{"id":"https://openalex.org/W4414424179","doi":"https://doi.org/10.1016/j.amc.2026.130188","title":"Neumann series of Bessel functions in direct and inverse spherically symmetric transmission eigenvalue problems","display_name":"Neumann series of Bessel functions in direct and inverse spherically symmetric transmission eigenvalue problems","publication_year":2026,"publication_date":"2026-06-03","ids":{"openalex":"https://openalex.org/W4414424179","doi":"https://doi.org/10.1016/j.amc.2026.130188"},"language":"en","primary_location":{"id":"doi:10.1016/j.amc.2026.130188","is_oa":true,"landing_page_url":"https://doi.org/10.1016/j.amc.2026.130188","pdf_url":null,"source":{"id":"https://openalex.org/S50372074","display_name":"Applied Mathematics and Computation","issn_l":"0096-3003","issn":["0096-3003","1873-5649"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320990","host_organization_name":"Elsevier BV","host_organization_lineage":["https://openalex.org/P4310320990"],"host_organization_lineage_names":["Elsevier BV"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Applied Mathematics and Computation","raw_type":"journal-article"},"type":"article","indexed_in":["arxiv","crossref","datacite"],"open_access":{"is_oa":true,"oa_status":"hybrid","oa_url":"https://doi.org/10.1016/j.amc.2026.130188","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5086367676","display_name":"Vladislav V. Kravchenko","orcid":"https://orcid.org/0000-0001-9180-858X"},"institutions":[{"id":"https://openalex.org/I137534880","display_name":"Southern Federal University","ror":"https://ror.org/01tv9ph92","country_code":"RU","type":"education","lineage":["https://openalex.org/I137534880"]},{"id":"https://openalex.org/I68368234","display_name":"Centro de Investigaci\u00f3n y de Estudios Avanzados del Instituto Polit\u00e9cnico Nacional","ror":"https://ror.org/009eqmr18","country_code":"MX","type":"facility","lineage":["https://openalex.org/I59361560","https://openalex.org/I68368234"]}],"countries":["MX","RU"],"is_corresponding":false,"raw_author_name":"Vladislav V. Kravchenko","raw_affiliation_strings":["Departamento de Matem\u00e1ticas, Cinvestav, Unidad Quer\u00e9taro, Libramiento Norponiente 2000, Quer\u00e9taro, 76230, Mexico","Regional Mathematical Center, Southern Federal University, Bol\u2019shaya Sadovaya 105/42, Rostov-on-Don, 344090, Russia"],"raw_orcid":"https://orcid.org/0000-0001-9180-858X","affiliations":[{"raw_affiliation_string":"Departamento de Matem\u00e1ticas, Cinvestav, Unidad Quer\u00e9taro, Libramiento Norponiente 2000, Quer\u00e9taro, 76230, Mexico","institution_ids":["https://openalex.org/I68368234"]},{"raw_affiliation_string":"Regional Mathematical Center, Southern Federal University, Bol\u2019shaya Sadovaya 105/42, Rostov-on-Don, 344090, Russia","institution_ids":["https://openalex.org/I137534880"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5092649679","display_name":"L. Estefania Murcia\u2010Lozano","orcid":"https://orcid.org/0000-0002-3192-9918"},"institutions":[{"id":"https://openalex.org/I137534880","display_name":"Southern Federal University","ror":"https://ror.org/01tv9ph92","country_code":"RU","type":"education","lineage":["https://openalex.org/I137534880"]}],"countries":["RU"],"is_corresponding":false,"raw_author_name":"L. Estefania Murcia-Lozano","raw_affiliation_strings":["Regional Mathematical Center, Southern Federal University, Bol\u2019shaya Sadovaya 105/42, Rostov-on-Don, 344090, Russia"],"raw_orcid":"https://orcid.org/0000-0002-3192-9918","affiliations":[{"raw_affiliation_string":"Regional Mathematical Center, Southern Federal University, Bol\u2019shaya Sadovaya 105/42, Rostov-on-Don, 344090, Russia","institution_ids":["https://openalex.org/I137534880"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5038423918","display_name":"Nikolaos