{"id":"https://openalex.org/W2044932602","doi":"https://doi.org/10.1002/(sici)1099-1476(199606)19:9<699::aid-mma789>3.0.co;2-4","title":"Scattering Frequencies and a Class of Perturbed Systems of Elastic Waves","display_name":"Scattering Frequencies and a Class of Perturbed Systems of Elastic Waves","publication_year":1996,"publication_date":"1996-06-01","ids":{"openalex":"https://openalex.org/W2044932602","doi":"https://doi.org/10.1002/(sici)1099-1476(199606)19:9<699::aid-mma789>3.0.co;2-4","mag":"2044932602"},"language":"en","primary_location":{"id":"doi:10.1002/(sici)1099-1476(199606)19:9<699::aid-mma789>3.0.co;2-4","doi":"https://doi.org/10.1002/(sici)1099-1476(199606)19:9<699::aid-mma789>3.0.co;2-4","is_oa":false,"landing_page_url":"https://doi.org/10.1002/(sici)1099-1476(199606)19:9<699::aid-mma789>3.0.co;2-4","pdf_url":null,"source":{"id":"https://openalex.org/S89452420","display_name":"Mathematical Methods in the Applied Sciences","issn_l":"0170-4214","issn":["0170-4214","1099-1476"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["anvur-scientific","cwts-core","dongbi-d","jufo-1","poland-100","russia-white-list-1","vabb-shw"],"host_organization":"https://openalex.org/P4310320595","host_organization_name":"Wiley","host_organization_lineage":["https://openalex.org/P4310320595"],"host_organization_lineage_names":["Wiley"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematical Methods in the Applied Sciences","raw_type":"journal-article"},"volume":null,"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/A5025757737","display_name":"Ruy Coimbra Char\u00e3o","orcid":"https://orcid.org/0000-0003-3016-9379","observed_orcids":["https://orcid.org/0000-0003-3016-9379","https://orcid.org/0000-0001-8597-6288"]},"institutions":[{"id":"https://openalex.org/I4104125","display_name":"Universidade Federal de Santa Catarina","ror":"https://ror.org/041akq887","country_code":"BR","type":"education","lineage":["https://openalex.org/I4104125"]}],"countries":["BR"],"is_corresponding":true,"raw_author_name":"Ruy Coimbra Char\u00e3o","raw_affiliation_strings":["Department of Mathematics, Federal University of Santa Catarina, Trindade, CP 476, Floriano\u0301polis, CEP 88040-900, Santa Catarina, Brazil"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Federal University of Santa Catarina, Trindade, CP 476, Floriano\u0301polis, CEP 88040-900, Santa Catarina, Brazil","institution_ids":["https://openalex.org/I4104125"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5031680265","display_name":"Gustavo Perla Menzala","orcid":"https://orcid.org/0000-0003-2250-9986","observed_orcids":["https://orcid.org/0000-0003-2250-9986"]},"institutions":[{"id":"https://openalex.org/I11385950","display_name":"Conselho Nacional de Desenvolvimento Cient\u00edfico e Tecnol\u00f3gico","ror":"https://ror.org/03swz6y49","country_code":"BR","type":"government","lineage":["https://openalex.org/I11385950","https://openalex.org/I4210151455"]}],"countries":["BR"],"is_corresponding":false,"raw_author_name":"Gustavo Perla Menzala","raw_affiliation_strings":["LNCC/CNPq, Rua Lauro Mu\u0308ller 455, Botafogo, CEP 22290, RJ, Brazil and IM/UFRJ, CP 68530, CEP 56018, RJ, Brazil"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"LNCC/CNPq, Rua Lauro Mu\u0308ller 455, Botafogo, CEP 22290, RJ, Brazil and IM/UFRJ, CP 68530, CEP 56018, RJ, Brazil","institution_ids":["https://openalex.org/I11385950"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5025757737"],"corresponding_institution_ids":["https://openalex.org/I4104125"],"apc_list":{"value":5000,"currency":"USD","value_usd":5000},"apc_paid":null,"fwci":0.5015,"has_fulltext":false,"cited_by_count":6,"citation_normalized_percentile":{"value":0.58896008,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"19","issue":"9","first_page":"699","last_page":"716"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11022","display_name":"Spectral Theory in Mathematical Physics","score":0.9922000169754028,"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":0.9922000169754028,"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/T11654","display_name":"Advanced Mathematical Physics Problems","score":0.0017999999690800905,"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/T11205","display_name":"Numerical methods in inverse problems","score":0.0013000000035390258,"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/elastic-waves","display_name":"elastic waves","score":0.8939999938011169},{"id":"https://openalex.org/keywords/impurities","display_name":"impurities","score":0.375},{"id":"https://openalex.org/keywords/isotropic-media","display_name":"isotropic media","score":0.7839999794960022},{"id":"https://openalex.org/keywords/complex-plane","display_name":"complex plane","score":0.40700000524520874},{"id":"https://openalex.org/keywords/discrete-spectrum","display_name":"discrete spectrum","score":0.5870000123977661},{"id":"https://openalex.org/keywords/asymptotic-behavior-at-infinity","display_name":"asymptotic behavior