{"id":"https://openalex.org/W2020239241","doi":"https://doi.org/10.1134/s0001434613070055","title":"Spectral and oscillatory properties of a linear pencil of fourth-order differential operators","display_name":"Spectral and oscillatory properties of a linear pencil of fourth-order differential operators","publication_year":2013,"publication_date":"2013-07-01","ids":{"openalex":"https://openalex.org/W2020239241","doi":"https://doi.org/10.1134/s0001434613070055","mag":"2020239241"},"language":"en","primary_location":{"id":"doi:10.1134/s0001434613070055","doi":"https://doi.org/10.1134/s0001434613070055","is_oa":false,"landing_page_url":"https://doi.org/10.1134/s0001434613070055","pdf_url":null,"source":{"id":"https://openalex.org/S16116274","display_name":"Mathematical Notes","issn_l":"0001-4346","issn":["0001-4346","1067-9073","1573-8876"],"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":["anvur-scientific","dongbi-b","jufo-1","norway-1","poland-40","russia-white-list-2"],"host_organization":"https://openalex.org/P4310320267","host_organization_name":"Pleiades Publishing","host_organization_lineage":["https://openalex.org/P4310320267","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Pleiades Publishing","Springer Nature"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematical Notes","raw_type":"journal-article"},"volume":null,"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/A5043637526","display_name":"Jamel Ben Amara","orcid":"https://orcid.org/0000-0001-7877-8216","observed_orcids":["https://orcid.org/0000-0001-7877-8216"]},"institutions":[{"id":"https://openalex.org/I179097149","display_name":"University of Carthage","ror":"https://ror.org/057x6za15","country_code":"TN","type":"education","lineage":["https://openalex.org/I179097149"]}],"countries":["TN"],"is_corresponding":true,"raw_author_name":"J. Ben Amara","raw_affiliation_strings":["University of 7th November at Carthage, Carthage, Tunisia","University of 7th November at Carthage"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"University of 7th November at Carthage, Carthage, Tunisia","institution_ids":["https://openalex.org/I179097149"]},{"raw_affiliation_string":"University of 7th November at Carthage","institution_ids":[]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5010299342","display_name":"\u0410\u043d\u0434\u0440\u0435\u0439 \u0410\u043d\u0434\u0440\u0435\u0435\u0432\u0438\u0447 \u0428\u043a\u0430\u043b\u0438\u043a\u043e\u0432","orcid":"https://orcid.org/0000-0002-9138-6628","observed_orcids":["https://orcid.org/0000-0002-9138-6628"]},"institutions":[{"id":"https://openalex.org/I19880235","display_name":"Lomonosov Moscow State University","ror":"https://ror.org/010pmpe69","country_code":"RU","type":"education","lineage":["https://openalex.org/I19880235"]}],"countries":["RU"],"is_corresponding":false,"raw_author_name":"A. A. Shkalikov","raw_affiliation_strings":["Moscow State University, Moscow, Russia","Moscow State  University"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Moscow State University, Moscow, Russia","institution_ids":["https://openalex.org/I19880235"]},{"raw_affiliation_string":"Moscow State  University","institution_ids":["https://openalex.org/I19880235"]}]},{"author_position":"last","author":{"id":null,"display_name":"A. A. Vladimirov","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I1313323035","display_name":"Russian Academy of Sciences","ror":"https://ror.org/05qrfxd25","country_code":"RU","type":"government","lineage":["https://openalex.org/I1313323035"]},{"id":"https://openalex.org/I2801535751","display_name":"Dorodnitsyn Computing Centre","ror":"https://ror.org/01vgda714","country_code":"RU","type":"facility","lineage":["https://openalex.org/I1313323035","https://openalex.org/I2801535751","https://openalex.org/I4210124601"]}],"countries":["RU"],"is_corresponding":false,"raw_author_name":"A. A. Vladimirov","raw_affiliation_strings":["Dorodnicyn Computing Center, Russian Academy of Sciences, Moscow, Russia","Russian Academy of Sciences"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Dorodnicyn Computing Center, Russian Academy of Sciences, Moscow, Russia","institution_ids":["https://openalex.org/I1313323035","https://openalex.org/I2801535751"]},{"raw_affiliation_string":"Russian Academy of Sciences","institution_ids":["https://openalex.org/I1313323035"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5043637526"],"corresponding_institution_ids":["https://openalex.org/I179097149"],"apc_list":null,"apc_paid":null,"fwci":0.4144,"has_fulltext":false,"cited_by_count":16,"citation_normalized_percentile":{"value":0.58226007,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":88,"max":97},"biblio":{"volume":"94","issue":"1-2","first_page":"49","last_page":"59"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11022","display_name":"Spectral Theory in Mathematical Physics","score":0.9961000084877014,"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":0.9961000084877014,"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":0.0019000000320374966,"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":0.0005000000237487257,"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/fourth-order-differential-operators","display_name":"fourth-order differential operators","score":0.9869999885559082},{"id":"https://openalex.org/keywords/spectral-properties","display_name":"spectral properties","score":0.7710000276565552},{"id":"https://openalex.org/keywords/oscillatory-properties","display_name":"oscillatory properties","score":0.9120000004768372},{"id":"https://openalex.org/keywords/eigenvalues","display_name":"eigenvalues","score":0.5910000205039978},{"id":"https://openalex.org/keywords/simple-eigenvalues","display_name":"simple