Determining the luminosity function of Swift long gamma-ray bursts with pseudo-redshifts

The determination of luminosity function (LF) of gamma-ray bursts (GRBs) is of an important role for the cosmological applications of the GRBs, which is however hindered seriously by some selection effects due to redshift measurements. In order to avoid these selection effects, we suggest to calculate pseudo-redshifts for Swift GRBs according to the empirical L-E_p relationship. Here, such a $L-E_p$ relationship is determined by reconciling the distributions of pseudo- and real redshifts of redshift-known GRBs. The values of E_p taken from Butler's GRB catalog are estimated with Bayesian statistics rather than observed. Using the GRB sample with pseudo-redshifts of a relatively large number, we fit the redshift-resolved luminosity distributions of the GRBs with a broken-power-law LF. The fitting results suggest that the LF could evolve with redshift by a redshift-dependent break luminosity, e.g., L_b=1.2\times10^{51}(1+z)^2\rm erg s^{-1}. The low- and high-luminosity indices are constrained to 0.8 and 2.0, respectively. It is found that the proportional coefficient between GRB event rate and star formation rate should correspondingly decrease with increasing redshifts.Comment: 5 pages, 5 figures, accepted for publication in ApJ

Modulation of the slow/common gating of CLC channels by intracellular cadmium.

Members of the CLC family of Cl(-) channels and transporters are homodimeric integral membrane proteins. Two gating mechanisms control the opening and closing of Cl(-) channels in this family: fast gating, which regulates opening and closing of the individual pores in each subunit, and slow (or common) gating, which simultaneously controls gating of both subunits. Here, we found that intracellularly applied Cd(2+) reduces the current of CLC-0 because of its inhibition on the slow gating. We identified CLC-0 residues C229 and H231, located at the intracellular end of the transmembrane domain near the dimer interface, as the Cd(2+)-coordinating residues. The inhibition of the current of CLC-0 by Cd(2+) was greatly enhanced by mutation of I225W and V490W at the dimer interface. Biochemical experiments revealed that formation of a disulfide bond within this Cd(2+)-binding site is also affected by mutation of I225W and V490W, indicating that these two mutations alter the structure of the Cd(2+)-binding site. Kinetic studies showed that Cd(2+) inhibition appears to be state dependent, suggesting that structural rearrangements may occur in the CLC dimer interface during Cd(2+) modulation. Mutations of I290 and I556 of CLC-1, which correspond to I225 and V490 of CLC-0, respectively, have been shown previously to cause malfunction of CLC-1 Cl(-) channel by altering the common gating. Our experimental results suggest that mutations of the corresponding residues in CLC-0 change the subunit interaction and alter the slow gating of CLC-0. The effect of these mutations on modulations of slow gating of CLC channels by intracellular Cd(2+) likely depends on their alteration of subunit interactions

Stability of braneworlds with non-minimally coupled multi-scalar fields

Linear stability of braneworld models constructed with multi-scalar fields is very different from that of single-scalar field models. It is well known that both the tensor and scalar perturbation equations of the later can always be written as a supersymmetric Schr\"{o}dinger equation, so it can be shown that the perturbations are stable at linear level. However, in general it is not true for multi-scalar field models and especially there is no effective method to deal with the stability problem of the scalar perturbations for braneworld models constructed with non-minimally coupled multi-scalar fields. In this paper we present a method to investigate the stability of such braneworld models. It is easy to find that the tensor perturbations are stable. For the stability problem of the scalar perturbations, we present a systematic covariant approach. The covariant quadratic order action and the corresponding first-order perturbed equations are derived. By introducing the orthonormal bases in field space and making the Kaluza-Klein decomposition, we show that the Kaluza-Klein modes of the scalar perturbations satisfy a set of coupled Schr\"{o}dinger-like equations, with which the stability of the scalar perturbations and localization of the scalar zero modes can be analyzed according to nodal theorem. The result depends on the explicit models. For superpotential derived barane models, the scalar perturbations are stable, but there exist normalizable scalar zero modes, which will result in unaccepted fifth force on the brane. We also use this method to analyze the $f(R)$ braneworld model with an explicit solution and find that the scalar perturbations are stable and the scalar zero modes can not be localized on the brane, which ensure that there is no extra long-range force and the Newtonian potential on the brane can be recovered.Comment: 13 pages, 3 figure