{"id":"https://openalex.org/W3139370441","doi":"https://doi.org/10.3934/nhm.2021008","title":"An inverse problem for quantum trees with observations at interior vertices","display_name":"An inverse problem for quantum trees with observations at interior vertices","publication_year":2021,"publication_date":"2021-01-01","ids":{"openalex":"https://openalex.org/W3139370441","doi":"https://doi.org/10.3934/nhm.2021008","mag":"3139370441"},"language":"en","primary_location":{"id":"doi:10.3934/nhm.2021008","is_oa":true,"landing_page_url":"https://doi.org/10.3934/nhm.2021008","pdf_url":"https://www.aimsciences.org/article/exportPdf?id=65cf7fe9-4a9f-4a52-b708-5ea1e1814ecb","source":{"id":"https://openalex.org/S21752972","display_name":"Networks and Heterogeneous Media","issn_l":"1556-1801","issn":["1556-1801","1556-181X"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310315844","host_organization_name":"American Institute of Mathematical Sciences","host_organization_lineage":["https://openalex.org/P4310315844"],"host_organization_lineage_names":["American Institute of Mathematical Sciences"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Networks &amp; Heterogeneous Media","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"diamond","oa_url":"https://www.aimsciences.org/article/exportPdf?id=65cf7fe9-4a9f-4a52-b708-5ea1e1814ecb","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5004625354","display_name":"Sergei Avdonin","orcid":"https://orcid.org/0000-0002-4368-708X"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Sergei Avdonin","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5046974837","display_name":"Julian Edward","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Julian Edward","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5004625354"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":3.6418,"has_fulltext":false,"cited_by_count":9,"citation_normalized_percentile":{"value":0.9323281,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":98},"biblio":{"volume":"16","issue":"2","first_page":"317","last_page":"317"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11022","display_name":"Spectral Theory in Mathematical Physics","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/T11022","display_name":"Spectral Theory in Mathematical Physics","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/T11261","display_name":"Quantum chaos and dynamical systems","score":0.9993000030517578,"subfield":{"id":"https://openalex.org/subfields/3109","display_name":"Statistical and Nonlinear Physics"},"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/T11205","display_name":"Numerical methods in inverse problems","score":0.9991999864578247,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5130308866500854},{"id":"https://openalex.org/keywords/quantum-graph","display_name":"Quantum graph","score":0.4743053913116455},{"id":"https://openalex.org/keywords/inverse","display_name":"Inverse","score":0.4713327884674072},{"id":"https://openalex.org/keywords/vertex","display_name":"Vertex (graph theory)","score":0.4541842043399811},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.44509467482566833},{"id":"https://openalex.org/keywords/boundary","display_name":"Boundary (topology)","score":0.4440065026283264},{"id":"https://openalex.org/keywords/inverse-problem","display_name":"Inverse problem","score":0.4287046790122986},{"id":"https://openalex.org/keywords/topology","display_name":"Topology (electrical circuits)","score":0.3657519817352295},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.3329940438270569},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.3287227749824524},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.18278464674949646}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5130308866500854},{"id":"https://openalex.org/C164886730","wikidata":"https://www.wikidata.org/wiki/Q7269054","display_name":"Quantum graph","level":3,"score":0.4743053913116455},{"id":"https://openalex.org/C207467116","wikidata":"https://www.wikidata.org/wiki/Q4385666","display_name":"Inverse","level":2,"score":0.4713327884674072},{"id":"https://openalex.org/C80899671","wikidata":"https://www.wikidata.org/wiki/Q1304193","display_name":"Vertex (graph theory)","level":3,"score":0.4541842043399811},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.44509467482566833},{"id":"https://openalex.org/C62354387","wikidata":"https://www.wikidata.org/wiki/Q875399","display_name":"Boundary (topology)","level":2,"score":0.4440065026283264},{"id":"https://openalex.org/C135252773","wikidata":"https://www.wikidata.org/wiki/Q1567213","display_name":"Inverse problem","level":2,"score":0.4287046790122986},{"id":"https://openalex.org/C184720557","wikidata":"https://www.wikidata.org/wiki/Q7825049","display_name":"Topology (electrical circuits)","level":2,"score":0.3657519817352295},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.3329940438270569},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.3287227749824524},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.18278464674949646}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.3934/nhm.2021008","is_oa":true,"landing_page_url":"https://doi.org/10.3934/nhm.2021008","pdf_url":"https://www.aimsciences.org/article/exportPdf?id=65cf7fe9-4a9f-4a52-b708-5ea1e1814ecb","source":{"id":"https://openalex.org/S21752972","display_name":"Networks and Heterogeneous