Get quick answers to your questions about the article from our AI researcher chatbot
{'id': 'https://openalex.org/W2155076729', 'doi': 'https://doi.org/10.1007/978-1-4612-5648-9_21', 'title': 'Intersections of Convex Bodies with Their Translates', 'display_name': 'Intersections of Convex Bodies with Their Translates', 'publication_year': 1981, 'publication_date': '1981-01-01', 'ids': {'openalex': 'https://openalex.org/W2155076729', 'doi': 'https://doi.org/10.1007/978-1-4612-5648-9_21', 'mag': '2155076729'}, 'language': 'en', 'primary_location': {'is_oa': False, 'landing_page_url': 'https://doi.org/10.1007/978-1-4612-5648-9_21', 'pdf_url': None, 'source': {'id': 'https://openalex.org/S4306463937', 'display_name': 'Springer eBooks', 'issn_l': None, 'issn': None, 'is_oa': False, 'is_in_doaj': False, 'is_core': False, 'host_organization': 'https://openalex.org/P4310319965', 'host_organization_name': 'Springer Nature', 'host_organization_lineage': ['https://openalex.org/P4310319965'], 'host_organization_lineage_names': ['Springer Nature'], 'type': 'ebook platform'}, 'license': None, 'license_id': None, 'version': None, 'is_accepted': False, 'is_published': False}, 'type': 'book-chapter', 'type_crossref': 'book-chapter', 'indexed_in': ['crossref'], 'open_access': {'is_oa': False, 'oa_status': 'closed', 'oa_url': None, 'any_repository_has_fulltext': False}, 'authorships': [{'author_position': 'first', 'author': {'id': 'https://openalex.org/A5023377473', 'display_name': 'Paul Goodey', 'orcid': None}, 'institutions': [{'id': 'https://openalex.org/I184558857', 'display_name': 'Royal Holloway University of London', 'ror': 'https://ror.org/04g2vpn86', 'country_code': 'GB', 'type': 'education', 'lineage': ['https://openalex.org/I124357947', 'https://openalex.org/I184558857']}], 'countries': ['GB'], 'is_corresponding': False, 'raw_author_name': 'P. R. Goodey', 'raw_affiliation_strings': ['Mathematics Department, Royal Holloway College, Englefield Green, Surrey,UK'], 'affiliations': [{'raw_affiliation_string': 'Mathematics Department, Royal Holloway College, Englefield Green, Surrey,UK', 'institution_ids': ['https://openalex.org/I184558857']}]}, {'author_position': 'last', 'author': {'id': 'https://openalex.org/A5011362597', 'display_name': 'M. M. Woodcock', 'orcid': None}, 'institutions': [{'id': 'https://openalex.org/I184558857', 'display_name': 'Royal Holloway University of London', 'ror': 'https://ror.org/04g2vpn86', 'country_code': 'GB', 'type': 'education', 'lineage': ['https://openalex.org/I124357947', 'https://openalex.org/I184558857']}], 'countries': ['GB'], 'is_corresponding': False, 'raw_author_name': 'M. M. Woodcock', 'raw_affiliation_strings': ['Mathematics Department, Royal Holloway College, Englefield Green, Surrey,UK'], 'affiliations': [{'raw_affiliation_string': 'Mathematics Department, Royal Holloway College, Englefield Green, Surrey,UK', 'institution_ids': ['https://openalex.org/I184558857']}]}], 'countries_distinct_count': 1, 'institutions_distinct_count': 1, 'corresponding_author_ids': [], 'corresponding_institution_ids': [], 'apc_list': None, 'apc_paid': None, 'fwci': 1.809, 'has_fulltext': False, 'cited_by_count': 12, 'citation_normalized_percentile': {'value': 0.786704, 'is_in_top_1_percent': False, 'is_in_top_10_percent': False}, 'cited_by_percentile_year': {'min': 82, 'max': 83}, 'biblio': {'volume': None, 'issue': None, 'first_page': '289', 'last_page': '296'}, 'is_retracted': False, 'is_paratext': False, 'primary_topic': {'id': 'https://openalex.org/T11830', 'display_name': 'Spatial Point Patterns in Science', 'score': 0.9485, '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/T11830', 'display_name': 'Spatial Point Patterns in Science', 'score': 0.9485, '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'}}], 'keywords': [{'id': 'https://openalex.org/keywords/convex-bodies', 'display_name': 'Convex Bodies', 'score': 0.60375}, {'id': 'https://openalex.org/keywords/convex-curve', 'display_name': 'Convex curve', 'score': 0.59974384}, {'id': 'https://openalex.org/keywords/ball', 'display_name': 'Ball (mathematics)', 'score': 0.5504377}], 'concepts': [{'id': 'https://openalex.org/C134912446', 'wikidata': 'https://www.wikidata.org/wiki/Q5166516', 'display_name': 'Convex body', 'level': 4, 'score': 0.8453474}, {'id': 'https://openalex.org/C112680207', 'wikidata': 'https://www.wikidata.org/wiki/Q714886', 