{"id":"https://openalex.org/W2912756416","doi":"https://doi.org/10.1007/s10444-019-09687-9","title":"Minkowski products of unit quaternion sets","display_name":"Minkowski products of unit quaternion sets","publication_year":2019,"publication_date":"2019-03-29","ids":{"openalex":"https://openalex.org/W2912756416","doi":"https://doi.org/10.1007/s10444-019-09687-9","mag":"2912756416"},"language":"en","primary_location":{"id":"doi:10.1007/s10444-019-09687-9","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s10444-019-09687-9","pdf_url":null,"source":{"id":"https://openalex.org/S57050787","display_name":"Advances in Computational Mathematics","issn_l":"1019-7168","issn":["1019-7168","1572-9044"],"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/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Advances in Computational Mathematics","raw_type":"journal-article"},"type":"article","indexed_in":["arxiv","crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/1901.07349","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":null,"display_name":"Rida T. Farouki","orcid":null},"institutions":[{"id":"https://openalex.org/I84218800","display_name":"University of California, Davis","ror":"https://ror.org/05rrcem69","country_code":"US","type":"education","lineage":["https://openalex.org/I84218800"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Rida T. Farouki","raw_affiliation_strings":["Department of Mechanical and Aerospace Engineering, University of California, Davis, CA, 95616, USA"],"affiliations":[{"raw_affiliation_string":"Department of Mechanical and Aerospace Engineering, University of California, Davis, CA, 95616, USA","institution_ids":["https://openalex.org/I84218800"]}]},{"author_position":"middle","author":{"id":null,"display_name":"Graziano Gentili","orcid":null},"institutions":[{"id":"https://openalex.org/I4402554200","display_name":"Liceo scientifico statale Ulisse Dini","ror":"https://ror.org/006xg2x43","country_code":null,"type":"education","lineage":["https://openalex.org/I4402554200"]},{"id":"https://openalex.org/I45084792","display_name":"University of Florence","ror":"https://ror.org/04jr1s763","country_code":"IT","type":"education","lineage":["https://openalex.org/I45084792"]}],"countries":["IT"],"is_corresponding":false,"raw_author_name":"Graziano Gentili","raw_affiliation_strings":["Dipartimento di Matematica e Informatica \u201cU. Dini,\u201d, Universit\u00e0 di Firenze, Viale Morgagni 67/A, I\u201350134, Firenze, Italy"],"affiliations":[{"raw_affiliation_string":"Dipartimento di Matematica e Informatica \u201cU. Dini,\u201d, Universit\u00e0 di Firenze, Viale Morgagni 67/A, I\u201350134, Firenze, Italy","institution_ids":["https://openalex.org/I45084792","https://openalex.org/I4402554200"]}]},{"author_position":"middle","author":{"id":null,"display_name":"Hwan Pyo Moon","orcid":null},"institutions":[{"id":"https://openalex.org/I205490536","display_name":"Dongguk University","ror":"https://ror.org/057q6n778","country_code":"KR","type":"education","lineage":["https://openalex.org/I205490536"]}],"countries":["KR"],"is_corresponding":false,"raw_author_name":"Hwan Pyo Moon","raw_affiliation_strings":["Department of Mathematics, Dongguk University\u2013Seoul, Seoul, 04620, Republic of Korea"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Dongguk University\u2013Seoul, Seoul, 04620, Republic of Korea","institution_ids":["https://openalex.org/I205490536"]}]},{"author_position":"last","author":{"id":null,"display_name":"Caterina Stoppato","orcid":null},"institutions":[{"id":"https://openalex.org/I45084792","display_name":"University of Florence","ror":"https://ror.org/04jr1s763","country_code":"IT","type":"education","lineage":["https://openalex.org/I45084792"]},{"id":"https://openalex.org/I4402554200","display_name":"Liceo scientifico statale Ulisse Dini","ror":"https://ror.org/006xg2x43","country_code":null,"type":"education","lineage":["https://openalex.org/I4402554200"]}],"countries":["IT"],"is_corresponding":false,"raw_author_name":"Caterina Stoppato","raw_affiliation_strings":["Dipartimento di Matematica e Informatica \u201cU. Dini,\u201d, Universit\u00e0 di Firenze, Viale Morgagni 67/A, I\u201350134, Firenze, Italy"],"affiliations":[{"raw_affiliation_string":"Dipartimento di Matematica e Informatica \u201cU. Dini,\u201d, Universit\u00e0 di Firenze, Viale Morgagni 