{"id":"https://openalex.org/W2540385142","doi":"https://doi.org/10.3103/s0146411617070185","title":"Network Model for the Problem of Integer Balancing of a Four-Dimensional Matrix","display_name":"Network Model for the Problem of Integer Balancing of a Four-Dimensional Matrix","publication_year":2017,"publication_date":"2017-12-01","ids":{"openalex":"https://openalex.org/W2540385142","doi":"https://doi.org/10.3103/s0146411617070185","mag":"2540385142"},"language":"en","primary_location":{"id":"doi:10.3103/s0146411617070185","is_oa":false,"landing_page_url":"https://doi.org/10.3103/s0146411617070185","pdf_url":null,"source":{"id":"https://openalex.org/S17203304","display_name":"Automatic Control and Computer Sciences","issn_l":"0146-4116","issn":["0146-4116","1558-108X"],"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/P4310320267","host_organization_name":"Pleiades Publishing","host_organization_lineage":["https://openalex.org/P4310320267","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Pleiades Publishing","Springer Nature"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Automatic Control and Computer Sciences","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/A5019524013","display_name":"\u0410. \u0412. \u0421\u043c\u0438\u0440\u043d\u043e\u0432","orcid":"https://orcid.org/0000-0002-0980-2507"},"institutions":[{"id":"https://openalex.org/I198371094","display_name":"Yaroslavl State University","ror":"https://ror.org/044s2fj67","country_code":"RU","type":"education","lineage":["https://openalex.org/I198371094"]}],"countries":["RU"],"is_corresponding":true,"raw_author_name":"A. V. Smirnov","raw_affiliation_strings":["Demidov Yaroslavl State University, Yaroslavl, 150003, Russia"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Demidov Yaroslavl State University, Yaroslavl, 150003, Russia","institution_ids":["https://openalex.org/I198371094"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5019524013"],"corresponding_institution_ids":["https://openalex.org/I198371094"],"apc_list":null,"apc_paid":null,"fwci":0.677,"has_fulltext":false,"cited_by_count":15,"citation_normalized_percentile":{"value":0.65900383,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":98},"biblio":{"volume":"51","issue":"7","first_page":"558","last_page":"566"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T13020","display_name":"Heat Transfer and Mathematical Modeling","score":0.10440000146627426,"subfield":{"id":"https://openalex.org/subfields/2210","display_name":"Mechanical 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/T13020","display_name":"Heat Transfer and Mathematical Modeling","score":0.10440000146627426,"subfield":{"id":"https://openalex.org/subfields/2210","display_name":"Mechanical 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/T13983","display_name":"Cybersecurity and Information Systems","score":0.08290000259876251,"subfield":{"id":"https://openalex.org/subfields/1705","display_name":"Computer Networks and Communications"},"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/T13964","display_name":"Educational Technology and Optimization","score":0.04670000076293945,"subfield":{"id":"https://openalex.org/subfields/1710","display_name":"Information Systems"},"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/rounding","display_name":"Rounding","score":0.6852081418037415},{"id":"https://openalex.org/keywords/integer","display_name":"Integer (computer science)","score":0.6366757154464722},{"id":"https://openalex.org/keywords/integer-matrix","display_name":"Integer matrix","score":0.5880244374275208},{"id":"https://openalex.org/keywords/matrix","display_name":"Matrix (chemical analysis)","score":0.5503038763999939},{"id":"https://openalex.org/keywords/multiplicity","display_name":"Multiplicity (mathematics)","score":0.5354585647583008},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5286633968353271},{"id":"https://openalex.org/keywords/flow-network","display_name":"Flow network","score":0.4757630228996277},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.4088807702064514},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.38381022214889526},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.3617432117462158},{"id":"https://openalex.org/keywords/nonnegative-matrix","display_name":"Nonnegative matrix","score":0.10511752963066101},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.10087162256240845},{"id":"https://openalex.org/keywords/symmetric-matrix","display_name":"Symmetric matrix","score":0.08923691511154175}],"concepts":[{"id":"https://openalex.org/C136625980","wikidata":"https://www.wikidata.org/wiki/Q663208","display_name":"Rounding","level":2,"score":0.6852081418037415},{"id":"https://openalex.org/C97137487","wikidata":"https://www.wikidata.org/wiki/Q729138","display_name":"Integer (computer science)","level":2,"score":0.6366757154464722},{"id":"https://openalex.org/C62555958","wikidata":"https://www.wikidata.org/wiki/Q6042601","display_name":"Integer matrix","level":5,"score":0.5880244374275208},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.5503038763999939},{"id":"https://openalex.org/C156004811","wikidata":"https://www.wikidata.org/wiki/Q2228257","display_name":"Multiplicity (mathematics)","level":2,"score":0.5354585647583008},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5286633968353271},{"id":"https://openalex.org/C114809511","wikidata":"https://www.wikidata.org/wiki/Q1412924","display_name":"Flow