Sturmian words are balanced, almost periodic, self-similar and hierarchical infinite sequences that have been studied in music theory in connection with diatonic scale theory and related subjects.[3][5] Carey and Camplitt 1996 give a brief but suggestive rhythmic example in which these properties are made manifest in a particularly visceral manner. The present paper expands upon this example, c...

A sequence {an} in a group G is a T -sequence if there is a Hausdorff group topology τ on G such that an τ −→ 0. In this paper, we provide several sufficient conditions for a sequence in an abelian group to be a T -sequence, and investigate special sequences in the Prüfer groups Z(p∞). We show that for p 6= 2, there is a Hausdorff group topology τ on Z(p∞) that is determined by a T -sequence, w...

Let G(x) = [ eIm 0 c−1e−iνx + c0 + c1e e−iλxIm ] , where cj ∈ Cm×m, α, ν > 0 and α+ ν = λ. For rational α/ν such matrices G are periodic, and their Wiener-Hopf factorization with respect to the real line R always exists and can be constructed explicitly. For irrational α/ν, a certain modification (called an almost periodic factorization) can be considered instead. The case of invertible c0 and ...

We introduce the Fourier-Stieltjes algebra in Rn which we denote by FS(Rn). It is a subalgebra of the algebra of bounded uniformly continuous functions in Rn, BUC(Rn), strictly containing the almost periodic functions, whose elements are invariant by translations and possess a mean-value. Thus, it is a so called algebra with mean value, a concept introduced by Zhikov and Krivenko (1986). Namely...

We study definably amenable groups in NIP theories, focusing on the problem raised in [10] of whether weak generic types coincide with almost periodic types, equivalently whether the union of minimal subflows of a suitable type space is closed. We give fairly definitive results in the o-minimal context, including a counterexample.

Let (Rn(x))n∈N0 be an orthogonal sequence inducing a polynomial hypergroup on N0. The basic facts on polynomial hypergroups and their characters can be found in the monograph [1] or in the papers [6, 7]. A recent review is [8]. The Banach space of almost periodic functions on hypergroups is introduced and studied by the author in [5]. Weakly almost periodic functions are the topic of [12]. It i...

The paper is a survey of notions and results related to classical and new generalizations of the notion of a periodic sequence. The topics related to almost periodicity in combinatorics on words, symbolic dynamics, expressibility in logical theories, algorithmic computability, Kolmogorov complexity, number theory, are discussed.

We characterize equicontinuous Delone dynamical systems as those coming from Delone sets with strongly almost periodic Dirac combs. Within the class of systems with finite local complexity the only equicontinuous systems are then shown to be the crystalline ones. On the other hand, within the class without finite local complexity, we exhibit examples of equicontinuous minimal Delone dynamical s...

This paper is concerned with a class of first order differential iterative equations. Under proper conditions, we employ a novel argument to establish a criterion on the existence of pseudo almost periodic solutions. The obtained result complements with some existing ones. © 2014 Elsevier Ltd. All rights reserved.