B E R N D    S I N G 

Senior Lecturer in Mathematics
University of the West Indies, Cave Hill, Barbados



All papers listed below can be downloaded as pdf files and/or gzipped postscript files.
Mathematical Diffraction Theory

J.-Y. Lee, D. Lenz, C. Richard, B. Sing, and N. Strungaru
Modulated crystals and almost periodic measures
Letters in Mathematical Physics 110, 3435-3472 (2020); arXiv:1907.07017
DOI: 10.1007/s11005-020-01337-2

B. Sing
Modulated Quasicrystals [pdf]
Z. Kristallographie 223, No. 11-12, 765-769 (2008) [Proceedings of the ICQ-10]
DOI: 10.1524/zkri.2008.1073
Poster prepared for the ICQ-10 in Zürich (DIN A4) [pdf]

The following article appeared in Z. Kristallographie and may be found here.
B. Sing and T.R. Welberry
Deformed model sets and distorted Penrose tilings [pdf]
Z. Kristallographie 221, No. 9, 621-634 (2006); mp_arc/06-199
DOI: 10.1524/zkri.2006.221.9.621
Poster prepared for the SET for BRITAIN Annual Reception at the House of Commons on 19 March 2007 (DIN A4) [ps.gz]

Author Posting. (c) Taylor & Francis, 2007. This is the author's version of the work. It is posted here by permission of Taylor & Francis for personal use, not for redistribution. The definitive version was published in Philosophical Magazine.
T.R. Welberry and B. Sing
Deformed Penrose tilings [pdf]
Philosophical Magazine 87, No. 18-21, 2877-2886 (2007) [Proceedings of the Aperiodic 2006]
DOI: 10.1080/14786430701364978

M. Baake and B. Sing
Diffraction spectrum of lattice gas models above Tc [ps.gz]
Lett. Math. Phys. 68, No. 3, 165-173 (2004); math-ph/0405064
DOI: 10.1023/B:MATH.0000045555.93532.6d
Poster prepared for the Workshop Mathematics and Physics of Disordered Systems in Oberwolfach (DIN A4) [ps.gz]
Presentation [ps.gz] at the Jahrestagung der DMV, Heidelberg, 14.9.04

M. Baake, R.V. Moody, C. Richard, and B. Sing
Which distributions of matter diffract? - Some answers [ps.gz]
in: H.-R. Trebin (ed.)
Quasicrystals: Structure and Physical Properties
Wiley-VCH, Berlin (2003), pp. 188-207; math-ph/0301019
DOI: 10.1002/3527606572.ch2
ISBN-13: 978-3-527-40399-8 (Online ISBN: 978-3-527-60657-3)
Presentation [pdf] at the Joint Colloquium GDR-CINQ and SPQK, Nancy, 27.5.03.

Pisot Substitutions & Cut and Project Schemes

PhD-thesis entitled Pisot Substitutions and Beyond is available on BieSOn:
If you cite this document, please include the above URN (in URL representation).

B. Sing
Non-unimodularity [pdf]
Actes des rencontres du CIRM 1, No. 1, 69-74 (2009).
DOI: 10.5802/acirm.12
Presentation [pdf] at the Workshop Numération: Mathématiques et Informatique, Luminy, 24.3.09.

B. Sing and V. Sirvent
Geometry of the common dynamics of flipped Pisot substitutions [pdf]
Monatshefte für Mathematik 155, No. 3-4, 431-448 (2008).
DOI: 10.1007/s00605-008-0004-z

Extended abstract [pdf] for the presentation given at the Mini-Workshop The Pisot Conjecture - From Substitution Dynamical Systems to Rauzy Fractals and Meyer Sets, Oberwolfach, 3.3.09.

Presentation [pdf] at the Workshop Computational and Combinatorial Aspects of Tilings, London, 30.7.08.

Presentation [pdf] at the Workshop Aspects of Aperiodic Order, Bielefeld, 3.7.08.

Presentation [pdf] at the Workshop Ordre apériodique: noveaux liens et anciens problèmes revisités, Luminy, 11.9.07.
Handout [pdf] distributed during the talk.

Presentation [pdf] at the Workshop Generalized substitutions, tilings and numeration, Ile de Porquerolles, 11.6.07.

Presentation [pdf] at the AMS 2007 Spring Southeastern Section Meeting, Davidson, NC, 4.3.07.

Presentation [pdf] at the Applied Mathematics Seminar, The Open University, Milton Keynes, 9.5.06.

Presentation [pdf] at the Workshop Generalized substitutions, tilings and numeration, Marseille, 7.3.06.

Presentation [pdf] at the Forschungsseminar Mathematische Physik, TU Chemnitz, 7.6.05.

Presentation [pdf] at the MASCOS Workshop on Algebraic Dynamics, Sydney, 15.2.05.

also see the article "Kolakoski-(3,1) is a (deformed) model set" (with M. Baake) below

Visible Point Sets

Presentation [pdf] at the Mathematical Physics Seminar, University of Bristol, 24.10.08.