at infinity","score":0.6499999761581421}],"concepts":[{"id":"https://openalex.org/C191486275","wikidata":"https://www.wikidata.org/wiki/Q210028","display_name":"Scattering","level":2,"score":0.7070275545120239},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7030553221702576},{"id":"https://openalex.org/C184050105","wikidata":"https://www.wikidata.org/wiki/Q273163","display_name":"Isotropy","level":2,"score":0.6789088845252991},{"id":"https://openalex.org/C7321624","wikidata":"https://www.wikidata.org/wiki/Q205","display_name":"Infinity","level":2,"score":0.6297941207885742},{"id":"https://openalex.org/C17825722","wikidata":"https://www.wikidata.org/wiki/Q17285","display_name":"Plane (geometry)","level":2,"score":0.5604678392410278},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.5535573959350586},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.549357533454895},{"id":"https://openalex.org/C179117685","wikidata":"https://www.wikidata.org/wiki/Q328998","display_name":"Complex plane","level":2,"score":0.5475533604621887},{"id":"https://openalex.org/C2778572836","wikidata":"https://www.wikidata.org/wiki/Q380933","display_name":"Space (punctuation)","level":2,"score":0.4439196288585663},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.4436599910259247},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.32490086555480957},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.24287667870521545},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.19737115502357483},{"id":"https://openalex.org/C41895202","wikidata":"https://www.wikidata.org/wiki/Q8162","display_name":"Linguistics","level":1,"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/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"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/C78458016","wikidata":"https://www.wikidata.org/wiki/Q840400","display_name":"Evolutionary biology","level":1,"score":0.0},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1002/(sici)1099-1476(199606)19:9<699::aid-mma789>3.0.co;2-4","doi":"https://doi.org/10.1002/(sici)1099-1476(199606)19:9<699::aid-mma789>3.0.co;2-4","is_oa":false,"landing_page_url":"https://doi.org/10.1002/(sici)1099-1476(199606)19:9<699::aid-mma789>3.0.co;2-4","pdf_url":null,"source":{"id":"https://openalex.org/S89452420","display_name":"Mathematical Methods in the Applied Sciences","issn_l":"0170-4214","issn":["0170-4214","1099-1476"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["anvur-scientific","cwts-core","dongbi-d","jufo-1","poland-100","russia-white-list-1","vabb-shw"],"host_organization":"https://openalex.org/P4310320595","host_organization_name":"Wiley","host_organization_lineage":["https://openalex.org/P4310320595"],"host_organization_lineage_names":["Wiley"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematical Methods in the Applied Sciences","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":16,"referenced_works":["https://openalex.org/W222749008","https://openalex.org/W571122171","https://openalex.org/W1981454809","https://openalex.org/W2007610584","https://openalex.org/W2077371597","https://openalex.org/W2083637536","https://openalex.org/W2085915575","https://openalex.org/W2092327885","https://openalex.org/W2117692113","https://openalex.org/W2118766761","https://openalex.org/W2996488364","https://openalex.org/W3022562852","https://openalex.org/W4237844829","https://openalex.org/W4245013082","https://openalex.org/W4252134205","https://openalex.org/W4285719527"],"related_works":["https://openalex.org/W2047707637","https://openalex.org/W2085915575","https://openalex.org/W2085414313","https://openalex.org/W2323454541","https://openalex.org/W360784334","https://openalex.org/W2037295825","https://openalex.org/W2489967298","https://openalex.org/W2045969093","https://openalex.org/W1970921574","https://openalex.org/W2026829390"],"abstract_inverted_index":{"We":[0,44,56],"consider":[1],"the":[2,11,17,38,46,49,65,75],"system":[3],"of":[4,13,16,48,71],"elastic":[5],"waves":[6],"in":[7],"three":[8],"dimensions":[9],"under":[10],"presence":[12],"an":[14],"impurity":[15],"medium":[18,30],"which":[19,68],"we":[20],"represent":[21],"by":[22],"a":[23,61],"real-valued":[24],"function":[25],"q(x)":[26],"(or":[27],"q(x,t)).":[28],"The":[29],"is":[31,60,69],"assumed":[32],"to":[33],"be":[34],"isotropic":[35],"and":[36],"occupies":[37],"whole":[39],"space":[40],"\u03a9":[41],"=":[42],"\u211d3.":[43],"study":[45],"location":[47],"scattering":[50,72],"frequencies":[51],"associated":[52],"with":[53],"such":[54],"phenomenon.":[55],"conclude":[57],"that":[58,82],"there":[59],"large":[62],"region":[63,77],"on":[64],"complex":[66],"plane":[67],"free":[70],"frequencies.":[73],"In":[74],"remaining":[76],"they":[78],"are":[79],"discrete":[80],"provided":[81],"q":[83],"satisfies":[84],"suitable":[85],"assumptions":[86],"concerning":[87],"its":[88],"behaviour":[89],"at":[90],"infinity.":[91]},"counts_by_year":[],"updated_date":"2026-10-14T16:39:01.820549","created_date":"2016-06-24T00:00:00"}
