For any countable group, and also for any locally compact second countable, compactly generated topological group, G, we show the existence of a “universal” hypercyclic (i.e. topologically transitive) representation on a Hilbert space, in the sense that it simultaneously models every possible ergodic probability measure preserving free action of G.

Based on data collected from a middle school, this study investigates how the quantity and quality of technology use aVect student learning outcomes. SpeciWcally, this study examines how technologies are used by students, what technology uses are popular among students, and what technology uses are eVective for increasing student academic achievement. Results suggest that the quantity of techno...

We study the dynamical behaviour of weighted shifts defined on sequence spaces a directed tree. In particular, we characterize their boundedness as well when they are hypercyclic, weakly mixing and mixing.

In an earlier paper we supplied indirect proof of the existence universal possible worlds that have topological property being hypercyclic, which means they can access every world in sequences approach arbitrarily closely to world. That states there are but it does not exhibit such a explicitly. We now explicitly construct two worlds. A continuous constructs with transreal co-ordinates directly...