Beta granules isolated from rat islets of Langerhans and subjected only to phosphotungstic acid had, in negatively stained images, a 50-A periodicity. This periodicity was also observed in thin-section profiles of beta granules in intact cells. In shadowed preparations, the granules were spherical in shape and had irregular edges and surface structure. The presence of such a periodicity in the ...

In the context of a distributive lattice we a) specify the sort of mappings that could be generally called ‘negations’ and b) study their behavior under iteration. We show that there are periodic and nonperiodic ones. Natural periodic negations exist with periods 2, 3 and 4 and pace 2, as well as natural non-periodic ones, arising from the interaction of interior and quasi interior mappings wit...

Many phenomena exhibit great regularity without being periodic. This is modeled using the notion of \pseudo-periodic" functions and the related \ -norm", which allow complex repetitive phenomena to be represented as a periodic process plus a set of parameters that de ne the deviations of the process from true periodicity. Applications to sunspot data and to heartbeat analysis explore practical ...

There has been experimental evidence pointing to at least two pitch mechanisms, the first involving low-order harmonics that are resolved along the basilar membrane, and the second a periodicity mechanism that depends only on the repetition rate of the time waveform on the basilar membrane. If this time waveform is derived from repeated bursts of sinusoidal tone, the second mechanism might be t...

In this paper we characterize the existence of periodic points of odd period greater than one for unimodal mappings of an interval onto itself. The interesting juxtaposition of this condition with the occurrence in inverse limits of the well-known Brouwer-Janiszewski-Knaster continuum is explored. Also obtained is a characterization of indecomposability of certain inverse limits using a single ...

The Bott periodicity theorem is of fundamental importance in many areas of mathematics, from algebraic topology to functional analysis. It appears unexpectedly in different guises and I would like to explain some of these as well as the influence it has had on the development of different fields. I will concentrate on two roles that periodicity plays. First, periodicity allows one to deloop cla...

The scope of the paper is the analysis of the impact of flow reversal on the dynamics of cascades of reactors (Fig.1). Periodic and chaotic oscillations occur in the analyzed system. There is a dependence between the oscillation period of the state variable of the system without flow reversal and the recurrence period of windows of chaos in the steady-state diagram of the system with flow rever...

We introduce a topology T on the space U of uniformly discrete subsets of the Euclidean space. Assume that S in U admits a unique autocorrelation measure. The diffraction measure of S is purely atomic if and only if S is almost periodic in (U,T ). This result relates idealized quasicrystals to almost periodicity. In the context of ergodic point processes, the autocorrelation measure is known to...

We consider the complexity of bi-in,nite words in one and two dimensions. A result of Morse and Hedlund in one dimension states that if the complexity, p (n), of a word satis,es p (n)6 n for some n, then the word is periodic. The corresponding question in two dimensions (whether p (m; n)6mn implies that is periodic) is known as the Nivat conjecture. In this paper, we strengthen the one-dimensio...

We explore a novel mechanism for control of periodicity in persistent current in a twisted normal metal loop threaded by a magnetic flux φ. A simple tight-binding model is used to describe the system. Quite interestingly we see that, depending on the number of twist p, the persistent current exhibits φ0/p (φ0 = ch/e, the elementary flux-quantum) periodicity. Such fractional periodicity provides...