{"id":"https://openalex.org/W3202965095","doi":"https://doi.org/10.3906/elk-2009-21","title":"On the closed-form evaluation of the PO integral using the Radon transform interpretation for linear triangles","display_name":"On the closed-form evaluation of the PO integral using the Radon transform interpretation for linear triangles","publication_year":2021,"publication_date":"2021-01-03","ids":{"openalex":"https://openalex.org/W3202965095","doi":"https://doi.org/10.3906/elk-2009-21","mag":"3202965095"},"language":"en","primary_location":{"id":"doi:10.3906/elk-2009-21","is_oa":true,"landing_page_url":"https://doi.org/10.3906/elk-2009-21","pdf_url":"https://journals.tubitak.gov.tr/cgi/viewcontent.cgi?article=1061&context=elektrik","source":{"id":"https://openalex.org/S32837994","display_name":"TURKISH JOURNAL OF ELECTRICAL ENGINEERING & COMPUTER SCIENCES","issn_l":"1300-0632","issn":["1300-0632","1303-6203"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310318422","host_organization_name":"Scientific and Technological Research Council of Turkey (TUBITAK)","host_organization_lineage":["https://openalex.org/P4310318422"],"host_organization_lineage_names":["Scientific and Technological Research Council of Turkey (TUBITAK)"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"TURKISH JOURNAL OF ELECTRICAL ENGINEERING & COMPUTER SCIENCES","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"diamond","oa_url":"https://journals.tubitak.gov.tr/cgi/viewcontent.cgi?article=1061&context=elektrik","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5000110482","display_name":"Aslihan Aktepe","orcid":"https://orcid.org/0000-0002-6492-6318"},"institutions":[{"id":"https://openalex.org/I109297418","display_name":"Gebze Technical University","ror":"https://ror.org/01sdnnq10","country_code":"TR","type":"education","lineage":["https://openalex.org/I109297418"]}],"countries":["TR"],"is_corresponding":false,"raw_author_name":"Aslihan AKTEPE","raw_affiliation_strings":["Department of Electronics Engineering , Gebze Technical University , Kocaeli , Turkey"],"raw_orcid":"https://orcid.org/0000-0002-6492-6318","affiliations":[{"raw_affiliation_string":"Department of Electronics Engineering , Gebze Technical University , Kocaeli , Turkey","institution_ids":["https://openalex.org/I109297418"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5024127529","display_name":"H. Arda \u00dclk\u00fc","orcid":"https://orcid.org/0000-0003-4682-3902"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"H\u00fcseyin Arda \u00dcLK\u00dc","raw_affiliation_strings":[],"raw_orcid":"https://orcid.org/0000-0003-4682-3902","affiliations":[]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.10652398,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"29","issue":"5","first_page":"2520","last_page":"2528"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11851","display_name":"Electromagnetic Compatibility and Measurements","score":0.9988999962806702,"subfield":{"id":"https://openalex.org/subfields/2208","display_name":"Electrical and Electronic Engineering"},"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/T11851","display_name":"Electromagnetic Compatibility and Measurements","score":0.9988999962806702,"subfield":{"id":"https://openalex.org/subfields/2208","display_name":"Electrical and Electronic Engineering"},"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/T10739","display_name":"Electromagnetic Scattering and Analysis","score":0.9986000061035156,"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"}},{"id":"https://openalex.org/T11263","display_name":"Electromagnetic Simulation and Numerical Methods","score":0.9965999722480774,"subfield":{"id":"https://openalex.org/subfields/2208","display_name":"Electrical and Electronic Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/radon-transform","display_name":"Radon transform","score":0.7729949951171875},{"id":"https://openalex.org/keywords/intersection","display_name":"Intersection (aeronautics)","score":0.7435019016265869},{"id":"https://openalex.org/keywords/interpretation","display_name":"Interpretation (philosophy)","score":0.7132896184921265},{"id":"https://openalex.org/keywords/plane","display_name":"Plane (geometry)","score":0.7023889422416687},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.5655291080474854},{"id":"https://openalex.org/keywords/integral-transform","display_name":"Integral transform","score":0.5619039535522461},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5476812124252319},{"id":"https://openalex.org/keywords/plane-wave","display_name":"Plane wave","score":0.5025670528411865},{"id":"https://openalex.org/keywords/field","display_name":"Field (mathematics)","score":0.48142191767692566},{"id":"https://openalex.org/keywords/domain","display_name":"Domain (mathematical analysis)","score":0.47123679518699646},{"id":"https://openalex.org/keywords/multiple-integral","display_name":"Multiple integral","score":0.4107131361961365},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.39282238483428955},{"id":"https://openalex.org/keywords/optics","display_name":"Optics","score":0.30384334921836853},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.27650773525238037},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.12611347436904907},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.10287880897521973},{"id":"https://openalex.org/keywords/engineering","display_name":"Engineering","score":0.07085344195365906}],"concepts":[{"id":"https://openalex.org/C197231052","wikidata":"https://www.wikidata.org/wiki/Q979829","display_name":"Radon transform","level":2,"score":0.7729949951171875},{"id":"https://openalex.org/C64543145","wikidata":"https://www.wikidata.org/wiki/Q162942","display_name":"Intersection (aeronautics)","level":2,"score":0.7435019016265869},{"id":"https://openalex.org/C527412718","wikidata":"https://www.wikidata.org/wiki/Q855395","display_name":"Interpretation (philosophy)","level":2,"score":0.7132896184921265},{"id":"https://openalex.org/C17825722","wikidata":"https://www.wikidata.org/wiki/Q17285","display_name":"Plane (geometry)","level":2,"score":0.7023889422416687},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.5655291080474854},{"id":"https://openalex.org/C200052193","wikidata":"https://www.wikidata.org/wiki/Q877802","display_name":"Integral transform","level":2,"score":0.5619039535522461},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5476812124252319},{"id":"https://openalex.org/C40308292","wikidata":"https://www.wikidata.org/wiki/Q122518","display_name":"Plane wave","level":2,"score":0.5025670528411865},{"id":"https://openalex.org/C9652623","wikidata":"https://www.wikidata.org/wiki/Q190109","display_name":"Field (mathematics)","level":2,"score":0.48142191767692566},{"id":"https://openalex.org/C36503486","wikidata":"https://www.wikidata.org/wiki/Q11235244","display_name":"Domain (mathematical analysis)","level":2,"score":0.47123679518699646},{"id":"https://openalex.org/C54865166","wikidata":"https://www.wikidata.org/wiki/Q844937","display_name":"Multiple integral","level":2,"score":0.4107131361961365},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.39282238483428955},{"id":"https://openalex.org/C120665830","wikidata":"https://www.wikidata.org/wiki/Q14620","display_name":"Optics","level":1,"score":0.30384334921836853},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.27650773525238037},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.12611347436904907},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.10287880897521973},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.07085344195365906},{"id":"https://openalex.org/C146978453","wikidata":"https://www.wikidata.org/wiki/Q3798668","display_name":"Aerospace engineering","level":1,"score":0.0},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.3906/elk-2009-21","is_oa":true,"landing_page_url":"https://doi.org/10.3906/elk-2009-21","pdf_url":"https://journals.tubitak.gov.tr/cgi/viewcontent.cgi?article=1061&context=elektrik","source":{"id":"https://openalex.org/S32837994","display_name":"TURKISH JOURNAL OF ELECTRICAL ENGINEERING & COMPUTER SCIENCES","issn_l":"1300-0632","issn":["1300-0632","1303-6203"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310318422","host_organization_name":"Scientific and Technological Research Council of Turkey (TUBITAK)","host_organization_lineage":["https://openalex.org/P4310318422"],"host_organization_lineage_names":["Scientific and Technological Research Council of Turkey (TUBITAK)"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"TURKISH JOURNAL OF ELECTRICAL ENGINEERING & COMPUTER SCIENCES","raw_type":"journal-article"}],"best_oa_location":{"id":"doi:10.3906/elk-2009-21","is_oa":true,"landing_page_url":"https://doi.org/10.3906/elk-2009-21","pdf_url":"https://journals.tubitak.gov.tr/cgi/viewcontent.cgi?article=1061&context=elektrik","source":{"id":"https://openalex.org/S32837994","display_name":"TURKISH JOURNAL OF ELECTRICAL ENGINEERING & COMPUTER SCIENCES","issn_l":"1300-0632","issn":["1300-0632","1303-6203"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310318422","host_organization_name":"Scientific and Technological Research Council of Turkey (TUBITAK)","host_organization_lineage":["https://openalex.org/P4310318422"],"host_organization_lineage_names":["Scientific and Technological Research Council of Turkey (TUBITAK)"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"TURKISH JOURNAL OF ELECTRICAL ENGINEERING & COMPUTER SCIENCES","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W3202965095.pdf","grobid_xml":"https://content.openalex.org/works/W3202965095.grobid-xml"},"referenced_works_count":12,"referenced_works":["https://openalex.org/W1661893705","https://openalex.org/W1972678233","https://openalex.org/W2005381261","https://openalex.org/W2033929502","https://openalex.org/W2119796171","https://openalex.org/W2133345153","https://openalex.org/W2137249453","https://openalex.org/W2161752198","https://openalex.org/W2323769464","https://openalex.org/W2594059555","https://openalex.org/W2926556845","https://openalex.org/W3033309923"],"related_works":["https://openalex.org/W3204855225","https://openalex.org/W3011253205","https://openalex.org/W4377140949","https://openalex.org/W2026961978","https://openalex.org/W4366975566","https://openalex.org/W1990534075","https://openalex.org/W2148451986","https://openalex.org/W1486136704","https://openalex.org/W1986899128","https://openalex.org/W2030815520"],"abstract_inverted_index":{"This":[0],"letter":[1],"presents":[2],"the":[3,8,12,55,58,61,65,77,88,95],"complete":[4],"mathematical":[5],"formulation":[6],"for":[7,76],"closed-form":[9,53,96],"evaluation":[10],"of":[11,57,87,94],"time":[13],"domain":[14],"physical":[15],"optics":[16],"(PO)":[17],"integral":[18,49],"on":[19],"linear":[20],"triangular":[21],"patches":[22],"using":[23],"Radon":[24],"transform":[25],"(RT)":[26],"interpretation.":[27],"The":[28,47],"incident":[29,66],"field":[30],"is":[31,50,74,84,98],"assumed":[32],"to":[33],"be":[34],"an":[35],"impulsively":[36],"excited":[37],"plane":[38,62,89],"wave":[39],"and":[40,60,67,90],"scattered":[41],"fields":[42],"are":[43],"observed":[44],"at":[45],"far-zone.":[46],"PO":[48],"evaluated":[51],"in":[52],"as":[54],"intersection":[56,86],"triangle":[59],"formed":[63],"by":[64],"observation":[68],"directions.":[69],"In":[70],"addition,":[71],"a":[72],"formula":[73],"suggested":[75],"special":[78],"case,":[79],"which":[80],"occurs":[81],"if":[82],"there":[83],"no":[85],"all":[91],"scatterer.":[92],"Accuracy":[93],"expressions":[97],"demonstrated":[99],"via":[100],"numerical":[101],"examples.":[102]},"counts_by_year":[],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}