Get quick answers to your questions about the article from our AI researcher chatbot
{'id': 'https://openalex.org/W4297752088', 'doi': 'https://doi.org/10.48550/arxiv.1307.6620', 'title': 'Energy of solenoidal vector fields on spherical domains', 'display_name': 'Energy of solenoidal vector fields on spherical domains', 'publication_year': 2013, 'publication_date': '2013-01-01', 'ids': {'openalex': 'https://openalex.org/W4297752088', 'doi': 'https://doi.org/10.48550/arxiv.1307.6620'}, 'language': 'en', 'primary_location': {'is_oa': True, 'landing_page_url': 'https://arxiv.org/abs/1307.6620', 'pdf_url': None, 'source': {'id': 'https://openalex.org/S4306400194', 'display_name': 'arXiv (Cornell University)', 'issn_l': None, 'issn': None, 'is_oa': True, 'is_in_doaj': False, 'is_core': False, 'host_organization': 'https://openalex.org/I205783295', 'host_organization_name': 'Cornell University', 'host_organization_lineage': ['https://openalex.org/I205783295'], 'host_organization_lineage_names': ['Cornell University'], 'type': 'repository'}, 'license': 'other-oa', 'license_id': 'https://openalex.org/licenses/other-oa', 'version': 'submittedVersion', 'is_accepted': False, 'is_published': False}, 'type': 'preprint', 'type_crossref': 'posted-content', 'indexed_in': ['arxiv', 'datacite'], 'open_access': {'is_oa': True, 'oa_status': 'green', 'oa_url': 'https://arxiv.org/abs/1307.6620', 'any_repository_has_fulltext': True}, 'authorships': [{'author_position': 'first', 'author': {'id': 'https://openalex.org/A5020277802', 'display_name': 'Fabiano Brito', 'orcid': None}, 'institutions': [], 'countries': [], 'is_corresponding': False, 'raw_author_name': 'Brito, Fabiano', 'raw_affiliation_strings': [], 'affiliations': []}, {'author_position': 'last', 'author': {'id': 'https://openalex.org/A5101998105', 'display_name': 'André Luís Gomes', 'orcid': 'https://orcid.org/0000-0003-0950-497X'}, 'institutions': [], 'countries': [], 'is_corresponding': False, 'raw_author_name': 'Gomes, André', 'raw_affiliation_strings': [], 'affiliations': []}], 'institution_assertions': [], 'countries_distinct_count': 0, 'institutions_distinct_count': 0, 'corresponding_author_ids': [], 'corresponding_institution_ids': [], 'apc_list': None, 'apc_paid': None, 'fwci': None, 'has_fulltext': False, 'cited_by_count': 0, 'citation_normalized_percentile': {'value': 0.0, 'is_in_top_1_percent': False, 'is_in_top_10_percent': False}, 'cited_by_percentile_year': {'min': 0, 'max': 65}, 'biblio': {'volume': None, 'issue': None, 'first_page': None, 'last_page': None}, 'is_retracted': False, 'is_paratext': False, 'primary_topic': {'id': 'https://openalex.org/T12100', 'display_name': 'Multiscale Methods for Heterogeneous Systems', 'score': 0.9903, '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'}}, 'topics': [{'id': 'https://openalex.org/T12100', 'display_name': 'Multiscale Methods for Heterogeneous Systems', 'score': 0.9903, '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/T12037', 'display_name': 'Quaternionic Analysis and Applications', 'score': 0.9365, '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/T13234', 'display_name': 'p-adic Models in Mathematical Physics', 'score': 0.9256, '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/unit-vector', 'display_name': 'Unit vector', 'score': 0.45926276}, {'id': 'https://openalex.org/keywords/mathematical-physics', 'display_name': 'Mathematical Physics', 'score': 0.434227}, {'id': 'https://openalex.org/keywords/unit-sphere', 'display_name': 'Unit sphere', 'score': 0.42226547}, {'id': 'https://openalex.org/keywords/spherical-cap', 'display_name': 'Spherical cap', 'score': 0.41173878}], 'concepts': [{'id': 'https://openalex.org/C7451433', 