{"id":"https://openalex.org/W4309744081","doi":"https://doi.org/10.3390/a15110436","title":"Higher-Order Curvatures of Plane and Space Parametrized Curves","display_name":"Higher-Order Curvatures of Plane and Space Parametrized Curves","publication_year":2022,"publication_date":"2022-11-18","ids":{"openalex":"https://openalex.org/W4309744081","doi":"https://doi.org/10.3390/a15110436"},"language":"en","primary_location":{"id":"doi:10.3390/a15110436","is_oa":true,"landing_page_url":"https://doi.org/10.3390/a15110436","pdf_url":"https://www.mdpi.com/1999-4893/15/11/436/pdf?version=1669105883","source":{"id":"https://openalex.org/S190629608","display_name":"Algorithms","issn_l":"1999-4893","issn":["1999-4893"],"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":"Algorithms","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://www.mdpi.com/1999-4893/15/11/436/pdf?version=1669105883","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5057264745","display_name":"Mircea Cr\u00e2\u015fm\u0103reanu","orcid":"https://orcid.org/0000-0002-5230-2751"},"institutions":[{"id":"https://openalex.org/I138164181","display_name":"Alexandru Ioan Cuza University","ror":"https://ror.org/022kvet57","country_code":"RO","type":"education","lineage":["https://openalex.org/I138164181"]}],"countries":["RO"],"is_corresponding":true,"raw_author_name":"Mircea Crasmareanu","raw_affiliation_strings":["Faculty of Mathematics, University \u201cAlexandru Ioan Cuza\u201d, 700506 Iasi, Romania","Faculty of Mathematics, University \"Alexandru Ioan Cuza\", 700506 Iasi, Romania"],"affiliations":[{"raw_affiliation_string":"Faculty of Mathematics, University \u201cAlexandru Ioan Cuza\u201d, 700506 Iasi, Romania","institution_ids":["https://openalex.org/I138164181"]},{"raw_affiliation_string":"Faculty of Mathematics, University \"Alexandru Ioan Cuza\", 700506 Iasi, Romania","institution_ids":["https://openalex.org/I138164181"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5057264745"],"corresponding_institution_ids":["https://openalex.org/I138164181"],"apc_list":{"value":1400,"currency":"CHF","value_usd":1515},"apc_paid":{"value":1400,"currency":"CHF","value_usd":1515},"fwci":1.0547,"has_fulltext":false,"cited_by_count":3,"citation_normalized_percentile":{"value":0.74728927,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":96},"biblio":{"volume":"15","issue":"11","first_page":"436","last_page":"436"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10229","display_name":"Geometric Analysis and Curvature Flows","score":0.9994999766349792,"subfield":{"id":"https://openalex.org/subfields/2604","display_name":"Applied Mathematics"},"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/T10229","display_name":"Geometric Analysis and Curvature Flows","score":0.9994999766349792,"subfield":{"id":"https://openalex.org/subfields/2604","display_name":"Applied Mathematics"},"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/T13080","display_name":"Advanced Differential Geometry Research","score":0.9961000084877014,"subfield":{"id":"https://openalex.org/subfields/3103","display_name":"Astronomy and Astrophysics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11366","display_name":"Elasticity and Material Modeling","score":0.9894000291824341,"subfield":{"id":"https://openalex.org/subfields/2204","display_name":"Biomedical 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/frenet\u2013serret-formulas","display_name":"Frenet\u2013Serret formulas","score":0.9246684312820435},{"id":"https://openalex.org/keywords/plane-curve","display_name":"Plane curve","score":0.7705428600311279},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7214370369911194},{"id":"https://openalex.org/keywords/curvature","display_name":"Curvature","score":0.7211481332778931},{"id":"https://openalex.org/keywords/space","display_name":"Space (punctuation)","score":0.6262016296386719},{"id":"https://openalex.org/keywords/plane","display_name":"Plane (geometry)","score":0.6086299419403076},{"id":"https://openalex.org/keywords/order","display_name":"Order (exchange)","score":0.6048849821090698},{"id":"https://openalex.org/keywords/torsion-of-a-curve","display_name":"Torsion of a curve","score":0.5818231701850891},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.5554889440536499},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.5387049913406372},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.381496787071228},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.37778612971305847},{"id":"https://openalex.org/keywords/center-of-curvature","display_name":"Center of curvature","score":0.29509103298187256},{"id":"https://openalex.org/keywords/mean-curvature","display_name":"Mean curvature","score":0.23378422856330872},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.0760917067527771}],"concepts":[{"id":"https://openalex.org/C162546045","wikidata":"https://www.wikidata.org/wiki/Q947922","display_name":"Frenet\u2013Serret formulas","level":3,"score":0.9246684312820435},{"id":"https://openalex.org/C43809302","wikidata":"https://www.wikidata.org/wiki/Q1060874","display_name":"Plane