Twisted vertex operators and unitary Lie algebras

A representation of the central extension of the unitary Lie algebra coordinated with a skew Laurent polynomial ring is constructed using vertex operators over an integral Z_2-lattice. The irreducible decomposition of the representation is explicitly computed and described. As a by-product, some fundamental representations of affine Kac-Moody Lie algebra of type $A_n^{(2)}$ are recovered by the new method.Comment: 26 page

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

Can preservice physical educators’ implicit attitude toward students with disabilities be changed by adapted physical education training program? Based on an Implicit Association Test

Purpose: Aim to explore whether preservice physical educators’ implicit attitude toward students with disabilities could be improved by a mid-term adapted physical education training program. Design: A randomized and controlled trial was deployed in the current experiment. Subjects were randomly divided into two groups (Experimental group and control group) after the pre-test of IAT. Post-test IAT was conducted for two groups after the training program for the experimental group. Findings: Chinese preservice physical educators’ implicit attitudes toward students with disabilities were negative. They also had a prejudice against students with disabilities. But the implicit attitudes toward students with disabilities could be improved by mid-term adapted physical education training. Furthermore, gender and contact experience with disabilities had no significant influence on the change in their implicit attitude