{"id":"https://openalex.org/W2077530085","doi":"https://doi.org/10.1080/00207160410001708832","title":"An axial four-index transportation problem and its algebraic characterizations","display_name":"An axial four-index transportation problem and its algebraic characterizations","publication_year":2004,"publication_date":"2004-06-01","ids":{"openalex":"https://openalex.org/W2077530085","doi":"https://doi.org/10.1080/00207160410001708832","mag":"2077530085"},"language":"en","primary_location":{"id":"doi:10.1080/00207160410001708832","is_oa":false,"landing_page_url":"https://doi.org/10.1080/00207160410001708832","pdf_url":null,"source":{"id":"https://openalex.org/S124867444","display_name":"International Journal of Computer Mathematics","issn_l":"0020-7160","issn":["0020-7160","1026-7425","1029-0265"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320547","host_organization_name":"Taylor & Francis","host_organization_lineage":["https://openalex.org/P4310320547"],"host_organization_lineage_names":["Taylor & Francis"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Computer 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/A5061654693","display_name":"Serap Bulut","orcid":"https://orcid.org/0000-0002-6506-4588"},"institutions":[{"id":"https://openalex.org/I193615760","display_name":"Dokuz Eyl\u00fcl University","ror":"https://ror.org/00dbd8b73","country_code":"TR","type":"education","lineage":["https://openalex.org/I193615760"]}],"countries":["TR"],"is_corresponding":true,"raw_author_name":"S. Aysun Bulut","raw_affiliation_strings":["Division of Mathematics, Faculty of Engineering , Dokuz Eyl\u00fcl University , 35100, Bornova, Izmir, Turkey"],"affiliations":[{"raw_affiliation_string":"Division of Mathematics, Faculty of Engineering , Dokuz Eyl\u00fcl University , 35100, Bornova, Izmir, Turkey","institution_ids":["https://openalex.org/I193615760"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5113599683","display_name":"Hamza Bulut","orcid":null},"institutions":[{"id":"https://openalex.org/I193615760","display_name":"Dokuz Eyl\u00fcl University","ror":"https://ror.org/00dbd8b73","country_code":"TR","type":"education","lineage":["https://openalex.org/I193615760"]}],"countries":["TR"],"is_corresponding":false,"raw_author_name":"Hamza Bulut","raw_affiliation_strings":["Division of Mathematics, Faculty of Engineering , Dokuz Eyl\u00fcl University , 35100, Bornova, Izmir, Turkey"],"affiliations":[{"raw_affiliation_string":"Division of Mathematics, Faculty of Engineering , Dokuz Eyl\u00fcl University , 35100, Bornova, Izmir, Turkey","institution_ids":["https://openalex.org/I193615760"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5061654693"],"corresponding_institution_ids":["https://openalex.org/I193615760"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":4,"citation_normalized_percentile":{"value":0.09742604,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":"81","issue":"6","first_page":"765","last_page":"773"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12709","display_name":"Optimization and Mathematical Programming","score":0.9970999956130981,"subfield":{"id":"https://openalex.org/subfields/2207","display_name":"Control and Systems Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T12709","display_name":"Optimization and Mathematical Programming","score":0.9970999956130981,"subfield":{"id":"https://openalex.org/subfields/2207","display_name":"Control and Systems 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/T10698","display_name":"Transportation Planning and Optimization","score":0.9889000058174133,"subfield":{"id":"https://openalex.org/subfields/3313","display_name":"Transportation"},"field":{"id":"https://openalex.org/fields/33","display_name":"Social Sciences"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},{"id":"https://openalex.org/T10963","display_name":"Advanced Optimization Algorithms Research","score":0.9384999871253967,"subfield":{"id":"https://openalex.org/subfields/2612","display_name":"Numerical Analysis"},"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":0.8213987946510315},{"id":"https://openalex.org/keywords/eigenvalues-and-eigenvectors","display_name":"Eigenvalues and eigenvectors","score":0.6682186126708984},{"id":"https://openalex.org/keywords/algebraic-number","display_name":"Algebraic number","score":0.6465190649032593},{"id":"https://openalex.org/keywords/index","display_name":"Index (typography)","score":0.5481458306312561},{"id":"https://openalex.org/keywords/order","display_name":"Order (exchange)","score":0.5406690239906311},{"id":"https://openalex.org/keywords/flow-network","display_name":"Flow network","score":0.539076566696167},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.4634762704372406},{"id":"https://openalex.org/keywords/matrix","display_name":"Matrix (chemical