@article{Popova_Strilets_2021, title={ Criteria for the existence of systems of subspaces related to a certain class of unicyclic graphs}, volume={73}, url={https://umj.imath.kiev.ua/index.php/umj/article/view/6354}, DOI={10.37863/umzh.v73i4.6354}, abstractNote={<p>UDC 512.552.4<br>We study the configurations of subspaces of a Hilbert space associated with a unicyclic graph, which is a cycle of length $m\geqslant 3$ and has, at each vertex of the cycle, a chains of length $s\geqslant 1$ glued to the vertex. <br>There is a one-to-one correspondence between the vertices and subspaces. <br>If an edge connects two vertices, then the angle between subspaces is equal to $\psi\in(0;\pi/2),$ otherwise the subspaces are orthogonal. <br>Applying the theorem on reduction of unicyclic graph, we prove that nonzero configurations exist if and only if $\cos\psi\in(0;\tau_{m,s}].$ <br>We obtain formulas for $\tau_{m,s}$ and show that~$\bigcap\limits_{m,s}(0;\tau_{m,s}] = (0;2/5].$</p&gt;}, number={4}, journal={Ukrains’kyi Matematychnyi Zhurnal}, author={Popova, N. D. and Strilets, O. V.}, year={2021}, month={Apr.}, pages={556 - 565} }