{"id":"https://openalex.org/W4224224417","doi":"https://doi.org/10.1155/2022/6488709","title":"Mikhlin\u2019s Integral Equation and the Integral Equation with the Generalized Neumann Kernel on Simply Connected Domains","display_name":"Mikhlin\u2019s Integral Equation and the Integral Equation with the Generalized Neumann Kernel on Simply Connected Domains","publication_year":2022,"publication_date":"2022-04-20","ids":{"openalex":"https://openalex.org/W4224224417","doi":"https://doi.org/10.1155/2022/6488709"},"language":"en","primary_location":{"id":"doi:10.1155/2022/6488709","is_oa":true,"landing_page_url":"http://doi.org/10.1155/2022/6488709","pdf_url":"https://downloads.hindawi.com/journals/cmm/2022/6488709.pdf","source":{"id":"https://openalex.org/S4210240678","display_name":"Computational and Mathematical Methods","issn_l":"2577-7408","issn":["2577-7408"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310320595","host_organization_name":"Wiley","host_organization_lineage":["https://openalex.org/P4310320595"],"host_organization_lineage_names":["Wiley"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Computational and Mathematical Methods","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://downloads.hindawi.com/journals/cmm/2022/6488709.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5072345813","display_name":"Samir Naqos","orcid":null},"institutions":[{"id":"https://openalex.org/I4576418","display_name":"University of Technology Malaysia","ror":"https://ror.org/026w31v75","country_code":"MY","type":"education","lineage":["https://openalex.org/I4576418"]}],"countries":["MY"],"is_corresponding":false,"raw_author_name":"Samir Naqos","raw_affiliation_strings":["Department of Mathematical Sciences, Faculty of Science, Universiti Teknologi Malaysia, 81310 Johor Bahru, Johor, Malaysia"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematical Sciences, Faculty of Science, Universiti Teknologi Malaysia, 81310 Johor Bahru, Johor, Malaysia","institution_ids":["https://openalex.org/I4576418"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5002942731","display_name":"Ali H. M. Murid","orcid":"https://orcid.org/0000-0001-9843-228X"},"institutions":[{"id":"https://openalex.org/I4576418","display_name":"University of Technology Malaysia","ror":"https://ror.org/026w31v75","country_code":"MY","type":"education","lineage":["https://openalex.org/I4576418"]}],"countries":["MY"],"is_corresponding":true,"raw_author_name":"Ali H. M. Murid","raw_affiliation_strings":["Department of Mathematical Sciences, Faculty of Science, Universiti Teknologi Malaysia, 81310 Johor Bahru, Johor, Malaysia"],"raw_orcid":"https://orcid.org/0000-0001-9843-228X","affiliations":[{"raw_affiliation_string":"Department of Mathematical Sciences, Faculty of Science, Universiti Teknologi Malaysia, 81310 Johor Bahru, Johor, Malaysia","institution_ids":["https://openalex.org/I4576418"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5051511553","display_name":"Mohamed M. S. Nasser","orcid":"https://orcid.org/0000-0002-2561-0978"},"institutions":[{"id":"https://openalex.org/I60342839","display_name":"Qatar University","ror":"https://ror.org/00yhnba62","country_code":"QA","type":"education","lineage":["https://openalex.org/I60342839"]}],"countries":["QA"],"is_corresponding":false,"raw_author_name":"Mohamed M. S. Nasser","raw_affiliation_strings":["Mathematics Program, Department of Mathematics, Statistics and Physics, College of Arts and Sciences, Qatar University, 2713 Doha, Qatar"],"raw_orcid":"https://orcid.org/0000-0002-2561-0978","affiliations":[{"raw_affiliation_string":"Mathematics Program, Department of Mathematics, Statistics and Physics, College of Arts and Sciences, Qatar University, 2713 Doha, Qatar","institution_ids":["https://openalex.org/I60342839"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5002942731"],"corresponding_institution_ids":["https://openalex.org/I4576418"],"apc_list":{"value":750,"currency":"USD","value_usd":750},"apc_paid":{"value":750,"currency":"USD","value_usd":750},"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.02791896,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"2022","issue":null,"first_page":"1","last_page":"18"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10514","display_name":"Numerical methods in engineering","score":0.9987999796867371,"subfield":{"id":"https://openalex.org/subfields/2211","display_name":"Mechanics of Materials"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T10514","display_name":"Numerical methods in engineering","score":0.9987999796867371,"subfield":{"id":"https://openalex.org/subfields/2211","display_name":"Mechanics of Materials"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11205","display_name":"Numerical