Pallikarakis","orcid":"https://orcid.org/0000-0002-2385-6747"},"institutions":[{"id":"https://openalex.org/I174458059","display_name":"National Technical University of Athens","ror":"https://ror.org/03cx6bg69","country_code":"GR","type":"education","lineage":["https://openalex.org/I174458059"]}],"countries":["GR"],"is_corresponding":true,"raw_author_name":"Nikolaos Pallikarakis","raw_affiliation_strings":["Department of Mathematics, National Technical University of Athens, Zografou Campus, Athens, 15780, Greece"],"raw_orcid":"https://orcid.org/0000-0002-2385-6747","affiliations":[{"raw_affiliation_string":"Department of Mathematics, National Technical University of Athens, Zografou Campus, Athens, 15780, Greece","institution_ids":["https://openalex.org/I174458059"]}]}],"institutions":[],"countries_distinct_count":3,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5038423918"],"corresponding_institution_ids":["https://openalex.org/I174458059"],"apc_list":{"value":3550,"currency":"USD","value_usd":3550},"apc_paid":{"value":3550,"currency":"USD","value_usd":3550},"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.04643226,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"531","issue":null,"first_page":"130188","last_page":"130188"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11205","display_name":"Numerical methods in inverse problems","score":0.9977999925613403,"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":0.9977999925613403,"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/T12037","display_name":"Algebraic and Geometric Analysis","score":0.9840999841690063,"subfield":{"id":"https://openalex.org/subfields/2604","display_name":"Applied Mathematics"},"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/T12100","display_name":"Advanced Mathematical Modeling in Engineering","score":0.9832000136375427,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/eigenvalues-and-eigenvectors","display_name":"Eigenvalues and eigenvectors","score":0.7411999702453613},{"id":"https://openalex.org/keywords/bessel-function","display_name":"Bessel function","score":0.6807000041007996},{"id":"https://openalex.org/keywords/inverse-scattering-problem","display_name":"Inverse scattering problem","score":0.6154999732971191},{"id":"https://openalex.org/keywords/inverse","display_name":"Inverse","score":0.6065000295639038},{"id":"https://openalex.org/keywords/neumann-series","display_name":"Neumann series","score":0.47870001196861267},{"id":"https://openalex.org/keywords/inverse-problem","display_name":"Inverse problem","score":0.4683000147342682},{"id":"https://openalex.org/keywords/helmholtz-equation","display_name":"Helmholtz equation","score":0.43720000982284546},{"id":"https://openalex.org/keywords/sign-function","display_name":"Sign function","score":0.3993000090122223},{"id":"https://openalex.org/keywords/sign","display_name":"Sign (mathematics)","score":0.3662000000476837}],"concepts":[{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.7411999702453613},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.73089998960495},{"id":"https://openalex.org/C107706756","wikidata":"https://www.wikidata.org/wiki/Q219637","display_name":"Bessel function","level":2,"score":0.6807000041007996},{"id":"https://openalex.org/C174558057","wikidata":"https://www.wikidata.org/wiki/Q11639409","display_name":"Inverse scattering problem","level":3,"score":0.6154999732971191},{"id":"https://openalex.org/C207467116","wikidata":"https://www.wikidata.org/wiki/Q4385666","display_name":"Inverse","level":2,"score":0.6065000295639038},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.6053000092506409},{"id":"https://openalex.org/C137343772","wikidata":"https://www.wikidata.org/wiki/Q584910","display_name":"Neumann series","level":2,"score":0.47870001196861267},{"id":"https://openalex.org/C135252773","wikidata":"https://www.wikidata.org/wiki/Q1567213","display_name":"Inverse