{"id":"https://openalex.org/W2509089377","doi":"https://doi.org/10.1137/16m1058704","title":"Stekloff Eigenvalues in Inverse Scattering","display_name":"Stekloff Eigenvalues in Inverse Scattering","publication_year":2016,"publication_date":"2016-01-01","ids":{"openalex":"https://openalex.org/W2509089377","doi":"https://doi.org/10.1137/16m1058704","mag":"2509089377"},"language":"en","primary_location":{"id":"doi:10.1137/16m1058704","is_oa":false,"landing_page_url":"https://doi.org/10.1137/16m1058704","pdf_url":null,"source":{"id":"https://openalex.org/S77200987","display_name":"SIAM Journal on Applied Mathematics","issn_l":"0036-1399","issn":["0036-1399","1095-712X"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Applied Mathematics","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5016533774","display_name":"Fioralba Cakoni","orcid":"https://orcid.org/0000-0002-4648-8780"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"F. Cakoni","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5051750967","display_name":"David Colton","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"D. Colton","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5073819137","display_name":"Shixu Meng","orcid":"https://orcid.org/0000-0002-5118-5426"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"S. Meng","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5028510993","display_name":"Peter Monk","orcid":"https://orcid.org/0000-0002-6539-5897"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"P. Monk","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5016533774"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":11.0078,"has_fulltext":false,"cited_by_count":84,"citation_normalized_percentile":{"value":0.99052831,"is_in_top_1_percent":true,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":97,"max":100},"biblio":{"volume":"76","issue":"4","first_page":"1737","last_page":"1763"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11205","display_name":"Numerical methods in inverse problems","score":0.9998999834060669,"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"}},"topics":[{"id":"https://openalex.org/T11205","display_name":"Numerical methods in inverse problems","score":0.9998999834060669,"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/T10514","display_name":"Numerical methods in engineering","score":0.9983999729156494,"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/T10739","display_name":"Electromagnetic Scattering and Analysis","score":0.9975000023841858,"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/scattering","display_name":"Scattering","score":0.707036018371582},{"id":"https://openalex.org/keywords/eigenvalues-and-eigenvectors","display_name":"Eigenvalues and eigenvectors","score":0.6884397864341736},{"id":"https://openalex.org/keywords/inverse-scattering-problem","display_name":"Inverse scattering problem","score":0.6536720395088196},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.5874476432800293},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5202832818031311},{"id":"https://openalex.org/keywords/boundary","display_name":"Boundary (topology)","score":0.48249006271362305},{"id":"https://openalex.org/keywords/field","display_name":"Field (mathematics)","score":0.4797550439834595},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.4658316969871521},{"id":"https://openalex.org/keywords/ball","display_name":"Ball (mathematics)","score":0.46157750487327576},{"id":"https://openalex.org/keywords/refractive-index","display_name":"Refractive index","score":0.4347851574420929},{"id":"https://openalex.org/keywords/boundary-value-problem","display_name":"Boundary value problem","score":0.4250714182853699},{"id":"https://openalex.org/keywords/inverse","display_name":"Inverse","score":0.4139944016933441},{"id":"https://openalex.org/keywords/optics","display_name":"Optics","score":0.38083407282829285},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.31925690174102783},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.15210601687431335},{"id":"https://openalex.org/keywords/quantum-mechanics","display_name":"Quantum mechanics","score":0.1384325623512268}],"concepts":[{"id":"https://openalex.org/C191486275","wikidata":"https://www.wikidata.org/wiki/Q210028","display_name":"Scattering","level":2,"score":0.707036018371582},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.6884397864341736},{"id":"https://openalex.org/C174558057","wikidata":"https://www.wikidata.org/wiki/Q11639409","display_name":"Inverse scattering problem","level":3,"score":0.6536720395088196},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.5874476432800293},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5202832818031311},{"id":"https://openalex.org/C62354387","wikidata":"https://www.wikidata.org/wiki/Q875399","display_name":"Boundary (topology)","level":2,"score":0.48249006271362305},{"id":"https://openalex.org/C9652623","wikidata":"https://www.wikidata.org/wiki/Q190109","display_name":"Field (mathematics)","level":2,"score":0.4797550439834595},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.4658316969871521},{"id":"https://openalex.org/C122041747","wikidata":"https://www.wikidata.org/wiki/Q838611","display_name":"Ball (mathematics)","level":2,"score":0.46157750487327576},{"id":"https://openalex.org/C42067758","wikidata":"https://www.wikidata.org/wiki/Q174102","display_name":"Refractive index","level":2,"score":0.4347851574420929},{"id":"https://openalex.org/C182310444","wikidata":"https://www.wikidata.org/wiki/Q1332643","display_name":"Boundary value problem","level":2,"score":0.4250714182853699},{"id":"https://openalex.org/C207467116","wikidata":"https://www.wikidata.org/wiki/Q4385666","display_name":"Inverse","level":2,"score":0.4139944016933441},{"id":"https://openalex.org/C120665830","wikidata":"https://www.wikidata.org/wiki/Q14620","display_name":"Optics","level":1,"score":0.38083407282829285},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.31925690174102783},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.15210601687431335},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.1384325623512268}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1137/16m1058704","is_oa":false,"landing_page_url":"https://doi.org/10.1137/16m1058704","pdf_url":null,"source":{"id":"https://openalex.org/S77200987","display_name":"SIAM Journal on Applied Mathematics","issn_l":"0036-1399","issn":["0036-1399","1095-712X"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Applied Mathematics","raw_type":"journal-article"},{"id":"pmh:oai:alma.01RUT_INST:11675610680004646","is_oa":false,"landing_page_url":"https://scholarship.libraries.rutgers.edu/esploro/outputs/journalArticle/STEKLOFF-EIGENVALUES-IN-INVERSE-SCATTERING/991031716232404646","pdf_url":null,"source":{"id":"https://openalex.org/S4210197018","display_name":"View","issn_l":"2688-268X","issn":["2688-268X","2688-3988"],"is_oa":false,"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":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G4586480135","display_name":null,"funder_award_id":"FA9550-13-1-0199","funder_id":"https://openalex.org/F4320338279","funder_display_name":"Air Force Office of Scientific Research"},{"id":"https://openalex.org/G5705050557","display_name":null,"funder_award_id":"DMS1602802","funder_id":"https://openalex.org/F4320337380","funder_display_name":"Division of Mathematical Sciences"}],"funders":[{"id":"https://openalex.org/F4320337380","display_name":"Division of Mathematical Sciences","ror":"https://ror.org/051fftw81"},{"id":"https://openalex.org/F4320338279","display_name":"Air Force Office of Scientific Research","ror":"https://ror.org/011e9bt93"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":13,"referenced_works":["https://openalex.org/W614932401","https://openalex.org/W1413004681","https://openalex.org/W1584097495","https://openalex.org/W1970446082","https://openalex.org/W1979418974","https://openalex.org/W1986817086","https://openalex.org/W1991135623","https://openalex.org/W2020695975","https://openalex.org/W2027842332","https://openalex.org/W2027989454","https://openalex.org/W3021722416","https://openalex.org/W3103805365","https://openalex.org/W4285719527"],"related_works":["https://openalex.org/W2165749285","https://openalex.org/W2061199333","https://openalex.org/W2062626603","https://openalex.org/W3193665957","https://openalex.org/W4297492740","https://openalex.org/W2474979212","https://openalex.org/W2562455930","https://openalex.org/W2001036795","https://openalex.org/W127450631","https://openalex.org/W2154748900"],"abstract_inverted_index":{"We":[0],"consider":[1],"a":[2,48,91,105],"problem":[3,43,80],"in":[4,7,11,32,111,142,150,154,173],"nondestructive":[5],"testing":[6],"which":[8],"small":[9],"changes":[10,31,149,153,168],"the":[12,58,61,68,72,82,88,98,101,108,125,134,155,164,170],"(possibly":[13],"complex":[14],"valued)":[15],"refractive":[16,135,171],"index":[17,136,172],"$n(x)$":[18,151],"of":[19,23,60,76,90,100,166],"an":[20,77],"inhomogeneous":[21],"medium":[22],"compact":[24],"support":[25,99],"are":[26,161],"to":[27,38,67,123,129,140,152,169],"be":[28,121],"determined":[29],"from":[30],"measured":[33,62],"far":[34,50,63,73],"field":[35,51,64,74],"data":[36],"due":[37,66],"incident":[39],"plane":[40],"waves.":[41],"The":[42],"is":[44,57,96,115,137,146],"studied":[45],"by":[46],"considering":[47],"modified":[49],"operator":[52],"${\\cal":[53,118],"F}$":[54,119],"whose":[55],"kernel":[56],"difference":[59],"pattern":[65,75],"scattering":[69,79,102,109],"object":[70,103,110],"and":[71,158],"auxiliary":[78],"with":[81],"Stekloff":[83,126,156],"boundary":[84,89],"condition":[85],"imposed":[86],"on":[87],"domain":[92],"$B$,":[93,130],"where":[94],"$B$":[95],"either":[97],"or":[104],"ball":[106],"containing":[107],"its":[112],"interior.":[113],"It":[114],"shown":[116],"that":[117],"can":[120],"used":[122],"determine":[124],"eigenvalues":[127,157],"corresponding":[128],"where,":[131],"if":[132],"$B\\not=D$,":[133],"set":[138],"equal":[139],"one":[141],"$B\\setminus\\overline{D}$.":[143],"A":[144],"formula":[145],"obtained":[147],"relating":[148],"numerical":[159],"examples":[160],"given":[162],"showing":[163],"effectiveness":[165],"determining":[167],"this":[174],"way.":[175]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":8},{"year":2024,"cited_by_count":6},{"year":2023,"cited_by_count":11},{"year":2022,"cited_by_count":9},{"year":2021,"cited_by_count":16},{"year":2020,"cited_by_count":13},{"year":2019,"cited_by_count":8},{"year":2018,"cited_by_count":8},{"year":2017,"cited_by_count":4}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}