{"id":"https://openalex.org/W3210190883","doi":"https://doi.org/10.31590/ejosat.1014593","title":"The Curvature Property of a Linear Dynamical System","display_name":"The Curvature Property of a Linear Dynamical System","publication_year":2021,"publication_date":"2021-11-01","ids":{"openalex":"https://openalex.org/W3210190883","doi":"https://doi.org/10.31590/ejosat.1014593","mag":"3210190883"},"language":"en","primary_location":{"id":"doi:10.31590/ejosat.1014593","doi":"https://doi.org/10.31590/ejosat.1014593","is_oa":true,"landing_page_url":"https://doi.org/10.31590/ejosat.1014593","pdf_url":"https://dergipark.org.tr/en/download/article-file/2045734","source":{"id":"https://openalex.org/S4210197137","display_name":"European Journal of Science and Technology","issn_l":"2148-2683","issn":["2148-2683"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/P4327628574","host_organization_name":"European Journal of Science and Technology","host_organization_lineage":["https://openalex.org/P4327628574"],"host_organization_lineage_names":["European Journal of Science and Technology"],"type":"journal"},"license":"cc-by-nc","license_id":"https://openalex.org/licenses/cc-by-nc","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"European Journal of Science and Technology","raw_type":"journal-article"},"parent_works":[],"lineage":["https://openalex.org/W3210190883"],"child_works_count":0,"type":"article","is_traditional":true,"indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"diamond","oa_url":"https://dergipark.org.tr/en/download/article-file/2045734","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5073808492","display_name":"T. Bayrakdar","orcid":"https://orcid.org/0000-0001-8777-5842","observed_orcids":["https://orcid.org/0000-0001-8777-5842"]},"institutions":[{"id":"https://openalex.org/I12387023","display_name":"Trakya University","ror":"https://ror.org/00xa0xn82","country_code":"TR","type":"education","lineage":["https://openalex.org/I12387023"]}],"countries":["TR"],"is_corresponding":false,"raw_author_name":"Tuna BAYRAKDAR","raw_affiliation_strings":["Trakya University, Faculty of Sciences, Departmant of Mathematics, Edirne, Turkey,"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Trakya University, Faculty of Sciences, Departmant of Mathematics, Edirne, Turkey,","institution_ids":["https://openalex.org/I12387023"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5062453768","display_name":"Z. Ok Bayrakdar","orcid":"https://orcid.org/0000-0002-2187-2102","observed_orcids":["https://orcid.org/0000-0002-2187-2102"]},"institutions":[{"id":"https://openalex.org/I41641357","display_name":"Ege University","ror":"https://ror.org/02eaafc18","country_code":"TR","type":"education","lineage":["https://openalex.org/I41641357"]}],"countries":["TR"],"is_corresponding":false,"raw_author_name":"Zahide OK BAYRAKDAR","raw_affiliation_strings":["Ege University, Faculty of Sciences, Departmant of Physics, \u0130zmir, Turkey,"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Ege University, Faculty of Sciences, Departmant of Physics, \u0130zmir, Turkey,","institution_ids":["https://openalex.org/I41641357"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.686,"has_fulltext":true,"cited_by_count":2,"citation_normalized_percentile":{"value":0.57413945,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":93,"max":95},"biblio":{"volume":null,"issue":null,"first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T13080","display_name":"Advanced Differential Geometry Research","score":0.9911999702453613,"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/T13080","display_name":"Advanced Differential Geometry Research","score":0.9911999702453613,"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/T10229","display_name":"Geometric Analysis and Curvature Flows","score":0.004100000020116568,"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/T12396","display_name":"Advanced Differential Equations and Dynamical Systems","score":0.0015999999595806003,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/linear-dynamical-systems","display_name":"linear dynamical systems","score":0.9559999704360962},{"id":"https://openalex.org/keywords/scalar-curvature","display_name":"scalar curvature","score":0.8640000224113464},{"id":"https://openalex.org/keywords/riemannian-manifolds","display_name":"Riemannian manifolds","score":0.875},{"id":"https://openalex.org/keywords/two-dimensional-autonomous-systems","display_name":"two-dimensional autonomous systems","score":0.8149999976158142},{"id":"https://openalex.org/keywords/nonpositive-curvature","display_name":"nonpositive curvature","score":0.7599999904632568},{"id":"https://openalex.org/keywords/smooth-dynamical-systems","display_name":"smooth dynamical systems","score":0.5270000100135803}],"concepts":[{"id":"https://openalex.org/C12520029","wikidata":"https://www.wikidata.org/wiki/Q1147161","display_name":"Scalar curvature","level":3,"score":0.7988232374191284},{"id":"https://openalex.org/C79379906","wikidata":"https://www.wikidata.org/wiki/Q3174497","display_name":"Dynamical systems theory","level":2,"score":0.6358071565628052},{"id":"https://openalex.org/C195065555","wikidata":"https://www.wikidata.org/wiki/Q214881","display_name":"Curvature","level":2,"score":0.6337282061576843},{"id":"https://openalex.org/C529865628","wikidata":"https://www.wikidata.org/wiki/Q1790740","display_name":"Manifold (fluid mechanics)","level":2,"score":0.606162428855896},{"id":"https://openalex.org/C57691317","wikidata":"https://www.wikidata.org/wiki/Q1289248","display_name":"Scalar (mathematics)","level":2,"score":0.5970537066459656},{"id":"https://openalex.org/C2779593128","wikidata":"https://www.wikidata.org/wiki/Q632814","display_name":"Riemannian manifold","level":2,"score":0.5319787859916687},{"id":"https://openalex.org/C33962884","wikidata":"https://www.wikidata.org/wiki/Q378637","display_name":"Dynamical system (definition)","level":3,"score":0.48645874857902527},{"id":"https://openalex.org/C14196021","wikidata":"https://www.wikidata.org/wiki/Q7240881","display_name":"Prescribed scalar curvature problem","level":5,"score":0.46902480721473694},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.46154502034187317},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.4536213278770447},{"id":"https://openalex.org/C114275822","wikidata":"https://www.wikidata.org/wiki/Q621512","display_name":"Linear dynamical system","level":3,"score":0.442230224609375},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.43271175026893616},{"id":"https://openalex.org/C37914503","wikidata":"https://www.wikidata.org/wiki/Q156495","display_name":"Mathematical physics","level":1,"score":0.38054582476615906},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.36312294006347656},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.2737649381160736},{"id":"https://openalex.org/C42448751","wikidata":"https://www.wikidata.org/wiki/Q855622","display_name":"Sectional curvature","level":4,"score":0.2081209421157837},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.09931421279907227},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.046210676431655884},{"id":"https://openalex.org/C78519656","wikidata":"https://www.wikidata.org/wiki/Q101333","display_name":"Mechanical engineering","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.31590/ejosat.1014593","doi":"https://doi.org/10.31590/ejosat.1014593","is_oa":true,"landing_page_url":"https://doi.org/10.31590/ejosat.1014593","pdf_url":"https://dergipark.org.tr/en/download/article-file/2045734","source":{"id":"https://openalex.org/S4210197137","display_name":"European Journal of Science and Technology","issn_l":"2148-2683","issn":["2148-2683"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/P4327628574","host_organization_name":"European Journal of Science and Technology","host_organization_lineage":["https://openalex.org/P4327628574"],"host_organization_lineage_names":["European Journal of Science and Technology"],"type":"journal"},"license":"cc-by-nc","license_id":"https://openalex.org/licenses/cc-by-nc","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"European Journal of Science and Technology","raw_type":"journal-article"},{"id":"pmh:oai:dergipark.org.tr:article/1014593","doi":null,"is_oa":true,"landing_page_url":"https://dergipark.org.tr/tr/pub/ejosat/issue/64234/1014593","pdf_url":null,"source":{"id":"https://openalex.org/S4210197137","display_name":"European Journal of Science and Technology","issn_l":"2148-2683","issn":["2148-2683"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/P4327628574","host_organization_name":"European Journal of Science and Technology","host_organization_lineage":["https://openalex.org/P4327628574"],"host_organization_lineage_names":["European Journal of Science and Technology"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"European Journal of Science and Technology","raw_type":"info:eu-repo/semantics/article"}],"best_oa_location":{"id":"doi:10.31590/ejosat.1014593","doi":"https://doi.org/10.31590/ejosat.1014593","is_oa":true,"landing_page_url":"https://doi.org/10.31590/ejosat.1014593","pdf_url":"https://dergipark.org.tr/en/download/article-file/2045734","source":{"id":"https://openalex.org/S4210197137","display_name":"European Journal of Science and Technology","issn_l":"2148-2683","issn":["2148-2683"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/P4327628574","host_organization_name":"European Journal of Science and Technology","host_organization_lineage":["https://openalex.org/P4327628574"],"host_organization_lineage_names":["European Journal of Science and Technology"],"type":"journal"},"license":"cc-by-nc","license_id":"https://openalex.org/licenses/cc-by-nc","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"European Journal of Science and Technology","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/W3210190883.pdf","grobid_xml":"https://content.openalex.org/works/W3210190883.grobid-xml"},"referenced_works_count":3,"referenced_works":["https://openalex.org/W1513060653","https://openalex.org/W2792644458","https://openalex.org/W2975896356"],"related_works":["https://openalex.org/W2047079486","https://openalex.org/W2963068960","https://openalex.org/W2593229498","https://openalex.org/W4301624622","https://openalex.org/W1973735886","https://openalex.org/W2389198623","https://openalex.org/W7102414841","https://openalex.org/W2043908043","https://openalex.org/W2180919483"],"abstract_inverted_index":{"In":[0],"this":[1],"work":[2],"a":[3,12,25],"two-dimensional":[4],"smooth":[5],"autonomous":[6],"dynamical":[7,27],"system":[8,28],"is":[9,18,31,35],"regarded":[10],"as":[11],"three-dimensional":[13],"Riemannian":[14],"manifold":[15,34],"and":[16,39],"it":[17],"shown":[19],"that":[20],"the":[21],"scalar":[22],"curvature":[23],"of":[24],"linear":[26],"$\\text{d}x/\\text{d}t=ax+by$,":[29],"$\\text{d}y/\\text{d}t=cx+dy$":[30],"non-positive.":[32],"The":[33],"scalar-flat":[36],"iff":[37],"$b=-c$":[38],"$a=d=0$.":[40]},"counts_by_year":[{"year":2024,"cited_by_count":2}],"updated_date":"2026-11-14T11:04:58.165337","created_date":"2021-11-08T00:00:00"}