67/A, I\u201350134, Firenze, Italy","institution_ids":["https://openalex.org/I45084792","https://openalex.org/I4402554200"]}]}],"institutions":[],"countries_distinct_count":3,"institutions_distinct_count":4,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I84218800"],"apc_list":{"value":2390,"currency":"EUR","value_usd":2990},"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":1,"citation_normalized_percentile":{"value":0.03855711,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":"45","issue":"3","first_page":"1607","last_page":"1629"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12037","display_name":"Algebraic and Geometric Analysis","score":0.6388999819755554,"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/T12037","display_name":"Algebraic and Geometric Analysis","score":0.6388999819755554,"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/T11822","display_name":"Analytic and geometric function theory","score":0.09000000357627869,"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/T11830","display_name":"Point processes and geometric inequalities","score":0.023099999874830246,"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/quaternion","display_name":"Quaternion","score":0.8479999899864197},{"id":"https://openalex.org/keywords/minkowski-space","display_name":"Minkowski space","score":0.7372000217437744},{"id":"https://openalex.org/keywords/stereographic-projection","display_name":"Stereographic projection","score":0.6243000030517578},{"id":"https://openalex.org/keywords/rotation","display_name":"Rotation (mathematics)","score":0.5415999889373779},{"id":"https://openalex.org/keywords/boundary","display_name":"Boundary (topology)","score":0.5054000020027161},{"id":"https://openalex.org/keywords/product","display_name":"Product (mathematics)","score":0.4830999970436096},{"id":"https://openalex.org/keywords/unit-vector","display_name":"Unit vector","score":0.48010000586509705},{"id":"https://openalex.org/keywords/unit","display_name":"Unit (ring theory)","score":0.4569000005722046},{"id":"https://openalex.org/keywords/type","display_name":"Type (biology)","score":0.4560999870300293}],"concepts":[{"id":"https://openalex.org/C200127275","wikidata":"https://www.wikidata.org/wiki/Q173853","display_name":"Quaternion","level":2,"score":0.8479999899864197},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7991999983787537},{"id":"https://openalex.org/C79464548","wikidata":"https://www.wikidata.org/wiki/Q464794","display_name":"Minkowski space","level":2,"score":0.7372000217437744},{"id":"https://openalex.org/C119001982","wikidata":"https://www.wikidata.org/wiki/Q866099","display_name":"Stereographic projection","level":2,"score":0.6243000030517578},{"id":"https://openalex.org/C74050887","wikidata":"https://www.wikidata.org/wiki/Q848368","display_name":"Rotation (mathematics)","level":2,"score":0.5415999889373779},{"id":"https://openalex.org/C62354387","wikidata":"https://www.wikidata.org/wiki/Q875399","display_name":"Boundary (topology)","level":2,"score":0.5054000020027161},{"id":"https://openalex.org/C90673727","wikidata":"https://www.wikidata.org/wiki/Q901718","display_name":"Product (mathematics)","level":2,"score":0.4830999970436096},{"id":"https://openalex.org/C84316537","wikidata":"https://www.wikidata.org/wiki/Q36255","display_name":"Unit vector","level":2,"score":0.48010000586509705},{"id":"https://openalex.org/C122637931","wikidata":"https://www.wikidata.org/wiki/Q118084","display_name":"Unit (ring theory)","level":2,"score":0.4569000005722046},{"id":"https://openalex.org/C2777299769","wikidata":"https://www.wikidata.org/wiki/Q3707858","display_name":"Type (biology)","level":2,"score":0.4560999870300293},{"id":"https://openalex.org/C175694140","wikidata":"https://www.wikidata.org/wiki/Q980329","display_name":"Orthographic projection","level":2,"score":0.4465999901294708},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.4154999852180481},{"id":"https://openalex.org/C126875415","wikidata":"https://www.wikidata.org/wiki/Q203425","display_name":"Unit circle","level":2,"score":0.41280001401901245},{"id":"https://openalex.org/C145941777","wikidata":"https://www.wikidata.org/wiki/Q5310237","display_name":"Dual quaternion","level":3,"score":0.4050999879837036},{"id":"https://openalex.org/C79013991","wikidata":"https://www.wikidata.org/wiki/Q1097021","display_name":"Minkowski's theorem","level":3,"score":0.3898000121116638},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.3889999985694885},{"id":"https://openalex.org/C57493831","wikidata":"https://www.wikidata.org/wiki/Q3134666","display_name":"Projection (relational algebra)","level":2,"score":0.3871999979019165},{"id":"https://openalex.org/C10233890","wikidata":"https://www.wikidata.org/wiki/Q1322294","display_name":"Minkowski