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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...
Autores principales: | , |
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Formato: | Online Artículo Texto |
Lenguaje: | English |
Publicado: |
2020
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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. |
format | Online Article Text |
id | pubmed-7274743 |
institution | National Center for Biotechnology Information |
language | English |
publishDate | 2020 |
record_format | MEDLINE/PubMed |
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 |
work_keys_str_mv | AT zamecnikovahana nonlocallaplaceoperatorinaspacewiththefuzzypartition AT perfilievairina nonlocallaplaceoperatorinaspacewiththefuzzypartition |