'display_name': 'Regular polygon', 'level': 2, 'score': 0.7387714}, {'id': 'https://openalex.org/C134786449', 'wikidata': 'https://www.wikidata.org/wiki/Q3391255', 'display_name': 'Planar', 'level': 2, 'score': 0.6305003}, {'id': 'https://openalex.org/C128618672', 'wikidata': 'https://www.wikidata.org/wiki/Q3001187', 'display_name': 'Convex curve', 'level': 5, 'score': 0.59974384}, {'id': 'https://openalex.org/C114614502', 'wikidata': 'https://www.wikidata.org/wiki/Q76592', 'display_name': 'Combinatorics', 'level': 1, 'score': 0.5912566}, {'id': 'https://openalex.org/C122041747', 'wikidata': 'https://www.wikidata.org/wiki/Q838611', 'display_name': 'Ball (mathematics)', 'level': 2, 'score': 0.5504377}, {'id': 'https://openalex.org/C33923547', 'wikidata': 'https://www.wikidata.org/wiki/Q395', 'display_name': 'Mathematics', 'level': 0, 'score': 0.5236687}, {'id': 'https://openalex.org/C2524010', 'wikidata': 'https://www.wikidata.org/wiki/Q8087', 'display_name': 'Geometry', 'level': 1, 'score': 0.45853907}, {'id': 'https://openalex.org/C189950617', 'wikidata': 'https://www.wikidata.org/wiki/Q937228', 'display_name': 'Property (philosophy)', 'level': 2, 'score': 0.42362428}, {'id': 'https://openalex.org/C49870271', 'wikidata': 'https://www.wikidata.org/wiki/Q193657', 'display_name': 'Convex set', 'level': 4, 'score': 0.41174918}, {'id': 'https://openalex.org/C202444582', 'wikidata': 'https://www.wikidata.org/wiki/Q837863', 'display_name': 'Pure mathematics', 'level': 1, 'score': 0.3931238}, {'id': 'https://openalex.org/C206194317', 'wikidata': 'https://www.wikidata.org/wiki/Q1138624', 'display_name': 'Convex hull', 'level': 3, 'score': 0.29808018}, {'id': 'https://openalex.org/C41008148', 'wikidata': 'https://www.wikidata.org/wiki/Q21198', 'display_name': 'Computer science', 'level': 0, 'score': 0.12346694}, {'id': 'https://openalex.org/C157972887', 'wikidata': 'https://www.wikidata.org/wiki/Q463359', 'display_name': 'Convex optimization', 'level': 3, 'score': 0.082288474}, {'id': 'https://openalex.org/C121684516', 'wikidata': 'https://www.wikidata.org/wiki/Q7600677', 'display_name': 'Computer graphics (images)', 'level': 1, 'score': 0.04758033}, {'id': 'https://openalex.org/C138885662', 'wikidata': 'https://www.wikidata.org/wiki/Q5891', 'display_name': 'Philosophy', 'level': 0, 'score': 0.0}, {'id': 'https://openalex.org/C111472728', 'wikidata': 'https://www.wikidata.org/wiki/Q9471', 'display_name': 'Epistemology', 'level': 1, 'score': 0.0}], 'mesh': [], 'locations_count': 1, 'locations': [{'is_oa': False, 'landing_page_url': 'https://doi.org/10.1007/978-1-4612-5648-9_21', 'pdf_url': None, 'source': {'id': 'https://openalex.org/S4306463937', 'display_name': 'Springer eBooks', 'issn_l': None, 'issn': None, 'is_oa': False, 'is_in_doaj': False, 'is_core': False, 'host_organization': 'https://openalex.org/P4310319965', 'host_organization_name': 'Springer Nature', 'host_organization_lineage': ['https://openalex.org/P4310319965'], 'host_organization_lineage_names': ['Springer Nature'], 'type': 'ebook platform'}, 'license': None, 'license_id': None, 'version': None, 'is_accepted': False, 'is_published': False}], 'best_oa_location': None, 'sustainable_development_goals': [{'display_name': 'Sustainable cities and communities', 'score': 0.42, 'id': 'https://metadata.un.org/sdg/11'}], 'grants': [], 'datasets': [], 'versions': [], 'referenced_works_count': 8, 'referenced_works': ['https://openalex.org/W1995231387', 'https://openalex.org/W1996931690', 'https://openalex.org/W1999551708', 'https://openalex.org/W2023812709', 'https://openalex.org/W2037369788', 'https://openalex.org/W2323547349', 'https://openalex.org/W4251582310', 'https://openalex.org/W4285719527'], 'related_works': ['https://openalex.org/W72541825', 'https://openalex.org/W4386395423', 'https://openalex.org/W4287712648', 'https://openalex.org/W3120597765', 'https://openalex.org/W3043508332', 'https://openalex.org/W2332930690', 'https://openalex.org/W2284613544', 'https://openalex.org/W2155076729', 'https://openalex.org/W2044260792', 'https://openalex.org/W1427726556'], 'abstract_inverted_index': None, 'cited_by_api_url': 'https://api.openalex.org/works?filter=cites:W2155076729', 'counts_by_year': [{'year': 2022, 'cited_by_count': 1}, {'year': 2021, 'cited_by_count': 1}, {'year': 2012, 'cited_by_count': 1}], 'updated_date': '2024-09-12T03:43:58.448275', 'created_date': '2016-06-24'}