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Vol 213, No 12 (2022)
- Year: 2022
- Articles: 7
- URL: https://journal-vniispk.ru/0368-8666/issue/view/7496
Controllability of difference approximation for a control system with continuous time
Abstract
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.
Matematicheskii Sbornik. 2022;213(12):3-30
3-30
Realization of geodesic flows with a linear first integral by billiards with slipping
Abstract
An arbitrary geodesic flow on the projective plane or Klein bottle with an additional, linear in the momentum, first integral is modelled using billiards with slipping on table complexes. The requisite table of a circular topological billiard with slipping is constructed algorithmically. Furthermore, linear integrals of geodesic flows can be reduced to the same canonical integral of a circular planar billiard. Bibliography: 36 titles.
Matematicheskii Sbornik. 2022;213(12):31-52
31-52
A circle criterion for a generalized cross graph in terms of minimal excluded minors
Abstract
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.
Matematicheskii Sbornik. 2022;213(12):53-67
53-67
Hodge level of weighted complete intersections of general type
Abstract
We show that smooth varieties of general type that are well-formed weighted complete intersections of Cartier divisors have the maximal Hodge level, that is, their rightmost middle Hodge numbers do not vanish. We show that this does not hold in the quasi-smooth case.Bibliography: 23 titles.
Matematicheskii Sbornik. 2022;213(12):68-85
68-85
86-108
The Hartogs extension phenomenon in almost homogeneous algebraic varieties
Abstract
We study the Hartogs extension phenomenon in noncompact almost homogeneous algebraic varieties, and we prove a cohomological and a weight criterion for the Hartogs phenomenon. In the case of spherical varieties we prove a criterion for the Hartogs phenomenon in terms of coloured fans.Bibliography: 28 titles.
Matematicheskii Sbornik. 2022;213(12):109-136
109-136
Convergence criterion for quantum relative entropy and its use
Abstract
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.
Matematicheskii Sbornik. 2022;213(12):137-174
137-174