{"id":"https://openalex.org/W2000687303","doi":"https://doi.org/10.1007/bf03322121","title":"Asymptotical Formulas For Solutions Of Linear Differential Systems Of The First Order","display_name":"Asymptotical Formulas For Solutions Of Linear Differential Systems Of The First Order","publication_year":1999,"publication_date":"1999-11-01","ids":{"openalex":"https://openalex.org/W2000687303","doi":"https://doi.org/10.1007/bf03322121","mag":"2000687303"},"language":"en","primary_location":{"id":"doi:10.1007/bf03322121","doi":"https://doi.org/10.1007/bf03322121","is_oa":false,"landing_page_url":"https://doi.org/10.1007/bf03322121","pdf_url":null,"source":{"id":"https://openalex.org/S939935174","display_name":"Results in Mathematics","issn_l":"0378-6218","issn":["0378-6218","1420-9012","1422-6383"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["anvur-scientific","cwts-core","dongbi-d","jufo-1","norway-1","poland-100","russia-white-list-1","vabb-shw"],"host_organization":"https://openalex.org/P4310320186","host_organization_name":"Birkh\u00e4user","host_organization_lineage":["https://openalex.org/P4310320186","https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Birkh\u00e4user","Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Results in Mathematics","raw_type":"journal-article"},"parent_works":[],"lineage":["https://openalex.org/W2000687303"],"child_works_count":0,"type":"article","is_traditional":true,"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/A5111544573","display_name":"Victor Sergeevich Rykhlov","orcid":"https://orcid.org/0000-0003-1556-7707","observed_orcids":["https://orcid.org/0000-0003-1556-7707"]},"institutions":[{"id":"https://openalex.org/I125219893","display_name":"Saratov State University","ror":"https://ror.org/05jcsqx24","country_code":"RU","type":"education","lineage":["https://openalex.org/I125219893"]}],"countries":["RU"],"is_corresponding":true,"raw_author_name":"Viktor S. Rykhlov","raw_affiliation_strings":["Department of Mechanics & Mathematics, Saratov State University, Astrakhan-skaya str. 83, 410026, Saratov, Russia","Saratov State University"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mechanics & Mathematics, Saratov State University, Astrakhan-skaya str. 83, 410026, Saratov, Russia","institution_ids":["https://openalex.org/I125219893"]},{"raw_affiliation_string":"Saratov State University","institution_ids":["https://openalex.org/I125219893"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5111544573"],"corresponding_institution_ids":["https://openalex.org/I125219893"],"apc_list":{"value":3090,"currency":"USD","value_usd":3090},"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":31,"citation_normalized_percentile":{"value":0.0,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":88,"max":98},"biblio":{"volume":"36","issue":"3-4","first_page":"342","last_page":"353"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11022","display_name":"Spectral Theory in Mathematical Physics","score":0.6654999852180481,"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"}},"topics":[{"id":"https://openalex.org/T11022","display_name":"Spectral Theory in Mathematical Physics","score":0.6654999852180481,"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"}},{"id":"https://openalex.org/T10541","display_name":"Nonlinear Differential Equations Analysis","score":0.22419999539852142,"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/T12589","display_name":"Differential Equations and Boundary Problems","score":0.03200000151991844,"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/linear-differential-systems","display_name":"linear differential systems","score":0.7720000147819519},{"id":"https://openalex.org/keywords/first-order-systems","display_name":"first-order systems","score":0.7649999856948853},{"id":"https://openalex.org/keywords/asymptotic-formula","display_name":"asymptotic formula","score":0.9739999771118164},{"id":"https://openalex.org/keywords/exponential-asymptotics","display_name":"exponential asymptotics","score":0.7129999995231628},{"id":"https://openalex.org/keywords/large-parameter","display_name":"large parameter","score":0.4620000123977661},{"id":"https://openalex.org/keywords/matrix-functions","display_name":"matrix functions","score":0.6110000014305115},{"id":"https://openalex.org/keywords/characteristic-equation","display_name":"characteristic equation","score":0.48100000619888306},{"id":"https://openalex.org/keywords/remainder-term","display_name":"remainder term","score":0.6039999723434448}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.9448880553245544},{"id":"https://openalex.org/C39613435","wikidata":"https://www.wikidata.org/wiki/Q846677","display_name":"Remainder","level":2,"score":0.7191134095191956},{"id":"https://openalex.org/C2778067643","wikidata":"https://www.wikidata.org/wiki/Q166507","display_name":"Interval (graph theory)","level":2,"score":0.6122533082962036},{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.5868523716926575},{"id":"https://openalex.org/C2777299769","wikidata":"https://www.wikidata.org/wiki/Q3707858","display_name":"Type (biology)","level":2,"score":0.5709916353225708},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.5425903797149658},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.5127564668655396},{"id":"https://openalex.org/C151376022","wikidata":"https://www.wikidata.org/wiki/Q168698","display_name":"Exponential function","level":2,"score":0.5102500915527344},{"id":"https://openalex.org/C78045399","wikidata":"https://www.wikidata.org/wiki/Q11214","display_name":"Differential equation","level":2,"score":0.491271436214447},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.4603549838066101},{"id":"https://openalex.org/C61797465","wikidata":"https://www.wikidata.org/wiki/Q1188986","display_name":"Term (time)","level":2,"score":0.4575168192386627},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.39598992466926575},{"id":"https://openalex.org/C94375191","wikidata":"https://www.wikidata.org/wiki/Q11205","display_name":"Arithmetic","level":1,"score":0.08917033672332764},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"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/C10138342","wikidata":"https://www.wikidata.org/wiki/Q43015","display_name":"Finance","level":1,"score":0.0},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C18903297","wikidata":"https://www.wikidata.org/wiki/Q7150","display_name":"Ecology","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/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","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:10.1007/bf03322121","doi":"https://doi.org/10.1007/bf03322121","is_oa":false,"landing_page_url":"https://doi.org/10.1007/bf03322121","pdf_url":null,"source":{"id":"https://openalex.org/S939935174","display_name":"Results in Mathematics","issn_l":"0378-6218","issn":["0378-6218","1420-9012","1422-6383"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["anvur-scientific","cwts-core","dongbi-d","jufo-1","norway-1","poland-100","russia-white-list-1","vabb-shw"],"host_organization":"https://openalex.org/P4310320186","host_organization_name":"Birkh\u00e4user","host_organization_lineage":["https://openalex.org/P4310320186","https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Birkh\u00e4user","Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Results in Mathematics","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":8,"referenced_works":["https://openalex.org/W2008897700","https://openalex.org/W2037437566","https://openalex.org/W2039677277","https://openalex.org/W2043841630","https://openalex.org/W2050719987","https://openalex.org/W4232258487","https://openalex.org/W4301859990","https://openalex.org/W6600489504"],"related_works":["https://openalex.org/W2050719987","https://openalex.org/W2971029343","https://openalex.org/W3042272349","https://openalex.org/W3048129252","https://openalex.org/W2605728592","https://openalex.org/W1009383642","https://openalex.org/W2050471646","https://openalex.org/W4387902514"],"abstract_inverted_index":null,"counts_by_year":[{"year":2026,"cited_by_count":2},{"year":2024,"cited_by_count":5},{"year":2023,"cited_by_count":2},{"year":2022,"cited_by_count":2},{"year":2021,"cited_by_count":6},{"year":2020,"cited_by_count":4},{"year":2019,"cited_by_count":1},{"year":2018,"cited_by_count":1},{"year":2017,"cited_by_count":2}],"updated_date":"2026-11-14T11:04:58.165337","created_date":"2016-06-24T00:00:00"}