'wikidata': 'https://www.wikidata.org/wiki/Q1265039', 'display_name': 'Solenoidal vector field', 'level': 3, 'score': 0.9961109}, {'id': 'https://openalex.org/C91188154', 'wikidata': 'https://www.wikidata.org/wiki/Q186247', 'display_name': 'Vector field', 'level': 2, 'score': 0.69439983}, {'id': 'https://openalex.org/C112280298', 'wikidata': 'https://www.wikidata.org/wiki/Q5156582', 'display_name': 'Complex lamellar vector field', 'level': 4, 'score': 0.6056642}, {'id': 'https://openalex.org/C129782007', 'wikidata': 'https://www.wikidata.org/wiki/Q162886', 'display_name': 'Euclidean geometry', 'level': 2, 'score': 0.57402754}, {'id': 'https://openalex.org/C36503486', 'wikidata': 'https://www.wikidata.org/wiki/Q11235244', 'display_name': 'Domain (mathematical analysis)', 'level': 2, 'score': 0.5680417}, {'id': 'https://openalex.org/C62354387', 'wikidata': 'https://www.wikidata.org/wiki/Q875399', 'display_name': 'Boundary (topology)', 'level': 2, 'score': 0.5218612}, {'id': 'https://openalex.org/C2027888', 'wikidata': 'https://www.wikidata.org/wiki/Q521126', 'display_name': 'Vector potential', 'level': 3, 'score': 0.47034246}, {'id': 'https://openalex.org/C77237485', 'wikidata': 'https://www.wikidata.org/wiki/Q7917842', 'display_name': 'Vector spherical harmonics', 'level': 3, 'score': 0.4694756}, {'id': 'https://openalex.org/C122637931', 'wikidata': 'https://www.wikidata.org/wiki/Q118084', 'display_name': 'Unit (ring theory)', 'level': 2, 'score': 0.46006858}, {'id': 'https://openalex.org/C84316537', 'wikidata': 'https://www.wikidata.org/wiki/Q36255', 'display_name': 'Unit vector', 'level': 2, 'score': 0.45926276}, {'id': 'https://openalex.org/C134306372', 'wikidata': 'https://www.wikidata.org/wiki/Q7754', 'display_name': 'Mathematical analysis', 'level': 1, 'score': 0.45198572}, {'id': 'https://openalex.org/C121332964', 'wikidata': 'https://www.wikidata.org/wiki/Q413', 'display_name': 'Physics', 'level': 0, 'score': 0.4476289}, {'id': 'https://openalex.org/C120174047', 'wikidata': 'https://www.wikidata.org/wiki/Q847073', 'display_name': 'Euclidean distance', 'level': 2, 'score': 0.4363558}, {'id': 'https://openalex.org/C33923547', 'wikidata': 'https://www.wikidata.org/wiki/Q395', 'display_name': 'Mathematics', 'level': 0, 'score': 0.42516115}, {'id': 'https://openalex.org/C191948623', 'wikidata': 'https://www.wikidata.org/wiki/Q1307800', 'display_name': 'Unit sphere', 'level': 2, 'score': 0.42226547}, {'id': 'https://openalex.org/C186370098', 'wikidata': 'https://www.wikidata.org/wiki/Q442787', 'display_name': 'Energy (signal processing)', 'level': 2, 'score': 0.41806662}, {'id': 'https://openalex.org/C2778664614', 'wikidata': 'https://www.wikidata.org/wiki/Q575597', 'display_name': 'Spherical cap', 'level': 2, 'score': 0.41173878}, {'id': 'https://openalex.org/C2524010', 'wikidata': 'https://www.wikidata.org/wiki/Q8087', 'display_name': 'Geometry', 'level': 1, 'score': 0.3148036}, {'id': 'https://openalex.org/C115260700', 'wikidata': 'https://www.wikidata.org/wiki/Q11408', 'display_name': 'Magnetic field', 'level': 2, 'score': 0.1645279}, {'id': 'https://openalex.org/C62520636', 'wikidata': 'https://www.wikidata.org/wiki/Q944', 'display_name': 'Quantum mechanics', 'level': 1, 'score': 0.07277861}, {'id': 'https://openalex.org/C3768446', 'wikidata': 'https://www.wikidata.org/wiki/Q877100', 'display_name': 'Spherical harmonics', 'level': 2, 'score': 0.0}, {'id': 'https://openalex.org/C145420912', 'wikidata': 'https://www.wikidata.org/wiki/Q853077', 'display_name': 'Mathematics education', 'level': 1, 'score': 0.0}], 'mesh': [], 'locations_count': 3, 'locations': [{'is_oa': True, 'landing_page_url': 'https://arxiv.org/abs/1307.6620', 'pdf_url': None, 