Topological Entropy and Mixing Invariant Extremal Distributional Chaos
We show that there exists a mixing dynamical system with an invariant, extremal and transitive distributionally scrambled set. Meanwhile, we prove that such a complex dynamical system has zero topological entropy. Finally, we extend the method of constructing the “strong” distributionally scrambled set and show that the new dynamical system has a positive topological entropy.
F-sensitivity and multi-sensitivity of hyperspatial dynamical systems
Abstract Let f be a continuous self-map defined on a compact metric space X and f ¯ be a continuous self-map naturally induced by f on the hyperspace K ( X ) of all nonempty compact subsets of X endowed with a Hausdorff metric. Firstly, a few sufficient and necessary conditions to ensure a dynamical system be F -sensitive or multi-sensitive are obtained. Then, the following results are proved: (1) If ( X , f ) is a non-minimal M-system, then ( K ( X ) , f ¯ ) has F s -sensitive pairs almost everywhere. (2) If ( K ( X ) , f ¯ ) or ( K ( Y ) , g ¯ ) is F -sensitive, then ( K ( X × Y ) , f × g ¯ ) is F -sensitive. (3) ( K ( X × Y ) , f × g ¯ ) is multi-sensitive if and only if ( K ( X ) , f ¯ ) or ( K ( Y ) , g ¯ ) is multi-sensitive, if and only if ( X , f ) or ( Y , g ) is multi-sensitive. Moreover, it is proved that f × g is multi-sensitive if and only if f or g is multi-sensitive. This is a positive answer to a question posed in R. Li and X. Zhou (2013) [18] .
Investigation of scatter radiation of non-circular X-ray scan trajectories
Modern interventional X-ray devices are highly maneuverable and allow complex 3D imaging trajectories. New scan trajectories enable not only optimized object sampling but also introduce new approaches for dynamic 3D imaging. In this paper, we investigated the scatter radiation of two different scan trajectories. The scatter radiation was sampled by a rail setup with dosimeters at defined positions. After data analysis, contour maps were generated which show for four exemplary heights the scatter radiation distribution. The alternative scan trajectory showed smaller dose exposures at heights correlated to upper torso and head areas of a model physician. Keywords—Image acquisition, alternative scan trajectory, circular tomosynthesis, scatter radiation distribution