{"id":"https://openalex.org/W2054841976","doi":"https://doi.org/10.1137/0405029","title":"IInfinite Graphs with Nonconstant Dirichlet Finite Harmonic Functions","display_name":"IInfinite Graphs with Nonconstant Dirichlet Finite Harmonic Functions","publication_year":1992,"publication_date":"1992-08-01","ids":{"openalex":"https://openalex.org/W2054841976","doi":"https://doi.org/10.1137/0405029","mag":"2054841976"},"language":"en","primary_location":{"id":"doi:10.1137/0405029","is_oa":false,"landing_page_url":"https://doi.org/10.1137/0405029","pdf_url":null,"source":{"id":"https://openalex.org/S117679221","display_name":"SIAM Journal on Discrete Mathematics","issn_l":"0895-4801","issn":["0895-4801","1095-7146"],"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 Discrete 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/A5110865628","display_name":"Donald I. Cartwright","orcid":null},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Donald I. Cartwright","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5045303057","display_name":"Wolfgang Woess","orcid":"https://orcid.org/0000-0002-7065-7126"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Wolfgang Woess","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5110865628"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":1.8325,"has_fulltext":false,"cited_by_count":16,"citation_normalized_percentile":{"value":0.84330794,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":"5","issue":"3","first_page":"380","last_page":"385"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11022","display_name":"Spectral Theory in Mathematical Physics","score":0.9984999895095825,"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":0.9984999895095825,"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/T10304","display_name":"Geometric and Algebraic Topology","score":0.9980999827384949,"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/T10229","display_name":"Geometric Analysis and Curvature Flows","score":0.9962999820709229,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8800634145736694},{"id":"https://openalex.org/keywords/harmonic-function","display_name":"Harmonic function","score":0.7874549627304077},{"id":"https://openalex.org/keywords/harmonic","display_name":"Harmonic","score":0.6236356496810913},{"id":"https://openalex.org/keywords/dirichlet-distribution","display_name":"Dirichlet distribution","score":0.6093959212303162},{"id":"https://openalex.org/keywords/harmonic-measure","display_name":"Harmonic measure","score":0.5699573755264282},{"id":"https://openalex.org/keywords/class","display_name":"Class (philosophy)","score":0.521141529083252},{"id":"https://openalex.org/keywords/boundary","display_name":"Boundary (topology)","score":0.5039679408073425},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.46481189131736755},{"id":"https://openalex.org/keywords/harmonic-number","display_name":"Harmonic number","score":0.4564935266971588},{"id":"https://openalex.org/keywords/dirichlet-problem","display_name":"Dirichlet problem","score":0.4529383182525635},{"id":"https://openalex.org/keywords/plane","display_name":"Plane (geometry)","score":0.44057032465934753},{"id":"https://openalex.org/keywords/dirichlet-boundary-condition","display_name":"Dirichlet boundary condition","score":0.43362611532211304},{"id":"https://openalex.org/keywords/boundary-value-problem","display_name":"Boundary value problem","score":0.41037434339523315},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.13428834080696106},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.05049237608909607},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.04642757773399353}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8800634145736694},{"id":"https://openalex.org/C627467","wikidata":"https://www.wikidata.org/wiki/Q599027","display_name":"Harmonic function","level":2,"score":0.7874549627304077},{"id":"https://openalex.org/C127934551","wikidata":"https://www.wikidata.org/wiki/Q1148098","display_name":"Harmonic","level":2,"score":0.6236356496810913},{"id":"https://openalex.org/C169214877","wikidata":"https://www.wikidata.org/wiki/Q981016","display_name":"Dirichlet distribution","level":3,"score":0.6093959212303162},{"id":"https://openalex.org/C53688716","wikidata":"https://www.wikidata.org/wiki/Q5659270","display_name":"Harmonic measure","level":3,"score":0.5699573755264282},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.521141529083252},{"id":"https://openalex.org/C62354387","wikidata":"https://www.wikidata.org/wiki/Q875399","display_name":"Boundary (topology)","level":2,"score":0.5039679408073425},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.46481189131736755},{"id":"https://openalex.org/C28581250","wikidata":"https://www.wikidata.org/wiki/Q13407133","display_name":"Harmonic number","level":3,"score":0.4564935266971588},{"id":"https://openalex.org/C2779560616","wikidata":"https://www.wikidata.org/wiki/Q1192869","display_name":"Dirichlet problem","level":3,"score":0.4529383182525635},{"id":"https://openalex.org/C17825722","wikidata":"https://www.wikidata.org/wiki/Q17285","display_name":"Plane (geometry)","level":2,"score":0.44057032465934753},{"id":"https://openalex.org/C110167270","wikidata":"https://www.wikidata.org/wiki/Q1193699","display_name":"Dirichlet boundary condition","level":3,"score":0.43362611532211304},{"id":"https://openalex.org/C182310444","wikidata":"https://www.wikidata.org/wiki/Q1332643","display_name":"Boundary value problem","level":2,"score":0.41037434339523315},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.13428834080696106},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.05049237608909607},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.04642757773399353},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.0},{"id":"https://openalex.org/C35235930","wikidata":"https://www.wikidata.org/wiki/Q187235","display_name":"Riemann zeta function","level":2,"score":0.0},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/0405029","is_oa":false,"landing_page_url":"https://doi.org/10.1137/0405029","pdf_url":null,"source":{"id":"https://openalex.org/S117679221","display_name":"SIAM Journal on Discrete Mathematics","issn_l":"0895-4801","issn":["0895-4801","1095-7146"],"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 Discrete Mathematics","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":14,"referenced_works":["https://openalex.org/W1494036437","https://openalex.org/W1502669108","https://openalex.org/W1560594658","https://openalex.org/W1969697615","https://openalex.org/W1972481868","https://openalex.org/W2028588440","https://openalex.org/W2028978432","https://openalex.org/W2038098381","https://openalex.org/W2052074622","https://openalex.org/W2101226606","https://openalex.org/W2188147912","https://openalex.org/W2317192174","https://openalex.org/W4206069707","https://openalex.org/W4293217885"],"related_works":["https://openalex.org/W1979009627","https://openalex.org/W1972832342","https://openalex.org/W1977410499","https://openalex.org/W2073803215","https://openalex.org/W1965393501","https://openalex.org/W2942292628","https://openalex.org/W4235175322","https://openalex.org/W1969439884","https://openalex.org/W2059988602","https://openalex.org/W2379505354"],"abstract_inverted_index":{"A":[0],"class":[1],"of":[2,30],"infinite":[3],"graphs":[4],"that":[5],"can":[6],"be":[7],"embedded":[8],"uniformly":[9],"in":[10],"the":[11],"hyperbolic":[12],"plane":[13],"and":[14],"carry":[15],"nonconstant":[16],"harmonic":[17,33],"functions":[18,34],"with":[19],"finite":[20],"Dirichlet":[21],"sum":[22],"is":[23,39],"exhibited.":[24],"In":[25],"fact,":[26],"a":[27],"general":[28],"method":[29],"constructing":[31],"such":[32],"\u201cwith":[35],"prescribed":[36],"boundary":[37],"values\u201d":[38],"provided.":[40]},"counts_by_year":[{"year":2018,"cited_by_count":1},{"year":2012,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}