{"id":"https://openalex.org/W4306362426","doi":"https://doi.org/10.3390/axioms11100557","title":"Plane Section Curves on Surfaces of NCP Functions","display_name":"Plane Section Curves on Surfaces of NCP Functions","publication_year":2022,"publication_date":"2022-10-14","ids":{"openalex":"https://openalex.org/W4306362426","doi":"https://doi.org/10.3390/axioms11100557"},"language":"en","primary_location":{"id":"doi:10.3390/axioms11100557","is_oa":true,"landing_page_url":"https://doi.org/10.3390/axioms11100557","pdf_url":"https://www.mdpi.com/2075-1680/11/10/557/pdf?version=1666606772","source":{"id":"https://openalex.org/S4210173132","display_name":"Axioms","issn_l":"2075-1680","issn":["2075-1680"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Axioms","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://www.mdpi.com/2075-1680/11/10/557/pdf?version=1666606772","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5072600558","display_name":"Shun-wei Li","orcid":null},"institutions":[{"id":"https://openalex.org/I134161618","display_name":"National Taiwan Normal University","ror":"https://ror.org/059dkdx38","country_code":"TW","type":"education","lineage":["https://openalex.org/I134161618"]}],"countries":["TW"],"is_corresponding":false,"raw_author_name":"Shun-Wei Li","raw_affiliation_strings":["Department of Mathematics, National Taiwan Normal University, Taipei 11677, Taiwan"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, National Taiwan Normal University, Taipei 11677, Taiwan","institution_ids":["https://openalex.org/I134161618"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5100677277","display_name":"Yu-Lin Chang","orcid":"https://orcid.org/0000-0002-6915-7490"},"institutions":[{"id":"https://openalex.org/I134161618","display_name":"National Taiwan Normal University","ror":"https://ror.org/059dkdx38","country_code":"TW","type":"education","lineage":["https://openalex.org/I134161618"]}],"countries":["TW"],"is_corresponding":true,"raw_author_name":"Yu-Lin Chang","raw_affiliation_strings":["Department of Mathematics, National Taiwan Normal University, Taipei 11677, Taiwan"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, National Taiwan Normal University, Taipei 11677, Taiwan","institution_ids":["https://openalex.org/I134161618"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5061633817","display_name":"Jein-Shan Chen","orcid":"https://orcid.org/0000-0002-4596-9419"},"institutions":[{"id":"https://openalex.org/I134161618","display_name":"National Taiwan Normal University","ror":"https://ror.org/059dkdx38","country_code":"TW","type":"education","lineage":["https://openalex.org/I134161618"]}],"countries":["TW"],"is_corresponding":false,"raw_author_name":"Jein-Shan Chen","raw_affiliation_strings":["Department of Mathematics, National Taiwan Normal University, Taipei 11677, Taiwan"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, National Taiwan Normal University, Taipei 11677, Taiwan","institution_ids":["https://openalex.org/I134161618"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5100677277"],"corresponding_institution_ids":["https://openalex.org/I134161618"],"apc_list":{"value":1400,"currency":"CHF","value_usd":1515},"apc_paid":{"value":1400,"currency":"CHF","value_usd":1515},"fwci":0.3091,"has_fulltext":true,"cited_by_count":1,"citation_normalized_percentile":{"value":0.52011202,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":"11","issue":"10","first_page":"557","last_page":"557"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10963","display_name":"Advanced Optimization Algorithms Research","score":0.9995999932289124,"subfield":{"id":"https://openalex.org/subfields/2612","display_name":"Numerical Analysis"},"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/T10963","display_name":"Advanced Optimization Algorithms Research","score":0.9995999932289124,"subfield":{"id":"https://openalex.org/subfields/2612","display_name":"Numerical Analysis"},"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/T10571","display_name":"Robotic Mechanisms and Dynamics","score":0.9923999905586243,"subfield":{"id":"https://openalex.org/subfields/2207","display_name":"Control