Get quick answers to your questions about the article from our AI researcher chatbot
{'id': 'https://openalex.org/W2240454606', 'doi': 'https://doi.org/10.2140/apde.2016.9.1903', 'title': 'Invariant distributions and the geodesic ray transform', 'display_name': 'Invariant distributions and the geodesic ray transform', 'publication_year': 2016, 'publication_date': '2016-12-11', 'ids': {'openalex': 'https://openalex.org/W2240454606', 'doi': 'https://doi.org/10.2140/apde.2016.9.1903', 'mag': '2240454606'}, 'language': 'en', 'primary_location': {'is_oa': False, 'landing_page_url': 'https://doi.org/10.2140/apde.2016.9.1903', 'pdf_url': None, 'source': {'id': 'https://openalex.org/S2477993565', 'display_name': 'Analysis & PDE', 'issn_l': '1948-206X', 'issn': ['1948-206X', '2157-5045'], 'is_oa': False, 'is_in_doaj': False, 'is_core': True, 'host_organization': 'https://openalex.org/P4310320446', 'host_organization_name': 'Mathematical Sciences Publishers', 'host_organization_lineage': ['https://openalex.org/P4310320446'], 'host_organization_lineage_names': ['Mathematical Sciences Publishers'], 'type': 'journal'}, 'license': None, 'license_id': None, 'version': None, 'is_accepted': False, 'is_published': False}, 'type': 'article', 'type_crossref': 'journal-article', 'indexed_in': ['arxiv', 'crossref', 'datacite'], 'open_access': {'is_oa': True, 'oa_status': 'green', 'oa_url': 'http://arxiv.org/pdf/1511.04547', 'any_repository_has_fulltext': True}, 'authorships': [{'author_position': 'first', 'author': {'id': 'https://openalex.org/A5025386563', 'display_name': 'Gabriel P. Paternain', 'orcid': None}, 'institutions': [{'id': 'https://openalex.org/I241749', 'display_name': 'University of Cambridge', 'ror': 'https://ror.org/013meh722', 'country_code': 'GB', 'type': 'education', 'lineage': ['https://openalex.org/I241749']}], 'countries': ['GB'], 'is_corresponding': False, 'raw_author_name': 'Gabriel P. Paternain', 'raw_affiliation_strings': ['Department of Pure Mathematics and Mathematical Statistics, University of Cambridge, Cambridge CB3 0WB, United Kingdom'], 'affiliations': [{'raw_affiliation_string': 'Department of Pure Mathematics and Mathematical Statistics, University of Cambridge, Cambridge CB3 0WB, United Kingdom', 'institution_ids': ['https://openalex.org/I241749']}]}, {'author_position': 'last', 'author': {'id': 'https://openalex.org/A5101420612', 'display_name': 'Hanming Zhou', 'orcid': 'https://orcid.org/0000-0002-2188-4445'}, 'institutions': [{'id': 'https://openalex.org/I241749', 'display_name': 'University of Cambridge', 'ror': 'https://ror.org/013meh722', 'country_code': 'GB', 'type': 'education', 'lineage': ['https://openalex.org/I241749']}], 'countries': ['GB'], 'is_corresponding': False, 'raw_author_name': 'Hanming Zhou', 'raw_affiliation_strings': ['Department of Pure Mathematics and Mathematical Statistics, University of Cambridge, Cambridge CB3 0WB, United Kingdom'], 'affiliations': [{'raw_affiliation_string': 'Department of Pure Mathematics and Mathematical Statistics, University of Cambridge, Cambridge CB3 0WB, United Kingdom', 'institution_ids': ['https://openalex.org/I241749']}]}], 'countries_distinct_count': 1, 'institutions_distinct_count': 1, 'corresponding_author_ids': [], 'corresponding_institution_ids': [], 'apc_list': None, 'apc_paid': None, 'fwci': 2.629, 'has_fulltext': True, 'fulltext_origin': 'pdf', 'cited_by_count': 11, 'citation_normalized_percentile': {'value': 0.658789, 'is_in_top_1_percent': False, 'is_in_top_10_percent': False}, 'cited_by_percentile_year': {'min': 87, 'max': 88}, 'biblio': {'volume': '9', 'issue': '8', 'first_page': '1903', 'last_page': '1930'}, 'is_retracted': False, 'is_paratext': False, 'primary_topic': {'id': 'https://openalex.org/T11205', 'display_name': 