{"id":"https://openalex.org/W3189040639","doi":"https://doi.org/10.3390/sym13081391","title":"Minimum Time Problem Controlled by Affine Connection","display_name":"Minimum Time Problem Controlled by Affine Connection","publication_year":2021,"publication_date":"2021-07-31","ids":{"openalex":"https://openalex.org/W3189040639","doi":"https://doi.org/10.3390/sym13081391","mag":"3189040639"},"language":"en","primary_location":{"id":"doi:10.3390/sym13081391","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym13081391","pdf_url":"https://www.mdpi.com/2073-8994/13/8/1391/pdf?version=1627721612","source":{"id":"https://openalex.org/S190787756","display_name":"Symmetry","issn_l":"2073-8994","issn":["2073-8994"],"is_oa":true,"is_in_doaj":false,"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":"Symmetry","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://www.mdpi.com/2073-8994/13/8/1391/pdf?version=1627721612","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5005064873","display_name":"Constantin Udri\u015fte","orcid":"https://orcid.org/0000-0002-7132-6900"},"institutions":[{"id":"https://openalex.org/I61641377","display_name":"Universitatea Na\u021bional\u0103 de \u0218tiin\u021b\u0103 \u0219i Tehnologie Politehnica Bucure\u0219ti","ror":"https://ror.org/0558j5q12","country_code":"RO","type":"education","lineage":["https://openalex.org/I61641377"]}],"countries":["RO"],"is_corresponding":true,"raw_author_name":"Constantin Udriste","raw_affiliation_strings":["Department of Mathematics and Informatics, Faculty of Applied Sciences, University Politehnica of Bucharest, Splaiul Independentei 313, Sector 6, 060042 Bucharest, Romania"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics and Informatics, Faculty of Applied Sciences, University Politehnica of Bucharest, Splaiul Independentei 313, Sector 6, 060042 Bucharest, Romania","institution_ids":["https://openalex.org/I61641377"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5047066905","display_name":"Ionel \u0162evy","orcid":"https://orcid.org/0000-0001-9160-9185"},"institutions":[{"id":"https://openalex.org/I61641377","display_name":"Universitatea Na\u021bional\u0103 de \u0218tiin\u021b\u0103 \u0219i Tehnologie Politehnica Bucure\u0219ti","ror":"https://ror.org/0558j5q12","country_code":"RO","type":"education","lineage":["https://openalex.org/I61641377"]}],"countries":["RO"],"is_corresponding":false,"raw_author_name":"Ionel Tevy","raw_affiliation_strings":["Department of Mathematics and Informatics, Faculty of Applied Sciences, University Politehnica of Bucharest, Splaiul Independentei 313, Sector 6, 060042 Bucharest, Romania"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics and Informatics, Faculty of Applied Sciences, University Politehnica of Bucharest, Splaiul Independentei 313, Sector 6, 060042 Bucharest, Romania","institution_ids":["https://openalex.org/I61641377"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5005064873"],"corresponding_institution_ids":["https://openalex.org/I61641377"],"apc_list":{"value":2000,"currency":"CHF","value_usd":2165},"apc_paid":{"value":2000,"currency":"CHF","value_usd":2165},"fwci":0.3284,"has_fulltext":false,"cited_by_count":1,"citation_normalized_percentile":{"value":0.50890636,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":93},"biblio":{"volume":"13","issue":"8","first_page":"1391","last_page":"1391"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10229","display_name":"Geometric Analysis and Curvature Flows","score":0.9908000230789185,"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":0.9908000230789185,"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/T11304","display_name":"Advanced Neuroimaging Techniques and Applications","score":0.9337999820709229,"subfield":{"id":"https://openalex.org/subfields/2741","display_name":"Radiology, Nuclear Medicine and Imaging"},"field":{"id":"https://openalex.org/fields/27","display_name":"Medicine"},"domain":{"id":"https://openalex.org/domains/4","display_name":"Health Sciences"}},{"id":"https://openalex.org/T11830","display_name":"Point processes and geometric inequalities","score":0.9276000261306763,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/parallel-transport","display_name":"Parallel transport","score":0.7596997618675232},{"id":"https://openalex.org/keywords/connection","display_name":"Connection (principal bundle)","score":0.7578160762786865},{"id":"https://openalex.org/keywords/affine-connection","display_name":"Affine connection","score":0.7005717754364014},{"id":"https://openalex.org/keywords/tangent-bundle","display_name":"Tangent