{"id":"https://openalex.org/W2076373225","doi":"https://doi.org/10.1002/cta.4490220507","title":"Uncountable transfinite graphs and electrical networks","display_name":"Uncountable transfinite graphs and electrical networks","publication_year":1994,"publication_date":"1994-09-01","ids":{"openalex":"https://openalex.org/W2076373225","doi":"https://doi.org/10.1002/cta.4490220507","mag":"2076373225"},"language":"en","primary_location":{"id":"doi:10.1002/cta.4490220507","is_oa":false,"landing_page_url":"https://doi.org/10.1002/cta.4490220507","pdf_url":null,"source":{"id":"https://openalex.org/S92132303","display_name":"International Journal of Circuit Theory and Applications","issn_l":"0098-9886","issn":["0098-9886","1097-007X"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320595","host_organization_name":"Wiley","host_organization_lineage":["https://openalex.org/P4310320595"],"host_organization_lineage_names":["Wiley"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Circuit Theory and Applications","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/A5056301868","display_name":"A. H. Zemanian","orcid":null},"institutions":[{"id":"https://openalex.org/I59553526","display_name":"Stony Brook University","ror":"https://ror.org/05qghxh33","country_code":"US","type":"education","lineage":["https://openalex.org/I59553526"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"A. H. Zemanian","raw_affiliation_strings":["Electrical Engineering Department, University of Stony Brook, Stony Brook, NY 11794-2350, U.S.A","Electrical Engineering Department, University of Stony Brook, Stony Brook, NY 11794\u20102350, U.S.A"],"affiliations":[{"raw_affiliation_string":"Electrical Engineering Department, University of Stony Brook, Stony Brook, NY 11794-2350, U.S.A","institution_ids":["https://openalex.org/I59553526"]},{"raw_affiliation_string":"Electrical Engineering Department, University of Stony Brook, Stony Brook, NY 11794\u20102350, U.S.A","institution_ids":["https://openalex.org/I59553526"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5056301868"],"corresponding_institution_ids":["https://openalex.org/I59553526"],"apc_list":{"value":3660,"currency":"USD","value_usd":3660},"apc_paid":null,"fwci":0.4872,"has_fulltext":false,"cited_by_count":1,"citation_normalized_percentile":{"value":0.64008667,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"22","issue":"5","first_page":"387","last_page":"398"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12002","display_name":"Computability, Logic, AI Algorithms","score":0.9746000170707703,"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"}},"topics":[{"id":"https://openalex.org/T12002","display_name":"Computability, Logic, AI Algorithms","score":0.9746000170707703,"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"}},{"id":"https://openalex.org/T10363","display_name":"Low-power high-performance VLSI design","score":0.9731000065803528,"subfield":{"id":"https://openalex.org/subfields/2208","display_name":"Electrical and Electronic Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10720","display_name":"Complexity and Algorithms in Graphs","score":0.9354000091552734,"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/uncountable-set","display_name":"Uncountable set","score":0.9848846793174744},{"id":"https://openalex.org/keywords/transfinite-number","display_name":"Transfinite number","score":0.9663865566253662},{"id":"https://openalex.org/keywords/countable-set","display_name":"Countable set","score":0.8820115923881531},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6357839703559875},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.534816324710846},{"id":"https://openalex.org/keywords/continuum-hypothesis","display_name":"Continuum hypothesis","score":0.4920048415660858},{"id":"https://openalex.org/keywords/graph-theory","display_name":"Graph theory","score":0.43186473846435547},{"id":"https://openalex.org/keywords/topology","display_name":"Topology (electrical circuits)","score":0.3251088261604309},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.30079054832458496},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.08040326833724976}],"concepts":[{"id":"https://openalex.org/C142399903","wikidata":"https://www.wikidata.org/wiki/Q1128796","display_name":"Uncountable set","level":3,"score":0.9848846793174744},{"id":"https://openalex.org/C147358099","wikidata":"https://www.wikidata.org/wiki/Q1069891","display_name":"Transfinite number","level":2,"score":0.9663865566253662},{"id":"https://openalex.org/C110729354","wikidata":"https://www.wikidata.org/wiki/Q185478","display_name":"Countable set","level":2,"score":0.8820115923881531},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6357839703559875},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.534816324710846},{"id":"https://openalex.org/C96488702","wikidata":"https://www.wikidata.org/wiki/Q208416","display_name":"Continuum hypothesis","level":2,"score":0.4920048415660858},{"id":"https://openalex.org/C88230418","wikidata":"https://www.wikidata.org/wiki/Q131476","display_name":"Graph theory","level":2,"score":0.43186473846435547},{"id":"https://openalex.org/C184720557","wikidata":"https://www.wikidata.org/wiki/Q7825049","display_name":"Topology (electrical circuits)","level":2,"score":0.3251088261604309},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.30079054832458496},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.08040326833724976}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1002/cta.4490220507","is_oa":false,"landing_page_url":"https://doi.org/10.1002/cta.4490220507","pdf_url":null,"source":{"id":"https://openalex.org/S92132303","display_name":"International Journal of Circuit Theory and Applications","issn_l":"0098-9886","issn":["0098-9886","1097-007X"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320595","host_organization_name":"Wiley","host_organization_lineage":["https://openalex.org/P4310320595"],"host_organization_lineage_names":["Wiley"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Circuit Theory and Applications","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":10,"referenced_works":["https://openalex.org/W1536161473","https://openalex.org/W1601875069","https://openalex.org/W1972481868","https://openalex.org/W2011266178","https://openalex.org/W2016722882","https://openalex.org/W2045241897","https://openalex.org/W2058162908","https://openalex.org/W2172139881","https://openalex.org/W4253302775","https://openalex.org/W4300847361"],"related_works":["https://openalex.org/W3019662020","https://openalex.org/W2076373225","https://openalex.org/W2100222222","https://openalex.org/W2729526449","https://openalex.org/W2600675026","https://openalex.org/W4297571715","https://openalex.org/W2512721618","https://openalex.org/W4294167392","https://openalex.org/W1516534821","https://openalex.org/W1982606881"],"abstract_inverted_index":{"Abstract":[0],"Up":[1],"to":[2,33,99],"now":[3],"the":[4,19,22,48,56,60,67,70,82,97,102],"theory":[5,32,49,104],"of":[6,50,59,69,81],"infinite":[7],"and":[8,11,35,93,95],"transfinite":[9,51,61],"graphs":[10,34],"electrical":[12,87],"networks":[13,36],"has":[14],"been":[15],"established":[16],"only":[17,78],"for":[18],"case":[20],"where":[21],"branch":[23,39,71],"sets":[24],"are":[25,63],"countable.":[26],"This":[27],"work":[28],"extends":[29],"that":[30,43,77],"prior":[31,103],"with":[37],"uncountable":[38,86],"sets,":[40],"a":[41],"structure":[42,58],"arises":[44],"quite":[45],"naturally":[46],"in":[47,84,101],"graphs.":[52],"Moreover,":[53],"conditions":[54],"on":[55],"local":[57],"graph":[62],"given":[64],"which":[65],"insure":[66],"countability":[68,100],"set.":[72],"Finally,":[73],"it":[74],"is":[75,105],"shown":[76],"countably":[79],"many":[80],"branches":[83],"an":[85],"network":[88],"can":[89],"have":[90],"non\u2010zero":[91],"voltages":[92],"currents,":[94],"therefore":[96],"restriction":[98],"not":[106],"essentially":[107],"restrictive.":[108]},"counts_by_year":[],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