analysis)","score":0.4628450572490692},{"id":"https://openalex.org/keywords/transportation-theory","display_name":"Transportation theory","score":0.4558880925178528},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.25602662563323975},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.06990671157836914},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.05428117513656616}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8213987946510315},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.6682186126708984},{"id":"https://openalex.org/C9376300","wikidata":"https://www.wikidata.org/wiki/Q168817","display_name":"Algebraic number","level":2,"score":0.6465190649032593},{"id":"https://openalex.org/C2777382242","wikidata":"https://www.wikidata.org/wiki/Q6017816","display_name":"Index (typography)","level":2,"score":0.5481458306312561},{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.5406690239906311},{"id":"https://openalex.org/C114809511","wikidata":"https://www.wikidata.org/wiki/Q1412924","display_name":"Flow network","level":2,"score":0.539076566696167},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.4634762704372406},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.4628450572490692},{"id":"https://openalex.org/C31829261","wikidata":"https://www.wikidata.org/wiki/Q1929885","display_name":"Transportation theory","level":2,"score":0.4558880925178528},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.25602662563323975},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.06990671157836914},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.05428117513656616},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C10138342","wikidata":"https://www.wikidata.org/wiki/Q43015","display_name":"Finance","level":1,"score":0.0},{"id":"https://openalex.org/C159985019","wikidata":"https://www.wikidata.org/wiki/Q181790","display_name":"Composite material","level":1,"score":0.0},{"id":"https://openalex.org/C192562407","wikidata":"https://www.wikidata.org/wiki/Q228736","display_name":"Materials science","level":0,"score":0.0},{"id":"https://openalex.org/C136764020","wikidata":"https://www.wikidata.org/wiki/Q466","display_name":"World Wide Web","level":1,"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:10.1080/00207160410001708832","is_oa":false,"landing_page_url":"https://doi.org/10.1080/00207160410001708832","pdf_url":null,"source":{"id":"https://openalex.org/S124867444","display_name":"International Journal of Computer Mathematics","issn_l":"0020-7160","issn":["0020-7160","1026-7425","1029-0265"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320547","host_organization_name":"Taylor & Francis","host_organization_lineage":["https://openalex.org/P4310320547"],"host_organization_lineage_names":["Taylor & Francis"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Computer 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":12,"referenced_works":["https://openalex.org/W64250266","https://openalex.org/W1965840109","https://openalex.org/W1973551208","https://openalex.org/W1992901776","https://openalex.org/W2013348732","https://openalex.org/W2015898583","https://openalex.org/W2024537828","https://openalex.org/W2032268867","https://openalex.org/W2041290270","https://openalex.org/W2056679620","https://openalex.org/W2109798945","https://openalex.org/W2160117479"],"related_works":["https://openalex.org/W1978042415","https://openalex.org/W3086542228","https://openalex.org/W2017331178","https://openalex.org/W3083820578","https://openalex.org/W2976797620","https://openalex.org/W1982496263","https://openalex.org/W2090285349","https://openalex.org/W4297094229","https://openalex.org/W2182929911","https://openalex.org/W1992901776"],"abstract_inverted_index":{"In":[0],"this":[1],"study,":[2],"we":[3,58],"describe":[4],"an":[5,106],"axial":[6,50],"four-index":[7,51,66],"transportation":[8,52,67],"problem":[9,27,68],"of":[10,48,69,94,96],"order":[11,70],"1":[12,71],"\u00d7":[13,15,17,72,74,76,108],"m":[14,29,73,107,109],"n":[16,31,75],"1,":[18],"which":[19],"is":[20,79,105],"equivalent":[21],"to":[22],"a":[23],"circularization":[24],"network":[25],"flow":[26],"with":[28,60],"+":[30,32,37,39],"2":[33],"nodes":[34],"and":[35,54,88,100],"(m":[36],"1)(n":[38],"1)":[40],"arcs.":[41],"We":[42],"then":[43],"give":[44],"some":[45,61],"algebraic":[46,86],"characterizations":[47],"the":[49,56,64,97],"problem,":[53],"compare":[55],"results":[57,62],"obtained":[59],"on":[63],"planar":[65],"1.":[77,114],"It":[78],"shown":[80],"that":[81],"these":[82],"problems":[83],"have":[84],"common":[85],"characterizations,":[87],"can":[89],"be":[90],"solved":[91],"in":[92],"terms":[93],"eigenvectors":[95],"matrices":[98],"Jm":[99,104],"Jn":[101],",":[102],"where":[103],"matrix":[110],"whose":[111],"entries":[112],"are":[113]},"counts_by_year":[{"year":2019,"cited_by_count":1},{"year":2016,"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"}