{"id":"https://openalex.org/W2091055493","doi":"https://doi.org/10.1080/10556780500247766","title":"Solving rank one perturbed linear Diophantine systems by the ABS method","display_name":"Solving rank one perturbed linear Diophantine systems by the ABS method","publication_year":2006,"publication_date":"2006-06-27","ids":{"openalex":"https://openalex.org/W2091055493","doi":"https://doi.org/10.1080/10556780500247766","mag":"2091055493"},"language":"en","primary_location":{"id":"doi:10.1080/10556780500247766","is_oa":false,"landing_page_url":"https://doi.org/10.1080/10556780500247766","pdf_url":null,"source":{"id":"https://openalex.org/S103047102","display_name":"Optimization methods & software","issn_l":"1026-7670","issn":["1026-7670","1029-4937","1055-6788"],"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":"Optimization Methods and Software","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/A5022601560","display_name":"Keyvan Amini","orcid":"https://orcid.org/0000-0002-9264-3091"},"institutions":[{"id":"https://openalex.org/I1187138","display_name":"Razi University","ror":"https://ror.org/02ynb0474","country_code":"IR","type":"education","lineage":["https://openalex.org/I1187138"]}],"countries":["IR"],"is_corresponding":false,"raw_author_name":"Keyvan Amini","raw_affiliation_strings":["Razi University","department of Sciences Razi University, Kermanshah Iran;"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Razi University","institution_ids":["https://openalex.org/I1187138"]},{"raw_affiliation_string":"department of Sciences Razi University, Kermanshah Iran;","institution_ids":["https://openalex.org/I1187138"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5062019109","display_name":"Nezam Mahdavi\u2010Amiri","orcid":"https://orcid.org/0000-0002-2763-4279"},"institutions":[{"id":"https://openalex.org/I133529467","display_name":"Sharif University of Technology","ror":"https://ror.org/024c2fq17","country_code":"IR","type":"education","lineage":["https://openalex.org/I133529467"]}],"countries":["IR"],"is_corresponding":true,"raw_author_name":"Nezam Mahdavi-Amiri","raw_affiliation_strings":["Sharif University of Technology","Department of Mathematical Sciences, Sharif University of Technology,Tehran,Iran"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Sharif University of Technology","institution_ids":["https://openalex.org/I133529467"]},{"raw_affiliation_string":"Department of Mathematical Sciences, Sharif University of Technology,Tehran,Iran","institution_ids":["https://openalex.org/I133529467"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5062019109"],"corresponding_institution_ids":["https://openalex.org/I133529467"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":4,"citation_normalized_percentile":{"value":0.15206779,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":"21","issue":"5","first_page":"819","last_page":"831"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11435","display_name":"Polynomial and algebraic computation","score":0.9958000183105469,"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/T11435","display_name":"Polynomial and algebraic computation","score":0.9958000183105469,"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/T12069","display_name":"Commutative Algebra and Its Applications","score":0.9957000017166138,"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/T11017","display_name":"Chaos-based Image/Signal Encryption","score":0.9915000200271606,"subfield":{"id":"https://openalex.org/subfields/1707","display_name":"Computer Vision and Pattern Recognition"},"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/diophantine-equation","display_name":"Diophantine equation","score":0.9024025797843933},{"id":"https://openalex.org/keywords/rank","display_name":"Rank (graph theory)","score":0.7968392372131348},{"id":"https://openalex.org/keywords/integer","display_name":"Integer (computer science)","score":0.6850172281265259},{"id":"https://openalex.org/keywords/coefficient-matrix","display_name":"Coefficient matrix","score":0.6351501941680908},{"id":"https://openalex.org/keywords/diophantine-set","display_name":"Diophantine set","score":0.618678092956543},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.582815945148468},{"id":"https://openalex.org/keywords/matrix","display_name":"Matrix (chemical analysis)","score":0.5340859889984131},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.43377017974853516},{"id":"https://openalex.org/keywords/linear-system","display_name":"Linear