The simple one-zone homogeneous jet model usually provides a good framework to explain the emissive spectra of AGN jets. However, it is argued that the jet should have velocity structures to mediate the inconsistence of bulk motions obtained by different wavebands. The synchrotron self-Compton (SSC) models and External Compton (EC) models of AGN jets with continually longitudinal and transverse bulk velocity structures are constructed. The observed spectra show complex and interesting patterns in different velocity structures and viewing angles. These models are used to calculate the synchrotron and inverse Compton spectra of two typical BL Lac objects (BLO) (Mrk 421 and 0716+714) and one Flat Spectrum Radio Quasars (FSRQ) (3C 279), and to discuss the implications of jet bulk velocity structures in unification of the BLO and FR I radio galaxies (FRI). By calculating the synchrotron spectra and SSC spectra of BL Lac object jets with continually bulk velocity structures, we find that the spectra are much different from ones in jets with uniform velocity structure under the increase of viewing angles. The unification of BLO and FR I is less constrained by viewing angles and would be imprinted by velocity structures intrinsic to the jet themselves. Finally, we present the EC spectra of FSRQ and FR II radio galaxies (FR II) and find that they are weakly affected by velocity structures compared to synchrotron and SSC spectra. Nowadays, IBL (W Comae and 3C 66A), LBL (BL Lacertae), and FSRQ (3C 279) display the potential to emit at VHE energy band, which attract great deal of attention upon them. We model the high-energy spectrum of 3C 66A, which was observed recently with the Fermi-LAT and VERITAS telescopes. The spectrum has a hard change from the energy range of 0.2-100 GeV to 200-500 GeV in recent almost contemporaneous observations of two telescopes. (1) The de-absorbed VERITAS spectrum depends strongly on redshift, which is highly uncertain. If z=0.444 is adopted, we are able to use the SSC model to produce the Fermi-LAT component and the EC model to the VERITAS component. For the VHE observations of IBL, EC component might be observed. (2) However, if z=0.1, the intrinsic VERITAS spectrum will be softer, and there will be a smooth link between the Fermi-LAT and VERITAS spectra that can be explained using an SSC model. It might indicate that the redshift of this source is less than 0.444. The VHE photons will be absorbed by the extragalactic background light (EBL) through pair production. Absorption features imprinted on the $\gamma$-ray spectra of distant blazars by background light photons provide an indirect approach to study the EBL. The research of VHE emission of blazars and EBL could promote mutually. The upper limits on the EBL, using the TeV spectra recently observed in TeV blazars, are presented. BL Lac objects usually present no or weak emission lines, and their redshifts are not easily determined. Comparing the measured and intrinsic VHE spectra due to EBL absorption, we give the redshift upper limits of three blazars.
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