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The behavior of the characteristic angular size (as defined in the paper) of milliarcsecond structures of active galactic nuclei (AGN) is analyzed as a function of redshift (z). Such a dependence contains a well-known feature, a dependence of the apparent angular size of a standard rod on cosmological distance. However, in the discussed case, this general dependence is complicated by dependences of source linear size (l) on its luminosity (L) and redshift, l is proportional to Lbeta^ (1 + z) ⁿ^. A nonlinear regression model, containing as parameters characteristic linear size of AGN, indices β and n, and the cosmological deceleration parameter q₀_ was applied for observational data of the VLBI survey at 2. 3 GHz (Preston et al. 1985). Results of the regression models are discussed from the perspective of apparent and intrinsic properties of milliarcsecond structures of AGN. The best fit is obtained for parameters β = 0. 26 +/- 0. 03 and n = -0. 30 +/- 0. 90. In the particular case of the universe with the Robertson-Walker metric and zero cosmological constant, the estimated value q₀_ = 0. 16 +/- 0. 71 is somewhat favorable for the open cosmological models.
Leonid Gurvits (Fri,) studied this question.