{"id":"https://openalex.org/W288010477","doi":null,"title":"The Helmholtz decomposition of vector fields in some unbounded domains","display_name":"The Helmholtz decomposition of vector fields in some unbounded domains","publication_year":1994,"publication_date":"1994-01-01","ids":{"openalex":"https://openalex.org/W288010477","mag":"288010477"},"language":"en","primary_location":{"id":"mag:288010477","doi":null,"is_oa":false,"landing_page_url":"http://ci.nii.ac.jp/naid/110000070437","pdf_url":null,"source":{"id":"https://openalex.org/S2764972172","display_name":"Mathematics journal of Toyama University","issn_l":"0916-6009","issn":["0916-6009"],"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/P4310313209","host_organization_name":"University of Toyama","host_organization_lineage":["https://openalex.org/P4310313209"],"host_organization_lineage_names":["University of Toyama"],"type":"journal"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":false,"raw_source_name":"Mathematics journal of Toyama University","raw_type":null},"volume":null,"type":"article","indexed_in":[],"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/A5029080963","display_name":"Tetsuro Miyakawa","orcid":null,"observed_orcids":[]},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Tetsuro Miyakawa","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":["https://openalex.org/A5029080963"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":21,"citation_normalized_percentile":{"value":0.03343427,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":"17","issue":null,"first_page":"115","last_page":"149"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12589","display_name":"Differential Equations and Boundary Problems","score":0.23600000143051147,"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"}},"topics":[{"id":"https://openalex.org/T12589","display_name":"Differential Equations and Boundary Problems","score":0.23600000143051147,"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/T11049","display_name":"Advanced Harmonic Analysis Research","score":0.19699999690055847,"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/T13400","display_name":"Mathematical and Theoretical Analysis","score":0.10599999874830246,"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/helmholtz-decomposition","display_name":"Helmholtz decomposition","score":1.0},{"id":"https://openalex.org/keywords/vector-fields","display_name":"vector fields","score":0.9959999918937683},{"id":"https://openalex.org/keywords/unbounded-domains","display_name":"unbounded domains","score":0.9800000190734863},{"id":"https://openalex.org/keywords/divergence-free-vector-fields","display_name":"divergence-free vector fields","score":0.5870000123977661}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8075322508811951},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.5507907271385193},{"id":"https://openalex.org/C27592594","wikidata":"https://www.wikidata.org/wiki/Q865821","display_name":"Helmholtz free energy","level":2,"score":0.5466740727424622},{"id":"https://openalex.org/C91188154","wikidata":"https://www.wikidata.org/wiki/Q186247","display_name":"Vector field","level":2,"score":0.49514880776405334},{"id":"https://openalex.org/C124681953","wikidata":"https://www.wikidata.org/wiki/Q339062","display_name":"Decomposition","level":2,"score":0.4174403250217438},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.40203672647476196},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.1833607256412506},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0990128219127655},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.024629712104797363},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C18903297","wikidata":"https://www.wikidata.org/wiki/Q7150","display_name":"Ecology","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"mag:288010477","doi":null,"is_oa":false,"landing_page_url":"http://ci.nii.ac.jp/naid/110000070437","pdf_url":null,"source":{"id":"https://openalex.org/S2764972172","display_name":"Mathematics journal of Toyama University","issn_l":"0916-6009","issn":["0916-6009"],"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/P4310313209","host_organization_name":"University of Toyama","host_organization_lineage":["https://openalex.org/P4310313209"],"host_organization_lineage_names":["University of Toyama"],"type":"journal"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":null,"raw_source_name":"Mathematics journal of Toyama University","raw_type":null}],"best_oa_location":null,"sustainable_development_goals":[],"sustainable_development_goals_aurora":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W2321791236","https://openalex.org/W2481696235","https://openalex.org/W2015105054","https://openalex.org/W2014588923","https://openalex.org/W2058408533","https://openalex.org/W1982418511","https://openalex.org/W1976167505","https://openalex.org/W2014783444","https://openalex.org/W2480400398","https://openalex.org/W617333099","https://openalex.org/W2073197159","https://openalex.org/W2004919776","https://openalex.org/W2002592349","https://openalex.org/W1964309801","https://openalex.org/W1674480361","https://openalex.org/W1598074861","https://openalex.org/W1568190999","https://openalex.org/W2990096427","https://openalex.org/W1616578860","https://openalex.org/W1532211829"],"abstract_inverted_index":null,"counts_by_year":[{"year":2019,"cited_by_count":1},{"year":2018,"cited_by_count":3},{"year":2017,"cited_by_count":2},{"year":2016,"cited_by_count":1},{"year":2014,"cited_by_count":1},{"year":2013,"cited_by_count":1}],"updated_date":"2026-10-12T09:40:04.860316","created_date":"2025-10-10T00:00:00"}