Get quick answers to your questions about the article from our AI researcher chatbot
{'id': 'https://openalex.org/W2088739747', 'doi': 'https://doi.org/10.1007/s10208-012-9136-6', 'title': 'On Minimal Subspaces in Tensor Representations', 'display_name': 'On Minimal Subspaces in Tensor Representations', 'publication_year': 2012, 'publication_date': '2012-10-08', 'ids': {'openalex': 'https://openalex.org/W2088739747', 'doi': 'https://doi.org/10.1007/s10208-012-9136-6', 'mag': '2088739747'}, 'language': 'en', 'primary_location': {'is_oa': False, 'landing_page_url': 'https://doi.org/10.1007/s10208-012-9136-6', 'pdf_url': None, 'source': {'id': 'https://openalex.org/S151639445', 'display_name': 'Foundations of Computational Mathematics', 'issn_l': '1615-3375', 'issn': ['1615-3375', '1615-3383'], 'is_oa': False, 'is_in_doaj': False, 'is_core': True, 'host_organization': 'https://openalex.org/P4310319900', 'host_organization_name': 'Springer Science+Business Media', 'host_organization_lineage': ['https://openalex.org/P4310319965', 'https://openalex.org/P4310319900'], 'host_organization_lineage_names': ['Springer Nature', 'Springer Science+Business Media'], 'type': 'journal'}, 'license': None, 'license_id': None, 'version': None, 'is_accepted': False, 'is_published': False}, 'type': 'article', 'type_crossref': 'journal-article', 'indexed_in': ['crossref'], 'open_access': {'is_oa': False, 'oa_status': 'closed', 'oa_url': 'https://ddd.uab.cat/pub/artpub/2012/gsduab_3463/FalHac2012_Preprint.pdf', 'any_repository_has_fulltext': True}, 'authorships': [{'author_position': 'first', 'author': {'id': 'https://openalex.org/A5025468104', 'display_name': 'Antonio Falcó', 'orcid': 'https://orcid.org/0000-0001-6225-0935'}, 'institutions': [{'id': 'https://openalex.org/I2800982320', 'display_name': 'Universidad Cardenal Herrera CEU', 'ror': 'https://ror.org/01tnh0829', 'country_code': 'ES', 'type': 'education', 'lineage': ['https://openalex.org/I2800982320', 'https://openalex.org/I2801318690']}], 'countries': ['ES'], 'is_corresponding': False, 'raw_author_name': 'Antonio Falcó', 'raw_affiliation_strings': ['Departamento de Ciencias Físicas, Matemáticas y de la Computación, Universidad CEU-Cardenal Herrera, Alfara del Patriarca (Valencia), Spain 46115#TAB#'], 'affiliations': [{'raw_affiliation_string': 'Departamento de Ciencias Físicas, Matemáticas y de la Computación, Universidad CEU-Cardenal Herrera, Alfara del Patriarca (Valencia), Spain 46115#TAB#', 'institution_ids': ['https://openalex.org/I2800982320']}]}, {'author_position': 'last', 'author': {'id': 'https://openalex.org/A5084653980', 'display_name': 'Wolfgang Hackbusch', 'orcid': 'https://orcid.org/0000-0002-4801-6189'}, 'institutions': [{'id': 'https://openalex.org/I149899117', 'display_name': 'Max Planck Society', 'ror': 'https://ror.org/01hhn8329', 'country_code': 'DE', 'type': 'nonprofit', 'lineage': ['https://openalex.org/I149899117']}], 'countries': ['DE'], 'is_corresponding': False, 'raw_author_name': 'Wolfgang Hackbusch', 'raw_affiliation_strings': ['Max-Planck-Institut Mathematik in den Naturwissenschaften, Leipzig, Germany 04103#TAB#'], 'affiliations': [{'raw_affiliation_string': 'Max-Planck-Institut Mathematik in den Naturwissenschaften, Leipzig, Germany 04103#TAB#', 'institution_ids': ['https://openalex.org/I149899117']}]}], 'institution_assertions': [], 'countries_distinct_count': 2, 'institutions_distinct_count': 2, 'corresponding_author_ids': [], 'corresponding_institution_ids': [], 'apc_list': {'value': 2390, 'currency': 'EUR', 'value_usd': 2990, 'provenance': 'doaj'}, 'apc_paid': None, 'fwci': 2.018, 'has_fulltext': True, 'fulltext_origin': 'pdf', 'cited_by_count': 60, 'citation_normalized_percentile': {'value': 0.987654, 'is_in_top_1_percent': False, 'is_in_top_10_percent': True}, 'cited_by_percentile_year': {'min': 