system","score":0.431146502494812},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.26010873913764954},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.23042798042297363},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.2171555757522583},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.16621097922325134},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.09393766522407532},{"id":"https://openalex.org/keywords/materials-science","display_name":"Materials science","score":0.05863410234451294}],"concepts":[{"id":"https://openalex.org/C206530611","wikidata":"https://www.wikidata.org/wiki/Q905896","display_name":"Diophantine equation","level":2,"score":0.9024025797843933},{"id":"https://openalex.org/C164226766","wikidata":"https://www.wikidata.org/wiki/Q7293202","display_name":"Rank (graph theory)","level":2,"score":0.7968392372131348},{"id":"https://openalex.org/C97137487","wikidata":"https://www.wikidata.org/wiki/Q729138","display_name":"Integer (computer science)","level":2,"score":0.6850172281265259},{"id":"https://openalex.org/C60866291","wikidata":"https://www.wikidata.org/wiki/Q5140577","display_name":"Coefficient matrix","level":3,"score":0.6351501941680908},{"id":"https://openalex.org/C40621787","wikidata":"https://www.wikidata.org/wiki/Q16251580","display_name":"Diophantine set","level":3,"score":0.618678092956543},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.582815945148468},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.5340859889984131},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.43377017974853516},{"id":"https://openalex.org/C6802819","wikidata":"https://www.wikidata.org/wiki/Q1072174","display_name":"Linear system","level":2,"score":0.431146502494812},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.26010873913764954},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.23042798042297363},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.2171555757522583},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.16621097922325134},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.09393766522407532},{"id":"https://openalex.org/C192562407","wikidata":"https://www.wikidata.org/wiki/Q228736","display_name":"Materials science","level":0,"score":0.05863410234451294},{"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/C159985019","wikidata":"https://www.wikidata.org/wiki/Q181790","display_name":"Composite material","level":1,"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},{"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:10.1080/10556780500247766","is_oa":false,"landing_page_url":"https://doi.org/10.1080/10556780500247766","pdf_url":null,"source":{"id":"https://openalex.org/S103047102","display_name":"Optimization methods & software","issn_l":"1026-7670","issn":["1026-7670","1029-4937","1055-6788"],"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":"Optimization Methods and Software","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320321157","display_name":"Sharif University of Technology","ror":"https://ror.org/024c2fq17"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":11,"referenced_works":["https://openalex.org/W1482956368","https://openalex.org/W1496314268","https://openalex.org/W1963547452","https://openalex.org/W1976474062","https://openalex.org/W1977211467","https://openalex.org/W1987275843","https://openalex.org/W2070990624","https://openalex.org/W2089514214","https://openalex.org/W2333117240","https://openalex.org/W4232058104","https://openalex.org/W4301808069"],"related_works":["https://openalex.org/W1980135287","https://openalex.org/W217056885","https://openalex.org/W2791276029","https://openalex.org/W2374840809","https://openalex.org/W2388294645","https://openalex.org/W2362898981","https://openalex.org/W2978626527","https://openalex.org/W2383836448","https://openalex.org/W2366914979","https://openalex.org/W2386596835"],"abstract_inverted_index":{"We":[0],"show":[1],"how":[2],"to":[3,24],"update":[4],"the":[5,14,19],"general":[6],"solution":[7],"of":[8],"linear":[9],"Diophantine":[10],"systems":[11],"obtained":[12],"by":[13],"integer":[15],"ABS":[16],"method":[17],"when":[18],"coefficient":[20],"matrix":[21],"is":[22],"subjected":[23],"a":[25],"rank":[26],"one":[27],"change.":[28]},"counts_by_year":[{"year":2019,"cited_by_count":1},{"year":2013,"cited_by_count":1}],"updated_date":"2026-07-29T09:40:50.615796","created_date":"2025-10-10T00:00:00"}