'Inverse Problems in Mathematical Physics and Imaging', 'score': 0.999, '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/T11205', 'display_name': 'Inverse Problems in Mathematical Physics and Imaging', 'score': 0.999, '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/T10229', 'display_name': 'Optimal Transport in Geometry and Analysis', 'score': 0.9972, '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/T11245', 'display_name': 'Isogeometric Analysis in Computational Engineering', 'score': 0.9852, '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': [{'id': 'https://openalex.org/keywords/geometric-applications', 'display_name': 'Geometric Applications', 'score': 0.473785}], 'concepts': [{'id': 'https://openalex.org/C33923547', 'wikidata': 'https://www.wikidata.org/wiki/Q395', 'display_name': 'Mathematics', 'level': 0, 'score': 0.859846}, {'id': 'https://openalex.org/C7451433', 'wikidata': 'https://www.wikidata.org/wiki/Q1265039', 'display_name': 'Solenoidal vector field', 'level': 3, 'score': 0.8560441}, {'id': 'https://openalex.org/C165818556', 'wikidata': 'https://www.wikidata.org/wiki/Q213488', 'display_name': 'Geodesic', 'level': 2, 'score': 0.778825}, {'id': 'https://openalex.org/C190470478', 'wikidata': 'https://www.wikidata.org/wiki/Q2370229', 'display_name': 'Invariant (physics)', 'level': 2, 'score': 0.68611807}, {'id': 'https://openalex.org/C112680207', 'wikidata': 'https://www.wikidata.org/wiki/Q714886', 'display_name': 'Regular polygon', 'level': 2, 'score': 0.53134686}, {'id': 'https://openalex.org/C134306372', 'wikidata': 'https://www.wikidata.org/wiki/Q7754', 'display_name': 'Mathematical analysis', 'level': 1, 'score': 0.49316186}, {'id': 'https://openalex.org/C202444582', 'wikidata': 'https://www.wikidata.org/wiki/Q837863', 'display_name': 'Pure mathematics', 'level': 1, 'score': 0.4790034}, {'id': 'https://openalex.org/C2524010', 'wikidata': 'https://www.wikidata.org/wiki/Q8087', 'display_name': 'Geometry', 'level': 1, 'score': 0.23483855}, {'id': 'https://openalex.org/C91188154', 'wikidata': 'https://www.wikidata.org/wiki/Q186247', 'display_name': 'Vector field', 'level': 2, 'score': 0.2183969}, {'id': 'https://openalex.org/C37914503', 'wikidata': 'https://www.wikidata.org/wiki/Q156495', 'display_name': 'Mathematical physics', 'level': 1, 'score': 0.13387534}], 'mesh': [], 'locations_count': 6, 'locations': [{'is_oa': False, 'landing_page_url': 'https://doi.org/10.2140/apde.2016.9.1903', 'pdf_url': None, 'source': {'id': 'https://openalex.org/S2477993565', 'display_name': 'Analysis & PDE', 'issn_l': '1948-206X', 'issn': ['1948-206X', '2157-5045'], 'is_oa': False, 'is_in_doaj': False, 'is_core': True, 'host_organization': 'https://openalex.org/P4310320446', 'host_organization_name': 'Mathematical Sciences Publishers', 'host_organization_lineage': ['https://openalex.org/P4310320446'], 'host_organization_lineage_names': ['Mathematical Sciences Publishers'], 'type': 'journal'}, 'license': None, 'license_id': None, 'version': None, 'is_accepted': False, 'is_published': False}, {'is_oa': True, 'landing_page_url': 'http://arxiv.org/abs/1511.04547', 'pdf_url': 'http://arxiv.org/pdf/1511.04547', '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': True, 'landing_page_url': 'https://www.repository.cam.ac.uk/handle/1810/261055', 'pdf_url': 'https://www.repository.cam.ac.uk/bitstream/1810/261055/4/apde-v9-n8-p04-p.pdf', 'source': {'id': 'https://openalex.org/S4306401777', 'display_name': 'Apollo (University of Cambridge)', 'issn_l': None, 'issn': None, 'is_oa': True, 'is_in_doaj': False, 'is_core': False, 'host_organization': 'https://openalex.org/I241749', 'host_organization_name': 'University of Cambridge', 'host_organization_lineage': ['https://openalex.org/I241749'], 