The formation rate of long gamma-ray bursts (GRBs) could follow the cosmic star formation rate (SFR) incorporating with cosmic metallicity evolution. Therefore, the luminosity function (LF) of GRBs can in principle be explored by modeling the redshift-luminosity distributions of {\it Swift} observed GRBs. For an assumed LF form as $\Phi_z(L)\propto e^{-L_p/L}\left({L/L_p}\right)^{-\nu}(1+z)^\delta$, we found that (1) the approximate broken-power law distribution of the luminosities of the {\it Swift} observed GRBs is probably caused by the luminosity selection of the telescope by reducing the number of the GRBs with low luminosities, (2) the evolution of the LF could approach to be very weak, i.e., $\delta\sim 0$, if the GRB environments are metal-poor as $Z_{\rm}<(0.1-0.3)Z_{\odot}$, and (3) the slope of the LF can be derived to be within $\nu\sim(1.55-1.72)$ by fitting the redshift distribution of the GRBs and qualitatively explaining the luminosity distribution. Finally, we also suggest an empirical detection efficiency as a function of flux for the {\it Swift} Burst Alert Telescope (BAT) in order to model the $\log N-\log P$ distribution of the GRBs.
We made a detailed study of the properties of the electron layer near the Quark surface of strange stars with strong ($\sim 10^{14}-10^{17}$G) magnetic Fields. The electrostatic potential and the electric field at the quark surface Were calculated as functions of the magnetic field intensity of bare...