{"id":"https://openalex.org/W7222932915","doi":"https://doi.org/10.21167/cqdv27e27012","title":"A representa\u00e7\u00e3o-FM para a fun\u00e7\u00e3o quadr\u00e1tica - Parte 1","display_name":"A representa\u00e7\u00e3o-FM para a fun\u00e7\u00e3o quadr\u00e1tica - Parte 1","publication_year":2026,"publication_date":"2026-10-19","ids":{"openalex":"https://openalex.org/W7222932915","doi":"https://doi.org/10.21167/cqdv27e27012"},"language":"en","primary_location":{"id":"doi:10.21167/cqdv27e27012","doi":"https://doi.org/10.21167/cqdv27e27012","is_oa":true,"landing_page_url":"https://doi.org/10.21167/cqdv27e27012","pdf_url":"https://revistas.bauru.unesp.br/index.php/revistacqd/article/download/555/480","source":{"id":"https://openalex.org/S4210181422","display_name":"C Q D - Revista Eletr\u00f4nica Paulista de Matem\u00e1tica","issn_l":"2316-9664","issn":["2316-9664"],"is_oa":true,"is_in_doaj":true,"is_core":false,"listed_in":["doaj"],"host_organization":"https://openalex.org/P4310312394","host_organization_name":"L\u00e1zaro, C. and Rodrigues, T.","host_organization_lineage":["https://openalex.org/P4310312394"],"host_organization_lineage_names":["L\u00e1zaro, C. and Rodrigues, T."],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"C.Q.D. - Revista Eletr\u00f4nica Paulista de Matem\u00e1tica","raw_type":"journal-article"},"volume":null,"type":"article","is_traditional":true,"indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"diamond","oa_url":"https://revistas.bauru.unesp.br/index.php/revistacqd/article/download/555/480","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5032945288","display_name":"Lu\u00eds Cl\u00e1udio Yamaoka","orcid":"https://orcid.org/0000-0002-3963-7338","observed_orcids":["https://orcid.org/0000-0002-3963-7338"]},"institutions":[{"id":"https://openalex.org/I88273585","display_name":"Universidade Federal de S\u00e3o Paulo","ror":"https://ror.org/02k5swt12","country_code":"BR","type":"education","lineage":["https://openalex.org/I88273585"]}],"countries":["BR"],"is_corresponding":true,"raw_author_name":"Lu\u00eds Cl\u00e1udio Yamaoka","raw_affiliation_strings":["Universidade Federal de S\u00e3o Paulo"],"raw_orcid":"https://orcid.org/0000-0002-3963-7338","affiliations":[{"raw_affiliation_string":"Universidade Federal de S\u00e3o Paulo","institution_ids":["https://openalex.org/I88273585"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5032945288"],"corresponding_institution_ids":["https://openalex.org/I88273585"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.71591108,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":"e27012","last_page":"e27012"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10588","display_name":"Mathematical Dynamics and Fractals","score":0.4050000011920929,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"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/T10588","display_name":"Mathematical Dynamics and Fractals","score":0.4050000011920929,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"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/T11822","display_name":"Analytic and geometric function theory","score":0.16910000145435333,"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/T13806","display_name":"Mathematical and Computational Methods","score":0.13169999420642853,"subfield":{"id":"https://openalex.org/subfields/2611","display_name":"Modeling and Simulation"},"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/quadratic-functions","display_name":"quadratic functions","score":0.6779999732971191},{"id":"https://openalex.org/keywords/roots-of-quadratic-equations","display_name":"roots of quadratic