{"id":"https://openalex.org/W1497279842","doi":"https://doi.org/10.48550/arxiv.math/0412472","title":"Reconstruction of Centrally Symmetrical Convex Bodies by Projection Curvature Radii","display_name":"Reconstruction of Centrally Symmetrical Convex Bodies by Projection Curvature Radii","publication_year":2004,"publication_date":"2004-12-23","ids":{"openalex":"https://openalex.org/W1497279842","doi":"https://doi.org/10.48550/arxiv.math/0412472","mag":"1497279842"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:math/0412472","doi":null,"is_oa":true,"landing_page_url":"http://arxiv.org/abs/math/0412472","pdf_url":"https://arxiv.org/pdf/math/0412472","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"volume":null,"type":"preprint","is_traditional":true,"indexed_in":["arxiv","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/math/0412472","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5049308073","display_name":"Rafik H. Aramyan","orcid":"https://orcid.org/0000-0003-4003-3088","observed_orcids":["https://orcid.org/0000-0003-4003-3088"]},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Aramyan, Rafik","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":["https://openalex.org/A5049308073"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":true,"cited_by_count":1,"citation_normalized_percentile":null,"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11830","display_name":"Point processes and geometric inequalities","score":0.9984999895095825,"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":"Point processes and geometric inequalities","score":0.9984999895095825,"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/T13080","display_name":"Advanced Differential Geometry Research","score":0.00019999999494757503,"subfield":{"id":"https://openalex.org/subfields/2608","display_name":"Geometry and Topology"},"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/T10948","display_name":"Advanced Combinatorial Mathematics","score":0.00019999999494757503,"subfield":{"id":"https://openalex.org/subfields/2607","display_name":"Discrete Mathematics and Combinatorics"},"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":0.6899999976158142},{"id":"https://openalex.org/keywords/central-symmetry","display_name":"central symmetry","score":0.8159999847412109},{"id":"https://openalex.org/keywords/reconstruction-era","display_name":"Reconstruction","score":0.44699999690055847},{"id":"https://openalex.org/keywords/existence-and-uniqueness-of-solutions","display_name":"existence and uniqueness of solutions","score":0.9679999947547913},{"id":"https://openalex.org/keywords/convex-geometry","display_name":"convex geometry","score":0.5609999895095825}],"concepts":[{"id":"https://openalex.org/C2777021972","wikidata":"https://www.wikidata.org/wiki/Q22976830","display_name":"Uniqueness","level":2,"score":0.6816756725311279},{"id":"https://openalex.org/C112680207","wikidata":"https://www.wikidata.org/wiki/Q714886","display_name":"Regular polygon","level":2,"score":0.6801912784576416},{"id":"https://openalex.org/C57493831","wikidata":"https://www.wikidata.org/wiki/Q3134666","display_name":"Projection (relational algebra)","level":2,"score":0.6772856116294861},{"id":"https://openalex.org/C195065555","wikidata":"https://www.wikidata.org/wiki/Q214881","display_name":"Curvature","level":2,"score":0.670783519744873},{"id":"https://openalex.org/C134912446","wikidata":"https://www.wikidata.org/wiki/Q5166516","display_name":"Convex body","level":4,"score":0.5853053331375122},{"id":"https://openalex.org/C178635117","wikidata":"https://www.wikidata.org/wiki/Q747499","display_name":"RADIUS","level":2,"score":0.5674193501472473},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.5537859797477722},{"id":"https://openalex.org/C11665553","wikidata":"https://www.wikidata.org/wiki/Q1136069","display_name":"Radius of curvature","level":5,"score":0.5331204533576965},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5241094827651978},{"id":"https://openalex.org/C145446738","wikidata":"https://www.wikidata.org/wiki/Q319913","display_name":"Convex function","level":3,"score":0.4459965229034424},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.4436423182487488},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.41705307364463806},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.36022987961769104},{"id":"https://openalex.org/C175017881","wikidata":"https://www.wikidata.org/wiki/Q1318998","display_name":"Mean curvature","level":3,"score":0.3375941514968872},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.20955955982208252},{"id":"https://openalex.org/C157972887","wikidata":"https://www.wikidata.org/wiki/Q463359","display_name":"Convex optimization","level":3,"score":0.19388887286186218},{"id":"https://openalex.org/C127813850","wikidata":"https://www.wikidata.org/wiki/Q6803617","display_name":"Mean curvature flow","level":4,"score":0.15483006834983826},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.11583259701728821},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C38652104","wikidata":"https://www.wikidata.org/wiki/Q3510521","display_name":"Computer security","level":1,"score":0.0},{"id":"https://openalex.org/C78458016","wikidata":"https://www.wikidata.org/wiki/Q840400","display_name":"Evolutionary biology","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:math/0412472","doi":null,"is_oa":true,"landing_page_url":"http://arxiv.org/abs/math/0412472","pdf_url":"https://arxiv.org/pdf/math/0412472","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},{"id":"doi:10.48550/arxiv.math/0412472","doi":"https://doi.org/10.48550/arxiv.math/0412472","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.math/0412472","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:math/0412472","doi":null,"is_oa":true,"landing_page_url":"http://arxiv.org/abs/math/0412472","pdf_url":"https://arxiv.org/pdf/math/0412472","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W1497279842.pdf","grobid_xml":"https://content.openalex.org/works/W1497279842.grobid-xml"},"referenced_works_count":4,"referenced_works":["https://openalex.org/W158064062","https://openalex.org/W1592589209","https://openalex.org/W1974945857","https://openalex.org/W2314082730"],"related_works":["https://openalex.org/W1635562360","https://openalex.org/W2151416090","https://openalex.org/W7014838027","https://openalex.org/W2022882967","https://openalex.org/W7097798693","https://openalex.org/W2078349565","https://openalex.org/W2315675514","https://openalex.org/W4300961705","https://openalex.org/W1970256154","https://openalex.org/W577391194"],"abstract_inverted_index":{"The":[0],"article":[1],"considers":[2],"the":[3,16,43],"problem":[4],"of":[5,9],"existence":[6],"and":[7,29],"uniqueness":[8],"centrally":[10],"symmetrical":[11],"convex":[12],"body":[13,44],"for":[14,41],"which":[15],"projection":[17],"curvature":[18],"radius":[19],"function":[20],"coincides":[21],"with":[22],"a":[23,36],"given":[24],"flag":[25],"function.":[26],"A":[27],"necessary":[28],"sufficient":[30],"condition":[31],"is":[32,47],"found":[33],"that":[34],"ensures":[35],"positive":[37],"answer.":[38],"An":[39],"algorithm":[40],"construction":[42],"in":[45],"question":[46],"proposed":[48]},"counts_by_year":[],"updated_date":"2026-11-04T10:54:05.112534","created_date":"2016-06-24T00:00:00"}