Asymmetric nuclear matter and neutron-skin in extended relativistic mean field model

The density dependence of the symmetry energy, instrumental in understanding the behaviour of the asymmetric nuclear matter, is investigated within the extended relativistic mean field (ERMF) model which includes the contributions from the self and mixed interaction terms for the scalar-isoscalar ($\sigma$), vector-isoscalar ($\omega$) and vector-isovector ($\rho$) mesons upto the quartic order. Each of the 26 different parameterizations of the ERMF model employed are compatible with the bulk properties of the finite nuclei. The behaviour of the symmetry energy for several parameter sets are found to be consistent with the empirical constraints on them as extracted from the analyses of the isospin diffusion data. The neutron-skin thickness in the $^{208}$Pb nucleus for these parameter sets of the ERMF model lie in the range of $\sim 0.20 - 0.24$ fm which is in harmony with the ones predicted by the Skyrme Hartree-Fock model. We also investigate the role of various mixed interaction terms which are crucial for the density dependence of the symmetry energy.Comment: 14 pages, 4 figures, Physical Review C (in press

A preliminary study of a very large space radiometric antenna

An approach used to compute the size of a special radiometric reflector antenna is presented. Operating at 1 GHz, this reflector is required to produce 200 simultaneous contiguous beams, each with a 3 dB footprint of 1 km from an assumed satellite height of 650 km. The overall beam efficiency for each beam is required to be more than 90%

Discovery of a Quasi-Periodic Oscillation in the Ultraluminous X-ray Source IC 342 X-1: XMM-Newton Results

We report the discovery of a quasi-periodic oscillation (QPO) at 642 mHz in an {\it XMM-Newton} observation of the ultraluminous X-ray source (ULX) IC 342 X-1. The QPO has a centroid at $\nu_{QPO} = 642 \pm 20$ mHz, a coherence factor of $Q = 11.6$, and an amplitude (rms) of 4.1\% with significance of $3.6\sigma$. The energy dependence study shows that the QPO is stronger in the energy range 0.3 - 5.0 keV. A subsequent observation (6 days later) does not show any signature of the QPO in the power density spectrum. The broadband energy spectra (0.3 - 40.0 keV) obtained by quasi-simultaneous observations of {\it XMM-Newton} and {\it NuSTAR} can be well described by an absorbed {\it diskbb} plus {\it cutoffpl} model. The best fitted spectral parameters are power-law index ($\Gamma$) $\sim$ 1.1, cutoff energy ($E_c$) $\sim$ 7.9 keV and disc temperature ($kT_{in}$) $\sim$ 0.33 keV, where the QPO is detected. The unabsorbed bolometric luminosity is $\sim$ 5.34$\times$ 10$^{39}$ erg~s$^{-1}$. Comparing with the well known X-ray binary GRS 1915+105, our results are consistent with the mass of the compact object in IC 342 X-1 being in the range $\sim 20 - 65 ~ M_\odot$. We discuss the possible implications of our results.Comment: 7 pages, 3 figures (2 colour), in press (MNRAS

A generalization of starlike functions of order alpha

For every $q\in(0,1)$ and $0\le \alpha<1$ we define a class of analytic functions, the so-called $q$-starlike functions of order $\alpha$, on the open unit disk. We study this class of functions and explore some inclusion properties with the well-known class of starlike functions of order $\alpha$. The paper is also devoted to the discussion on the Herglotz representation formula for analytic functions $zf'(z)/f(z)$ when $f(z)$ is $q$-starlike of order $\alpha$. As an application we also discuss the Bieberbach conjecture problem for the $q$-starlike functions of order $\alpha$. Further application includes the study of the order of $q$-starlikeness of the well-known basic hypergeometric functions introduced by Heine.Comment: 13 pages, 4 figures, submitted to a journa