eigenvalues","score":0.7960000038146973},{"id":"https://openalex.org/keywords/zeros-of-eigenfunctions","display_name":"eigenfunction zeros","score":0.8100000023841858},{"id":"https://openalex.org/keywords/sturm-liouville-operators","display_name":"Sturm-Liouville operators","score":0.6010000109672546}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8704909682273865},{"id":"https://openalex.org/C134949993","wikidata":"https://www.wikidata.org/wiki/Q2068617","display_name":"Pencil (optics)","level":2,"score":0.7847273349761963},{"id":"https://openalex.org/C70915906","wikidata":"https://www.wikidata.org/wiki/Q1058681","display_name":"Differential operator","level":2,"score":0.7222898602485657},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.6931235194206238},{"id":"https://openalex.org/C128803854","wikidata":"https://www.wikidata.org/wiki/Q1307821","display_name":"Eigenfunction","level":3,"score":0.6529399752616882},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.5914568901062012},{"id":"https://openalex.org/C13982400","wikidata":"https://www.wikidata.org/wiki/Q1129902","display_name":"Linear differential equation","level":3,"score":0.5912298560142517},{"id":"https://openalex.org/C1576492","wikidata":"https://www.wikidata.org/wiki/Q3739929","display_name":"Matrix pencil","level":3,"score":0.4874284565448761},{"id":"https://openalex.org/C110342517","wikidata":"https://www.wikidata.org/wiki/Q1129902","display_name":"Constant coefficients","level":2,"score":0.4837751090526581},{"id":"https://openalex.org/C93226319","wikidata":"https://www.wikidata.org/wiki/Q193137","display_name":"Differential (mechanical device)","level":2,"score":0.4317362904548645},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.37076544761657715},{"id":"https://openalex.org/C78045399","wikidata":"https://www.wikidata.org/wiki/Q11214","display_name":"Differential equation","level":2,"score":0.31619006395339966},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.09022259712219238},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.05821004509925842},{"id":"https://openalex.org/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1134/s0001434613070055","doi":"https://doi.org/10.1134/s0001434613070055","is_oa":false,"landing_page_url":"https://doi.org/10.1134/s0001434613070055","pdf_url":null,"source":{"id":"https://openalex.org/S16116274","display_name":"Mathematical Notes","issn_l":"0001-4346","issn":["0001-4346","1067-9073","1573-8876"],"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":["anvur-scientific","dongbi-b","jufo-1","norway-1","poland-40","russia-white-list-2"],"host_organization":"https://openalex.org/P4310320267","host_organization_name":"Pleiades Publishing","host_organization_lineage":["https://openalex.org/P4310320267","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Pleiades Publishing","Springer Nature"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematical Notes","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"sustainable_development_goals_aurora":[],"study_designs":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320321079","display_name":"Russian Foundation for Basic Research","ror":"https://ror.org/02mh1ke95"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":24,"referenced_works":["https://openalex.org/W593634829","https://openalex.org/W609892630","https://openalex.org/W614920821","https://openalex.org/W1540163279","https://openalex.org/W1575147392","https://openalex.org/W1576911969","https://openalex.org/W1985433917","https://openalex.org/W2010559691","https://openalex.org/W2034265344","https://openalex.org/W2040653548","https://openalex.org/W2058513936","https://openalex.org/W2059800177","https://openalex.org/W2065116436","https://openalex.org/W2074809607","https://openalex.org/W2094322837","https://openalex.org/W2141981259","https://openalex.org/W2165075469","https://openalex.org/W2315800462","https://openalex.org/W2321623140","https://openalex.org/W2788908630","https://openalex.org/W3021722416","https://openalex.org/W3101920821","https://openalex.org/W4253939733","https://openalex.org/W4300657400"],"related_works":["https://openalex.org/W2047937394","https://openalex.org/W2330447052","https://openalex.org/W4387938021","https://openalex.org/W2390920986","https://openalex.org/W3138597860","https://openalex.org/W1992815519","https://openalex.org/W2949838652","https://openalex.org/W4289785680","https://openalex.org/W2116399163","https://openalex.org/W1987060762"],"abstract_inverted_index":{"The":[0],"paper":[1],"deals":[2],"with":[3],"the":[4,19,24,31,36,55,64,69,75,79],"spectral":[5],"and":[6,30],"oscillatory":[7],"properties":[8],"of":[9,54,66,68,78],"a":[10],"linear":[11],"operator":[12],"pencil":[13,56],"A":[14,21],"\u2212":[15,39],"\u03bbB":[16],",":[17],"where":[18],"coefficient":[20,32],"corresponds":[22,34],"to":[23,35,74],"differential":[25,37],"expression":[26,38],"(":[27],"py":[28],"\u2033)\u2033":[29],"B":[33],"y":[40],"\u2033":[41],"+":[42],"cry":[43],".":[44],"In":[45],"particular,":[46],"it":[47],"is":[48,72],"shown":[49],"that":[50],"all":[51],"negative":[52],"eigenvalues":[53],"are":[57],"simple":[58],"and,":[59],"under":[60],"some":[61],"additional":[62],"conditions,":[63],"number":[65,77],"zeros":[67],"corresponding":[70,80],"eigenfunctions":[71],"related":[73],"serial":[76],"eigenvalue.":[81]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":2},{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":4},{"year":2021,"cited_by_count":1},{"year":2019,"cited_by_count":1},{"year":2018,"cited_by_count":2},{"year":2017,"cited_by_count":2},{"year":2016,"cited_by_count":1}],"updated_date":"2026-10-14T16:39:01.820549","created_date":"2025-10-10T00:00:00"}