methods in inverse problems","score":0.9976999759674072,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10739","display_name":"Electromagnetic Scattering and Analysis","score":0.9965000152587891,"subfield":{"id":"https://openalex.org/subfields/3107","display_name":"Atomic and Molecular Physics, and Optics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7711471319198608},{"id":"https://openalex.org/keywords/integral-equation","display_name":"Integral equation","score":0.7212531566619873},{"id":"https://openalex.org/keywords/laplaces-equation","display_name":"Laplace's equation","score":0.7044471502304077},{"id":"https://openalex.org/keywords/poisson-kernel","display_name":"Poisson kernel","score":0.6787423491477966},{"id":"https://openalex.org/keywords/summation-equation","display_name":"Summation equation","score":0.6463608145713806},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.5819403529167175},{"id":"https://openalex.org/keywords/volterra-integral-equation","display_name":"Volterra integral equation","score":0.5687935948371887},{"id":"https://openalex.org/keywords/integro-differential-equation","display_name":"Integro-differential equation","score":0.5420681834220886},{"id":"https://openalex.org/keywords/kernel","display_name":"Kernel (algebra)","score":0.5121960043907166},{"id":"https://openalex.org/keywords/electric-field-integral-equation","display_name":"Electric-field integral equation","score":0.42317843437194824},{"id":"https://openalex.org/keywords/laplace-transform","display_name":"Laplace transform","score":0.41093379259109497},{"id":"https://openalex.org/keywords/partial-differential-equation","display_name":"Partial differential equation","score":0.37974312901496887},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.16508707404136658},{"id":"https://openalex.org/keywords/riccati-equation","display_name":"Riccati equation","score":0.10999807715415955}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7711471319198608},{"id":"https://openalex.org/C27016315","wikidata":"https://www.wikidata.org/wiki/Q580101","display_name":"Integral equation","level":2,"score":0.7212531566619873},{"id":"https://openalex.org/C70615421","wikidata":"https://www.wikidata.org/wiki/Q339444","display_name":"Laplace's equation","level":3,"score":0.7044471502304077},{"id":"https://openalex.org/C8077415","wikidata":"https://www.wikidata.org/wiki/Q2596534","display_name":"Poisson kernel","level":2,"score":0.6787423491477966},{"id":"https://openalex.org/C143591791","wikidata":"https://www.wikidata.org/wiki/Q7637218","display_name":"Summation equation","level":3,"score":0.6463608145713806},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.5819403529167175},{"id":"https://openalex.org/C21965488","wikidata":"https://www.wikidata.org/wiki/Q2632613","display_name":"Volterra integral equation","level":3,"score":0.5687935948371887},{"id":"https://openalex.org/C70985411","wikidata":"https://www.wikidata.org/wiki/Q2380676","display_name":"Integro-differential equation","level":4,"score":0.5420681834220886},{"id":"https://openalex.org/C74193536","wikidata":"https://www.wikidata.org/wiki/Q574844","display_name":"Kernel (algebra)","level":2,"score":0.5121960043907166},{"id":"https://openalex.org/C3537527","wikidata":"https://www.wikidata.org/wiki/Q5357276","display_name":"Electric-field integral equation","level":3,"score":0.42317843437194824},{"id":"https://openalex.org/C97937538","wikidata":"https://www.wikidata.org/wiki/Q199691","display_name":"Laplace transform","level":2,"score":0.41093379259109497},{"id":"https://openalex.org/C93779851","wikidata":"https://www.wikidata.org/wiki/Q271977","display_name":"Partial differential equation","level":2,"score":0.37974312901496887},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.16508707404136658},{"id":"https://openalex.org/C45473103","wikidata":"https://www.wikidata.org/wiki/Q851503","display_name":"Riccati equation","level":3,"score":0.10999807715415955}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1155/2022/6488709","is_oa":true,"landing_page_url":"http://doi.org/10.1155/2022/6488709","pdf_url":"https://downloads.hindawi.com/journals/cmm/2022/6488709.pdf","source":{"id":"https://openalex.org/S4210240678","display_name":"Computational and Mathematical Methods","issn_l":"2577-7408","issn":["2577-7408"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310320595","host_organization_name":"Wiley","host_organization_lineage":["https://openalex.org/P4310320595"],"host_organization_lineage_names":["Wiley"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Computational and Mathematical