{"id":"https://openalex.org/W2157508176","doi":"https://doi.org/10.1093/imamci/dnt041","title":"Construction of algebraic-differential equations with given smooth and impulsive behaviour","display_name":"Construction of algebraic-differential equations with given smooth and impulsive behaviour","publication_year":2013,"publication_date":"2013-12-03","ids":{"openalex":"https://openalex.org/W2157508176","doi":"https://doi.org/10.1093/imamci/dnt041","mag":"2157508176"},"language":"en","primary_location":{"id":"doi:10.1093/imamci/dnt041","is_oa":false,"landing_page_url":"https://doi.org/10.1093/imamci/dnt041","pdf_url":null,"source":{"id":"https://openalex.org/S162756791","display_name":"IMA Journal of Mathematical Control and Information","issn_l":"0265-0754","issn":["0265-0754","1471-6887"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310311648","host_organization_name":"Oxford University Press","host_organization_lineage":["https://openalex.org/P4310311648","https://openalex.org/P4310311647"],"host_organization_lineage_names":["Oxford University Press","University of Oxford"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IMA Journal of Mathematical Control and Information","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5066594965","display_name":"Nicholas P. Karampetakis","orcid":"https://orcid.org/0000-0002-4578-5521"},"institutions":[{"id":"https://openalex.org/I21370196","display_name":"Aristotle University of Thessaloniki","ror":"https://ror.org/02j61yw88","country_code":"GR","type":"education","lineage":["https://openalex.org/I21370196"]}],"countries":["GR"],"is_corresponding":true,"raw_author_name":"N. P. Karampetakis","raw_affiliation_strings":["Department of Mathematics, Aristotle University of Thessaloniki, Thessaloniki 54623, Greece"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Aristotle University of Thessaloniki, Thessaloniki 54623, Greece","institution_ids":["https://openalex.org/I21370196"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5066594965"],"corresponding_institution_ids":["https://openalex.org/I21370196"],"apc_list":{"value":2582,"currency":"GBP","value_usd":3167},"apc_paid":null,"fwci":1.3941,"has_fulltext":false,"cited_by_count":6,"citation_normalized_percentile":{"value":0.81695468,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":"32","issue":"1","first_page":"195","last_page":"224"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12396","display_name":"Advanced Differential Equations and Dynamical Systems","score":0.9980000257492065,"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/T12396","display_name":"Advanced Differential Equations and Dynamical Systems","score":0.9980000257492065,"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/T10792","display_name":"Matrix Theory and Algorithms","score":0.995199978351593,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T13234","display_name":"advanced mathematical theories","score":0.9937999844551086,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7515395283699036},{"id":"https://openalex.org/keywords/polynomial","display_name":"Polynomial","score":0.6413635611534119},{"id":"https://openalex.org/keywords/space","display_name":"Space (punctuation)","score":0.5843061208724976},{"id":"https://openalex.org/keywords/algebraic-number","display_name":"Algebraic number","score":0.5668824911117554},{"id":"https://openalex.org/keywords/matrix","display_name":"Matrix (chemical analysis)","score":0.538698136806488},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.536004364490509},{"id":"https://openalex.org/keywords/algebraic-equation","display_name":"Algebraic equation","score":0.531333327293396},{"id":"https://openalex.org/keywords/zero","display_name":"Zero (linguistics)","score":0.4871535003185272},{"id":"https://openalex.org/keywords/differential-equation","display_name":"Differential equation","score":0.48451346158981323},{"id":"https://openalex.org/keywords/matrix-polynomial","display_name":"Matrix polynomial","score":0.4804741442203522},{"id":"https://openalex.org/keywords/differential-algebraic-geometry","display_name":"Differential algebraic geometry","score":0.46485841274261475},{"id":"https://openalex.org/keywords/differential","display_name":"Differential (mechanical device)","score":0.4629579186439514},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.42688101530075073},{"id":"https://openalex.org/keywords/differential-algebraic-equation","display_name":"Differential algebraic equation","score":0.4148932993412018},{"id":"https://openalex.org/keywords/ordinary-differential-equation","display_name":"Ordinary differential equation","score":0.18137532472610474},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.12610918283462524},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.09194552898406982},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.08597278594970703}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7515395283699036},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.6413635611534119},{"id":"https://openalex.org/C2778572836","wikidata":"https://www.wikidata.org/wiki/Q380933","display_name":"Space (punctuation)","level":2,"score":0.5843061208724976},{"id":"https://openalex.org/C9376300","wikidata":"https://www.wikidata.org/wiki/Q168817","display_name":"Algebraic