problem","level":2,"score":0.4683000147342682},{"id":"https://openalex.org/C18591234","wikidata":"https://www.wikidata.org/wiki/Q860615","display_name":"Helmholtz equation","level":3,"score":0.43720000982284546},{"id":"https://openalex.org/C4250","wikidata":"https://www.wikidata.org/wiki/Q236813","display_name":"Sign function","level":2,"score":0.3993000090122223},{"id":"https://openalex.org/C139676723","wikidata":"https://www.wikidata.org/wiki/Q1193832","display_name":"Sign (mathematics)","level":2,"score":0.3662000000476837},{"id":"https://openalex.org/C143724316","wikidata":"https://www.wikidata.org/wiki/Q312468","display_name":"Series (stratigraphy)","level":2,"score":0.34630000591278076},{"id":"https://openalex.org/C75553542","wikidata":"https://www.wikidata.org/wiki/Q178161","display_name":"A priori and a posteriori","level":2,"score":0.33799999952316284},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.326200008392334},{"id":"https://openalex.org/C74193536","wikidata":"https://www.wikidata.org/wiki/Q574844","display_name":"Kernel (algebra)","level":2,"score":0.32269999384880066},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.322299987077713},{"id":"https://openalex.org/C63479239","wikidata":"https://www.wikidata.org/wiki/Q7353546","display_name":"Robustness (evolution)","level":3,"score":0.3215000033378601},{"id":"https://openalex.org/C48753275","wikidata":"https://www.wikidata.org/wiki/Q11216","display_name":"Numerical analysis","level":2,"score":0.3188999891281128},{"id":"https://openalex.org/C42067758","wikidata":"https://www.wikidata.org/wiki/Q174102","display_name":"Refractive index","level":2,"score":0.3151000142097473},{"id":"https://openalex.org/C67105901","wikidata":"https://www.wikidata.org/wiki/Q903737","display_name":"Scattering theory","level":3,"score":0.30550000071525574},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.30320000648498535},{"id":"https://openalex.org/C204323151","wikidata":"https://www.wikidata.org/wiki/Q905424","display_name":"Range (aeronautics)","level":2,"score":0.3028999865055084},{"id":"https://openalex.org/C2778067643","wikidata":"https://www.wikidata.org/wiki/Q166507","display_name":"Interval (graph theory)","level":2,"score":0.2784999907016754},{"id":"https://openalex.org/C2780586882","wikidata":"https://www.wikidata.org/wiki/Q7520643","display_name":"Simple (philosophy)","level":2,"score":0.27649998664855957},{"id":"https://openalex.org/C179117685","wikidata":"https://www.wikidata.org/wiki/Q328998","display_name":"Complex plane","level":2,"score":0.2752000093460083},{"id":"https://openalex.org/C186080144","wikidata":"https://www.wikidata.org/wiki/Q358733","display_name":"Series expansion","level":2,"score":0.2721000015735626},{"id":"https://openalex.org/C182365436","wikidata":"https://www.wikidata.org/wiki/Q50701","display_name":"Variable (mathematics)","level":2,"score":0.2720000147819519},{"id":"https://openalex.org/C140532419","wikidata":"https://www.wikidata.org/wiki/Q249748","display_name":"Spectral radius","level":3,"score":0.26660001277923584},{"id":"https://openalex.org/C156778621","wikidata":"https://www.wikidata.org/wiki/Q1365748","display_name":"Spectrum (functional analysis)","level":2,"score":0.2547000050544739}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1016/j.amc.2026.130188","is_oa":true,"landing_page_url":"https://doi.org/10.1016/j.amc.2026.130188","pdf_url":null,"source":{"id":"https://openalex.org/S50372074","display_name":"Applied Mathematics and Computation","issn_l":"0096-3003","issn":["0096-3003","1873-5649"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320990","host_organization_name":"Elsevier BV","host_organization_lineage":["https://openalex.org/P4310320990"],"host_organization_lineage_names":["Elsevier BV"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Applied Mathematics and