Recently, in connection with C*-algebra theory, the first author and Danilo Royer introduced ultragraph shift spaces. In this paper we define a family of metrics for the topology in such spaces, and use these metrics to study the existence of chaos in the shift. In particular we characterize all ultragraph shift spaces that have Li-Yorke chaos (an uncountable scrambled set), and prove that such property implies the existence of a perfect and scrambled set in the ultragraph shift space. Furthermore, this scrambled set can be chosen compact, what is not the case for a labelled edge shift (with the product topology) of an infinite graph.MSC 2010: 37B10, 37B20, 37D40, 54H20,We begin with some standard definitions regarding ultragraphs, as introduced in [16] and [23]. After this we recall the definition of an ultragraph shift space X, as given in [8], and then define a family of metrics for the topology in X.
BackgroundDefinition 2.1. An ultragraph is a quadruple G = (G 0 , G 1 , r, s) consisting of two countable sets G 0 , G 1 , a map s : G 1 → G 0 , and a map r : G 1 → P (G 0 ) \ {∅}, where P (G 0 ) stands for the power set of G 0 .
Motivated by C*-algebra theory, ultragraph edge shift spaces generalize shifts of finite type to the infinite alphabet case. In this paper we study several notions of chaos for ultragraph shift spaces. More specifically, we show that Li-Yorke, Devaney and distributional chaos are equivalent conditions for ultragraph shift spaces, and characterize this condition in terms of a combinatorial property of the underlying ultragraph. Furthermore, we prove that such properties imply the existence of a compact, perfect set which is distributionally scrambled of type 1 in the ultragraph shift space (a result that is not known for a labelled edge shift (with the product topology) of an infinite graph).MSC 2010: 37B10, 37B20, 37D40, 54H20,
Logging companies are extremely important in the economy of the country, but the large number of occupational accidents is of concern in this sector. It is therefore essential to act preventively in the cause of these accidents by identifying and controlling hazards. Thus, the objective of this work was to elaborate an Occupational Health and Safety Risk Matrix in a logging plant in Criciúma - SC. To this end, the applied matrix is based on the requirements set forth in BS OHSAS 18001: 2007. As a result it was observed that the greatest risk is incorrect posture and intense physical effort, as well as noise and projection of wood residues in the eyes and skin. It was inferred that with the matrix it was possible to identify the points in which a company should seek quick solutions to minimize the risks to which its employees are subjected daily.
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