network","level":2,"score":0.4757630228996277},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4088807702064514},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.38381022214889526},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3617432117462158},{"id":"https://openalex.org/C139018669","wikidata":"https://www.wikidata.org/wiki/Q6961560","display_name":"Nonnegative matrix","level":4,"score":0.10511752963066101},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.10087162256240845},{"id":"https://openalex.org/C54848796","wikidata":"https://www.wikidata.org/wiki/Q339011","display_name":"Symmetric matrix","level":3,"score":0.08923691511154175},{"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/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C111919701","wikidata":"https://www.wikidata.org/wiki/Q9135","display_name":"Operating system","level":1,"score":0.0},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","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/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.3103/s0146411617070185","is_oa":false,"landing_page_url":"https://doi.org/10.3103/s0146411617070185","pdf_url":null,"source":{"id":"https://openalex.org/S17203304","display_name":"Automatic Control and Computer Sciences","issn_l":"0146-4116","issn":["0146-4116","1558-108X"],"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/P4310320267","host_organization_name":"Pleiades Publishing","host_organization_lineage":["https://openalex.org/P4310320267","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Pleiades Publishing","Springer Nature"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Automatic Control and Computer Sciences","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":11,"referenced_works":["https://openalex.org/W925666063","https://openalex.org/W1964119857","https://openalex.org/W2011039300","https://openalex.org/W2045588107","https://openalex.org/W2062754819","https://openalex.org/W2088158318","https://openalex.org/W2210271247","https://openalex.org/W2401610261","https://openalex.org/W2402311713","https://openalex.org/W3144909185","https://openalex.org/W4285719527"],"related_works":["https://openalex.org/W2048541553","https://openalex.org/W2366105249","https://openalex.org/W1975527650","https://openalex.org/W2185598862","https://openalex.org/W2963641145","https://openalex.org/W2023301239","https://openalex.org/W2381311028","https://openalex.org/W4385335055","https://openalex.org/W4387316460","https://openalex.org/W3028475238"],"abstract_inverted_index":{"The":[0,11,70,172,178,250],"problem":[1,71,125,201,213,238,243],"of":[2,5,13,24,40,78,119,126,135,146,162,180,202,214,224,247,252],"integer":[3,76,199,264],"balancing":[4,200,237,265],"a":[6,160,181,220,271],"four-dimensional":[7,236],"matrix":[8,28,77,206],"is":[9,46,72,140,159,267],"studied.":[10,142],"elements":[12,55,93],"the":[14,25,41,43,54,67,79,87,92,95,99,104,107,122,124,128,133,193,198,212,216,231,235,240,245,254,259,263],"inner":[15],"part":[16],"(all":[17],"four":[18,110],"indices":[19,60,112],"are":[20,29,51,61,144,167,176,188,191,229],"greater":[21],"than":[22],"zero)":[23],"given":[26],"real":[27],"summed":[30],"in":[31,132,219,244],"each":[32,35,170],"direction":[33],"and":[34,37,153,157,184],"two-":[36],"three-dimensional":[38],"section":[39],"matrix;":[42],"total":[44],"sum":[45],"also":[47,141],"found.":[48],"These":[49],"sums":[50],"placed":[52],"into":[53],"where":[56],"one":[57,89],"or":[58,98],"more":[59],"equal":[62],"to":[63,66,73,211,239],"zero":[64,111],"(according":[65],"summing":[68],"directions).":[69],"find":[74],"an":[75,203],"same":[80,105],"structure,":[81],"which":[82,166,257],"can":[83],"be":[84,114],"produced":[85,115],"from":[86],"initial":[88],"by":[90],"replacing":[91],"with":[94,109,116,169],"largest":[96],"previous":[97],"smallest":[100],"following":[101],"integer.":[102],"At":[103],"time,":[106],"element":[108],"should":[113],"standard":[117],"rules":[118,175,232],"rounding-off.":[120],"In":[121],"article":[123],"finding":[127,215,253],"maximum":[129,217,241,255],"multiple":[130,151,156,222],"flow":[131,218,242],"network":[134,173,183,223,246],"any":[136],"natural":[137],"multiplicity":[138,225,248],"k":[139,163,226],"There":[143,190,228],"arcs":[145,152],"three":[147],"types:":[148],"ordinary":[149],"arcs,":[150,165],"multi-arcs.":[154],"Each":[155],"multi-arc":[158],"union":[161],"linked":[164],"adjusted":[168],"other.":[171],"constructing":[174],"described.":[177],"definitions":[179],"divisible":[182,221],"some":[185],"associated":[186],"subjects":[187],"stated.":[189],"defined":[192],"basic":[194],"principles":[195],"for":[196,233,262,269],"reducing":[197,234],"l":[204,208],"-dimensional":[205],"(":[207],"\u2265":[209],"3)":[210],".":[227],"stated":[230],"5.":[249],"algorithm":[251],"flow,":[256],"meets":[258],"solvability":[260],"conditions":[261],"problem,":[266],"formulated":[268],"such":[270],"network.":[272]},"counts_by_year":[{"year":2025,"cited_by_count":2},{"year":2024,"cited_by_count":4},{"year":2023,"cited_by_count":2},{"year":2022,"cited_by_count":2},{"year":2021,"cited_by_count":1},{"year":2018,"cited_by_count":3},{"year":2017,"cited_by_count":1}],"updated_date":"2026-07-31T08:31:51.225901","created_date":"2025-10-10T00:00:00"}
