Bernd Sing

University of the West Indies at Cave Hill, Barbados | UWI · Department of Computer Science, Mathematics and Physics

Modulated crystals and quasicrystals can simultaneously be described as modulated quasicrystals, a class of point sets introduced by de Bruijn in 1987. With appropriate modulation functions, modulated quasicrystals themselves constitute a substantial subclass of strongly almost periodic point measures. We re-analyze these structures using methods f...

The dates of the transition between winter and summer (W2S) and between summer and winter (S2W) regional-scale atmospheric regimes have been defined using daily weather types above and around the Caribbean basin from 1979 to 2017. The uncertainties due to either the use of two different reanalyses (i.e., NCEP-DOE and ERA-Interim) or the parametriza...

A practical model for identification of children at risk of excess energy intake in the developing world – CORRIGENDUM - Pamela S Gaskin, Peter Chami, Justin Ward, Gabriela Goodman, Bernd Sing, Maria D Jackson, Hedy Broome

Modulated crystals and quasicrystals can simultaneously be described as modulated quasicrystals, a class of point sets introduced by de Bruijn in 1987. With appropriate modulation functions, modulated quasicrystals themselves constitute a substantial subclass of strongly almost periodic point measures. We re-analyse these structures using methods f...

Objective We describe diet quality by demographic factors and weight status among Barbadian children and examine associations with excess energy intake (EI). A screening tool for the identification of children at risk of excess EI was developed. Design In a cross-sectional survey, the Diet Quality Index–International (DQI-I) was used to assess die...

We consider the family of integral operators $(K_{\alpha}f)(x)$ from $L^p[0,1]$ to $L^q[0,1]$ given by $$(K_{\alpha}f)(x)=\int_0^1(1-xy)^{\alpha -1}\,f(y)\,\operatorname{d}\!y, \qquad 0<\alpha<1.$$ The main objective is to find upper bounds for the Kolmogorov widths, where the $n$th Kolmogorov width is the infimum of the deviation of $(K_{\alpha}f)...

We perform a survival analysis on the records of the burials at the Westbury Cemetery, Barbados, between 1877 and 1976. The goal of the paper is to observe the stratified life expectancies of persons of particular time appropriate occupations. Comparing different occupations through time, amongst each other and to the general population, enables us...

We investigate polynomials, called m-polynomials, whose generator polynomial has coefficients that can be arranged as a matrix, where q is a positive integer greater than one. Orthogonality relations are established and coefficients are obtained for the expansion of a polynomial in terms of m-polynomials. We conclude this article by an implementati...

This study contrasts the pattern of low-frequency (LF) and high-frequency (HF) climate variability in the eastern Caribbean. A low-pass Butterworth filter is used to study oscillations in rainfall and regional SST on time scales of greater and less than 8 yr in the period 1901–2002. The results show that the southern and northern Antilles are domin...

We propose a two parameter ratio-product-ratio estimator for a finite population mean in a simple random sample without replacement following the methodology in Ray and Sahai (1980), Sahai and Ray (1980), Sahai and Sahai (1985) and Singh and Ruiz Espejo (2003). The bias and mean square error of our proposed estimator are obtained to the first degre...

Our goal in this article is to review the known properties of the mysterious Kolakoski sequence and at the same time look at generalizations of it over arbitrary two letter alphabets. Our primary focus will here be the case where one of the letters is odd while the other is even, since in the other cases the sequences in question can be rewritten a...

In this article we study the common dynamics of two different Pisot substitutions σ 1 and σ 2 having the same incidence matrix. This common dynamics arises in the study of the adic systems associated with the substitutions σ 1 and σ 2. Since the adic systems considered here have geometric realizations given by solutions to graph-directed iterated f...

Monte Carlo (MC) simulation of a model quasicrystal (2D Penrose rhomb tiling) shows that the kinds of local distortions that result from size-effect-like relaxations are in fact very similar to mathematical constructions called deformed model sets. Of particular interest is the fact that these deformed model sets are pure point-diffractive, i.e. th...

Computing modular coincidences can show whether a given substitution system, which is supported on a point lattice in Rd, consists of model sets or not. We prove the computatibility of this problem and determine an upper bound for the number of iterations needed. The main tool is a simple algorithm for computing modular coincidences, which is essen...

We investigate graph-directed iterated function systems in mixed Euclidean and p-adic spaces. Hausdorff measure and Hausdorff dimension in such spaces are defined, and an upper bound for the Hausdorff dimension is obtained. The relation between the Haar measure and the Hausdorff measure is clarified. Finally, we discus an example in ${Bbb R}\times{...

Computing modular coincidences can show whether a given substitution system, which is supported on a point lattice in R^d, consists of model sets or not. We prove the computatibility of this problem and determine an upper bound for the number of iterations needed. The main tool is a simple algorithm for computing modular coincidences, which is esse...

In this article, we show how the mathematical concept of a deformed model set can be used to gain in- sight into the diffraction pattern of quasicrystalline struc- tures. We explain what a deformed model set is, what its characteristic features are and how it relates to certain dis- order phenomena in solids. We then apply this concept to distorted...

This thesis consists (mainly) of three parts: At first, we define Hausdorff measures for product spaces of local fields. We look at iterated function systems on such spaces, the Hausdorff dimension of their attractor is estimated. Afterwards, model sets (respectively cut and project sets) are introduced. For point sets generated by a substitution r...

The diffraction spectra of lattice gas models on ℤd with finite-range ferromagnetic two-body interactions above T c or with certain rates of decay of the potential are considered. We show that these diffraction spectra almost surely exist, are ℤd-periodic and consist of a pure point part and an absolutely continuous part with continuous density.

(Generalized) Kolakoski sequences are built of two symbols – similar to the Fibonacci-chain – and can be constructed by a very simple rule. They are general enough to allow a richness of structures: e.g., some show pure point diffraction spectrum, others diffuse scattering. We will illustrate the methods to classify these sequences and to calculate...

This review revolves around the question which general distribution of scatterers (in a Euclidean space) results in a pure point diffraction spectrum. Firstly, we treat mathematical diffration theory and state conditions under which such a distribution has pure point diffraction. We explain how a cut and project scheme naturally appears in this con...

We consider (generalized) Kolakoski sequences on an alphabet with two even numbers. They can be related to a primitive substitution rule of constant length l. Using this connection, we prove that they have pure point dynamical and pure point diffractive spectrum, where we make use of the strong interplay between these two concepts. Since these sequ...

Unlike the (classical) Kolakoski sequence on the alphabet {1,2}, its analogue on {1,3} can be related to a primitive substitution rule. Using this connection, we prove that the corresponding bi-infinite fixed point is a regular generic model set and thus has a pure point diffraction spectrum. The Kolakoski-(3,1) sequence is then obtained as a defor...

The freezing of argon in silica powder is observed to generate bands of pure solid argon in the same manner as in the phenomenon of ice lens formation in the freezing of moist ground. A first principles dynamical theory describes the mechanism of lens formation by the thermomolecular pressure-driven flow of interfacially melted films at the lens-so...

Frost heave in wet soils and powders is a well known natural occurrence. Frost heave, though, is not an exclusive property of water. A fluid coexisting with its solid phase below its normal freezing point and placed in a temperature gradient will support a thermomolecular pressure difference directed toward lower temperature. We will report on qual...

There is some confusion in the literature what "modulated quasicrystals" are: Some people treat "modulated quasicrystals" and "deformed model sets" as exchangeable termini (compare [6, 9, 5]), others claim that "[. . .] the projection method becomes powerless against incommensurate modulated structures" (e.g., [12, p. 148]). We use a mathematical a...