equations","score":0.5699999928474426},{"id":"https://openalex.org/keywords/complex-plane","display_name":"complex plane","score":0.42800000309944153},{"id":"https://openalex.org/keywords/cartesian-plane","display_name":"Cartesian plane","score":0.4169999957084656},{"id":"https://openalex.org/keywords/pointwise-convergence","display_name":"pointwise convergence","score":0.7599999904632568},{"id":"https://openalex.org/keywords/uniform-convergence","display_name":"uniform convergence","score":0.996999979019165},{"id":"https://openalex.org/keywords/sequences-of-functions","display_name":"sequences of functions","score":0.7599999904632568},{"id":"https://openalex.org/keywords/graph-of-quadratic-functions","display_name":"quadratic function graphs","score":0.4090000092983246}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7699999809265137},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.48890000581741333},{"id":"https://openalex.org/C65236422","wikidata":"https://www.wikidata.org/wiki/Q173740","display_name":"Cartesian product","level":2,"score":0.4560999870300293},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.4498000144958496},{"id":"https://openalex.org/C17825722","wikidata":"https://www.wikidata.org/wiki/Q17285","display_name":"Plane (geometry)","level":2,"score":0.4334000051021576},{"id":"https://openalex.org/C61445026","wikidata":"https://www.wikidata.org/wiki/Q217608","display_name":"Fixed point","level":2,"score":0.40470001101493835},{"id":"https://openalex.org/C179117685","wikidata":"https://www.wikidata.org/wiki/Q328998","display_name":"Complex plane","level":2,"score":0.38989999890327454},{"id":"https://openalex.org/C16038011","wikidata":"https://www.wikidata.org/wiki/Q62912","display_name":"Cartesian coordinate system","level":2,"score":0.3409000039100647},{"id":"https://openalex.org/C195065555","wikidata":"https://www.wikidata.org/wiki/Q214881","display_name":"Curvature","level":2,"score":0.3343999981880188},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.33180001378059387},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.3077999949455261},{"id":"https://openalex.org/C2778112365","wikidata":"https://www.wikidata.org/wiki/Q3511065","display_name":"Sequence (biology)","level":2,"score":0.30709999799728394}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.21167/cqdv27e27012","doi":"https://doi.org/10.21167/cqdv27e27012","is_oa":true,"landing_page_url":"https://doi.org/10.21167/cqdv27e27012","pdf_url":"https://revistas.bauru.unesp.br/index.php/revistacqd/article/download/555/480","source":{"id":"https://openalex.org/S4210181422","display_name":"C Q D - Revista Eletr\u00f4nica Paulista de Matem\u00e1tica","issn_l":"2316-9664","issn":["2316-9664"],"is_oa":true,"is_in_doaj":true,"is_core":false,"listed_in":["doaj"],"host_organization":"https://openalex.org/P4310312394","host_organization_name":"L\u00e1zaro, C. and Rodrigues, T.","host_organization_lineage":["https://openalex.org/P4310312394"],"host_organization_lineage_names":["L\u00e1zaro, C. and Rodrigues, T."],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"C.Q.D. - Revista Eletr\u00f4nica Paulista de Matem\u00e1tica","raw_type":"journal-article"},{"id":"pmh:oai:doaj.org/article:76df27f308f44317b014f16cae0cb4d6","doi":null,"is_oa":false,"landing_page_url":"https://doaj.org/article/76df27f308f44317b014f16cae0cb4d6","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,"listed_in":[],"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"CQD Revista Eletr\u00f4nica Paulista de Matem\u00e1tica, Vol 27 (2026)","raw_type":"article"}],"best_oa_location":{"id":"doi:10.21167/cqdv27e27012","doi":"https://doi.org/10.21167/cqdv27e27012","is_oa":true,"landing_page_url":"https://doi.org/10.21167/cqdv27e27012","pdf_url":"https://revistas.bauru.unesp.br/index.php/revistacqd/article/download/555/480","source":{"id":"https://openalex.org/S4210181422","display_name":"C Q D - Revista Eletr\u00f4nica Paulista de Matem\u00e1tica","issn_l":"2316-9664","issn":["2316-9664"],"is_oa":true,"is_in_doaj":true,"is_core":false,"listed_in":["doaj"],"host_organization":"https://openalex.org/P4310312394","host_organization_name":"L\u00e1zaro, C. and Rodrigues, T.","host_organization_lineage":["https://openalex.org/P4310312394"],"host_organization_lineage_names":["L\u00e1zaro, C. and Rodrigues, T."],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"C.Q.D. - Revista Eletr\u00f4nica Paulista de Matem\u00e1tica","raw_type":"journal-article"},"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7222932915.pdf","grobid_xml":"https://content.openalex.org/works/W7222932915.grobid-xml"},"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W4240861168","https://openalex.org/W1234106844","https://openalex.org/W2794244528","https://openalex.org/W2320664181","https://openalex.org/W7057601834","https://openalex.org/W2285492500","https://openalex.org/W7124564129","https://openalex.org/W7099596189","https://openalex.org/W2008212902","https://openalex.org/W138959822"],"abstract_inverted_index":{"Given":[0],"\ud835\udc4f0":[1],"\u2208":[2,6,30,49,153,187],"R":[3,15,17,196],"and":[4,135,171,209],"\ud835\udc500":[5],"R,":[7],"let":[8],"the":[9,57,62,67,76,81,84,94,98,110,118,191],"families":[10],"of":[11,61,69,75,83,87,93,101,113,120,193],"functions":[12,121],"\ud835\udc39a":[13,21,70,105],":":[14,33,125,139,195],"\u2192":[16,35,197],"be":[18,37],"given":[19,38,128,144,199],"by":[20,39,129,145,200],"(\ud835\udc65)":[22],"=":[23,42,133,149,155,202],"\ud835\udc4e\ud835\udc652":[24],"+":[25,44,123,131,169],"\ud835\udc4f0x+":[26],"c0":[27,46],",":[28,47],"\ud835\udc4e":[29,48,186],"R*,":[31,188],"and\ud835\udc53a":[32],"C":[34,36],"\ud835\udc53a":[40,88],"(\ud835\udc67)":[41],"\ud835\udc4e\ud835\udc672":[43],"\ud835\udc4f0z+":[45],"R*.":[50],"When":[51],"we":[52,55,189],"vary":[53],"\ud835\udc4e,":[54],"obtain":[56],"FaM-representation,":[58],"which":[59,66,80],"consists":[60],"Cartesian":[63],"plane":[64,78],"in":[65,79,97],"graph":[68],"evolves":[71],"and,":[72],"right":[73],"below,":[74],"complex":[77],"paths":[82],"2":[85,111],"roots":[86,112],"are":[89],"traced.":[90],"The":[91],"importance":[92],"FaM-representation":[95],"lies":[96],"simultaneous":[99],"analysis":[100],"what":[102,107],"happens":[103,108],"to":[104,109,165,177],"with":[106],"\ud835\udc53a.":[114],"We":[115],"show":[116],"that":[117],"sequences":[119],"\ud835\udc39n":[122,130,136,146,168,172],"-1":[124,138],"[0,+\u221e[\u2192":[126],"[0,+\u221e[":[127],"-1(\ud835\udc4a)":[132,148],"(\ud835\udc4a/\ud835\udc5b)1/2":[134],"-":[137,147,150,173],"[0,+\u221e[\u2192]":[140],"\u2212":[141],"\u221e,":[142],"0]":[143],"(\ud835\udc4a/\ud835\udc5b)1/2,":[151],"\ud835\udc5b":[152],"N":[154],"{1,":[156],"2,":[157],"3,":[158],"...},":[159],"converge":[160,175],"pointwise,":[161],"but":[162],"not":[163],"uniformly,":[164],"0;":[166],"while":[167],"-1|[0,M]":[170,174],"uniformly":[176],"0,":[178],"for":[179],"fixed":[180,207],"\ud835\udc40":[181],">":[182],"0.":[183],"For":[184],"each":[185],"determine":[190],"curvature":[192],"\ud835\udf06a":[194],"R2":[198],"\ud835\udf06a(\ud835\udc65)":[201],"(\ud835\udc65,":[203],"a\ud835\udc652)":[204],"at":[205],"a":[206],"\ud835\udc650,":[208],"give":[210],"examples.":[211]},"counts_by_year":[],"updated_date":"2026-11-04T10:54:05.112534","created_date":"2026-10-20T00:00:00"}