On algebraic construction of certain integrable and super-integrable systems

We propose a new construction of two-dimensional natural bi-Hamiltonian systems associated with a very simple Lie algebra. The presented construction allows us to distinguish three families of super-integrable monomial potentials for which one additional first integral is quadratic, and the second one can be of arbitrarily high degree with respect to the momenta. Many integrable systems with additional integrals of degree greater than two in momenta are given. Moreover, an example of a super-integrable system with first integrals of degree two, four and six in the momenta is found.Comment: 37 page

Non-linear stability in photogravitational non-planar restricted three body problem with oblate smaller primary

We have discussed non-linear stability in photogravitational non-planar restricted three body problem with oblate smaller primary. By photogravitational we mean that both primaries are radiating. We normalised the Hamiltonian using Lie transform as in Coppola and Rand (1989). We transformed the system into Birkhoff's normal form. Lie transforms reduce the system to an equivalent simpler system which is immediately solvable. Applying Arnold's theorem, we have found non-linear stability criteria. We conclude that $L_6$ is stable. We plotted graphs for $(\omega_1, D_2).$ They are rectangular hyperbola.Comment: Accepted for publication in Astrophysics & Space Scienc

Straight Line Orbits in Hamiltonian Flows

We investigate periodic straight-line orbits (SLO) in Hamiltonian force fields using both direct and inverse methods. A general theorem is proven for natural Hamiltonians quadratic in the momenta in arbitrary dimension and specialized to two and three dimension. Next we specialize to homogeneous potentials and their superpositions, including the familiar H\'enon-Heiles problem. It is shown that SLO's can exist for arbitrary finite superpositions of $N$-forms. The results are applied to a family of generalized H\'enon-Heiles potentials having discrete rotational symmetry. SLO's are also found for superpositions of these potentials.Comment: laTeX with 6 figure

CCD BV and 2MASS photometric study of the open cluster NGC 1513

We present CCD BV and JHK$_{s}$ 2MASS photometric data for the open cluster NGC 1513. We observed 609 stars in the direction of the cluster up to a limiting magnitude of $V\sim19$ mag. The star count method shows that the centre of the cluster lies at $\alpha_{2000}=04^{h}09^{m}36^{s}$, $\delta_{2000}=49^{\circ}28^{'}43^{''}$ and its angular size is $r=10$ arcmin. The optical and near-infrared two-colour diagrams reveal the colour excesses in the direction of the cluster as $E(B-V)=0.68\pm0.06$, $E(J-H)=0.21\pm0.02$ and $E(J-K_{s})=0.33\pm0.04$ mag. These results are consistent with normal interstellar extinction values. Optical and near-infrared Zero Age Main-Sequences (ZAMS) provided an average distance modulus of $(m-M)_{0}=10.80\pm0.13$ mag, which can be translated into a distance of $1440\pm80$ pc. Finally, using Padova isochrones we determined the metallicity and age of the cluster as $Z=0.015\pm 0.004$ ($[M/H]=-0.10 \pm 0.10$ dex) and $\log (t/yr) = 8.40\pm0.04$, respectively.Comment: 15 pages, 12 figures and 4 tables, accepted for publication in Astrophysics & Space Scienc

Minimum Energy Configurations in the NN-Body Problem and the Celestial Mechanics of Granular Systems

Minimum energy configurations in celestial mechanics are investigated. It is shown that this is not a well defined problem for point-mass celestial mechanics but well-posed for finite density distributions. This naturally leads to a granular mechanics extension of usual celestial mechanics questions such as relative equilibria and stability. This paper specifically studies and finds all relative equilibria and minimum energy configurations for $N=1,2,3$ and develops hypotheses on the relative equilibria and minimum energy configurations for $N\gg 1$ bodies.Comment: Accepted for publication in Celestial Mechanics and Dynamical Astronom

On the HU aquarii planetary system hypothesis

In this paper, we investigate the eclipse timing of the polar binary HUAquarii that has been observed for almost two decades. Recently, Qian et al. attributed large (O-C) deviations between the eclipse ephemeris and observations to a compact system of two massive Jovian companions. We improve the Keplerian, kinematic model of the light travel time effect and re-analyse the whole currently available data set. We add almost 60 new, yet unpublished, mostly precision light curves obtained using the time high-resolution photopolarimeter Optical Timing Analyzer (OPTIMA), as well as photometric observations performed at the Monitoring Network of Telescopes/North, Physics Innovations Robotic Astronomical Telescope Explorer and Carlos Sánchez Telescope. We determine new mid-egress times with a mean uncertainty at the level of 1s or better. We claim that because the observations that currently exist in the literature are non-homogeneous with respect to spectral windows (ultraviolet, X-ray, visual and polarimetric mode) and the reported mid-egress measurements errors, they may introduce systematics that affect orbital fits. Indeed, we find that the published data, when taken literally, cannot be explained by any unique solution. Many qualitatively different and best-fit two-planet configurations, including self-consistent, Newtonian N-body solutions may be able to explain the data. However, using high-resolution, precision OPTIMA light curves, we find that the (O-C) deviations are best explained by the presence of a single circumbinary companion orbiting at a distance of ~4.5au with a small eccentricity and having ~7 Jupiter masses. This object could be the next circumbinary planet detected from the ground, similar to the announced companions around close binaries HWVir, NNSer, UZFor, DPLeo, FSAur or SZHer, and planets of this type around Kepler-16, Kepler-34 and Kepler-35. © 2012 The Authors Monthly Notices of the Royal Astronomical Society © 2012 RAS

Involvement of Fas-mediated apoptosis in the inhibitory effects of interferon-a in chronic myelogenous leukemia

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Analysis of Short-Circuit Transients in the LHC Main Dipole Circuit

In each of the 8 sectors of the Large Hadron Collider (LHC) there exists one main dipole circuit, where 154 superconducting dipole magnets are connected in series. In the case a short to ground event occurs, the current flows through the circuit fuse that is present in the grounding subcircuit. A simulation scheme utilising a common interface between PSpice and Matlab is proposed in order to include the intermittent blow-up behaviour of the fuse in the simulations and increase the accuracy of the circuit model. The worst-case values of the voltage to ground in the circuit and the conditions under which they occur are identified from the simulations where the intermittent behaviour of the fuse is included in the model. A comparison with the values in the case where the fuse behaviour is not simulated is presented. Potential solutions to reduce the peak voltages in the circuit are also discussed