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Connectedness of a class of planar self-affine tiles

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Title: Connectedness of a class of planar self-affine tiles
Authors: Deng, Qi-Rong1 qrdeng@fjnu.edu.cn, Lau, Ka-sing2 kslau@math.cuhk.edu.hk
Source: Journal of Mathematical Analysis & Applications. Aug2011, Vol. 380 Issue 2, p493-500. 8p.
Subjects: Set theory, Matrices (Mathematics), Mathematical forms, Number theory, Triangularization (Mathematics), Mathematical analysis
Abstract: Abstract: We consider a class of planar self-affine tiles T that are generated by the lower triangular expanding matrices and the product-form digit sets. We give necessary and sufficient conditions for T to be connected and disk-like. Also for the disconnect case, we give a condition that enumerates the number of connected components of T. [Copyright &y& Elsevier]
Copyright of Journal of Mathematical Analysis & Applications is the property of Academic Press Inc. and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)
Database: Engineering Source
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DbLabel: Engineering Source
An: 60028899
AccessLevel: 6
PubType: Academic Journal
PubTypeId: academicJournal
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  Data: Connectedness of a class of planar self-affine tiles
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  Data: <searchLink fieldCode="AR" term="%22Deng%2C+Qi-Rong%22">Deng, Qi-Rong</searchLink><relatesTo>1</relatesTo><i> qrdeng@fjnu.edu.cn</i><br /><searchLink fieldCode="AR" term="%22Lau%2C+Ka-sing%22">Lau, Ka-sing</searchLink><relatesTo>2</relatesTo><i> kslau@math.cuhk.edu.hk</i>
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  Data: <searchLink fieldCode="JN" term="%22Journal+of+Mathematical+Analysis+%26+Applications%22">Journal of Mathematical Analysis & Applications</searchLink>. Aug2011, Vol. 380 Issue 2, p493-500. 8p.
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  Data: <searchLink fieldCode="DE" term="%22Set+theory%22">Set theory</searchLink><br /><searchLink fieldCode="DE" term="%22Matrices+%28Mathematics%29%22">Matrices (Mathematics)</searchLink><br /><searchLink fieldCode="DE" term="%22Mathematical+forms%22">Mathematical forms</searchLink><br /><searchLink fieldCode="DE" term="%22Number+theory%22">Number theory</searchLink><br /><searchLink fieldCode="DE" term="%22Triangularization+%28Mathematics%29%22">Triangularization (Mathematics)</searchLink><br /><searchLink fieldCode="DE" term="%22Mathematical+analysis%22">Mathematical analysis</searchLink>
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  Label: Abstract
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  Data: Abstract: We consider a class of planar self-affine tiles T that are generated by the lower triangular expanding matrices and the product-form digit sets. We give necessary and sufficient conditions for T to be connected and disk-like. Also for the disconnect case, we give a condition that enumerates the number of connected components of T. [Copyright &y& Elsevier]
– Name: AbstractSuppliedCopyright
  Label:
  Group: Ab
  Data: <i>Copyright of Journal of Mathematical Analysis & Applications is the property of Academic Press Inc. and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.)
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        Value: 10.1016/j.jmaa.2011.03.043
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      – SubjectFull: Mathematical forms
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      – SubjectFull: Triangularization (Mathematics)
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      – TitleFull: Connectedness of a class of planar self-affine tiles
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              Text: Aug2011
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