and Systems 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/T10791","display_name":"Advanced Control Systems Optimization","score":0.9836999773979187,"subfield":{"id":"https://openalex.org/subfields/2207","display_name":"Control and Systems Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/convexity","display_name":"Convexity","score":0.852338433265686},{"id":"https://openalex.org/keywords/plane-curve","display_name":"Plane curve","score":0.7103993892669678},{"id":"https://openalex.org/keywords/differentiable-function","display_name":"Differentiable function","score":0.7076176404953003},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6979807615280151},{"id":"https://openalex.org/keywords/inflection-point","display_name":"Inflection point","score":0.6539578437805176},{"id":"https://openalex.org/keywords/plane","display_name":"Plane (geometry)","score":0.5825756788253784},{"id":"https://openalex.org/keywords/section","display_name":"Section (typography)","score":0.5496417880058289},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.5108680129051208},{"id":"https://openalex.org/keywords/regular-polygon","display_name":"Regular polygon","score":0.4728665053844452},{"id":"https://openalex.org/keywords/interval","display_name":"Interval (graph theory)","score":0.42666542530059814},{"id":"https://openalex.org/keywords/quartic-plane-curve","display_name":"Quartic plane curve","score":0.42424148321151733},{"id":"https://openalex.org/keywords/quadratic-equation","display_name":"Quadratic equation","score":0.4190019369125366},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.405928373336792},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.1951107680797577},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.08658525347709656}],"concepts":[{"id":"https://openalex.org/C72134830","wikidata":"https://www.wikidata.org/wiki/Q5166524","display_name":"Convexity","level":2,"score":0.852338433265686},{"id":"https://openalex.org/C43809302","wikidata":"https://www.wikidata.org/wiki/Q1060874","display_name":"Plane curve","level":2,"score":0.7103993892669678},{"id":"https://openalex.org/C202615002","wikidata":"https://www.wikidata.org/wiki/Q783507","display_name":"Differentiable function","level":2,"score":0.7076176404953003},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6979807615280151},{"id":"https://openalex.org/C74545648","wikidata":"https://www.wikidata.org/wiki/Q212794","display_name":"Inflection point","level":2,"score":0.6539578437805176},{"id":"https://openalex.org/C17825722","wikidata":"https://www.wikidata.org/wiki/Q17285","display_name":"Plane (geometry)","level":2,"score":0.5825756788253784},{"id":"https://openalex.org/C2780129039","wikidata":"https://www.wikidata.org/wiki/Q1931107","display_name":"Section (typography)","level":2,"score":0.5496417880058289},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.5108680129051208},{"id":"https://openalex.org/C112680207","wikidata":"https://www.wikidata.org/wiki/Q714886","display_name":"Regular polygon","level":2,"score":0.4728665053844452},{"id":"https://openalex.org/C2778067643","wikidata":"https://www.wikidata.org/wiki/Q166507","display_name":"Interval (graph theory)","level":2,"score":0.42666542530059814},{"id":"https://openalex.org/C84181032","wikidata":"https://www.wikidata.org/wiki/Q1857574","display_name":"Quartic plane curve","level":3,"score":0.42424148321151733},{"id":"https://openalex.org/C129844170","wikidata":"https://www.wikidata.org/wiki/Q41299","display_name":"Quadratic equation","level":2,"score":0.4190019369125366},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.405928373336792},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.1951107680797577},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.08658525347709656},{"id":"https://openalex.org/C106159729","wikidata":"https://www.wikidata.org/wiki/Q2294553","display_name":"Financial