Let φ be a one-dimensional surjective cellular automaton map. We prove that if φ is a closing map, then the configurations which are both spatially and temporally periodic are dense. (If φ is not a closing map, then we do not know whether the temporally periodic configurations must be dense.) The results are special cases of results for shifts of finite type, and the proofs use symbolic dynamic...

Let X denote a locally compact metric space and φ : X → X be a continuous map. In the 1970s L. Zadeh presented an extension principle, helping us to fuzzify the dynamical system (X, φ), i.e., to obtain a map Φ for the space of fuzzy sets on X. We extend an idea mentioned in [P. Diamond, A. Pokrovskii, Chaos, entropy and a generalized extension principle, Fuzzy Sets and Systems 61 (1994)] and we...

Correspondence: [email protected]. edu.tw Department of Applied Mathematics, National Hsinchu University of Education, No. 521, Nanda Rd., Hsinchu City 300, Taiwan Abstract In this article, we introduce the notions of cyclic weaker φ ○ -contractions and cyclic weaker (φ, )-contractions in complete metric spaces and prove two theorems which assure the existence and uniqueness of a fixed point for ...

Let Φ be a trace-preserving, positivity-preserving linear map on the algebra of complex 2 × 2 matrices, and let Ω be any finite-dimensional completely positive map. For p = 2 and p ≥ 4, we prove that the maximal p-norm of the product map Φ⊗Ω is the product of the maximal p-norms of Φ and Ω. Restricting Φ to the class of completely positive maps, this settles the multiplicativity question for al...

We investigate the interrelationships between the dynamical properties of commuting continuous maps of a compact metric space. Let X be a compact metric space. First we show the following. If τ : X → X is an expansive onto continuous map with the pseudo-orbit tracing property (POTP) and if there is a topologically mixing continuous map φ : X → X with τφ = φτ , then τ is topologically mixing. If...

Weinberger in 1973 has shown that under the Generalized Riemann Hypothesis for Dedekind zeta functions, an algebraic number field with infinite unit group is Euclidean if and only if it is a principal ideal domain. Using a method recently introduced by us, we give two examples of cubic fields which are Euclidean but not norm–Euclidean. Let R be the ring of integers of an algebraic number field ...

Kluwer Academic Publishers 2000 Homological Perturbation Theory – A theory that concerns itself with of a collection of techniques for deriving chain complexes which are both smaller and chain homotopy equivalent to a given chain complex (cf. also Complex (in homological algebra)). It is motivated by the desire to find effective algorithms in homological algebra. The cornerstone of the theory i...

in this paper, a concept of generalized weakly contraction mappings in partially ordered fuzzy metric spaces is introduced and  coincidence point  theorems on partially ordered fuzzy metric spaces are proved. also, as the corollary of these theorems, some common fixed point theorems on partially ordered fuzzy metric spaces are presented.