Browsing by Author "Savchenko, А."
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Item Frechet distance on the set of compact trees(2015) Lozinska, O.; Savchenko, А.; Zarichnyi, M.; Савченко, О. Г.We introduce a counterpart of the Fr echet distance for the rooted trees in a metric space. Some properties and possible generalizations of this distance are discussed.Item FUZZY HYPERSPACE MONAD(2010) Savchenko, А.; Савченко, А.; Савченко, О. Г.The hyperspace of a fuzzy metric space is defined by J. Rodr´ıguez-L´opez and S. Romaguera. In this paper, it is shown that the hyperspace construction determines a functor on the category of fuzzy metric spaces and nonexpanding maps. We also prove that this functor determines a monad on this category and that the G-symmetric power functor can be extended over the Kleisli category of this monad. Доказано, что гиперпространство нечеткого метрического пространства, определеное Родрiгесом-Лопесом и Ромагуэрой определяет функтор на категории нечетких метрических пространств и их нерастягивающих отображений. Этот функтор дополняется до монады, на категорию Клейсли которой продолжается функтор G-симметрической степени.Item Geodesic mappings of compact quasi-Einstein spaces, I(2020) Kiosak, V.; Savchenko, А.; Kovalova, G.; Савченко, О. Г.The paper treats a particular type of pseudo-Riemannian spaces, namely quasi-Einstein spaces with gradient defining vector. These spaces are a generalization of well-known Einstein spaces. There are three types of these spaces that admit locally geodesic mappings. Authors proved a “theorem of disappearance” for compact quasi-Einstein spaces of main type.Item Probability measure monad on the category of fuzzy ultrametric spaces(2011) Savchenko, А.; Zarichnyi, M.; Савченко, О. Г.It is proved that the probability measure functor comprises a monad on the category of fuzzy ultrametric spaces and nonexpanding maps. It is also proved that the G-symmetric power functor admits an extension on the Kleisli category of this monad (i.e. the category of fuzzy ultrametric spaces and nonexpanding measure-valued maps).Item Triples of infinite iterations of hyperspaces of maxнplus compact convex sets(2016) Savchenko, А.; Zarichnyi, M.; Савченко, О. Г.Geometrу of the innite iterated hуperspace of compact max-plus convex sets, their completions and compactications is investigated.