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We present the first near-IR spectroscopy and joint analyses of multiwavelength observations for SDSS J082747.14+425241.1, a dust-reddened, weak broad emission-line quasar (WLQ) undergoing a remarkable broad-absorption line (BAL) transformation. The systemic redshift is more precisely measured to be z = 2.070 ± 0.001 using H β compared to z = 2.040 ± 0.003 using Mg ii from the literature, signifying an extreme Mg ii blueshift of 2140 ± 530 km sâˆ'1 relative to H β. Using the H β -based single-epoch scaling relation with a systematic uncertainty of 0.3 dex, its black hole (BH) mass and Eddington ratio are estimated to be M BH ∼ 6.1 Ă— 108 M ⊙ and λ Edd ∼ 0.71, indicative of being in a rapidly accreting phase. Our investigations confirm the WLQ nature and the LoBAL â†' HiBAL transformation, along with a factor of 2 increase in the Mg ii +Fe ii emission strength and a decrease of 0.1 in E (B âˆ' V) over two decades. The kinetic power of this LoBAL wind at R ∼ 15 pc from its BH is estimated to be ∼43% of the Eddington luminosity, sufficient for quasar feedback upon its host galaxy albeit with an order-of-magnitude uncertainty. This quasar provides a clear example of the long-sought scenario where LoBAL quasars are surrounded by dust cocoons, and wide-angle nuclear winds play a key role in the transition of red quasars evolving into the commonly seen blue quasars. [ABSTRACT FROM AUTHOR]

We study the luminosity function and formation rate of long gamma-ray bursts (GRBs) by using a maximum likelihood method. This is the first time this method is applied to a well-defined sample of GRBs that is complete in redshift. The sample is composed of 99 bursts detected by the Swift satellite, 81 of them with measured redshift and luminosity for a completeness level of |$82\, {\rm per\, cent}$|⁠. We confirm that a strong redshift evolution in luminosity (with an evolution index of |$\delta =2.22^{+0.32}_{-0.31}$|⁠) or in density (⁠|$\delta =1.92^{+0.20}_{-0.21}$|⁠) is needed in order to reproduce the observations well. But since the predicted redshift and luminosity distributions in the two scenarios are very similar, it is difficult to distinguish between these two kinds of evolutions only on the basis of the current sample. Furthermore, we also consider an empirical density case in which the GRB rate density is directly described as a broken power-law function and the luminosity function is taken to be non-evolving. In this case, we find that the GRB formation rate rises like |$(1+z)^{3.85^{+0.48}_{-0.45}}$| for |$z\lesssim 2$| and is proportional to |$(1+z)^{-1.07^{+0.98}_{-1.12}}$| for |$z\gtrsim 2$|⁠. The local GRB rate is |$1.49^{+0.63}_{-0.64}$|  Gpc−3 yr−1. The GRB rate may be consistent with the cosmic star formation rate (SFR) at |$z\lesssim 2$|⁠ , but shows an enhancement compared to the SFR at |$z\gtrsim 2$|⁠. [ABSTRACT FROM AUTHOR]