Media","issn_l":"1556-1801","issn":["1556-1801","1556-181X"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310315844","host_organization_name":"American Institute of Mathematical Sciences","host_organization_lineage":["https://openalex.org/P4310315844"],"host_organization_lineage_names":["American Institute of Mathematical Sciences"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Networks &amp; Heterogeneous Media","raw_type":"journal-article"},{"id":"pmh:oai:doaj.org/article:078a423c5d004e3eb5a7df4af102b5c0","is_oa":false,"landing_page_url":"https://doaj.org/article/078a423c5d004e3eb5a7df4af102b5c0","pdf_url":null,"source":{"id":"https://openalex.org/S4306401280","display_name":"DOAJ (DOAJ: Directory of Open Access Journals)","issn_l":null,"issn":null,"is_oa":false,"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":"Networks and Heterogeneous Media, Vol 16, Iss 2, Pp 317-339 (2021)","raw_type":"article"}],"best_oa_location":{"id":"doi:10.3934/nhm.2021008","is_oa":true,"landing_page_url":"https://doi.org/10.3934/nhm.2021008","pdf_url":"https://www.aimsciences.org/article/exportPdf?id=65cf7fe9-4a9f-4a52-b708-5ea1e1814ecb","source":{"id":"https://openalex.org/S21752972","display_name":"Networks and Heterogeneous Media","issn_l":"1556-1801","issn":["1556-1801","1556-181X"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310315844","host_organization_name":"American Institute of Mathematical Sciences","host_organization_lineage":["https://openalex.org/P4310315844"],"host_organization_lineage_names":["American Institute of Mathematical Sciences"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Networks &amp; Heterogeneous Media","raw_type":"journal-article"},"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/11","score":0.5799999833106995,"display_name":"Sustainable cities and communities"}],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W3139370441.pdf","grobid_xml":"https://content.openalex.org/works/W3139370441.grobid-xml"},"referenced_works_count":52,"referenced_works":["https://openalex.org/W178164902","https://openalex.org/W303892284","https://openalex.org/W1248197218","https://openalex.org/W1595841226","https://openalex.org/W1596846276","https://openalex.org/W1601216305","https://openalex.org/W1667867929","https://openalex.org/W1963923369","https://openalex.org/W1979775628","https://openalex.org/W1983631021","https://openalex.org/W1992217172","https://openalex.org/W1998972521","https://openalex.org/W1999004587","https://openalex.org/W2003672268","https://openalex.org/W2007175988","https://openalex.org/W2010172912","https://openalex.org/W2013923843","https://openalex.org/W2017350456","https://openalex.org/W2021073395","https://openalex.org/W2021830868","https://openalex.org/W2021861292","https://openalex.org/W2025501339","https://openalex.org/W2026384322","https://openalex.org/W2028396877","https://openalex.org/W2032638919","https://openalex.org/W2079460691","https://openalex.org/W2085006025","https://openalex.org/W2094509119","https://openalex.org/W2101798517","https://openalex.org/W2115336412","https://openalex.org/W2119398442","https://openalex.org/W2137557306","https://openalex.org/W2142874024","https://openalex.org/W2165893315","https://openalex.org/W2167712193","https://openalex.org/W2212399862","https://openalex.org/W2267395098","https://openalex.org/W2510507472","https://openalex.org/W2515780510","https://openalex.org/W2544345206","https://openalex.org/W2554612069","https://openalex.org/W2938599412","https://openalex.org/W2963640439","https://openalex.org/W2963813581","https://openalex.org/W2969262714","https://openalex.org/W2990307889","https://openalex.org/W3092663332","https://openalex.org/W3103142786","https://openalex.org/W3104574451","https://openalex.org/W3105843469","https://openalex.org/W4247854531","https://openalex.org/W4251965993"],"related_works":["https://openalex.org/W1719252778","https://openalex.org/W3107333841","https://openalex.org/W2031098440","https://openalex.org/W4307385446","https://openalex.org/W4386875525","https://openalex.org/W2466894780","https://openalex.org/W3092119098","https://openalex.org/W2003008160","https://openalex.org/W2381713449","https://openalex.org/W2731724293"],"abstract_inverted_index":{"<p":[0],"style='text-indent:20px;'>In":[1],"this":[2],"paper":[3],"we":[4,43,74],"consider":[5],"a":[6,16],"non-standard":[7],"dynamical":[8],"inverse":[9],"problem":[10],"for":[11],"the":[12,29,33,59,76,81,83,86,89,92],"wave":[13],"equation":[14],"on":[15],"metric":[17],"tree":[18],"graph.":[19,34],"We":[20],"assume":[21],"that":[22,42],"positive":[23],"masses":[24,90],"may":[25],"be":[26],"attached":[27],"to":[28,67],"internal":[30,72],"vertices":[31],"of":[32,38,80,85],"Another":[35],"specific":[36],"feature":[37],"our":[39],"investigation":[40],"is":[41],"use":[44],"only":[45],"one":[46,50,64,68],"boundary":[47,51,65,69],"actuator":[48],"and":[49,70,78,88],"sensor,":[52],"all":[53,71],"other":[54],"observations":[55],"being":[56],"internal.":[57],"Using":[58],"Dirichlet-to-Neumann":[60],"map":[61],"(acting":[62],"from":[63],"vertex":[66],"vertices)":[73],"recover":[75],"topology":[77],"geometry":[79],"graph,":[82],"coefficients":[84],"equations":[87],"at":[91],"vertices.":[93]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2024,"cited_by_count":2},{"year":2023,"cited_by_count":3},{"year":2022,"cited_by_count":2},{"year":2021,"cited_by_count":1}],"updated_date":"2026-05-06T08:25:59.206177","created_date":"2025-10-10T00:00:00"}
