  Results of a pilot project with the participation of the "Kvazar-KVO" radio
interferometry array in observations carried out with the European VLBI Network
are presented. The aim of the project was to conduct and analyze
multi-frequency (1.7, 2.3, 5.0, 8.4 GHz) observations of the parsec-scale jets
of 24 active galactic nuclei. Three observing sessions were successfully
carried out in October 2008. Maps of the radio intensity distributions have
been constructed in all four frequencies using phase referencing. A method for
measuring the frequency-dependent shift of the position of the VLBI core by
applying relative astrometry to observations of close triplets of radio sources
has been developed. The fundamental possibility of detecting core shifts in
ultra-compact sources for which traditional methods based on the achromatic
positions of optically thin regions of the jet are not suitable is
demonstrated. The conditions for successful measurement of this shift are
discussed; these are determined by the closeness of the calibrator used, the
effective resolution of the system, the quality of the filling of the $uv$
plane, the relative orientations of the jets in the triplets, and the
brightnesses of the sources.
