Rotation of Polarization Angle in Gamma-Ray Burst Prompt Phase−-\uppercase\expandafter{\romannumeral2}. The Influence of The Parameters

In addition to the light curve and energy spectrum, polarization is also important for the study of Gamma-ray burst (GRB) prompt emission. Rotation of the polarization angle (PA) with time will cause depolarization of the time-integrated polarization degree. However, it is rarely studied before. Here, we use the magnetic reconnection model with a large-scale ordered aligned magnetic field in the emitting region to study the influence of the key parameters on the PA rotations. We find that half-opening angle of the jet $\theta_{j}$, the observational angle $\theta_{V}$, and the bulk Lorentz factor $\Gamma$ all have significant impacts on the PA rotations. For a fixed $\theta_{j}\Gamma_{0}$ value ($\Gamma_{0}$ is the normalization factor of $\Gamma$), regardless of concrete $\theta_{j}$ and $\Gamma_{0}$ values, PA rotation within $T_{90}$ ($\triangle$PA) remains roughly unchanged for a $q\equiv\theta_{V}/\theta_{j}$ value. As $\theta_{j}\Gamma_{0}$ value increases, the $q$ range for $\triangle$PA$>10^{\circ}$ becomes smaller. The most significant PA rotation with $\triangle$PA$\thicksim90^{\circ}$ will happen when $\theta_{j}\Gamma_{0}\thicksim100$ and $1.1\leq q\leq1.2$. For the top-hat jet, observations of the PA rotation within $T_{90}$ will imply a slightly off-axis observation.Comment: 9 pages, 7 figures, submitte

A systematic study on the binding energy of Λ\Lambda hypernuclei

In this paper, we calculated the binding energy per baryon of the $\Lambda$ hypernuclei systemically, using the relativistic mean field theory (RMF) in a statistic frame. Some resemble properties are found among most of the hypernuclei found in experiments. The data show that a $\Lambda$ hypernucleus will be more stable, if it is composed of a $\Lambda$ hyperon adding to a stable normal nuclear core, or a $\Lambda$ hyperon replacing a neutron in a stable normal nuclear core. According to our calculations, existences of some new $\Lambda$ hypernuclei are predicted under the frame of RMF.Comment: 8 pages, 6 figures, 3 table

On coincidence and common fixed point theorems of eight self-maps satisfying an FM-contraction condition

In this paper, a new type of contraction for several self-mappings of a metric space, called FM-contraction, is introduced. This extends the one presented for a single map by Wardowski [Fixed points of a new type of contractive mappings in complete metric spaces, Fixed Point Theory Appl., 2012:94, 2012]. Coincidence and common fixed point of eight self mappings satisfying FM-contraction conditions are established via common limit range property without exploiting the completeness of the space or the continuity of the involved maps. Coincidence and common fixed point of eight self-maps satisfying FM-contraction conditions via the common property (E.A.) are also studied. Our results generalize, extend and improve the analogous recent results in the literature, and some examples are presented to justify the validity of our main results