{"id":"https://openalex.org/W3046689063","doi":"https://doi.org/10.3390/sym12081266","title":"Oscillation Properties of Singular Quantum Trees","display_name":"Oscillation Properties of Singular Quantum Trees","publication_year":2020,"publication_date":"2020-08-01","ids":{"openalex":"https://openalex.org/W3046689063","doi":"https://doi.org/10.3390/sym12081266","mag":"3046689063"},"language":"en","primary_location":{"id":"doi:10.3390/sym12081266","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym12081266","pdf_url":"https://www.mdpi.com/2073-8994/12/8/1266/pdf?version=1596642461","source":{"id":"https://openalex.org/S190787756","display_name":"Symmetry","issn_l":"2073-8994","issn":["2073-8994"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Symmetry","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://www.mdpi.com/2073-8994/12/8/1266/pdf?version=1596642461","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5045088561","display_name":"Monika Homa","orcid":"https://orcid.org/0000-0003-4890-9419"},"institutions":[{"id":"https://openalex.org/I98559091","display_name":"Rzesz\u00f3w University","ror":"https://ror.org/03pfsnq21","country_code":"PL","type":"education","lineage":["https://openalex.org/I98559091"]},{"id":"https://openalex.org/I4210137370","display_name":"Institute of Mathematics","ror":"https://ror.org/04hrrh248","country_code":"PL","type":"facility","lineage":["https://openalex.org/I4210137370","https://openalex.org/I99542240"]}],"countries":["PL"],"is_corresponding":false,"raw_author_name":"Monika Homa","raw_affiliation_strings":["Institute of Mathematics, the University of Rzesz\u00f3w, 1 Pigonia str., 35-310 Rzesz\u00f3w, Poland"],"affiliations":[{"raw_affiliation_string":"Institute of Mathematics, the University of Rzesz\u00f3w, 1 Pigonia str., 35-310 Rzesz\u00f3w, Poland","institution_ids":["https://openalex.org/I98559091","https://openalex.org/I4210137370"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5073010879","display_name":"Rostyslav Hryniv","orcid":"https://orcid.org/0000-0003-0394-9791"},"institutions":[{"id":"https://openalex.org/I4210137370","display_name":"Institute of Mathematics","ror":"https://ror.org/04hrrh248","country_code":"PL","type":"facility","lineage":["https://openalex.org/I4210137370","https://openalex.org/I99542240"]},{"id":"https://openalex.org/I98559091","display_name":"Rzesz\u00f3w University","ror":"https://ror.org/03pfsnq21","country_code":"PL","type":"education","lineage":["https://openalex.org/I98559091"]}],"countries":["PL"],"is_corresponding":true,"raw_author_name":"Rostyslav Hryniv","raw_affiliation_strings":["Institute of Mathematics, the University of Rzesz\u00f3w, 1 Pigonia str., 35-310 Rzesz\u00f3w, Poland"],"affiliations":[{"raw_affiliation_string":"Institute of Mathematics, the University of Rzesz\u00f3w, 1 Pigonia str., 35-310 Rzesz\u00f3w, Poland","institution_ids":["https://openalex.org/I98559091","https://openalex.org/I4210137370"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5073010879"],"corresponding_institution_ids":["https://openalex.org/I4210137370","https://openalex.org/I98559091"],"apc_list":{"value":2000,"currency":"CHF","value_usd":2165},"apc_paid":{"value":2000,"currency":"CHF","value_usd":2165},"fwci":0.0,"has_fulltext":true,"cited_by_count":2,"citation_normalized_percentile":{"value":0.20552644,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":95},"biblio":{"volume":"12","issue":"8","first_page":"1266","last_page":"1266"},"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/T11476","display_name":"Graph theory and applications","score":0.9970999956130981,"subfield":{"id":"https://openalex.org/subfields/2608","display_name":"Geometry and Topology"},"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":0.9947999715805054,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7700268030166626},{"id":"https://openalex.org/keywords/oscillation","display_name":"Oscillation (cell