Vol 213, No 12 (2022)

For a control system with continuous time a discrete control system approximating it is constructed and shown to be locally controllable with respect to a trajectory admissible for the continuous system in question. Examples illustrating this result are given. Bibliography: 10 titles.

Geelen and Oum described classes of minimal excluded pivot-minors for a simple graph to be a circle graphand for a delta-matroid to be Eulerian. Pivot-equivalence classes of circle simple graphs and delta-matroids arise in the investigation of Eulerian cycles on cross graphs (4-valent graphs with cross structure). The results established by Geelen and Oum rely on some lemmas in their work, which are shown below to be not quite correct.We consider generalized cross graphs, which arise in the description of rotating circuits on cross graphs. For such graphs we derive a circle criterion: we reproduce and augment the arguments due to Geelen and Oum, and we improve some incorrectly formulated statements. As a result, we obtain the same list of 166 inequivalent graphs, the minimal excluded minors for a generalized cross graph to be a circle graph.Bibliography: 14 titles.

We prove the Jordan property for groups of bimeromorphic self-maps of three-dimensional compact Kähler varieties of nonnegative Kodaira dimension and positive irregularity.Bibliography: 32 titles.

A criterion and necessary conditions for the convergence (local continuity) of quantum relative entropy are obtained. Some applications of these results are considered. In particular, the preservation of the local continuity of quantum relative entropy under completely positive linear maps is established.Bibliography: 29 titles.