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.
THE CHAIN PROPERTIES AND LI-YORKE SENSITIVITY OF ZADEH'S EXTENSION ON THE SPACE OF UPPER SEMI-CONTINUOUS FUZZY SETS
Some characterizations on the chain recurrence, chain transitivity, chain mixing property,shadowing and $h$-shadowing for Zadeh's extension are obtained. Besides, it is provedthat a dynamical system is spatiotemporally chaotic provided that the Zadeh's extensionis Li-Yorke sensitive.
Ultrastructural observations of the spermiogenesis in the Parotoplaninae (Plathelminthes, Proseriata) with special reference to a striated appendage of the intercentriolar body
SummaryThe spermiogenesis of three species of the Parotoplaninae (Otoplanidae, Proseriata) is described based on electron-microscopical observations. Special reference is given to organelles which do not persist in mature male gametes. One of these organelles is a striated appendage of the intercentriolar body. This differentiation has not been reported from any other plathelminth taxa up to now. The striated appendage, which may serve as a strengthening element, is hypothesized to be an autapomorphic feature of the Parotoplaninae.