{"id":"https://openalex.org/W4321360157","doi":"https://doi.org/10.3103/s0146411622070161","title":"On Properties of a Regular Simplex Inscribed into a Ball","display_name":"On Properties of a Regular Simplex Inscribed into a Ball","publication_year":2022,"publication_date":"2022-12-01","ids":{"openalex":"https://openalex.org/W4321360157","doi":"https://doi.org/10.3103/s0146411622070161"},"language":"en","primary_location":{"id":"doi:10.3103/s0146411622070161","is_oa":false,"landing_page_url":"https://doi.org/10.3103/s0146411622070161","pdf_url":null,"source":{"id":"https://openalex.org/S17203304","display_name":"Automatic Control and Computer Sciences","issn_l":"0146-4116","issn":["0146-4116","1558-108X"],"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/P4310320267","host_organization_name":"Pleiades Publishing","host_organization_lineage":["https://openalex.org/P4310320267","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Pleiades Publishing","Springer Nature"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Automatic Control and Computer Sciences","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/A5001284414","display_name":"\u041c. \u0412. \u041d\u0435\u0432\u0441\u043a\u0438\u0439","orcid":"https://orcid.org/0000-0002-6392-7618"},"institutions":[{"id":"https://openalex.org/I198371094","display_name":"Yaroslavl State University","ror":"https://ror.org/044s2fj67","country_code":"RU","type":"education","lineage":["https://openalex.org/I198371094"]}],"countries":["RU"],"is_corresponding":true,"raw_author_name":"M. V. Nevskii","raw_affiliation_strings":["Demidov Yaroslavl State University, 150003, Yaroslavl, Russia"],"raw_orcid":"https://orcid.org/0000-0002-6392-7618","affiliations":[{"raw_affiliation_string":"Demidov Yaroslavl State University, 150003, Yaroslavl, Russia","institution_ids":["https://openalex.org/I198371094"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5001284414"],"corresponding_institution_ids":["https://openalex.org/I198371094"],"apc_list":null,"apc_paid":null,"fwci":0.1497,"has_fulltext":false,"cited_by_count":2,"citation_normalized_percentile":{"value":0.42131325,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":95},"biblio":{"volume":"56","issue":"7","first_page":"778","last_page":"787"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11797","display_name":"graph theory and CDMA systems","score":0.9973000288009644,"subfield":{"id":"https://openalex.org/subfields/2208","display_name":"Electrical and Electronic Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T11797","display_name":"graph theory and CDMA systems","score":0.9973000288009644,"subfield":{"id":"https://openalex.org/subfields/2208","display_name":"Electrical and Electronic Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T12504","display_name":"Mathematics and Applications","score":0.9968000054359436,"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/T10792","display_name":"Matrix Theory and Algorithms","score":0.9921000003814697,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/inscribed-figure","display_name":"Inscribed figure","score":0.9179345369338989},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.8328192234039307},{"id":"https://openalex.org/keywords/simplex","display_name":"Simplex","score":0.6580145359039307},{"id":"https://openalex.org/keywords/ball","display_name":"Ball (mathematics)","score":0.6369500756263733},{"id":"https://openalex.org/keywords/computer-graphics","display_name":"Computer graphics (images)","score":0.3417116403579712},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.1661599576473236},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.14038574695587158}],"concepts":[{"id":"https://openalex.org/C44074806","wikidata":"https://www.wikidata.org/wiki/Q1066790","display_name":"Inscribed figure","level":2,"score":0.9179345369338989},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.8328192234039307},{"id":"https://openalex.org/C62438384","wikidata":"https://www.wikidata.org/wiki/Q331350","display_name":"Simplex","level":2,"score":0.6580145359039307},{"id":"https://openalex.org/C122041747","wikidata":"https://www.wikidata.org/wiki/Q838611","display_name":"Ball (mathematics)","level":2,"score":0.6369500756263733},{"id":"https://openalex.org/C121684516","wikidata":"https://www.wikidata.org/wiki/Q7600677","display_name":"Computer graphics (images)","level":1,"score":0.3417116403579712},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.1661599576473236},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.14038574695587158}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.3103/s0146411622070161","is_oa":false,"landing_page_url":"https://doi.org/10.3103/s0146411622070161","pdf_url":null,"source":{"id":"https://openalex.org/S17203304","display_name":"Automatic Control and Computer Sciences","issn_l":"0146-4116","issn":["0146-4116","1558-108X"],"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/P4310320267","host_organization_name":"Pleiades Publishing","host_organization_lineage":["https://openalex.org/P4310320267","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Pleiades Publishing","Springer Nature"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Automatic Control and Computer Sciences","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":8,"referenced_works":["https://openalex.org/W1965099828","https://openalex.org/W1985555142","https://openalex.org/W2090669554","https://openalex.org/W2791071004","https://openalex.org/W2919432614","https://openalex.org/W3010205600","https://openalex.org/W3083515074","https://openalex.org/W4234040099"],"related_works":["https://openalex.org/W2377586623","https://openalex.org/W2375579303","https://openalex.org/W1993615288","https://openalex.org/W2372469834","https://openalex.org/W3010490071","https://openalex.org/W4287829386","https://openalex.org/W4297831611","https://openalex.org/W2950445380","https://openalex.org/W4321360157","https://openalex.org/W2268632128"],"abstract_inverted_index":{"Let":[0,147],"$$B$$":[1,217],"be":[2,11,107,150],"a":[3,12,43,55,151,160,193],"Euclidean":[4],"ball":[5],"in":[6,156,216],"$${{\\mathbb{R}}^{n}}$$":[7,61],"and":[8],"let":[9],"$$C(B)$$":[10,103,105],"space":[13],"of":[14,45,47,57,97,159,210],"continuous":[15],"functions":[16,59],"$$f:B":[17],"\\to":[18,67],"\\mathbb{R}$$":[19],"with":[20,72,143,174,214],"the":[21,73,81,110,131,137,154,157,165,169,175,207],"uniform":[22],"norm":[23,96,209],"$${{\\left\\|":[24,112,177,199],"f":[25],"\\right\\|}_{{C(B)}}}:":[26],"=":[27,84,88,115,182,230],"\\mathop":[28,116],"{\\max":[29,117],"}\\limits_{x":[30,118],"\\in":[31,76,119,172],"B}":[32,120],"\\left|":[33],"{f(x)}":[34],"\\right|.$$":[35],"By":[36],"$${{\\Pi":[37],"}_{1}}\\left(":[38,69],"{{{\\mathbb{R}}^{n}}}":[39,70],"\\right)$$":[40,71],"we":[41,191],"mean":[42],"set":[44,56],"polynomials":[46,134],"degree":[48],"$$":[49,188],"\\leqslant":[50],"1$$":[51,93],",":[52,86],"i.":[53],"e.,":[54],"linear":[58],"on":[60],".":[62,94,146,189,218,232],"The":[63,95],"interpolation":[64,212],"projector":[65,152,213],"$$P:C(B)":[66],"{{\\Pi":[68],"nodes":[74,155,215],"$${{x}^{{(j)}}}":[75],"B$$":[77,173],"is":[78,204],"defined":[79],"by":[80,109],"equalities":[82],"$$Pf({{x}^{{(j)}}})":[83],"f({{x}^{{(j)}}})$$":[85],"$$j":[87],"1,$$":[89],"...,":[90],"$$n":[91,229],"+":[92],"$$P$$":[98],"as":[99],"an":[100,211],"operator":[101],"from":[102],"to":[104,136,206],"can":[106],"calculated":[108],"formula":[111],"P":[113,148],"\\right\\|}_{B}}":[114,181],"\\sum":[121,183],"{\\left|":[122,184],"{{{\\lambda":[123,185],"}_{j}}(x)}":[124],"\\right|}":[125,187],".$$":[126],"Here":[127],"$${{\\lambda":[128],"}_{j}}$$":[129],"are":[130],"basic":[132],"Lagrange":[133],"corresponding":[135],"$$n$$":[138],"-dimensional":[139],"nondegenerate":[140],"simplex":[141,162],"$$S$$":[142],"vertices":[144,158],"$${{x}^{{(j)}}}$$":[145],"'":[149],"having":[153],"regular":[161],"inscribed":[163],"into":[164],"ball.":[166],"We":[167,219],"describe":[168],"points":[170],"$$y":[171],"property":[176],"{P{\\kern":[178,200],"1pt}":[179,201],"'}":[180,202],"}_{j}}(y)}":[186],"Also":[190],"formulate":[192],"geometric":[194],"conjecture":[195,223],"which":[196],"implies":[197],"that":[198,221],"\\right\\|}_{B}}$$":[203],"equal":[205],"minimal":[208],"prove":[220],"this":[222],"holds":[224],"true":[225],"at":[226],"least":[227],"for":[228],"1,2,3,4$$":[231]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2023,"cited_by_count":1}],"updated_date":"2026-08-21T09:56:20.448147","created_date":"2025-10-10T00:00:00"}