96, 'max': 97}, 'biblio': {'volume': '12', 'issue': '6', 'first_page': '765', 'last_page': '803'}, 'is_retracted': False, 'is_paratext': False, 'primary_topic': {'id': 'https://openalex.org/T12303', 'display_name': 'Tensor decomposition and applications', 'score': 1.0, 'subfield': {'id': 'https://openalex.org/subfields/2605', 'display_name': 'Computational 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/T12303', 'display_name': 'Tensor decomposition and applications', 'score': 1.0, 'subfield': {'id': 'https://openalex.org/subfields/2605', 'display_name': 'Computational 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/T11366', 'display_name': 'Elasticity and Material Modeling', 'score': 0.9802, 'subfield': {'id': 'https://openalex.org/subfields/2204', 'display_name': 'Biomedical Engineering'}, 'field': {'id': 'https://openalex.org/fields/22', 'display_name': 'Engineering'}, 'domain': {'id': 'https://openalex.org/domains/3', 'display_name': 'Physical Sciences'}}, {'id': 'https://openalex.org/T10339', 'display_name': 'Advanced Numerical Methods in Computational Mathematics', 'score': 0.9761, 'subfield': {'id': 'https://openalex.org/subfields/2206', 'display_name': 'Computational Mechanics'}, 'field': {'id': 'https://openalex.org/fields/22', 'display_name': 'Engineering'}, 'domain': {'id': 'https://openalex.org/domains/3', 'display_name': 'Physical Sciences'}}], 'keywords': [], 'concepts': [{'id': 'https://openalex.org/C93776189', 'wikidata': 'https://www.wikidata.org/wiki/Q1404488', 'display_name': 'Tensor product of Hilbert spaces', 'level': 4, 'score': 0.8410075}, {'id': 'https://openalex.org/C33923547', 'wikidata': 'https://www.wikidata.org/wiki/Q395', 'display_name': 'Mathematics', 'level': 0, 'score': 0.8269834}, {'id': 'https://openalex.org/C51255310', 'wikidata': 'https://www.wikidata.org/wiki/Q1163016', 'display_name': 'Tensor product', 'level': 2, 'score': 0.80070794}, {'id': 'https://openalex.org/C101783463', 'wikidata': 'https://www.wikidata.org/wiki/Q3406761', 'display_name': 'Tensor product of modules', 'level': 5, 'score': 0.7010559}, {'id': 'https://openalex.org/C124007464', 'wikidata': 'https://www.wikidata.org/wiki/Q428091', 'display_name': 'Tensor contraction', 'level': 3, 'score': 0.6202351}, {'id': 'https://openalex.org/C41678559', 'wikidata': 'https://www.wikidata.org/wiki/Q7700713', 'display_name': 'Tensor product of algebras', 'level': 5, 'score': 0.6143287}, {'id': 'https://openalex.org/C178099376', 'wikidata': 'https://www.wikidata.org/wiki/Q7825044', 'display_name': 'Topological tensor product', 'level': 4, 'score': 0.61406}, {'id': 'https://openalex.org/C202444582', 'wikidata': 'https://www.wikidata.org/wiki/Q837863', 'display_name': 'Pure mathematics', 'level': 1, 'score': 0.5794724}, {'id': 'https://openalex.org/C155281189', 'wikidata': 'https://www.wikidata.org/wiki/Q3518150', 'display_name': 'Tensor (intrinsic definition)', 'level': 2, 'score': 0.56011355}, {'id': 'https://openalex.org/C20178491', 'wikidata': 'https://www.wikidata.org/wiki/Q2204117', 'display_name': 'Symmetric tensor', 'level': 3, 'score': 0.555297}, {'id': 'https://openalex.org/C132954091', 'wikidata': 'https://www.wikidata.org/wiki/Q194397', 'display_name': 'Banach space', 'level': 2, 'score': 0.5487554}, {'id': 'https://openalex.org/C12362212', 'wikidata': 'https://www.wikidata.org/wiki/Q728435', 'display_name': 'Linear subspace', 'level': 2, 'score': 0.5441036}, {'id': 'https://openalex.org/C148125525', 'wikidata': 'https://www.wikidata.org/wiki/Q904927', 'display_name': 'Tensor density', 'level': 4, 'score': 0.4594558}, {'id': 'https://openalex.org/C128107574', 'wikidata': 'https://www.wikidata.org/wiki/Q182003', 'display_name': 'Injective function', 'level': 2, 'score': 0.4187923}, {'id': 'https://openalex.org/C166077713', 'wikidata': 