We make use of the recent large sample of 17 042 Mg Ⅱ absorption systems from Quider et al. to analyze the evolution of the redshift number density. Regardless of the strength of the absorption line, we find that the evolution of the redshift number density can be clearly distinguished into three different phases. In the intermediate redshift epoch (0.6■ z ■1.6), the evolution of the redshift number density is consistent with the non-evolution curve, however, the non-evolution curve over-predicts the values of the redshift number density in the early (z ■ 0.6) and late (z ■ 1.6) epochs. Based on the invariant cross-section of the absorber, the lack of evolution in the redshift number density compared to the non-evolution curve implies the galaxy number density does not evolve during the middle epoch. The flat evolution of the redshift number density tends to correspond to a shallow evolution in the galaxy merger rate during the late epoch, and the steep decrease of the redshift number density might be ascribed to the small mass of halos during the early epoch.
We find exact solutions to the Klein-Gordon equation in the vicinity of Schwarzschild black holes.For particles with a zero angular momentum,the convergence range of the solution is r < 4M.One of the solutions describes an exponential enhancement of the density of particles in the vicinity of Schwarzschild black holes,which might be the mechanism of gamma-ray bursts.