'host_organization_lineage_names': ['University of Cambridge'], 'type': 'repository'}, 'license': None, 'license_id': None, 'version': 'submittedVersion', 'is_accepted': False, 'is_published': False}, {'is_oa': True, 'landing_page_url': 'https://arxiv.org/abs/1511.04547', 'pdf_url': 'https://arxiv.org/pdf/1511.04547', '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': True, 'landing_page_url': 'https://projecteuclid.org/euclid.apde/1510843378', 'pdf_url': 'https://projecteuclid.org/journals/analysis-and-pde/volume-9/issue-8/Invariant-distributions-and-the-geodesic-ray-transform/10.2140/apde.2016.9.1903.pdf', 'source': {'id': 'https://openalex.org/S4306400787', 'display_name': 'Project Euclid (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.1511.04547', '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': 'http://arxiv.org/abs/1511.04547', 'pdf_url': 'http://arxiv.org/pdf/1511.04547', '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}, 'sustainable_development_goals': [{'display_name': 'Sustainable cities and communities', 'id': 'https://metadata.un.org/sdg/11', 'score': 0.5}], 'grants': [], 'datasets': [], 'versions': ['https://openalex.org/W2240454606', 'https://openalex.org/W3102736872'], 'referenced_works_count': 26, 'referenced_works': ['https://openalex.org/W1586142979', 'https://openalex.org/W1602383637', 'https://openalex.org/W1802177642', 'https://openalex.org/W1975849239', 'https://openalex.org/W1987794161', 'https://openalex.org/W1993230286', 'https://openalex.org/W1999383731', 'https://openalex.org/W2032833911', 'https://openalex.org/W2033733331', 'https://openalex.org/W2056987756', 'https://openalex.org/W2074863718', 'https://openalex.org/W2104912029', 'https://openalex.org/W2111991040', 'https://openalex.org/W2126829454', 'https://openalex.org/W2156316288', 'https://openalex.org/W2169251826', 'https://openalex.org/W2253659007', 'https://openalex.org/W2963168736', 'https://openalex.org/W2963221109', 'https://openalex.org/W2963589863', 'https://openalex.org/W2964137612', 'https://openalex.org/W3100855699', 'https://openalex.org/W4234046331', 'https://openalex.org/W4239729298', 'https://openalex.org/W653922175', 'https://openalex.org/W76216095'], 'related_works': ['https://openalex.org/W4391375266', 'https://openalex.org/W4297752088', 'https://openalex.org/W3193153203', 'https://openalex.org/W2996354014', 'https://openalex.org/W2594626177', 'https://openalex.org/W2343442984', 'https://openalex.org/W223118542', 'https://openalex.org/W2025438663', 'https://openalex.org/W2018229445', 'https://openalex.org/W1979120450'], 'abstract_inverted_index': {'We': [0], 'establish': [1], 'an': [2], 'equivalence': [3], 'principle': [4], 'between': [5], 'the': [6, 10, 19, 32], 'solenoidal': [7, 35], 'injectivity': [8], 'of': [9, 21, 34, 44], 'geodesic': [11], 'ray': [12], 'transform': [13], 'acting': [14], 'on': [15], 'symmetric': [16], 'm-tensors': [17], 'and': [18], 'existence': [20], 'invariant': [22], 'distributions': [23], 'or': [24], 'smooth': [25], 'first': [26], 'integrals': [27], 'with': [28, 38, 51], 'prescribed': [29], 'projection': [30], 'over': [31], 'set': [33], 'm-tensors.We': [36], 'work': [37], 'compact': [39], 'simple': [40], 'manifolds,': [41], 'but': [42], 'several': [43], 'our': [45], 'results': [46], 'apply': [47], 'to': [48], 'nontrapping': [49], 'manifolds': [50], 'strictly': [52], 'convex': [53], 'boundary.': [54]}, 'cited_by_api_url': 'https://api.openalex.org/works?filter=cites:W2240454606', 'counts_by_year': [{'year': 2019, 'cited_by_count': 1}, {'year': 2018, 'cited_by_count': 1}, {'year': 2017, 'cited_by_count': 1}, {'year': 2016, 'cited_by_count': 6}, {'year': 2014, 'cited_by_count': 1}], 'updated_date': '2024-09-12T11:02:50.328482', 'created_date': '2016-06-24'}