'https://www.wikidata.org/wiki/Q1758924', 'display_name': 'Tensor field', 'level': 3, 'score': 0.3535143}, {'id': 'https://openalex.org/C136119220', 'wikidata': 'https://www.wikidata.org/wiki/Q1000660', 'display_name': 'Algebra over a field', 'level': 2, 'score': 0.35350406}, {'id': 'https://openalex.org/C134306372', 'wikidata': 'https://www.wikidata.org/wiki/Q7754', 'display_name': 'Mathematical analysis', 'level': 1, 'score': 0.25094402}, {'id': 'https://openalex.org/C520416788', 'wikidata': 'https://www.wikidata.org/wiki/Q5419229', 'display_name': 'Exact solutions in general relativity', 'level': 2, 'score': 0.20541713}, {'id': 'https://openalex.org/C55112680', 'wikidata': 'https://www.wikidata.org/wiki/Q190549', 'display_name': 'Functional analysis', 'level': 3, 'score': 0.13257593}, {'id': 'https://openalex.org/C55493867', 'wikidata': 'https://www.wikidata.org/wiki/Q7094', 'display_name': 'Biochemistry', 'level': 1, 'score': 0.0}, {'id': 'https://openalex.org/C185592680', 'wikidata': 'https://www.wikidata.org/wiki/Q2329', 'display_name': 'Chemistry', 'level': 0, 'score': 0.0}, {'id': 'https://openalex.org/C104317684', 'wikidata': 'https://www.wikidata.org/wiki/Q7187', 'display_name': 'Gene', 'level': 2, 'score': 0.0}], 'mesh': [], 'locations_count': 4, 'locations': [{'is_oa': False, 'landing_page_url': 'https://doi.org/10.1007/s10208-012-9136-6', 'pdf_url': None, 'source': {'id': 'https://openalex.org/S151639445', 'display_name': 'Foundations of Computational Mathematics', 'issn_l': '1615-3375', 'issn': ['1615-3375', '1615-3383'], 'is_oa': False, 'is_in_doaj': False, 'is_core': True, 'host_organization': 'https://openalex.org/P4310319900', 'host_organization_name': 'Springer Science+Business Media', 'host_organization_lineage': ['https://openalex.org/P4310319965', 'https://openalex.org/P4310319900'], 'host_organization_lineage_names': ['Springer Nature', 'Springer Science+Business Media'], 'type': 'journal'}, 'license': None, 'license_id': None, 'version': None, 'is_accepted': False, 'is_published': False}, {'is_oa': True, 'landing_page_url': 'http://ddd.uab.cat/record/150486', 'pdf_url': 'https://ddd.uab.cat/pub/artpub/2012/gsduab_3463/FalHac2012_Preprint.pdf', 'source': {'id': 'https://openalex.org/S4306402641', 'display_name': 'LA Referencia (Red Federada de Repositorios Institucionales de Publicaciones Científicas)', 'issn_l': None, 'issn': None, 'is_oa': True, 'is_in_doaj': False, 'is_core': False, 'host_organization': 'https://openalex.org/I4383465926', 'host_organization_name': 'LA Referencia', 'host_organization_lineage': ['https://openalex.org/I4383465926'], 'host_organization_lineage_names': ['LA Referencia'], 'type': 'repository'}, 'license': 'public-domain', 'license_id': 'https://openalex.org/licenses/public-domain', 'version': 'acceptedVersion', 'is_accepted': True, 'is_published': False}, {'is_oa': True, 'landing_page_url': 'http://hdl.handle.net/10637/5396', 'pdf_url': 'https://repositorioinstitucional.ceu.es/bitstream/10637/5396/4/Minimal_Falco_FOCM_2012.pdf', 'source': {'id': 'https://openalex.org/S4306401561', 'display_name': 'CEU Repositorio Institucional (Fundación Universitaria San Pablo CEU)', 'issn_l': None, 'issn': None, 'is_oa': True, 'is_in_doaj': False, 'is_core': False, 'host_organization': 'https://openalex.org/I118091203', 'host_organization_name': 'Universidad San Pablo CEU', 'host_organization_lineage': ['https://openalex.org/I118091203'], 'host_organization_lineage_names': ['Universidad San Pablo CEU'], 'type': 'repository'}, 'license': 'public-domain', 'license_id': 'https://openalex.org/licenses/public-domain', 'version': 'submittedVersion', 'is_accepted': False, 'is_published': False}, {'is_oa': True, 'landing_page_url': 'http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.641.1260', 'pdf_url': 'http://www.mis.mpg.de/preprints/2010/preprint2010_70.pdf', 