We consider the range of possible dynamics cellular automata (CA) on two-sided beta-shifts [Formula: see text] and its relation to direct topological factorizations. show that any reversible CA has an almost equicontinuous direction whenever is not sofic. This corollary non-sofic are topologically prime, i.e. they conjugate factorizations two nontrivial subshifts text]. also give a simple crite...

in this note we first redefine the notion of a fuzzy hypervectorspace (see [1]) and then introduce some further concepts of fuzzy hypervectorspaces, such as fuzzy convex and balance fuzzy subsets in fuzzy hypervectorspaces over valued fields. finally, we briefly discuss on the convex (balanced)hull of a given fuzzy set of a hypervector space.

‎in this paper, a new class of fuzzy sets called fuzzy strongly ${{g}^{*}}$-closed sets is introduced and its properties are investigated. moreover, we study some more properties of this type of closed spaces.

We consider a class of fragmentation equations in which the distribution of daughter particles formed when a parent particle fragments is governed by a homogeneous function. A systematic procedure is presented for constructing a space of distributions in which initial-value problems involving singular initial conditions can be analysed. This procedure makes use of results on sun dual semigroups...

for all k. This shows that the sequence of functions is uniformly equicontinuous. Let now t ∈ R and assume that the sequence (|fk(t)|) is unbounded. Then it follows from the estimate that the sequence (min[t−1,t+1] |fk|) is unbounded and therefore also that (‖fk‖L2) is unbounded, contradiction. We conclude the the sequence ‖fk(t)‖ is bounded, for every t ∈ R. Let now T > 0. Then it follows by A...

We consider flows (X,T), given by actions (t,x)→tx, on a compact metric space X with discrete T as an acting group. study new class of - the Strongly Rigid (SR) flows, that are properly contained in distal (D) and contain all equicontinuous (EQ) flows. Thus, EQflows⫋SRflows⫋Dflows. The concepts equicontinuity, strong rigidity distality coincide for induced flow (2X,T). observe strongly rigid (X...