economics","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/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.3390/axioms11100557","is_oa":true,"landing_page_url":"https://doi.org/10.3390/axioms11100557","pdf_url":"https://www.mdpi.com/2075-1680/11/10/557/pdf?version=1666606772","source":{"id":"https://openalex.org/S4210173132","display_name":"Axioms","issn_l":"2075-1680","issn":["2075-1680"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Axioms","raw_type":"journal-article"},{"id":"pmh:oai:doaj.org/article:322a370f49f04ac7a33d43309c2da5b0","is_oa":true,"landing_page_url":"https://doaj.org/article/322a370f49f04ac7a33d43309c2da5b0","pdf_url":null,"source":{"id":"https://openalex.org/S112646816","display_name":"SHILAP Revista de lepidopterolog\u00eda","issn_l":"0300-5267","issn":["0300-5267","2340-4078"],"is_oa":true,"is_in_doaj":true,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Axioms, Vol 11, Iss 10, p 557 (2022)","raw_type":"article"},{"id":"pmh:oai:mdpi.com:/2075-1680/11/10/557/","is_oa":true,"landing_page_url":"https://dx.doi.org/10.3390/axioms11100557","pdf_url":null,"source":{"id":"https://openalex.org/S4306400947","display_name":"MDPI (MDPI AG)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I4210097602","host_organization_name":"Multidisciplinary Digital Publishing Institute (Switzerland)","host_organization_lineage":["https://openalex.org/I4210097602"],"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":"Axioms; Volume 11; Issue 10; Pages: 557","raw_type":"Text"}],"best_oa_location":{"id":"doi:10.3390/axioms11100557","is_oa":true,"landing_page_url":"https://doi.org/10.3390/axioms11100557","pdf_url":"https://www.mdpi.com/2075-1680/11/10/557/pdf?version=1666606772","source":{"id":"https://openalex.org/S4210173132","display_name":"Axioms","issn_l":"2075-1680","issn":["2075-1680"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Axioms","raw_type":"journal-article"},"sustainable_development_goals":[{"display_name":"Sustainable cities and communities","id":"https://metadata.un.org/sdg/11","score":0.6299999952316284}],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4306362426.pdf","grobid_xml":"https://content.openalex.org/works/W4306362426.grobid-xml"},"referenced_works_count":20,"referenced_works":["https://openalex.org/W1972573855","https://openalex.org/W2001508169","https://openalex.org/W2066038730","https://openalex.org/W2090694590","https://openalex.org/W2146112192","https://openalex.org/W2149255010","https://openalex.org/W2151902790","https://openalex.org/W2164576999","https://openalex.org/W2282602389","https://openalex.org/W2586481538","https://openalex.org/W2807303275","https://openalex.org/W3003184393","https://openalex.org/W3007399760","https://openalex.org/W3037866958","https://openalex.org/W3157244600","https://openalex.org/W4249840661","https://openalex.org/W6667087212","https://openalex.org/W6683931076","https://openalex.org/W6732989827","https://openalex.org/W6774222127"],"related_works":["https://openalex.org/W1996226968","https://openalex.org/W2099571829","https://openalex.org/W1647114756","https://openalex.org/W4298245680","https://openalex.org/W1893041278","https://openalex.org/W2916840102","https://openalex.org/W2372775297","https://openalex.org/W2950363176","https://openalex.org/W3190473241","https://openalex.org/W2526303471"],"abstract_inverted_index":{"The":[0,23,80],"goal":[1],"of":[2,27,40,65,76,82],"this":[3,59],"paper":[4],"is":[5,85],"to":[6,88],"investigate":[7],"the":[8,16,37,41,51,54,63,71,77],"curves":[9,29,42,55,78,84],"intersected":[10],"by":[11],"a":[12],"vertical":[13],"plane":[14],"with":[15,62],"surfaces":[17],"based":[18],"on":[19],"certain":[20],"NCP":[21],"functions.":[22],"convexity":[24],"and":[25,67],"differentiability":[26,66],"these":[28,83],"are":[30,56],"studied":[31],"as":[32],"well.":[33],"In":[34],"most":[35],"cases,":[36],"inflection":[38],"points":[39],"cannot":[43],"be":[44],"expressed":[45],"exactly.":[46],"Therefore,":[47],"we":[48,69],"instead":[49],"estimate":[50],"interval":[52],"where":[53],"convex":[57],"under":[58],"situation.":[60],"Then,":[61],"help":[64],"convexity,":[68],"obtain":[70],"local":[72],"minimum":[73],"or":[74],"maximum":[75],"accordingly.":[79],"study":[81],"very":[86],"useful":[87],"binary":[89],"quadratic":[90],"programming.":[91]},"counts_by_year":[{"year":2023,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2022-10-17T00:00:00"}