Universal size properties of "star-ring" polymer structure in disordered environment

We consider the complex polymer system, consisting of ring polymer connected to the $f_1$-branched star-like structure, in good solvent in presence of structural inhomogeneities. We assume, that structural defects are correlated at large distances $x$ according to a power law $~x^{-a}$. Applying the direct polymer renormalization approach, we evaluate the universal size characteristics such as the ratio of the radii of gyration of star-ring and star topologies, and compare the effective sizes of single branches in complex structures and isolated polymers of the same total molecular weight. The non-trivial impact of disorder on these quantities is analyzed.