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High energy photon radiations of gamma-ray bursts(GRBs)and active galactic nuclei(AGNs)are dominated by their jet radiations.We examine whether the synchrotron radiations of jets in BL Lacs,flat spectrum radio quasars(FSRQs),and Narrow Line Seyfert 1 galaxies(NLS1s)follow the relation between the prompt gamma-ray emission and the initial Lorentz factor(Г0)of GRBs.It is shown that the AGN sample does not agree with the Lp-Ep,z-Г0 relation of GRBs.In addition,we obtain a tight relation of Lsyn ∝ Es0y4n5,p±0.15δ3.50±0.25 for FSRQs and NLS1 galaxies,where Lsyn is the luminosity at peak photon energy Esyn,p of the synchrotron radiations.This relation is different from the Lp-Ep,z-Г0 relation of GRBs.The dependence of Lsyn to δ is consistent with the expectation of the Doppler boosting effect for the FSRQs and NLS1 galaxies,but it is not for GRBs.We argue that Г0 may be a representative of the kinetic power of the radiating region and the tight Lp-Ep,z-Г0 relation is shaped by the radiation physics and 1 the jet power together.