bundle","score":0.6104532480239868},{"id":"https://openalex.org/keywords/controllability","display_name":"Controllability","score":0.605404257774353},{"id":"https://openalex.org/keywords/covariant-derivative","display_name":"Covariant derivative","score":0.5908926129341125},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5842125415802002},{"id":"https://openalex.org/keywords/manifold","display_name":"Manifold (fluid mechanics)","score":0.4939480423927307},{"id":"https://openalex.org/keywords/affine-transformation","display_name":"Affine transformation","score":0.486505925655365},{"id":"https://openalex.org/keywords/bounded-function","display_name":"Bounded function","score":0.47562792897224426},{"id":"https://openalex.org/keywords/curvature","display_name":"Curvature","score":0.4722425639629364},{"id":"https://openalex.org/keywords/levi-civita-connection","display_name":"Levi-Civita connection","score":0.44589921832084656},{"id":"https://openalex.org/keywords/tangent","display_name":"Tangent","score":0.4166833162307739},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.36271896958351135},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.3020904064178467},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.2735937237739563},{"id":"https://openalex.org/keywords/pseudo-riemannian-manifold","display_name":"Pseudo-Riemannian manifold","score":0.2293846309185028},{"id":"https://openalex.org/keywords/tangent-space","display_name":"Tangent space","score":0.21650710701942444},{"id":"https://openalex.org/keywords/ricci-curvature","display_name":"Ricci curvature","score":0.210985004901886},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.16745799779891968}],"concepts":[{"id":"https://openalex.org/C106953101","wikidata":"https://www.wikidata.org/wiki/Q1814838","display_name":"Parallel transport","level":2,"score":0.7596997618675232},{"id":"https://openalex.org/C13355873","wikidata":"https://www.wikidata.org/wiki/Q2920850","display_name":"Connection (principal bundle)","level":2,"score":0.7578160762786865},{"id":"https://openalex.org/C105561566","wikidata":"https://www.wikidata.org/wiki/Q1371213","display_name":"Affine connection","level":3,"score":0.7005717754364014},{"id":"https://openalex.org/C28903235","wikidata":"https://www.wikidata.org/wiki/Q746550","display_name":"Tangent bundle","level":3,"score":0.6104532480239868},{"id":"https://openalex.org/C48209547","wikidata":"https://www.wikidata.org/wiki/Q1331104","display_name":"Controllability","level":2,"score":0.605404257774353},{"id":"https://openalex.org/C19492387","wikidata":"https://www.wikidata.org/wiki/Q2287715","display_name":"Covariant derivative","level":2,"score":0.5908926129341125},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5842125415802002},{"id":"https://openalex.org/C529865628","wikidata":"https://www.wikidata.org/wiki/Q1790740","display_name":"Manifold (fluid mechanics)","level":2,"score":0.4939480423927307},{"id":"https://openalex.org/C92757383","wikidata":"https://www.wikidata.org/wiki/Q382497","display_name":"Affine transformation","level":2,"score":0.486505925655365},{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.47562792897224426},{"id":"https://openalex.org/C195065555","wikidata":"https://www.wikidata.org/wiki/Q214881","display_name":"Curvature","level":2,"score":0.4722425639629364},{"id":"https://openalex.org/C129049296","wikidata":"https://www.wikidata.org/wiki/Q548675","display_name":"Levi-Civita connection","level":5,"score":0.44589921832084656},{"id":"https://openalex.org/C138187205","wikidata":"https://www.wikidata.org/wiki/Q131251","display_name":"Tangent","level":2,"score":0.4166833162307739},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.36271896958351135},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.3020904064178467},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.2735937237739563},{"id":"https://openalex.org/C121705324","wikidata":"https://www.wikidata.org/wiki/Q1510587","display_name":"Pseudo-Riemannian manifold","level":4,"score":0.2293846309185028},{"id":"https://openalex.org/C157157409","wikidata":"https://www.wikidata.org/wiki/Q909601","display_name":"Tangent space","level":2,"score":0.21650710701942444},{"id":"https://openalex.org/C12089564","wikidata":"https://www.wikidata.org/wiki/Q1195879","display_name":"Ricci curvature","level":3,"score":0.210985004901886},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.16745799779891968},{"id":"https://openalex.org/C78519656","wikidata":"https://www.wikidata.org/wiki/Q101333","display_name":"Mechanical