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Nonlocal Laplace Operator in a Space with the Fuzzy Partition

Differential operators play an important role in the mathematical modeling of dynamic processes and the analysis of various structures. However, there are certain limitations in their use. To remove them, nonlocal differential operators have been proposed. In this work, we focus on nonlocal Laplace...

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Autores principales: Zámečníková, Hana, Perfilieva, Irina
Formato: Online Artículo Texto
Lenguaje:English
Publicado: 2020
Materias:
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC7274743/
http://dx.doi.org/10.1007/978-3-030-50153-2_22
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author Zámečníková, Hana
Perfilieva, Irina
author_facet Zámečníková, Hana
Perfilieva, Irina
author_sort Zámečníková, Hana
collection PubMed
description Differential operators play an important role in the mathematical modeling of dynamic processes and the analysis of various structures. However, there are certain limitations in their use. To remove them, nonlocal differential operators have been proposed. In this work, we focus on nonlocal Laplace operator, which has become increasingly useful in image processing. We introduce the representation of F-transform based Laplace operator in a space with a fuzzy partition. Many useful properties of this operator are proposed and their proofs are also included.
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spelling pubmed-72747432020-06-08 Nonlocal Laplace Operator in a Space with the Fuzzy Partition Zámečníková, Hana Perfilieva, Irina Information Processing and Management of Uncertainty in Knowledge-Based Systems Article Differential operators play an important role in the mathematical modeling of dynamic processes and the analysis of various structures. However, there are certain limitations in their use. To remove them, nonlocal differential operators have been proposed. In this work, we focus on nonlocal Laplace operator, which has become increasingly useful in image processing. We introduce the representation of F-transform based Laplace operator in a space with a fuzzy partition. Many useful properties of this operator are proposed and their proofs are also included. 2020-05-16 /pmc/articles/PMC7274743/ http://dx.doi.org/10.1007/978-3-030-50153-2_22 Text en © Springer Nature Switzerland AG 2020 This article is made available via the PMC Open Access Subset for unrestricted research re-use and secondary analysis in any form or by any means with acknowledgement of the original source. These permissions are granted for the duration of the World Health Organization (WHO) declaration of COVID-19 as a global pandemic.
spellingShingle Article
Zámečníková, Hana
Perfilieva, Irina
Nonlocal Laplace Operator in a Space with the Fuzzy Partition
title Nonlocal Laplace Operator in a Space with the Fuzzy Partition
title_full Nonlocal Laplace Operator in a Space with the Fuzzy Partition
title_fullStr Nonlocal Laplace Operator in a Space with the Fuzzy Partition
title_full_unstemmed Nonlocal Laplace Operator in a Space with the Fuzzy Partition
title_short Nonlocal Laplace Operator in a Space with the Fuzzy Partition
title_sort nonlocal laplace operator in a space with the fuzzy partition
topic Article
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC7274743/
http://dx.doi.org/10.1007/978-3-030-50153-2_22
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