1 Introduction

One of the most important results of the CGRO/EGRET instrument in the field of extragalactic astronomy is the discovery that blazars (i.e., flat-spectrum radio quasars-(FSRQs) and BL Lac objects) emit most of their bolometric luminosity in the high $\gamma$-rays (E > 100 MeV) energy range. Many of the $\gamma$-ray emitters are also superluminal radio sources (von Montigny et al. 1995). The common properties of these EGRET-detected AGNs are the following: the $\gamma$-ray flux is dominant over the flux in lower energy bands; The $\gamma$-ray luminosity above 100 MeV ranges from less than $3 \ 10^{44}$ erg s^-1 to more than 10⁴⁹ erg s^-1 (assuming isotropic emission); many of the sources are strongly variable in the $\gamma$-ray band on timescales from days to months (Mukherjee et al. 1997), but large flux variability on short timescales of < 1 day is also detected (see below). Some correlations between $\gamma$-ray and the lower energetic bands are discussed (see Dondi & Ghisellini 1995; Fan 1997; Fan et al. 1998a; M$\ddot{\rm u}$cke et al. 1997; Xie et al. 1997; Zhou et al. 1997). These suggest that the $\gamma$-ray emission is likely from the jet.

Various models for $\gamma$-ray emission have been proposed: Namely, (1) the inverse Compton process on the external photons (ECS), in which the soft photons are directly from a nearby accretion disk (Dermer et al. 1992; Coppi et al. 1993) or from disk radiation reprocessed in some region of AGNs (e.g. broad emission line region) (Sikora et al. 1994; Blandford & Levinson 1995); (2) the synchrotron self-Compton model (SSC), in which the soft photons originate as synchrotron emission in the jet (Maraschi et al. 1992; Bloom & Marscher 1992, 1993; Zdziarski & Krolik 1993; Bloom & Marscher 1996; Marscher & Travis 1996); (3) synchrotron emission from ultrarelativistic electrons and positrons produced in a proton-induced cascade (PIC) (Mannheim & Biermann 1992; Mannheim 1993; Cheng & Ding 1994). TeV radiations are observed from 3 X-ray-selected BL Lacertae objects (XBLs): Mkn 421 (Punch et al. 1992); Mkn 501 (Quinn et al. 1996), and IES 2344+514 (Catanese et al. 1998). But there is no consensus yet on the dominant emission process (see $\rm 3C~273$ for instance, von Montigny et al. 1997); for PKS 0528+134, the lower and higher states can be fitted by different models (e.g. B$\ddot{\rm o}$ttcher & Collmar 1998).

The $\gamma$-rays are produced at a distance of $\sim$$100~ R_{\rm g}$ (Hartman et al. 1996), $205~R_{\rm g}$ (Xie et al. 1998), and hundreds of Schwarzshild radii (Ghisellini & Madau 1996; Celotti & Ghisellini 1998). We think that this distance is an important parameter, which can be used to constrain the mass of the central black hole. In this paper, we will use it to derive the central black hole mass and the Doppler factor for some blazars with short timescales. The paper is arranged as follows: in Sect. 2, we estimate the mass of the central black hole and the Doppler factor; in Sect. 3, we give some discussions and a brief summary.

H₀ = 75 km s^-1 Mpc^-1, and q₀ = 0.5 are adopted through out the paper.