Average cosmological invariant parameters (ACIPs) are calculated for six groups of BATSE cosmic gamma-ray bursts selected by their peak fluxes on the 1.024 s time scale. The ACIPs represent the average temporal and spectral properties of these events equally in the observer frame of reference and in the co-moving frames of outbursting emitters. The parameters are determined separately for rise fronts and for back slopes of bursts, defined as the time profiles before and after the main peaks, respectively. The ACIPs for the rise fronts are found to be different for different intensity groups, while the ACIPs for the back slopes show no significant dependence on intensity. We conclude that emitters of bursts manifest standard average properties only during the back slopes of bursts.
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