'source': {'id': 'https://openalex.org/S4306400194', 'display_name': 'arXiv (Cornell University)', 'issn_l': None, 'issn': None, 'is_oa': True, 'is_in_doaj': False, 'is_core': False, 'host_organization': 'https://openalex.org/I205783295', 'host_organization_name': 'Cornell University', 'host_organization_lineage': ['https://openalex.org/I205783295'], 'host_organization_lineage_names': ['Cornell University'], 'type': 'repository'}, 'license': 'other-oa', 'license_id': 'https://openalex.org/licenses/other-oa', 'version': 'submittedVersion', 'is_accepted': False, 'is_published': False}, {'is_oa': True, 'landing_page_url': 'http://arxiv.org/abs/1307.6620', 'pdf_url': 'http://arxiv.org/pdf/1307.6620', 'source': {'id': 'https://openalex.org/S4306400194', 'display_name': 'arXiv (Cornell University)', 'issn_l': None, 'issn': None, 'is_oa': True, 'is_in_doaj': False, 'is_core': False, 'host_organization': 'https://openalex.org/I205783295', 'host_organization_name': 'Cornell University', 'host_organization_lineage': ['https://openalex.org/I205783295'], 'host_organization_lineage_names': ['Cornell University'], 'type': 'repository'}, 'license': None, 'license_id': None, 'version': 'submittedVersion', 'is_accepted': False, 'is_published': False}, {'is_oa': False, 'landing_page_url': 'https://api.datacite.org/dois/10.48550/arxiv.1307.6620', 'pdf_url': None, 'source': {'id': 'https://openalex.org/S4393179698', 'display_name': 'DataCite API', 'issn_l': None, 'issn': None, 'is_oa': True, 'is_in_doaj': False, 'is_core': False, 'host_organization': 'https://openalex.org/I4210145204', 'host_organization_name': 'DataCite', 'host_organization_lineage': ['https://openalex.org/I4210145204'], 'host_organization_lineage_names': ['DataCite'], 'type': 'metadata'}, 'license': None, 'license_id': None, 'version': None}], 'best_oa_location': {'is_oa': True, 'landing_page_url': 'https://arxiv.org/abs/1307.6620', 'pdf_url': None, 'source': {'id': 'https://openalex.org/S4306400194', 'display_name': 'arXiv (Cornell University)', 'issn_l': None, 'issn': None, 'is_oa': True, 'is_in_doaj': False, 'is_core': False, 'host_organization': 'https://openalex.org/I205783295', 'host_organization_name': 'Cornell University', 'host_organization_lineage': ['https://openalex.org/I205783295'], 'host_organization_lineage_names': ['Cornell University'], 'type': 'repository'}, 'license': 'other-oa', 'license_id': 'https://openalex.org/licenses/other-oa', 'version': 'submittedVersion', 'is_accepted': False, 'is_published': False}, 'sustainable_development_goals': [{'score': 0.53, 'id': 'https://metadata.un.org/sdg/7', 'display_name': 'Affordable and clean energy'}], 'grants': [], 'datasets': [], 'versions': [], 'referenced_works_count': 0, 'referenced_works': [], 'related_works': ['https://openalex.org/W2996354014', 'https://openalex.org/W2765592855', 'https://openalex.org/W2478780871', 'https://openalex.org/W246067103', 'https://openalex.org/W223118542', 'https://openalex.org/W2180574938', 'https://openalex.org/W2008408871', 'https://openalex.org/W1983126371', 'https://openalex.org/W1512603899', 'https://openalex.org/W1459117173'], 'abstract_inverted_index': {'We': [0], 'present': [1], 'a': [2, 6, 17], 'boundary': [3], 'version': [4], 'of': [5, 20], 'theorem': [7], 'about': [8], 'solenoidal': [9], 'unit': [10], 'vector': [11], 'fields': [12], 'with': [13], 'minimum': [14], 'energy': [15], 'on': [16], 'spherical': [18], 'domain': [19], 'an': [21], 'odd': [22], 'dimensional': [23], 'Euclidean': [24], 'sphere.': [25]}, 'cited_by_api_url': 'https://api.openalex.org/works?filter=cites:W4297752088', 'counts_by_year': [], 'updated_date': '2024-09-15T08:38:26.690704', 'created_date': '2022-09-30'}