{"id":"https://openalex.org/W3200167502","doi":"https://doi.org/10.1155/2021/6396792","title":"On the Solutions of Three\u2010Variable Frobenius\u2010Related Problems Using Order Reduction Approach","display_name":"On the Solutions of Three\u2010Variable Frobenius\u2010Related Problems Using Order Reduction Approach","publication_year":2021,"publication_date":"2021-01-01","ids":{"openalex":"https://openalex.org/W3200167502","doi":"https://doi.org/10.1155/2021/6396792","mag":"3200167502"},"language":"en","primary_location":{"id":"doi:10.1155/2021/6396792","is_oa":true,"landing_page_url":"https://doi.org/10.1155/2021/6396792","pdf_url":"https://downloads.hindawi.com/journals/ijmms/2021/6396792.pdf","source":{"id":"https://openalex.org/S151851439","display_name":"International Journal of Mathematics and Mathematical Sciences","issn_l":"0161-1712","issn":["0161-1712","1687-0425"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310319869","host_organization_name":"Hindawi Publishing Corporation","host_organization_lineage":["https://openalex.org/P4310319869"],"host_organization_lineage_names":["Hindawi Publishing Corporation"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Mathematics and Mathematical Sciences","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://downloads.hindawi.com/journals/ijmms/2021/6396792.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5001633638","display_name":"Tian-Xiao He","orcid":"https://orcid.org/0000-0002-9405-5808"},"institutions":[{"id":"https://openalex.org/I184616310","display_name":"Illinois Wesleyan University","ror":"https://ror.org/021aqk126","country_code":"US","type":"education","lineage":["https://openalex.org/I184616310"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Tian-Xiao He","raw_affiliation_strings":["Department of Mathematics, Illinois Wesleyan University, Bloomington, IL 61702-2900, USA"],"raw_orcid":"https://orcid.org/0000-0002-9405-5808","affiliations":[{"raw_affiliation_string":"Department of Mathematics, Illinois Wesleyan University, Bloomington, IL 61702-2900, USA","institution_ids":["https://openalex.org/I184616310"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5004528157","display_name":"Peter J.-S. Shiue","orcid":"https://orcid.org/0000-0002-1832-9002"},"institutions":[{"id":"https://openalex.org/I133999245","display_name":"University of Nevada, Las Vegas","ror":"https://ror.org/0406gha72","country_code":"US","type":"education","lineage":["https://openalex.org/I133999245"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Peter J.-S. Shiue","raw_affiliation_strings":["Department of Mathematical Sciences, University of Nevada, Las Vegas, NV 89154-4020, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematical Sciences, University of Nevada, Las Vegas, NV 89154-4020, USA","institution_ids":["https://openalex.org/I133999245"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5013712373","display_name":"Rama Venkat","orcid":"https://orcid.org/0000-0001-5976-4468"},"institutions":[{"id":"https://openalex.org/I133999245","display_name":"University of Nevada, Las Vegas","ror":"https://ror.org/0406gha72","country_code":"US","type":"education","lineage":["https://openalex.org/I133999245"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Rama Venkat","raw_affiliation_strings":["Howard R. Hughes College of Engineering, University of Nevada, Las Vegas, NV 89154-4020, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Howard R. Hughes College of Engineering, University of Nevada, Las Vegas, NV 89154-4020, USA","institution_ids":["https://openalex.org/I133999245"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5001633638"],"corresponding_institution_ids":["https://openalex.org/I184616310"],"apc_list":{"value":1025,"currency":"USD","value_usd":1025},"apc_paid":{"value":1025,"currency":"USD","value_usd":1025},"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.28360958,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"2021","issue":"1","first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12069","display_name":"Commutative Algebra and Its Applications","score":0.9980999827384949,"subfield":{"id":"https://openalex.org/subfields/2602","display_name":"Algebra and Number Theory"},"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/T12069","display_name":"Commutative Algebra and Its Applications","score":0.9980999827384949,"subfield":{"id":"https://openalex.org/subfields/2602","display_name":"Algebra and Number Theory"},"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/T11435","display_name":"Polynomial and algebraic computation","score":0.9944000244140625,"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/T10287","display_name":"Algebraic structures and combinatorial models","score":0.9714000225067139,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8878535032272339},{"id":"https://openalex.org/keywords/variable","display_name":"Variable (mathematics)","score":0.6827551126480103},{"id":"https://openalex.org/keywords/reduction","display_name":"Reduction (mathematics)","score":0.6494722366333008},{"id":"https://openalex.org/keywords/conjecture","display_name":"Conjecture","score":0.5768136382102966},{"id":"https://openalex.org/keywords/order","display_name":"Order (exchange)","score":0.5720232129096985},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.4513513147830963},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.23488861322402954},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.2298632562160492},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.06223088502883911}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8878535032272339},{"id":"https://openalex.org/C182365436","wikidata":"https://www.wikidata.org/wiki/Q50701","display_name":"Variable (mathematics)","level":2,"score":0.6827551126480103},{"id":"https://openalex.org/C111335779","wikidata":"https://www.wikidata.org/wiki/Q3454686","display_name":"Reduction (mathematics)","level":2,"score":0.6494722366333008},{"id":"https://openalex.org/C2780990831","wikidata":"https://www.wikidata.org/wiki/Q319141","display_name":"Conjecture","level":2,"score":0.5768136382102966},{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.5720232129096985},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4513513147830963},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.23488861322402954},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.2298632562160492},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.06223088502883911},{"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}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1155/2021/6396792","is_oa":true,"landing_page_url":"https://doi.org/10.1155/2021/6396792","pdf_url":"https://downloads.hindawi.com/journals/ijmms/2021/6396792.pdf","source":{"id":"https://openalex.org/S151851439","display_name":"International Journal of Mathematics and Mathematical Sciences","issn_l":"0161-1712","issn":["0161-1712","1687-0425"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310319869","host_organization_name":"Hindawi Publishing Corporation","host_organization_lineage":["https://openalex.org/P4310319869"],"host_organization_lineage_names":["Hindawi Publishing Corporation"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Mathematics and Mathematical Sciences","raw_type":"journal-article"},{"id":"pmh:oai:doaj.org/article:c92981e6884a482b822c44c237dfc77f","is_oa":true,"landing_page_url":"https://doaj.org/article/c92981e6884a482b822c44c237dfc77f","pdf_url":null,"source":{"id":"https://openalex.org/S4306401280","display_name":"DOAJ (DOAJ: Directory of Open Access Journals)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"International Journal of Mathematics and Mathematical Sciences, Vol 2021 (2021)","raw_type":"article"},{"id":"pmh:oai:oasis.library.unlv.edu:math_fac_articles-1222","is_oa":true,"landing_page_url":"https://oasis.library.unlv.edu/math_fac_articles/222","pdf_url":null,"source":{"id":"https://openalex.org/S4377196371","display_name":"Digital Scholarship - UNLV (University of Nevada Reno)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I134113660","host_organization_name":"University of Nevada, Reno","host_organization_lineage":["https://openalex.org/I134113660"],"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":"Mathematical Sciences Faculty Research","raw_type":"article"}],"best_oa_location":{"id":"doi:10.1155/2021/6396792","is_oa":true,"landing_page_url":"https://doi.org/10.1155/2021/6396792","pdf_url":"https://downloads.hindawi.com/journals/ijmms/2021/6396792.pdf","source":{"id":"https://openalex.org/S151851439","display_name":"International Journal of Mathematics and Mathematical Sciences","issn_l":"0161-1712","issn":["0161-1712","1687-0425"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310319869","host_organization_name":"Hindawi Publishing Corporation","host_organization_lineage":["https://openalex.org/P4310319869"],"host_organization_lineage_names":["Hindawi Publishing Corporation"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Mathematics and Mathematical Sciences","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W3200167502.pdf","grobid_xml":"https://content.openalex.org/works/W3200167502.grobid-xml"},"referenced_works_count":15,"referenced_works":["https://openalex.org/W350260367","https://openalex.org/W1974439110","https://openalex.org/W2011246228","https://openalex.org/W2117945667","https://openalex.org/W2148266637","https://openalex.org/W2155565900","https://openalex.org/W2332901121","https://openalex.org/W2514354892","https://openalex.org/W2962954387","https://openalex.org/W3000040668","https://openalex.org/W3014547306","https://openalex.org/W3080414289","https://openalex.org/W4300915685","https://openalex.org/W6677646789","https://openalex.org/W6871983694"],"related_works":["https://openalex.org/W3194471551","https://openalex.org/W4375956809","https://openalex.org/W1581373162","https://openalex.org/W2784911598","https://openalex.org/W4297950433","https://openalex.org/W4287023968","https://openalex.org/W4288279572","https://openalex.org/W1973978937","https://openalex.org/W4286909116","https://openalex.org/W4292635168"],"abstract_inverted_index":{"This":[0],"paper":[1],"presents":[2],"a":[3,30,79,85,123],"new":[4],"approach":[5],"to":[6,17,54,71,83],"determine":[7],"the":[8,27,34,40,55,73,97],"number":[9,35],"of":[10,12,29,36,46,57,62,75,87,99,105],"solutions":[11,20,61,120],"three\u2010variable":[13,63,80],"Frobenius\u2010related":[14,31,64,81],"problems":[15],"and":[16],"find":[18],"their":[19],"by":[21],"using":[22],"order":[23,28,47,76,100,106],"reducing":[24],"methods.":[25],"Here,":[26],"problem":[32,56,82,118],"means":[33],"variables":[37],"appearing":[38],"in":[39],"problem.":[41],"We":[42],"present":[43],"two":[44,90],"types":[45],"reduction":[48],"methods":[49],"that":[50],"can":[51],"be":[52,84],"applied":[53],"finding":[58],"all":[59],"nonnegative":[60],"problems.":[65],"The":[66,93],"first":[67],"method":[68,95],"is":[69,112],"used":[70],"reduce":[72],"equation":[74,98],"three":[77,101,103],"from":[78],"system":[86],"equations":[88,104],"with":[89,114],"fixed":[91],"variables.":[92],"second":[94],"reduces":[96],"into":[102],"two,":[107],"for":[108],"which":[109],"an":[110,115],"algorithm":[111],"designed":[113],"interesting":[116],"open":[117],"on":[119],"left":[121],"as":[122],"conjecture.":[124]},"counts_by_year":[],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}