Presentation [pdf] at the Oberseminar Geometrie und Topologie, TU Dortmund, 30.6.08.

Presentation [pdf] at the 2007 British Combinatorial Conference, Reading, 12.7.07.

Lattice Substitution Systems

D. Frettlöh and B. Sing
Computing modular coincidences for substitution tilings and point sets [ps.gz] [pdf]
Discrete Comput. Geom. 37, No.3, 381-401 (2007); math.MG/0601067
DOI: 10.1007/s00454-006-1280-9

Iterated Function Systems & Hausdorff Measures

B. Sing
Iterated function systems in mixed Euclidean and p-adic spaces [ps.gz] [pdf]
in: M.M. Novak (ed.)
Complexus Mundi - Emergent Patterns in Nature
World Scientific, Singapore (2006), pp. 267-276; math.MG/0610687
DOI: 10.1142/9789812774217_0024
ISBN-13: 978-981-256-666-9
Presentation [pdf] at the Conference Fractal 2006, Wien, 12.2.06.


B. Sing
More Kolakoski sequences [pdf]
INTEGERS 11B, A14, 17 pages (2011) [Proceedings of the Leiden Numeration Conference 2010]; arXiv:1009.4061

B. Sing
Kolakoski sequences - an example of aperiodic order [ps.gz]
J. Non-Cryst. Solids 334-335, 100-104 (2004) [Proceedings of the ICQ-8]
DOI: 10.1016/j.jnoncrysol.2003.11.021
Poster prepared for the ICQ-8 (DIN A4) [ps.gz]

M. Baake and B. Sing
Kolakoski-(3,1) is a (deformed) model set [ps.gz] [pdf]
Canad. Math. Bull. 47, No. 2, 168-190 (2004); math.MG/0206098
DOI: 10.4153/CMB-2004-018-6

The following article appeared in J. Math. Phys. and may be found here.
B. Sing
Kolakoski-(2m,2n) are limit-periodic model sets [ps.gz] [pdf]
J. Math. Phys. 44, No. 2, 899-912 (2003); math-ph/0207037
DOI: 10.1063/1.1521239
© (2003) American Institute of Physics.
This article may be downloaded for personal use only.
Any other use requires prior permission of the author and the American Institute of Physics.

Diploma-thesis entitled Spektrale Eigenschaften der Kolakoski-Sequenzen is available as [ps.gz] and as [pdf.gz]


Duaine Lewis and Bernd Sing
An upper bound on the Kolmogorov widths of a certain family of integral operators [pdf]
Journal of Approximation Theory 240, 71-95 (2019); arXiv:1612.03183;
DOI: 10.1016/j.jat.2018.09.012

P.S. Chami, B. Sing and N. Sookoo
Generalizing Krawtchouk polynomials using Hadamard matrices [pdf]
ISRN Applied Mathematics 2014, Article ID 498135, 8 pages (2014); arXiv:1307.5777
DOI: 10.1155/2014/498135

Estimator Theory

P.S. Chami, B. Sing and D. Thomas
A two-parameter ratio-product-ratio estimator using auxiliary information [pdf]
ISRN Probability and Statistics 2012, Article ID 103860, 15 pages (2012); arXiv:1202.2395
DOI: 10.5402/2012/103860
Poster prepared for the Departmental Research Day 2012 [pdf]


I. Gouirand, V. Moron, and B. Sing
Seasonal atmospheric transitions in the Caribbean basin and Central America
Climate Dynamics 55, 1809-1828 (2020)
DOI: 10.1007/s00382-020-05356-6

I. Gouirand, M.R. Jury, and B. Sing
An analysis of low- and high-frequency summer climate variability around the Caribbean Antilles [pdf]
J. Climate 25, No. 11, 3942-3952 (2012)
DOI: 10.1175/JCLI-D-11-00269.1

Frost Heave

D-M. Zhu, O.E. Vilches, J.G. Dash, B. Sing, and J.S. Wettlaufer
Frost heave in argon [ps.gz]
Phys. Rev. Lett. 85, No. 23, 4908-4911 (2000)
DOI: 10.1103/PhysRevLett.85.4908

Public Health

P.S. Gaskin, P. Chami, J.A. Ward, G. Goodman, B. Sing, M.D. Jackson, and H. Broome
A practical model for identification of children at risk of excess energy intake in the developing world
Public Health Nutrition 22, 1979-1989 (2019)
DOI: 10.1017/S1368980019000296


P. Chami, T. Inniss, and B. Sing
Life in Bridgetown, Barbados, according to the Westbury Cemetery records 1877—1976
Economic Quality Control 30, No. 1, 39-47 (2015)
DOI: 10.1515/eqc-2015-6004


© 2004-2021 by Bernd Sing • • last update: 31.10.2021 (10/31/2021)