{"id":"https://openalex.org/W1981777427","doi":"https://doi.org/10.1137/s1064827500376211","title":"Application of an Inverse Problem for Symmetric Periodic Potentials","display_name":"Application of an Inverse Problem for Symmetric Periodic Potentials","publication_year":2001,"publication_date":"2001-01-01","ids":{"openalex":"https://openalex.org/W1981777427","doi":"https://doi.org/10.1137/s1064827500376211","mag":"1981777427"},"language":"en","primary_location":{"id":"doi:10.1137/s1064827500376211","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s1064827500376211","pdf_url":null,"source":{"id":"https://openalex.org/S165512578","display_name":"SIAM Journal on Scientific Computing","issn_l":"1064-8275","issn":["1064-8275","1095-7197"],"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 Scientific Computing","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/A5077403467","display_name":"Gaobiao Xiao","orcid":"https://orcid.org/0000-0001-5547-9475"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"G. B. Xiao","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5110831445","display_name":"K. Yashiro","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"K. Yashiro","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5038558435","display_name":"Ning Guan","orcid":"https://orcid.org/0000-0002-0686-522X"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"N. Guan","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5108507778","display_name":"S. Ohkawa","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"S. Ohkawa","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5077403467"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.9846,"has_fulltext":false,"cited_by_count":2,"citation_normalized_percentile":{"value":0.68835971,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"23","issue":"3","first_page":"1042","last_page":"1049"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11022","display_name":"Spectral Theory in Mathematical Physics","score":0.9997000098228455,"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":0.9997000098228455,"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":0.9973999857902527,"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/T11262","display_name":"Quantum Mechanics and Non-Hermitian Physics","score":0.9940999746322632,"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/lambda","display_name":"Lambda","score":0.8564282655715942},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8134354948997498},{"id":"https://openalex.org/keywords/inverse","display_name":"Inverse","score":0.4887261390686035},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.45808565616607666},{"id":"https://openalex.org/keywords/discriminant","display_name":"Discriminant","score":0.4514349102973938},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.4391743838787079},{"id":"https://openalex.org/keywords/delta","display_name":"Delta","score":0.4183870553970337},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.30113542079925537},{"id":"https://openalex.org/keywords/quantum-mechanics","display_name":"Quantum mechanics","score":0.11758092045783997},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.1144402027130127}],"concepts":[{"id":"https://openalex.org/C2778113609","wikidata":"https://www.wikidata.org/wiki/Q10897","display_name":"Lambda","level":2,"score":0.8564282655715942},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8134354948997498},{"id":"https://openalex.org/C207467116","wikidata":"https://www.wikidata.org/wiki/Q4385666","display_name":"Inverse","level":2,"score":0.4887261390686035},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.45808565616607666},{"id":"https://openalex.org/C78397625","wikidata":"https://www.wikidata.org/wiki/Q192487","display_name":"Discriminant","level":2,"score":0.4514349102973938},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.4391743838787079},{"id":"https://openalex.org/C5072461","wikidata":"https://www.wikidata.org/wiki/Q49506","display_name":"Delta","level":2,"score":0.4183870553970337},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.30113542079925537},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.11758092045783997},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.1144402027130127},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.0},{"id":"https://openalex.org/C1276947","wikidata":"https://www.wikidata.org/wiki/Q333","display_name":"Astronomy","level":1,"score":0.0},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/s1064827500376211","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s1064827500376211","pdf_url":null,"source":{"id":"https://openalex.org/S165512578","display_name":"SIAM Journal on Scientific Computing","issn_l":"1064-8275","issn":["1064-8275","1095-7197"],"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 Scientific Computing","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/10","display_name":"Reduced inequalities","score":0.75}],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":8,"referenced_works":["https://openalex.org/W594166105","https://openalex.org/W1569024867","https://openalex.org/W1970946031","https://openalex.org/W1981237273","https://openalex.org/W1998129089","https://openalex.org/W2012169079","https://openalex.org/W2027382864","https://openalex.org/W2159163188"],"related_works":["https://openalex.org/W4221046490","https://openalex.org/W4297616267","https://openalex.org/W2502651140","https://openalex.org/W3195406774","https://openalex.org/W4297615481","https://openalex.org/W4297616317","https://openalex.org/W2951695430","https://openalex.org/W3111070561","https://openalex.org/W4239373651","https://openalex.org/W2414832939"],"abstract_inverted_index":{"This":[0],"paper":[1],"gives":[2],"an":[3],"algorithm":[4],"for":[5],"constructing":[6],"symmetric":[7],"periodic":[8],"potential":[9],"q(x)":[10,49],"of":[11,17,35,43,55],"Hill's":[12,36],"equation":[13,37],"from":[14,22,40,52],"given":[15],"roots":[16,42,54],"$\\Delta(\\lambda)-2=0$.":[18],"The":[19],"problem":[20],"arises":[21],"synthesizing":[23],"dual-mode":[24],"ring":[25],"electrical":[26],"circuits.":[27],"In":[28],"the":[29,32,41,53,65],"presented":[30],"method,":[31],"discriminant":[33],"$\\Delta(\\lambda)$":[34],"is":[38,50],"determined":[39],"$\\Delta(\\lambda)-2=0$":[44],"at":[45],"first,":[46],"and":[47,58],"then":[48],"constructed":[51],"$\\Delta(\\lambda)\\pm":[56],"2=0$":[57],"$\\Delta(\\lambda)=0$.":[59],"Examples":[60],"are":[61],"provided":[62],"to":[63],"verify":[64],"algorithm.":[66]},"counts_by_year":[],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}