engineering","level":1,"score":0.0},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.3390/sym13081391","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym13081391","pdf_url":"https://www.mdpi.com/2073-8994/13/8/1391/pdf?version=1627721612","source":{"id":"https://openalex.org/S190787756","display_name":"Symmetry","issn_l":"2073-8994","issn":["2073-8994"],"is_oa":true,"is_in_doaj":false,"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":"Symmetry","raw_type":"journal-article"},{"id":"pmh:oai:doaj.org/article:8d47402ec05e42a483cf8b5d1b823d2e","is_oa":true,"landing_page_url":"https://doaj.org/article/8d47402ec05e42a483cf8b5d1b823d2e","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-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Symmetry, Vol 13, Iss 8, p 1391 (2021)","raw_type":"article"},{"id":"pmh:oai:mdpi.com:/2073-8994/13/8/1391/","is_oa":true,"landing_page_url":"https://dx.doi.org/10.3390/sym13081391","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":"Symmetry; Volume 13; Issue 8; Pages: 1391","raw_type":"Text"}],"best_oa_location":{"id":"doi:10.3390/sym13081391","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym13081391","pdf_url":"https://www.mdpi.com/2073-8994/13/8/1391/pdf?version=1627721612","source":{"id":"https://openalex.org/S190787756","display_name":"Symmetry","issn_l":"2073-8994","issn":["2073-8994"],"is_oa":true,"is_in_doaj":false,"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":"Symmetry","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W3189040639.pdf","grobid_xml":"https://content.openalex.org/works/W3189040639.grobid-xml"},"referenced_works_count":25,"referenced_works":["https://openalex.org/W571963652","https://openalex.org/W579208263","https://openalex.org/W1591476741","https://openalex.org/W1961133456","https://openalex.org/W2016394143","https://openalex.org/W2017696424","https://openalex.org/W2057252611","https://openalex.org/W2079127489","https://openalex.org/W2089105781","https://openalex.org/W2089465567","https://openalex.org/W2095131413","https://openalex.org/W2130805307","https://openalex.org/W2131971985","https://openalex.org/W2338744577","https://openalex.org/W2503014151","https://openalex.org/W2523400111","https://openalex.org/W2554690849","https://openalex.org/W2565928091","https://openalex.org/W2617088617","https://openalex.org/W3084163507","https://openalex.org/W3123018487","https://openalex.org/W3134113624","https://openalex.org/W4301484187","https://openalex.org/W6679640817","https://openalex.org/W6738522664"],"related_works":["https://openalex.org/W4200554484","https://openalex.org/W2117030100","https://openalex.org/W4210879025","https://openalex.org/W4389317490","https://openalex.org/W2078971009","https://openalex.org/W4309127226","https://openalex.org/W2618988779","https://openalex.org/W4206116550","https://openalex.org/W3189040639","https://openalex.org/W4236902948"],"abstract_inverted_index":{"Geometrically,":[0],"the":[1,5,10,13,16,19,24,54,60,68,82,112,116,137,147],"affine":[2,61],"connection":[3],"is":[4,158],"main":[6,64],"ingredient":[7],"that":[8],"underlies":[9],"covariant":[11],"derivative,":[12],"parallel":[14],"transport,":[15],"auto-parallel":[17,51,71,107],"curves,":[18,52,108],"torsion":[20],"tensor":[21,26],"field,":[22],"and":[23,45,53,79,109,115,142],"curvature":[25],"field":[27],"on":[28,81,133],"a":[29,40,75,86,99],"finite-dimensional":[30],"differentiable":[31],"manifold.":[32],"In":[33],"this":[34],"paper,":[35],"we":[36],"come":[37],"up":[38],"with":[39,122,155],"new":[41],"idea":[42],"of":[43,47,85,90,106,139,151],"controllability":[44,80],"observability":[46],"states":[48],"by":[49,59,74,98,103],"using":[50],"minimum":[55,94,152],"time":[56,95,114,154],"problem":[57,96],"controlled":[58,73,97],"connection.":[62],"The":[63,120],"contributions":[65],"refer":[66],"to":[67],"following:":[69],"(i)":[70],"curves":[72],"connection,":[76,100],"(ii)":[77],"reachability":[78],"tangent":[83],"bundle":[84],"manifold,":[87],"(iii)":[88],"examples":[89,132],"equiaffine":[91],"connections,":[92],"(iv)":[93],"(v)":[101],"connectivity":[102],"stochastic":[104],"perturbations":[105],"(vi)":[110],"computing":[111],"optimal":[113,117,128],"striking":[118,153],"time.":[119],"connections":[121],"bounded":[123],"pull-backs":[124],"result":[125],"in":[126],"bang\u2013bang":[127],"controls.":[129],"Some":[130],"significative":[131],"bi-dimensional":[134],"manifolds":[135],"clarify":[136],"intention":[138],"our":[140],"paper":[141],"suggest":[143],"possible":[144],"applications.":[145],"At":[146],"end,":[148],"an":[149],"example":[150],"simulation":[156],"results":[157],"presented.":[159]},"counts_by_year":[{"year":2021,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