curve","level":2,"score":0.7705428600311279},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7214370369911194},{"id":"https://openalex.org/C195065555","wikidata":"https://www.wikidata.org/wiki/Q214881","display_name":"Curvature","level":2,"score":0.7211481332778931},{"id":"https://openalex.org/C2778572836","wikidata":"https://www.wikidata.org/wiki/Q380933","display_name":"Space (punctuation)","level":2,"score":0.6262016296386719},{"id":"https://openalex.org/C17825722","wikidata":"https://www.wikidata.org/wiki/Q17285","display_name":"Plane (geometry)","level":2,"score":0.6086299419403076},{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.6048849821090698},{"id":"https://openalex.org/C84985374","wikidata":"https://www.wikidata.org/wiki/Q1892644","display_name":"Torsion of a curve","level":5,"score":0.5818231701850891},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.5554889440536499},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.5387049913406372},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.381496787071228},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.37778612971305847},{"id":"https://openalex.org/C161223928","wikidata":"https://www.wikidata.org/wiki/Q3775868","display_name":"Center of curvature","level":4,"score":0.29509103298187256},{"id":"https://openalex.org/C175017881","wikidata":"https://www.wikidata.org/wiki/Q1318998","display_name":"Mean curvature","level":3,"score":0.23378422856330872},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.0760917067527771},{"id":"https://openalex.org/C10138342","wikidata":"https://www.wikidata.org/wiki/Q43015","display_name":"Finance","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},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C78458016","wikidata":"https://www.wikidata.org/wiki/Q840400","display_name":"Evolutionary biology","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.3390/a15110436","is_oa":true,"landing_page_url":"https://doi.org/10.3390/a15110436","pdf_url":"https://www.mdpi.com/1999-4893/15/11/436/pdf?version=1669105883","source":{"id":"https://openalex.org/S190629608","display_name":"Algorithms","issn_l":"1999-4893","issn":["1999-4893"],"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":"Algorithms","raw_type":"journal-article"},{"id":"pmh:oai:doaj.org/article:5396482d2bca47cfa282565af13c06c0","is_oa":true,"landing_page_url":"https://doaj.org/article/5396482d2bca47cfa282565af13c06c0","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":"Algorithms, Vol 15, Iss 11, p 436 (2022)","raw_type":"article"},{"id":"pmh:oai:mdpi.com:/1999-4893/15/11/436/","is_oa":true,"landing_page_url":"https://dx.doi.org/10.3390/a15110436","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":"Algorithms; Volume 15; Issue 11; Pages: 436","raw_type":"Text"}],"best_oa_location":{"id":"doi:10.3390/a15110436","is_oa":true,"landing_page_url":"https://doi.org/10.3390/a15110436","pdf_url":"https://www.mdpi.com/1999-4893/15/11/436/pdf?version=1669105883","source":{"id":"https://openalex.org/S190629608","display_name":"Algorithms","issn_l":"1999-4893","issn":["1999-4893"],"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":"Algorithms","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4309744081.pdf","grobid_xml":"https://content.openalex.org/works/W4309744081.grobid-xml"},"referenced_works_count":9,"referenced_works":["https://openalex.org/W627232015","https://openalex.org/W1930529183","https://openalex.org/W1996753658","https://openalex.org/W2064152620","https://openalex.org/W2589165287","https://openalex.org/W2991084271","https://openalex.org/W3210057476","https://openalex.org/W4318825521","https://openalex.org/W6734062109"],"related_works":["https://openalex.org/W2075234962","https://openalex.org/W141339580","https://openalex.org/W2223994253","https://openalex.org/W1514629605","https://openalex.org/W2893463943","https://openalex.org/W3118120558","https://openalex.org/W3121806070","https://openalex.org/W4309744081","https://openalex.org/W4295915098","https://openalex.org/W2254103776"],"abstract_inverted_index":{"We":[0],"start":[1],"by":[2,11,30],"introducing":[3,55],"and":[4],"studying":[5],"two":[6],"sequences":[7,58],"of":[8,15,20,45,59,68,70],"curvatures":[9,27,60],"provided":[10],"the":[12,16,35,41,49,63],"higher-order":[13],"derivatives":[14],"usual":[17],"Frenet":[18],"equation":[19],"a":[21,31,71],"given":[22],"plane":[23],"curve":[24],"C.":[25,46],"These":[26],"are":[28,74],"expressed":[29],"recurrence":[32],"starting":[33,61],"with":[34,62],"pair":[36],"(0,\u2212k)":[37],"where":[38],"k":[39],"is":[40],"classical":[42],"curvature":[43],"function":[44],"Moreover,":[47],"for":[48],"space":[50],"curves,":[51],"we":[52],"succeed":[53],"in":[54],"three":[56],"recurrent":[57],"triple":[64],"(\u2212k,0,\u03c4).":[65],"Some":[66],"kinds":[67],"helices":[69],"higher":[72],"order":[73],"defined.":[75]},"counts_by_year":[{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":2}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}