{"id":"https://openalex.org/W2036738119","doi":"https://doi.org/10.1007/s00211-010-0332-5","title":"Computational existence proofs for spherical t-designs","display_name":"Computational existence proofs for spherical t-designs","publication_year":2010,"publication_date":"2010-10-01","ids":{"openalex":"https://openalex.org/W2036738119","doi":"https://doi.org/10.1007/s00211-010-0332-5","mag":"2036738119"},"language":"en","primary_location":{"id":"doi:10.1007/s00211-010-0332-5","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s00211-010-0332-5","pdf_url":null,"source":{"id":"https://openalex.org/S4210205683","display_name":"Numerische Mathematik","issn_l":"0029-599X","issn":["0029-599X","0945-3245"],"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":"Numerische Mathematik","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5100369445","display_name":"Xiaojun Chen","orcid":"https://orcid.org/0000-0002-6627-2637"},"institutions":[{"id":"https://openalex.org/I14243506","display_name":"Hong Kong Polytechnic University","ror":"https://ror.org/0030zas98","country_code":"HK","type":"education","lineage":["https://openalex.org/I14243506"]}],"countries":["HK"],"is_corresponding":true,"raw_author_name":"Xiaojun Chen","raw_affiliation_strings":["Department of Applied Mathematics, Hong Kong Polytechnic University, Kowloon, Hong Kong","Hong Kong Polytechnic University, Department of Applied Mathematics, Kowloon, Hong Kong#TAB#"],"affiliations":[{"raw_affiliation_string":"Department of Applied Mathematics, Hong Kong Polytechnic University, Kowloon, Hong Kong","institution_ids":["https://openalex.org/I14243506"]},{"raw_affiliation_string":"Hong Kong Polytechnic University, Department of Applied Mathematics, Kowloon, Hong Kong#TAB#","institution_ids":["https://openalex.org/I14243506"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5072635213","display_name":"Andreas Frommer","orcid":"https://orcid.org/0000-0002-6901-0114"},"institutions":[{"id":"https://openalex.org/I167360494","display_name":"University of Wuppertal","ror":"https://ror.org/00613ak93","country_code":"DE","type":"education","lineage":["https://openalex.org/I167360494"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Andreas Frommer","raw_affiliation_strings":["Department of Mathematics, University of Wuppertal, 42097, Wuppertal, Germany","University of Wuppertal, Department of Mathematics, 42097, Wuppertal, Germany#TAB#"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, University of Wuppertal, 42097, Wuppertal, Germany","institution_ids":["https://openalex.org/I167360494"]},{"raw_affiliation_string":"University of Wuppertal, Department of Mathematics, 42097, Wuppertal, Germany#TAB#","institution_ids":["https://openalex.org/I167360494"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5070913387","display_name":"Bruno Lang","orcid":"https://orcid.org/0000-0001-9197-4836"},"institutions":[{"id":"https://openalex.org/I167360494","display_name":"University of Wuppertal","ror":"https://ror.org/00613ak93","country_code":"DE","type":"education","lineage":["https://openalex.org/I167360494"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Bruno Lang","raw_affiliation_strings":["Department of Mathematics, University of Wuppertal, 42097, Wuppertal, Germany","University of Wuppertal, Department of Mathematics, 42097, Wuppertal, Germany#TAB#"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, University of Wuppertal, 42097, Wuppertal, Germany","institution_ids":["https://openalex.org/I167360494"]},{"raw_affiliation_string":"University of Wuppertal, Department of Mathematics, 42097, Wuppertal, Germany#TAB#","institution_ids":["https://openalex.org/I167360494"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5100369445"],"corresponding_institution_ids":["https://openalex.org/I14243506"],"apc_list":{"value":2390,"currency":"EUR","value_usd":2990},"apc_paid":null,"fwci":3.4437,"has_fulltext":false,"cited_by_count":56,"citation_normalized_percentile":{"value":0.92241701,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":"117","issue":"2","first_page":"289","last_page":"305"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11697","display_name":"Numerical Methods and Algorithms","score":0.9988999962806702,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T11697","display_name":"Numerical Methods and Algorithms","score":0.9988999962806702,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T12404","display_name":"Mathematical Approximation and Integration","score":0.9988999962806702,"subfield":{"id":"https://openalex.org/subfields/2612","display_name":"Numerical Analysis"},"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":"Advanced Numerical Analysis Techniques","score":0.9927999973297119,"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/interval-arithmetic","display_name":"Interval arithmetic","score":0.793889045715332},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7504749298095703},{"id":"https://openalex.org/keywords/unit-sphere","display_name":"Unit sphere","score":0.5938381552696228},{"id":"https://openalex.org/keywords/interval","display_name":"Interval (graph theory)","score":0.5682454705238342},{"id":"https://openalex.org/keywords/quadrature","display_name":"Quadrature (astronomy)","score":0.5550470948219299},{"id":"https://openalex.org/keywords/computation","display_name":"Computation","score":0.5519647598266602},{"id":"https://openalex.org/keywords/dimension","display_name":"Dimension (graph theory)","score":0.5507704019546509},{"id":"https://openalex.org/keywords/mathematical-proof","display_name":"Mathematical proof","score":0.5218818783760071},{"id":"https://openalex.org/keywords/matlab","display_name":"MATLAB","score":0.4817950129508972},{"id":"https://openalex.org/keywords/degree","display_name":"Degree (music)","score":0.4501150846481323},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.43171262741088867},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.39540135860443115},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.3756595253944397},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.3611583411693573},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.3390691578388214},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.28677046298980713},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.23635956645011902},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.22624242305755615},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.19411629438400269},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.10442876815795898}],"concepts":[{"id":"https://openalex.org/C191252586","wikidata":"https://www.wikidata.org/wiki/Q1671453","display_name":"Interval arithmetic","level":3,"score":0.793889045715332},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7504749298095703},{"id":"https://openalex.org/C191948623","wikidata":"https://www.wikidata.org/wiki/Q1307800","display_name":"Unit sphere","level":2,"score":0.5938381552696228},{"id":"https://openalex.org/C2778067643","wikidata":"https://www.wikidata.org/wiki/Q166507","display_name":"Interval (graph theory)","level":2,"score":0.5682454705238342},{"id":"https://openalex.org/C62869609","wikidata":"https://www.wikidata.org/wiki/Q28137","display_name":"Quadrature (astronomy)","level":2,"score":0.5550470948219299},{"id":"https://openalex.org/C45374587","wikidata":"https://www.wikidata.org/wiki/Q12525525","display_name":"Computation","level":2,"score":0.5519647598266602},{"id":"https://openalex.org/C33676613","wikidata":"https://www.wikidata.org/wiki/Q13415176","display_name":"Dimension (graph theory)","level":2,"score":0.5507704019546509},{"id":"https://openalex.org/C108710211","wikidata":"https://www.wikidata.org/wiki/Q11538","display_name":"Mathematical proof","level":2,"score":0.5218818783760071},{"id":"https://openalex.org/C2780365114","wikidata":"https://www.wikidata.org/wiki/Q169478","display_name":"MATLAB","level":2,"score":0.4817950129508972},{"id":"https://openalex.org/C2775997480","wikidata":"https://www.wikidata.org/wiki/Q586277","display_name":"Degree (music)","level":2,"score":0.4501150846481323},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.43171262741088867},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.39540135860443115},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3756595253944397},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.3611583411693573},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.3390691578388214},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.28677046298980713},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.23635956645011902},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.22624242305755615},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.19411629438400269},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.10442876815795898},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.0},{"id":"https://openalex.org/C111919701","wikidata":"https://www.wikidata.org/wiki/Q9135","display_name":"Operating system","level":1,"score":0.0},{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.0},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C119599485","wikidata":"https://www.wikidata.org/wiki/Q43035","display_name":"Electrical engineering","level":1,"score":0.0},{"id":"https://openalex.org/C24890656","wikidata":"https://www.wikidata.org/wiki/Q82811","display_name":"Acoustics","level":1,"score":0.0},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1007/s00211-010-0332-5","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s00211-010-0332-5","pdf_url":null,"source":{"id":"https://openalex.org/S4210205683","display_name":"Numerische Mathematik","issn_l":"0029-599X","issn":["0029-599X","0945-3245"],"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":"Numerische Mathematik","raw_type":"journal-article"},{"id":"pmh:oai:ira.lib.polyu.edu.hk:10397/20621","is_oa":false,"landing_page_url":"http://hdl.handle.net/10397/20621","pdf_url":null,"source":{"id":"https://openalex.org/S4306400205","display_name":"PolyU Institutional Research Archive (Hong Kong Polytechnic University)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I14243506","host_organization_name":"Hong Kong Polytechnic University","host_organization_lineage":["https://openalex.org/I14243506"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Journal/Magazine Article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":29,"referenced_works":["https://openalex.org/W178772886","https://openalex.org/W203078251","https://openalex.org/W845427635","https://openalex.org/W1514118425","https://openalex.org/W1518139620","https://openalex.org/W1522616537","https://openalex.org/W1532036648","https://openalex.org/W1571045421","https://openalex.org/W1592303155","https://openalex.org/W1605702526","https://openalex.org/W1934619092","https://openalex.org/W1974360466","https://openalex.org/W1976497332","https://openalex.org/W1981745143","https://openalex.org/W1985132689","https://openalex.org/W1989317678","https://openalex.org/W1989397443","https://openalex.org/W2008151474","https://openalex.org/W2016603857","https://openalex.org/W2044413922","https://openalex.org/W2060924166","https://openalex.org/W2066796569","https://openalex.org/W2070381457","https://openalex.org/W2087255259","https://openalex.org/W2091491976","https://openalex.org/W2113028138","https://openalex.org/W2584020404","https://openalex.org/W2798909945","https://openalex.org/W4231075076"],"related_works":["https://openalex.org/W2520934858","https://openalex.org/W2098412892","https://openalex.org/W2990487117","https://openalex.org/W43877154","https://openalex.org/W109635080","https://openalex.org/W4213384165","https://openalex.org/W2377262226","https://openalex.org/W2531534085","https://openalex.org/W4285295794","https://openalex.org/W34401233"],"abstract_inverted_index":null,"counts_by_year":[{"year":2025,"cited_by_count":5},{"year":2024,"cited_by_count":3},{"year":2023,"cited_by_count":7},{"year":2022,"cited_by_count":3},{"year":2021,"cited_by_count":1},{"year":2019,"cited_by_count":6},{"year":2018,"cited_by_count":5},{"year":2017,"cited_by_count":1},{"year":2016,"cited_by_count":6},{"year":2015,"cited_by_count":5},{"year":2014,"cited_by_count":4},{"year":2013,"cited_by_count":3},{"year":2012,"cited_by_count":3}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}