Observational Constraints on Cosmological Models with the Updated Long
  Gamma-Ray Bursts
  In the present work, by the help of the newly released Union2 compilation
which consists of 557 Type Ia supernovae (SNIa), we calibrate 109 long
Gamma-Ray Bursts (GRBs) with the well-known Amati relation, using the
cosmology-independent calibration method proposed by Liang {\it et al.}. We
have obtained 59 calibrated high-redshift GRBs which can be used to constrain
cosmological models without the circularity problem (we call them ``Hymnium''
GRBs sample for convenience). Then, we consider the joint constraints on 7
cosmological models from the latest observational data, namely, the combination
of 557 Union2 SNIa dataset, 59 calibrated Hymnium GRBs dataset (obtained in
this work), the shift parameter $R$ from the WMAP 7-year data, and the distance
parameter $A$ of the measurement of the baryon acoustic oscillation (BAO) peak
in the distribution of SDSS luminous red galaxies. We also briefly consider the
comparison of these 7 cosmological models.
