For any continuous self-map of a compact metric space, we prove saturation distributionally scrambled Mycielski sets under type shadowing and the chain transitivity. This extends result J. Li, S. Tu, Devaney chaos plus implies distributional chaos, Chaos 26 (2016), 093103, 6 pp.

We present a relation between the rotation of chain transitive sets and the rotation shadowing for annulus homeomorphisms isotopic to identity.

We present a terminating tableau calculus for graded hybrid logic with global modalities, reflexivity, transitivity and role hierarchies. Termination of the system is achieved through pattern-based blocking. Previous approaches to related logics all rely on chain-based blocking. Besides being conceptually simple and suitable for efficient implementation, the pattern-based approach gives us a NE...

We study two transitivity properties for group actions on buildings, called Weyl transitivity and strong transitivity. Following hints by Tits, we give examples involving anisotropic algebraic groups to show that strong transitivity is strictly stronger than Weyl transitivity. A surprising feature of the examples is that strong transitivity holds more often than expected.

We discuss the relation between (topological) transitivity and strong transitivity of dynamical systems. We show that a transitive and open self-map of a compact metric space satisfying a certain expanding condition is strongly transitive. We also prove a couple of results for interval maps; for example it is shown that a transitive piecewise monotone interval map is strongly transitive.

b) moderate stochastic transitivity: For a reciprocal fuzzy relation Q : x2 + [O, 11 on a finite set of alternatives X , we introduce the concept of U-transitivity which is based upon the ordering of the matrix elements qij, qjk and qki of Q for all triples of indices i, j and k. We show that U-transitivity generalizes both stochastic and fuzzy transitivity. The U-transitivity of the secalled u...