signaling)","score":0.7567301392555237},{"id":"https://openalex.org/keywords/eigenvalues-and-eigenvectors","display_name":"Eigenvalues and eigenvectors","score":0.6789005994796753},{"id":"https://openalex.org/keywords/simple","display_name":"Simple (philosophy)","score":0.6187489032745361},{"id":"https://openalex.org/keywords/metric","display_name":"Metric (unit)","score":0.6050000190734863},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.5297625660896301},{"id":"https://openalex.org/keywords/quantum","display_name":"Quantum","score":0.5163865685462952},{"id":"https://openalex.org/keywords/boundary","display_name":"Boundary (topology)","score":0.47172656655311584},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.4279361665248871},{"id":"https://openalex.org/keywords/boundary-value-problem","display_name":"Boundary value problem","score":0.41237694025039673},{"id":"https://openalex.org/keywords/quantum-mechanics","display_name":"Quantum mechanics","score":0.16218724846839905},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.12600725889205933}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7700268030166626},{"id":"https://openalex.org/C2778439541","wikidata":"https://www.wikidata.org/wiki/Q7106412","display_name":"Oscillation (cell signaling)","level":2,"score":0.7567301392555237},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.6789005994796753},{"id":"https://openalex.org/C2780586882","wikidata":"https://www.wikidata.org/wiki/Q7520643","display_name":"Simple (philosophy)","level":2,"score":0.6187489032745361},{"id":"https://openalex.org/C176217482","wikidata":"https://www.wikidata.org/wiki/Q860554","display_name":"Metric (unit)","level":2,"score":0.6050000190734863},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.5297625660896301},{"id":"https://openalex.org/C84114770","wikidata":"https://www.wikidata.org/wiki/Q46344","display_name":"Quantum","level":2,"score":0.5163865685462952},{"id":"https://openalex.org/C62354387","wikidata":"https://www.wikidata.org/wiki/Q875399","display_name":"Boundary (topology)","level":2,"score":0.47172656655311584},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.4279361665248871},{"id":"https://openalex.org/C182310444","wikidata":"https://www.wikidata.org/wiki/Q1332643","display_name":"Boundary value problem","level":2,"score":0.41237694025039673},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.16218724846839905},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.12600725889205933},{"id":"https://openalex.org/C21547014","wikidata":"https://www.wikidata.org/wiki/Q1423657","display_name":"Operations management","level":1,"score":0.0},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0},{"id":"https://openalex.org/C111472728","wikidata":"https://www.wikidata.org/wiki/Q9471","display_name":"Epistemology","level":1,"score":0.0},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C54355233","wikidata":"https://www.wikidata.org/wiki/Q7162","display_name":"Genetics","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.3390/sym12081266","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym12081266","pdf_url":"https://www.mdpi.com/2073-8994/12/8/1266/pdf?version=1596642461","source":{"id":"https://openalex.org/S190787756","display_name":"Symmetry","issn_l":"2073-8994","issn":["2073-8994"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Symmetry","raw_type":"journal-article"},{"id":"pmh:oai:doaj.org/article:00ec14b6874941faba73536317946b7d","is_oa":true,"landing_page_url":"https://doaj.org/article/00ec14b6874941faba73536317946b7d","pdf_url":null,"source":{"id":"https://openalex.org/S112646816","display_name":"SHILAP Revista de lepidopterolog\u00eda","issn_l":"0300-5267","issn":["0300-5267","2340-4078"],"is_oa":true,"is_in_doaj":true,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"journal"},"license":"cc-by-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Symmetry, Vol 12, Iss 8, p 1266 (2020)","raw_type":"article"},{"id":"pmh:oai:mdpi.com:/2073-8994/12/8/1266/","is_oa":true,"landing_page_url":"https://dx.doi.org/10.3390/sym12081266","pdf_url":null,"source":{"id":"https://openalex.org/S4306400947","display_name":"MDPI (MDPI AG)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I4210097602","host_organization_name":"Multidisciplinary Digital Publishing Institute (Switzerland)","host_organization_lineage":["https://openalex.org/I4210097602"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Symmetry","raw_type":"Text"}],"best_oa_location":{"id":"doi:10.3390/sym12081266","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym12081266","pdf_url":"https://www.mdpi.com/2073-8994/12/8/1266/pdf?version=1596642461","source":{"id":"https://openalex.org/S190787756","display_name":"Symmetry","issn_l":"2073-8994","issn":["2073-8994"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Symmetry","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W3046689063.pdf","grobid_xml":"https://content.openalex.org/works/W3046689063.grobid-xml"},"referenced_works_count":35,"referenced_works":["https://openalex.org/W84701144","https://openalex.org/W342268678","https://openalex.org/W963614142","https://openalex.org/W1866716260","https://openalex.org/W1967757921","https://openalex.org/W1991004274","https://openalex.org/W1995475407","https://openalex.org/W2016979060","https://openalex.org/W2029993762","https://openalex.org/W2031599158","https://openalex.org/W2059800177","https://openalex.org/W2080193431","https://openalex.org/W2120124313","https://openalex.org/W2153504110","https://openalex.org/W2171498293","https://openalex.org/W2310311511","https://openalex.org/W2321710858","https://openalex.org/W2756874281","https://openalex.org/W2962789371","https://openalex.org/W3098936281","https://openalex.org/W3099640657","https://openalex.org/W3105575315","https://openalex.org/W3123681079","https://openalex.org/W3146592959","https://openalex.org/W4231116741","https://openalex.org/W4238371686","https://openalex.org/W4250329484","https://openalex.org/W6603401641","https://openalex.org/W6603741294","https://openalex.org/W6611643084","https://openalex.org/W6629208752","https://openalex.org/W6635315704","https://openalex.org/W6639217917","https://openalex.org/W6789224213","https://openalex.org/W6831829772"],"related_works":["https://openalex.org/W2004735650","https://openalex.org/W1551019254","https://openalex.org/W2165749285","https://openalex.org/W2000010777","https://openalex.org/W2057473185","https://openalex.org/W2062626603","https://openalex.org/W2359162541","https://openalex.org/W2385067730","https://openalex.org/W3014273909","https://openalex.org/W2133690079"],"abstract_inverted_index":{"We":[0,93],"discuss":[1],"the":[2,6,13,58,72,81,106,112],"possibility":[3],"of":[4,15,46,103],"generalizing":[5],"Sturm":[7,60],"comparison":[8,73],"and":[9,32,37,79,109],"oscillation":[10,82,113],"theorems":[11],"to":[12,21,34,115],"case":[14],"singular":[16,26],"quantum":[17,66],"trees,":[18],"that":[19,52,71,80,86],"is,":[20,87],"Sturm-Liouville":[22],"differential":[23,47],"expressions":[24],"with":[25,90],"coefficients":[27],"acting":[28],"on":[29,49,55],"metric":[30,50],"trees":[31,51],"subject":[33],"some":[35,56,101],"boundary":[36],"interface":[38],"conditions.":[39],"As":[40],"there":[41],"may":[42],"exist":[43],"non-trivial":[44],"solutions":[45,104],"equations":[48],"vanish":[53],"identically":[54],"edges,":[57],"classical":[59],"theory":[61],"cannot":[62],"hold":[63],"globally":[64],"for":[65,88],"trees.":[67],"However,":[68],"we":[69],"show":[70],"theorem":[74,83],"holds":[75,84],"under":[76],"minimal":[77],"assumptions":[78],"generically,":[85],"operators":[89],"simple":[91,116],"spectra.":[92],"also":[94],"introduce":[95],"a":[96],"special":[97],"Pr\u00fcfer":[98],"angle,":[99],"establish":[100],"properties":[102],"in":[105],"non-generic":[107],"case,":[108],"then":[110],"extend":[111],"results":[114],"eigenvalues.":[117]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2014,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}