Methods","raw_type":"journal-article"},{"id":"pmh:oai:hindawi.com:10.1155/2022/6488709","is_oa":true,"landing_page_url":"https://doi.org/10.1155/2022/6488709","pdf_url":null,"source":{"id":"https://openalex.org/S4306400340","display_name":"Hindawi Journal of Chemistry (Hindawi)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I4210126990","host_organization_name":"Hindawi (United Kingdom)","host_organization_lineage":["https://openalex.org/I4210126990"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Research Article"}],"best_oa_location":{"id":"doi:10.1155/2022/6488709","is_oa":true,"landing_page_url":"http://doi.org/10.1155/2022/6488709","pdf_url":"https://downloads.hindawi.com/journals/cmm/2022/6488709.pdf","source":{"id":"https://openalex.org/S4210240678","display_name":"Computational and Mathematical Methods","issn_l":"2577-7408","issn":["2577-7408"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310320595","host_organization_name":"Wiley","host_organization_lineage":["https://openalex.org/P4310320595"],"host_organization_lineage_names":["Wiley"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Computational and Mathematical Methods","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G6417478499","display_name":null,"funder_award_id":"FRGS/1/2019/STG06/UTM/02/20","funder_id":"https://openalex.org/F4320323300","funder_display_name":"Universiti Teknologi Malaysia"},{"id":"https://openalex.org/G7918313871","display_name":null,"funder_award_id":"FRGS/1/2019/STG06/UTM/02/20","funder_id":"https://openalex.org/F4320321147","funder_display_name":"Ministry of Higher Education"}],"funders":[{"id":"https://openalex.org/F4320321147","display_name":"Ministry of Higher Education","ror":"https://ror.org/0512bh102"},{"id":"https://openalex.org/F4320323300","display_name":"Universiti Teknologi Malaysia","ror":"https://ror.org/026w31v75"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4224224417.pdf","grobid_xml":"https://content.openalex.org/works/W4224224417.grobid-xml"},"referenced_works_count":34,"referenced_works":["https://openalex.org/W149994525","https://openalex.org/W253784358","https://openalex.org/W1603041040","https://openalex.org/W1960199220","https://openalex.org/W1998527589","https://openalex.org/W2000915675","https://openalex.org/W2006069011","https://openalex.org/W2008398217","https://openalex.org/W2013776667","https://openalex.org/W2014208709","https://openalex.org/W2029141900","https://openalex.org/W2066855946","https://openalex.org/W2083216488","https://openalex.org/W2084826328","https://openalex.org/W2086261919","https://openalex.org/W2087058805","https://openalex.org/W2112155935","https://openalex.org/W2117648842","https://openalex.org/W2144243526","https://openalex.org/W2151634502","https://openalex.org/W2152961610","https://openalex.org/W2160829514","https://openalex.org/W2161697123","https://openalex.org/W2349468399","https://openalex.org/W2488815412","https://openalex.org/W2532373555","https://openalex.org/W2743652032","https://openalex.org/W2895666951","https://openalex.org/W3014485743","https://openalex.org/W3015514709","https://openalex.org/W3103628751","https://openalex.org/W4213212409","https://openalex.org/W4247024214","https://openalex.org/W6682299505"],"related_works":["https://openalex.org/W2945803575","https://openalex.org/W4367557662","https://openalex.org/W2118560105","https://openalex.org/W2526252530","https://openalex.org/W2096568474","https://openalex.org/W4240464390","https://openalex.org/W2585034204","https://openalex.org/W2011403244","https://openalex.org/W2946528495","https://openalex.org/W196098719"],"abstract_inverted_index":{"Mikhlin\u2019s":[0],"integral":[1,6,20,30,44,76],"equation":[2,7,21,31,45,96],"is":[3,22,46,56,67,87],"a":[4,47,70],"classical":[5],"for":[8,13,32],"solving":[9,33],"boundary":[10,99],"value":[11],"problems":[12],"Laplace\u2019s":[14,95],"equation.":[15],"The":[16,39,62],"kernel":[17,40],"of":[18,41,49,64],"the":[19,25,34,42,50,58],"known":[23],"as":[24],"Neumann":[26,51,60],"kernel.":[27,61],"Recently,":[28],"an":[29],"Riemann\u2013Hilbert":[35],"problem":[36],"was":[37],"derived.":[38],"new":[43],"generalization":[48],"kernel,":[52],"and":[53,83,107],"hence,":[54],"it":[55],"called":[57],"generalized":[59],"objective":[63],"this":[65],"paper":[66],"to":[68,93],"present":[69],"detailed":[71],"comparison":[72,86],"between":[73],"these":[74],"two":[75],"equations":[77,92],"with":[78,97,105],"emphasis":[79],"on":[80],"their":[81],"similarities":[82],"differences.":[84],"This":[85],"done":[88],"through":[89],"applying":[90],"both":[91],"solve":[94],"Dirichlet":[98],"conditions":[100],"in":[101],"simply":[102],"connected":[103],"domains":[104],"smooth":[106,109],"piecewise":[108],"boundaries.":[110]},"counts_by_year":[],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}
