The general idea in this paper is to study curves of the parametric equations where the parameter varies in a so-called time scale, which may be an arbitrary closed subset of the set of all real numbers. We introduce ...The general idea in this paper is to study curves of the parametric equations where the parameter varies in a so-called time scale, which may be an arbitrary closed subset of the set of all real numbers. We introduce the directional derivative according to the vector fields.展开更多
This article discusses the shapes of a class of regular curves defined by hyperbolic functions.We first make a preliminary judgment using its torsion and then get more precise descriptions using its curvature and alge...This article discusses the shapes of a class of regular curves defined by hyperbolic functions.We first make a preliminary judgment using its torsion and then get more precise descriptions using its curvature and algebraic invariants.In addition,we study the shape of the generalization of the curve.展开更多
Let X be a regular curve and n be a positive integer such that for every nonempty open set U⊂X,there is a nonempty connected open set V⊂U with the cardinality|∂_(X)(V)|≤n.We show that if X admits a sensitive action o...Let X be a regular curve and n be a positive integer such that for every nonempty open set U⊂X,there is a nonempty connected open set V⊂U with the cardinality|∂_(X)(V)|≤n.We show that if X admits a sensitive action of a group G,then G contains a free subsemigroup and the action has positive geometric entropy.As a corollary,X admits no sensitive nilpotent group action.展开更多
文摘The general idea in this paper is to study curves of the parametric equations where the parameter varies in a so-called time scale, which may be an arbitrary closed subset of the set of all real numbers. We introduce the directional derivative according to the vector fields.
基金Supported by the Curriculum Ideological and Political Teaching Research Project of Huzhou University (JGSZ202323)。
文摘This article discusses the shapes of a class of regular curves defined by hyperbolic functions.We first make a preliminary judgment using its torsion and then get more precise descriptions using its curvature and algebraic invariants.In addition,we study the shape of the generalization of the curve.
基金Supported by NSFC(Grant Nos.11771318 and 11790274)。
文摘Let X be a regular curve and n be a positive integer such that for every nonempty open set U⊂X,there is a nonempty connected open set V⊂U with the cardinality|∂_(X)(V)|≤n.We show that if X admits a sensitive action of a group G,then G contains a free subsemigroup and the action has positive geometric entropy.As a corollary,X admits no sensitive nilpotent group action.