'source': {'id': 'https://openalex.org/S4306400349', 'display_name': 'CiteSeer X (The Pennsylvania State University)', 'issn_l': None, 'issn': None, 'is_oa': True, 'is_in_doaj': False, 'is_core': False, 'host_organization': 'https://openalex.org/I130769515', 'host_organization_name': 'Pennsylvania State University', 'host_organization_lineage': ['https://openalex.org/I130769515'], 'host_organization_lineage_names': ['Pennsylvania State University'], 'type': 'repository'}, 'license': 'public-domain', 'license_id': 'https://openalex.org/licenses/public-domain', 'version': 'submittedVersion', 'is_accepted': False, 'is_published': False}], 'best_oa_location': {'is_oa': True, 'landing_page_url': 'http://ddd.uab.cat/record/150486', 'pdf_url': 'https://ddd.uab.cat/pub/artpub/2012/gsduab_3463/FalHac2012_Preprint.pdf', 'source': {'id': 'https://openalex.org/S4306402641', 'display_name': 'LA Referencia (Red Federada de Repositorios Institucionales de Publicaciones Científicas)', 'issn_l': None, 'issn': None, 'is_oa': True, 'is_in_doaj': False, 'is_core': False, 'host_organization': 'https://openalex.org/I4383465926', 'host_organization_name': 'LA Referencia', 'host_organization_lineage': ['https://openalex.org/I4383465926'], 'host_organization_lineage_names': ['LA Referencia'], 'type': 'repository'}, 'license': 'public-domain', 'license_id': 'https://openalex.org/licenses/public-domain', 'version': 'acceptedVersion', 'is_accepted': True, 'is_published': False}, 'sustainable_development_goals': [], 'grants': [], 'datasets': [], 'versions': [], 'referenced_works_count': 32, 'referenced_works': ['https://openalex.org/W1503042153', 'https://openalex.org/W1963826206', 'https://openalex.org/W1978632288', 'https://openalex.org/W2000215628', 'https://openalex.org/W2001292054', 'https://openalex.org/W2001518794', 'https://openalex.org/W2011347541', 'https://openalex.org/W2012810874', 'https://openalex.org/W2024165284', 'https://openalex.org/W2024182011', 'https://openalex.org/W2036604884', 'https://openalex.org/W2049444599', 'https://openalex.org/W2057577185', 'https://openalex.org/W2058999563', 'https://openalex.org/W2060200773', 'https://openalex.org/W2069086447', 'https://openalex.org/W2088025933', 'https://openalex.org/W2094085947', 'https://openalex.org/W2112823474', 'https://openalex.org/W2113055885', 'https://openalex.org/W2132267493', 'https://openalex.org/W2146552914', 'https://openalex.org/W2185658598', 'https://openalex.org/W2258054274', 'https://openalex.org/W2903005364', 'https://openalex.org/W2963858059', 'https://openalex.org/W3101417846', 'https://openalex.org/W4205354563', 'https://openalex.org/W4230023511', 'https://openalex.org/W4246335055', 'https://openalex.org/W50417968', 'https://openalex.org/W654155693'], 'related_works': ['https://openalex.org/W4301256940', 'https://openalex.org/W4298343018', 'https://openalex.org/W4297845514', 'https://openalex.org/W4205205188', 'https://openalex.org/W2948436065', 'https://openalex.org/W2558649412', 'https://openalex.org/W2469343812', 'https://openalex.org/W2201223056', 'https://openalex.org/W2088739747', 'https://openalex.org/W132488082'], 'abstract_inverted_index': None, 'cited_by_api_url': 'https://api.openalex.org/works?filter=cites:W2088739747', 'counts_by_year': [{'year': 2024, 'cited_by_count': 1}, {'year': 2023, 'cited_by_count': 2}, {'year': 2022, 'cited_by_count': 1}, {'year': 2021, 'cited_by_count': 4}, {'year': 2020, 'cited_by_count': 4}, {'year': 2019, 'cited_by_count': 5}, {'year': 2018, 'cited_by_count': 6}, {'year': 2017, 'cited_by_count': 8}, {'year': 2016, 'cited_by_count': 4}, {'year': 2015, 'cited_by_count': 4}, {'year': 2014, 'cited_by_count': 7}, {'year': 2013, 'cited_by_count': 6}, {'year': 2012, 'cited_by_count': 3}], 'updated_date': '2024-12-15T15:15:56.872523', 'created_date': '2016-06-24'}