and management teams are developed for each of the three situations listed above to explain why the different circumstances occur in different cases

Construction of classical superintegrable systems with higher order integrals of motion from ladder operators

We construct integrals of motion for multidimensional classical systems from ladder operators of one-dimensional systems. This method can be used to obtain new systems with higher order integrals. We show how these integrals generate a polynomial Poisson algebra. We consider a one-dimensional system with third order ladders operators and found a family of superintegrable systems with higher order integrals of motion. We obtain also the polynomial algebra generated by these integrals. We calculate numerically the trajectories and show that all bounded trajectories are closed.Comment: 10 pages, 4 figures, to appear in j.math.phys

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