Search for strong gravitational lensing effect in the current GRB data of BATSE

Because gamma-ray bursts (GRBs) trace the high-z Universe, there is an appreciable probability for a GRB to be gravitational lensed by galaxies in the universe. Herein we consider the gravitational lensing effect of GRBs contributed by the dark matter halos in galaxies. Assuming that all halos have the singular isothermal sphere (SIS) mass profile in the mass range $10^{10} h^{-1} M_\odot < M < 2\times 10^{13} h^{-1}M_\odot$ and all GRB samples follow the intrinsic redshift distribution and luminosity function derived from the Swift LGRBs sample, we calculated the gravitational lensing probability in BATSE, Swift/BAT and Fermi/GBM GRBs, respectively. With an derived probability result in BATSE GRBs, we searched for lensed GRB pairs in the BATSE 5B GRB Spectral catalog. The search did not find any convincing gravitationally lensed events. We discuss our result and future observations for GRB lensing observation.Comment: 18 pages, 8 figure

Constraining fast radio burst progenitors with gravitational lensing

Fast Radio Bursts (FRBs) are new transient radio sources discovered recently. Because of the angular resolution restriction in radio surveys, no optical counter part has been identified yet so it is hard to determine the progenitor of FRBs. In this paper we propose to use radio lensing survey to constrain FRB progenitors. We show that, different types of progenitors lead to different probabilities for a FRB to be gravitationally lensed by dark matter halos in foreground galaxies, since different type progenitors result in different redshift distributions of FRBs. For example, the redshift distribution of FRBs arising from double stars shifts toward lower redshift than of the FRBs arising from single stars, because double stars and single stars have different evolution timescales. With detailed calculations, we predict that the FRB sample size for producing one lensing event varies significantly for different FRB progenitor models. We argue that this fact can be used to distinguish different FRB models and also discuss the practical possibility of using lensing observation in radio surveys to constrain FRB progenitors.Comment: 14 pages, including 6 figures and 1 tabl

Teachers' recognition of school bullying according to background variables and type of bullying

How teachers identify and judge school bullying may affect their willingness to intervene in bullying situations and influence their strategies for doing so. This study aimed to investigate whether there were significant differences in teachers' identification of bullying incidents according to background variables (gender, teaching experience, and education level). The participants of this study were 150 primary school and middle school teachers in Taiwan, A 24-item Recognition of Bullying incidents Questionnaire (RBIQ) was used in this study to explore whether teachers can identify physical, verbal, and relational scenarios as bullying or non-bullying incidents. A mixed-model two way ANOVA was used to analyze this data. Results revealed that teachers' teaching experiences significantly interacted with behavioral types, and teachers' education levels also sigm candy interacted with behavioral types. In addition, no gender differences in the identification of bullying were observed. Overall, teachers were more likely to identifi physical bullying incidents than relational ones. The results of this study suggest that teachers should participate in training to help them identify bullying incidents, particularly when these involve relational bullying