addition","level":3,"score":0.3675999939441681},{"id":"https://openalex.org/C191948623","wikidata":"https://www.wikidata.org/wiki/Q1307800","display_name":"Unit sphere","level":2,"score":0.36480000615119934},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.34929999709129333},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.3292999863624573},{"id":"https://openalex.org/C65236422","wikidata":"https://www.wikidata.org/wiki/Q173740","display_name":"Cartesian product","level":2,"score":0.3021000027656555},{"id":"https://openalex.org/C92951342","wikidata":"https://www.wikidata.org/wiki/Q1411166","display_name":"Orthonormality","level":3,"score":0.29339998960494995},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.288100004196167},{"id":"https://openalex.org/C139002025","wikidata":"https://www.wikidata.org/wiki/Q3001212","display_name":"Lift (data mining)","level":2,"score":0.28459998965263367},{"id":"https://openalex.org/C2778572836","wikidata":"https://www.wikidata.org/wiki/Q380933","display_name":"Space (punctuation)","level":2,"score":0.26980000734329224},{"id":"https://openalex.org/C91855343","wikidata":"https://www.wikidata.org/wiki/Q214159","display_name":"Inner product space","level":2,"score":0.26969999074935913},{"id":"https://openalex.org/C151640129","wikidata":"https://www.wikidata.org/wiki/Q2835967","display_name":"Quaternion algebra","level":5,"score":0.26109999418258667},{"id":"https://openalex.org/C88977231","wikidata":"https://www.wikidata.org/wiki/Q681406","display_name":"Euler's rotation theorem","level":3,"score":0.2529999911785126},{"id":"https://openalex.org/C83633838","wikidata":"https://www.wikidata.org/wiki/Q1256564","display_name":"Rotation matrix","level":2,"score":0.2508000135421753}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1007/s10444-019-09687-9","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s10444-019-09687-9","pdf_url":null,"source":{"id":"https://openalex.org/S57050787","display_name":"Advances in Computational Mathematics","issn_l":"1019-7168","issn":["1019-7168","1572-9044"],"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/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Advances in Computational Mathematics","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:1901.07349","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1901.07349","pdf_url":"https://arxiv.org/pdf/1901.07349","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"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":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},{"id":"pmh:oai:flore.unifi.it:2158/1148312","is_oa":false,"landing_page_url":"http://hdl.handle.net/2158/1148312","pdf_url":null,"source":{"id":"https://openalex.org/S4306402033","display_name":"Florence Research (University of Florence)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I45084792","host_organization_name":"University of Florence","host_organization_lineage":["https://openalex.org/I45084792"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"info:eu-repo/semantics/article"},{"id":"pmh:oai:flore.unifi.it:2158/1172741","is_oa":true,"landing_page_url":"https://rdcu.be/b2k1q","pdf_url":null,"source":{"id":"https://openalex.org/S4306402033","display_name":"Florence Research (University of Florence)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I45084792","host_organization_name":"University of Florence","host_organization_lineage":["https://openalex.org/I45084792"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"info:eu-repo/semantics/article"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:1901.07349","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1901.07349","pdf_url":"https://arxiv.org/pdf/1901.07349","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"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":[],"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":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":15,"referenced_works":["https://openalex.org/W422477","https://openalex.org/W244957858","https://openalex.org/W972589330","https://openalex.org/W1566463023","https://openalex.org/W1580809199","https://openalex.org/W1982773511","https://openalex.org/W2035183661","https://openalex.org/W2045026024","https://openalex.org/W2052545723","https://openalex.org/W2055949355","https://openalex.org/W2080140653","https://openalex.org/W2088378949","https://openalex.org/W2098328565","https://openalex.org/W2108951449","https://openalex.org/W2610247417"],"related_works":[],"abstract_inverted_index":null,"counts_by_year":[{"year":2023,"cited_by_count":1}],"updated_date":"2026-03-20T23:20:44.827607","created_date":"2019-02-21T00:00:00"}