number","level":2,"score":0.5668824911117554},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.538698136806488},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.536004364490509},{"id":"https://openalex.org/C23917780","wikidata":"https://www.wikidata.org/wiki/Q50698","display_name":"Algebraic equation","level":3,"score":0.531333327293396},{"id":"https://openalex.org/C2780813799","wikidata":"https://www.wikidata.org/wiki/Q3274237","display_name":"Zero (linguistics)","level":2,"score":0.4871535003185272},{"id":"https://openalex.org/C78045399","wikidata":"https://www.wikidata.org/wiki/Q11214","display_name":"Differential equation","level":2,"score":0.48451346158981323},{"id":"https://openalex.org/C101044782","wikidata":"https://www.wikidata.org/wiki/Q6787887","display_name":"Matrix polynomial","level":3,"score":0.4804741442203522},{"id":"https://openalex.org/C26959085","wikidata":"https://www.wikidata.org/wiki/Q5275330","display_name":"Differential algebraic geometry","level":5,"score":0.46485841274261475},{"id":"https://openalex.org/C93226319","wikidata":"https://www.wikidata.org/wiki/Q193137","display_name":"Differential (mechanical device)","level":2,"score":0.4629579186439514},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.42688101530075073},{"id":"https://openalex.org/C186219872","wikidata":"https://www.wikidata.org/wiki/Q955889","display_name":"Differential algebraic equation","level":4,"score":0.4148932993412018},{"id":"https://openalex.org/C51544822","wikidata":"https://www.wikidata.org/wiki/Q465274","display_name":"Ordinary differential equation","level":3,"score":0.18137532472610474},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.12610918283462524},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.09194552898406982},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.08597278594970703},{"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/C159985019","wikidata":"https://www.wikidata.org/wiki/Q181790","display_name":"Composite material","level":1,"score":0.0},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0},{"id":"https://openalex.org/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","level":1,"score":0.0},{"id":"https://openalex.org/C41895202","wikidata":"https://www.wikidata.org/wiki/Q8162","display_name":"Linguistics","level":1,"score":0.0},{"id":"https://openalex.org/C192562407","wikidata":"https://www.wikidata.org/wiki/Q228736","display_name":"Materials science","level":0,"score":0.0},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1093/imamci/dnt041","is_oa":false,"landing_page_url":"https://doi.org/10.1093/imamci/dnt041","pdf_url":null,"source":{"id":"https://openalex.org/S162756791","display_name":"IMA Journal of Mathematical Control and Information","issn_l":"0265-0754","issn":["0265-0754","1471-6887"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310311648","host_organization_name":"Oxford University Press","host_organization_lineage":["https://openalex.org/P4310311648","https://openalex.org/P4310311647"],"host_organization_lineage_names":["Oxford University Press","University of Oxford"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IMA Journal of Mathematical Control and Information","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":8,"referenced_works":["https://openalex.org/W2012219987","https://openalex.org/W2024042397","https://openalex.org/W2027489104","https://openalex.org/W2085849252","https://openalex.org/W2146560209","https://openalex.org/W2147425165","https://openalex.org/W2406334773","https://openalex.org/W2798813531"],"related_works":["https://openalex.org/W2502480061","https://openalex.org/W21216597","https://openalex.org/W4288410816","https://openalex.org/W2924426067","https://openalex.org/W2517966731","https://openalex.org/W2051868556","https://openalex.org/W2490075509","https://openalex.org/W4234783915","https://openalex.org/W2023803998","https://openalex.org/W2107705030"],"abstract_inverted_index":{"This":[0],"paper":[1],"consists":[2],"of":[3,19,22,48,54,72,101],"two":[4],"parts.":[5],"In":[6,77],"the":[7,12,20,55,73,78,83,114],"first":[8],"part,":[9,80],"we":[10,81,94],"present":[11],"smooth":[13,88],"and":[14,24,50,59,68,89,103],"impulsive":[15,90],"solution":[16,42,91,116],"space":[17,43,92],"B":[18],"system":[21,100],"algebraic":[23,102],"differential":[25,104],"equations":[26,105],"A(\u03c1)":[27,106],"\u03b2(t)=0,":[28],"\u03c1\u2254d/dt,":[29],"where":[30],"A(\u03c1)\u2208\u211d[\u03c1]r":[31],"\u00d7":[32],"r":[33],"(with":[34],"detA":[35],"(\u03c1)":[36],"\u2260":[37],"0)":[38],"is":[39,44,64],"given.":[40],"The":[41],"given":[45,65,115],"in":[46],"terms":[47],"finite":[49,67],"infinite":[51,69],"Jordan":[52],"pairs":[53],"polynomial":[56,74],"matrix":[57,75],"A(\u03c1),":[58],"therefore":[60],"a":[61,87,99],"necessary":[62],"introduction":[63],"for":[66],"zero":[70],"structures":[71],"A(\u03c1).":[76],"second":[79],"study":[82],"inverse":[84],"problem:":[85],"Given":[86],"B,":[93],"try":[95],"to":[96],"find":[97],"out":[98],"\u03b2(t)":[107],"=":[108],"0,":[109],"\u03c1":[110],"\u2254":[111],"dt":[112],"with":[113],"space.":[117]},"counts_by_year":[{"year":2021,"cited_by_count":1},{"year":2019,"cited_by_count":1},{"year":2017,"cited_by_count":1},{"year":2016,"cited_by_count":1},{"year":2014,"cited_by_count":2}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}