{"id":"https://openalex.org/W2883241388","doi":"https://doi.org/10.1142/s0218196718500534","title":"Recognition of unimodal map germs from the plane to the plane by invariants","display_name":"Recognition of unimodal map germs from the plane to the plane by invariants","publication_year":2018,"publication_date":"2018-07-24","ids":{"openalex":"https://openalex.org/W2883241388","doi":"https://doi.org/10.1142/s0218196718500534","mag":"2883241388"},"language":"en","primary_location":{"id":"doi:10.1142/s0218196718500534","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218196718500534","pdf_url":null,"source":{"id":"https://openalex.org/S23260266","display_name":"International Journal of Algebra and Computation","issn_l":"0218-1967","issn":["0218-1967","1793-6500"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319815","host_organization_name":"World Scientific","host_organization_lineage":["https://openalex.org/P4310319815"],"host_organization_lineage_names":["World Scientific"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Algebra and Computation","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/A5027237167","display_name":"Saima Aslam","orcid":null},"institutions":[{"id":"https://openalex.org/I194348271","display_name":"Government College University, Faisalabad","ror":"https://ror.org/051zgra59","country_code":"PK","type":"education","lineage":["https://openalex.org/I194348271"]}],"countries":["PK"],"is_corresponding":false,"raw_author_name":"Saima Aslam","raw_affiliation_strings":["Department of Mathematics, Government College University, Faisalabad, Pakistan"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Government College University, Faisalabad, Pakistan","institution_ids":["https://openalex.org/I194348271"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5088782593","display_name":"Muhammad Ahsan Binyamin","orcid":"https://orcid.org/0000-0003-0717-7557"},"institutions":[{"id":"https://openalex.org/I194348271","display_name":"Government College University, Faisalabad","ror":"https://ror.org/051zgra59","country_code":"PK","type":"education","lineage":["https://openalex.org/I194348271"]}],"countries":["PK"],"is_corresponding":true,"raw_author_name":"Muhammad Ahsan Binyamin","raw_affiliation_strings":["Department of Mathematics, Government College University, Faisalabad, Pakistan"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Government College University, Faisalabad, Pakistan","institution_ids":["https://openalex.org/I194348271"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5035101218","display_name":"Gerhard Pfister","orcid":null},"institutions":[{"id":"https://openalex.org/I153267046","display_name":"University of Kaiserslautern","ror":"https://ror.org/04zrf7b53","country_code":"DE","type":"education","lineage":["https://openalex.org/I153267046"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Gerhard Pfister","raw_affiliation_strings":["Department of Mathematics, University of Kaiserslautern, Germany"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, University of Kaiserslautern, Germany","institution_ids":["https://openalex.org/I153267046"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5088782593"],"corresponding_institution_ids":["https://openalex.org/I194348271"],"apc_list":null,"apc_paid":null,"fwci":0.3794,"has_fulltext":false,"cited_by_count":6,"citation_normalized_percentile":{"value":0.57727169,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":"28","issue":"07","first_page":"1199","last_page":"1208"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10061","display_name":"Algebraic Geometry and Number Theory","score":0.9950000047683716,"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"}},"topics":[{"id":"https://openalex.org/T10061","display_name":"Algebraic Geometry and Number Theory","score":0.9950000047683716,"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"}},{"id":"https://openalex.org/T11673","display_name":"Advanced Topics in Algebra","score":0.9927999973297119,"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":0.9918000102043152,"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/mathematics","display_name":"Mathematics","score":0.8716182708740234},{"id":"https://openalex.org/keywords/plane","display_name":"Plane (geometry)","score":0.6933008432388306},{"id":"https://openalex.org/keywords/equivalence","display_name":"Equivalence (formal languages)","score":0.6011086702346802},{"id":"https://openalex.org/keywords/algebraically-closed-field","display_name":"Algebraically closed field","score":0.5875657796859741},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.4394330084323883},{"id":"https://openalex.org/keywords/basis","display_name":"Basis (linear algebra)","score":0.4301193058490753},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.4184383749961853},{"id":"https://openalex.org/keywords/field","display_name":"Field (mathematics)","score":0.4137600362300873},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.23455485701560974}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8716182708740234},{"id":"https://openalex.org/C17825722","wikidata":"https://www.wikidata.org/wiki/Q17285","display_name":"Plane (geometry)","level":2,"score":0.6933008432388306},{"id":"https://openalex.org/C2780069185","wikidata":"https://www.wikidata.org/wiki/Q7977945","display_name":"Equivalence (formal languages)","level":2,"score":0.6011086702346802},{"id":"https://openalex.org/C203701370","wikidata":"https://www.wikidata.org/wiki/Q1047547","display_name":"Algebraically closed field","level":2,"score":0.5875657796859741},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.4394330084323883},{"id":"https://openalex.org/C12426560","wikidata":"https://www.wikidata.org/wiki/Q189569","display_name":"Basis (linear algebra)","level":2,"score":0.4301193058490753},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.4184383749961853},{"id":"https://openalex.org/C9652623","wikidata":"https://www.wikidata.org/wiki/Q190109","display_name":"Field (mathematics)","level":2,"score":0.4137600362300873},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.23455485701560974}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1142/s0218196718500534","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218196718500534","pdf_url":null,"source":{"id":"https://openalex.org/S23260266","display_name":"International Journal of Algebra and Computation","issn_l":"0218-1967","issn":["0218-1967","1793-6500"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319815","host_organization_name":"World Scientific","host_organization_lineage":["https://openalex.org/P4310319815"],"host_organization_lineage_names":["World Scientific"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Algebra and Computation","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":8,"referenced_works":["https://openalex.org/W1970130627","https://openalex.org/W2009338421","https://openalex.org/W2037478209","https://openalex.org/W2066181227","https://openalex.org/W2078149121","https://openalex.org/W2175098281","https://openalex.org/W2553630605","https://openalex.org/W2962873494"],"related_works":["https://openalex.org/W2074052495","https://openalex.org/W3191608549","https://openalex.org/W2376336218","https://openalex.org/W2361715264","https://openalex.org/W4380343522","https://openalex.org/W2003007890","https://openalex.org/W2293427636","https://openalex.org/W2949390709","https://openalex.org/W4302824655","https://openalex.org/W2372890883"],"abstract_inverted_index":{"In":[0],"this":[1,47],"paper,":[2],"we":[3,49],"characterize":[4],"the":[5,11,14,31,44,55,58,62,65,69,78],"classification":[6,32],"of":[7,27,38,46,57],"unimodal":[8,59],"maps":[9,60],"from":[10,61],"plane":[12,15,63,66],"to":[13,18,53,64],"with":[16],"respect":[17],"[Formula:":[19,40],"see":[20,41],"text]-equivalence":[21],"given":[22],"by":[23],"Rieger":[24],"in":[25,77],"terms":[26],"invariants.":[28],"We":[29],"recall":[30],"over":[33],"an":[34,51],"algebraically":[35],"closed":[36],"field":[37],"characteristic":[39],"text].":[42],"On":[43],"basis":[45],"characterization,":[48],"present":[50],"algorithm":[52],"compute":[54],"type":[56],"without":[67],"computing":[68],"normal":[70],"form":[71],"and":[72],"also":[73],"give":[74],"its":[75],"implementation":[76],"computer":[79],"algebra":[80],"system":[81],"Singular.":[82]},"counts_by_year":[{"year":2023,"cited_by_count":3},{"year":2022,"cited_by_count":2},{"year":2020,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