Computation","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:2507.16554","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2507.16554","pdf_url":"https://arxiv.org/pdf/2507.16554","source":{"id":"https://openalex.org/S4393918464","display_name":"ArXiv.org","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},{"id":"doi:10.48550/arxiv.2507.16554","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2507.16554","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"article"}],"best_oa_location":{"id":"doi:10.1016/j.amc.2026.130188","is_oa":true,"landing_page_url":"https://doi.org/10.1016/j.amc.2026.130188","pdf_url":null,"source":{"id":"https://openalex.org/S50372074","display_name":"Applied Mathematics and Computation","issn_l":"0096-3003","issn":["0096-3003","1873-5649"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320990","host_organization_name":"Elsevier BV","host_organization_lineage":["https://openalex.org/P4310320990"],"host_organization_lineage_names":["Elsevier BV"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Applied Mathematics and Computation","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320321912","display_name":"Ministry of Education and Science of the Russian Federation","ror":"https://ror.org/00ghqgy32"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":[],"abstract_inverted_index":{"The":[0],"transmission":[1],"eigenvalue":[2,173],"problem":[3,171],"(TEP)":[4],"plays":[5],"a":[6,42,60,64,94,103,117,131,147,186,194],"central":[7],"role":[8],"in":[9,25,72],"inverse":[10,23,113,170],"scattering":[11],"theory.":[12],"Despite":[13],"substantial":[14],"theoretical":[15],"progress,":[16],"the":[17,57,84,112,122,138,151,164,168,180,200,203],"numerical":[18],"solution":[19],"of":[20,46,189,202],"direct":[21,85],"and":[22,35,135,166,183],"TEP":[24,58],"spherically":[26],"symmetric":[27],"domains":[28],"with":[29,102,108,192],"variable":[30],"refractive":[31,139,190],"index-":[32],"covering":[33],"real":[34],"complex":[36],"eigenvalues-remains":[37],"challenging.":[38],"This":[39],"study":[40],"introduces":[41],"novel":[43],"Neumann":[44],"Series":[45],"Bessel":[47],"Functions":[48],"(NSBF)":[49],"methodology":[50],"to":[51,162],"address":[52],"this":[53],"challenge.":[54],"After":[55],"reformulating":[56],"as":[59,106],"Sturm-Liouville":[61],"equation":[62],"via":[63,130],"Liouville":[65],"transformation,":[66],"we":[67,115],"expand":[68],"its":[69],"characteristic":[70],"function":[71],"an":[73],"NSBF":[74,96,153],"whose":[75],"coefficients":[76],"are":[77],"computed":[78],"by":[79,91,145],"simple":[80],"recursive":[81],"integration.":[82],"In":[83],"problem,":[86,114],"eigenvalues-real":[87],"or":[88,199],"complex-are":[89],"found":[90],"root-finding":[92],"on":[93,197],"truncated":[95],"partial":[97],"sum,":[98],"yielding":[99],"high":[100],"accuracy":[101,184],"few":[104],"coefficients,":[105],"demonstrated":[107],"various":[109],"examples.":[110],"For":[111],"develop":[116],"two-step":[118],"approach:":[119],"first,":[120],"recovering":[121],"transformed":[123],"interval":[124],"length":[125],"\u03b4":[126,198],"from":[127],"spectral":[128],"data":[129,174],"new":[132],"NSBF-based":[133],"algorithm,":[134],"second,":[136],"reconstructing":[137],"index":[140],"n":[141,207],"(":[142,208],"r":[143,209],")":[144,210],"solving":[146],"linear":[148],"system":[149],"for":[150],"first":[152],"coefficients.":[154],"A":[155],"spectrum":[156,165],"completion":[157],"technique":[158],"is":[159,175],"also":[160],"implemented":[161],"complete":[163],"solve":[167],"corresponding":[169],"when":[172],"limited.":[176],"Numerical":[177],"examples":[178],"confirm":[179],"method\u2019s":[181],"robustness":[182],"across":[185],"wide":[187],"range":[188],"indices,":[191],"no":[193],"priori":[195],"assumptions":[196],"sign":[201],"contrast":[204],"1":[205],"\u2212":[206],".":[211]},"counts_by_year":[],"updated_date":"2026-06-05T06:17:00.636019","created_date":"2025-10-10T00:00:00"}
