{"id":"https://openalex.org/W4412995691","doi":"https://doi.org/10.3390/axioms14080591","title":"Singularities of Fuzzy Friedmann\u2013Lema\u00eetre\u2013Robertson\u2013Walker Space","display_name":"Singularities of Fuzzy Friedmann\u2013Lema\u00eetre\u2013Robertson\u2013Walker Space","publication_year":2025,"publication_date":"2025-07-31","ids":{"openalex":"https://openalex.org/W4412995691","doi":"https://doi.org/10.3390/axioms14080591"},"language":"en","primary_location":{"id":"doi:10.3390/axioms14080591","is_oa":true,"landing_page_url":"https://doi.org/10.3390/axioms14080591","pdf_url":null,"source":{"id":"https://openalex.org/S4210173132","display_name":"Axioms","issn_l":"2075-1680","issn":["2075-1680"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Axioms","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://doi.org/10.3390/axioms14080591","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5100376055","display_name":"Yanlin Li","orcid":"https://orcid.org/0000-0003-1614-3228"},"institutions":[{"id":"https://openalex.org/I163151501","display_name":"Hangzhou Normal University","ror":"https://ror.org/014v1mr15","country_code":"CN","type":"education","lineage":["https://openalex.org/I163151501"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Yanlin Li","raw_affiliation_strings":["School of Mathematics, Hangzhou Normal University, Hangzhou 311121, China"],"affiliations":[{"raw_affiliation_string":"School of Mathematics, Hangzhou Normal University, Hangzhou 311121, China","institution_ids":["https://openalex.org/I163151501"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5035034381","display_name":"Fawaz Alharbi","orcid":"https://orcid.org/0000-0001-9786-8161"},"institutions":[{"id":"https://openalex.org/I199693650","display_name":"Umm al-Qura University","ror":"https://ror.org/01xjqrm90","country_code":"SA","type":"education","lineage":["https://openalex.org/I199693650"]}],"countries":["SA"],"is_corresponding":true,"raw_author_name":"Fawaz Alharbi","raw_affiliation_strings":["Department of Mathematics, Umm Al-Qura University, Makkah 21955, Saudi Arabia"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Umm Al-Qura University, Makkah 21955, Saudi Arabia","institution_ids":["https://openalex.org/I199693650"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5035046572","display_name":"A. E. El-Ahmady","orcid":"https://orcid.org/0000-0003-2333-6650"},"institutions":[{"id":"https://openalex.org/I21376657","display_name":"Tanta University","ror":"https://ror.org/016jp5b92","country_code":"EG","type":"education","lineage":["https://openalex.org/I21376657"]}],"countries":["EG"],"is_corresponding":false,"raw_author_name":"Abdulaziz E. El-Ahmady","raw_affiliation_strings":["Mathematics Department, Faculty of Science, Tanta University, Tanta 31527, Egypt"],"affiliations":[{"raw_affiliation_string":"Mathematics Department, Faculty of Science, Tanta University, Tanta 31527, Egypt","institution_ids":["https://openalex.org/I21376657"]}]}],"institutions":[],"countries_distinct_count":3,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5035034381"],"corresponding_institution_ids":["https://openalex.org/I199693650"],"apc_list":{"value":1400,"currency":"CHF","value_usd":1515},"apc_paid":{"value":1400,"currency":"CHF","value_usd":1515},"fwci":1.1206,"has_fulltext":false,"cited_by_count":1,"citation_normalized_percentile":{"value":0.82252503,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":96,"max":99},"biblio":{"volume":"14","issue":"8","first_page":"591","last_page":"591"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T13080","display_name":"Advanced Differential Geometry Research","score":0.9810000061988831,"subfield":{"id":"https://openalex.org/subfields/3103","display_name":"Astronomy and Astrophysics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T13080","display_name":"Advanced Differential Geometry Research","score":0.9810000061988831,"subfield":{"id":"https://openalex.org/subfields/3103","display_name":"Astronomy and Astrophysics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10229","display_name":"Geometric Analysis and Curvature Flows","score":0.9718000292778015,"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/T12504","display_name":"Mathematics and Applications","score":0.9445000290870667,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/gravitational-singularity","display_name":"Gravitational singularity","score":0.7338297963142395},{"id":"https://openalex.org/keywords/friedmann-equations","display_name":"Friedmann equations","score":0.533728301525116},{"id":"https://openalex.org/keywords/mathematical-physics","display_name":"Mathematical physics","score":0.491326242685318},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.43399083614349365},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.41123878955841064},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.16459015011787415},{"id":"https://openalex.org/keywords/astrophysics","display_name":"Astrophysics","score":0.07784336805343628},{"id":"https://openalex.org/keywords/cosmology","display_name":"Cosmology","score":0.07783150672912598}],"concepts":[{"id":"https://openalex.org/C12843","wikidata":"https://www.wikidata.org/wiki/Q201721","display_name":"Gravitational singularity","level":2,"score":0.7338297963142395},{"id":"https://openalex.org/C85405196","wikidata":"https://www.wikidata.org/wiki/Q467736","display_name":"Friedmann equations","level":4,"score":0.533728301525116},{"id":"https://openalex.org/C37914503","wikidata":"https://www.wikidata.org/wiki/Q156495","display_name":"Mathematical physics","level":1,"score":0.491326242685318},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.43399083614349365},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.41123878955841064},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.16459015011787415},{"id":"https://openalex.org/C44870925","wikidata":"https://www.wikidata.org/wiki/Q37547","display_name":"Astrophysics","level":1,"score":0.07784336805343628},{"id":"https://openalex.org/C26405456","wikidata":"https://www.wikidata.org/wiki/Q338","display_name":"Cosmology","level":2,"score":0.07783150672912598},{"id":"https://openalex.org/C172790937","wikidata":"https://www.wikidata.org/wiki/Q18343","display_name":"Dark energy","level":3,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.3390/axioms14080591","is_oa":true,"landing_page_url":"https://doi.org/10.3390/axioms14080591","pdf_url":null,"source":{"id":"https://openalex.org/S4210173132","display_name":"Axioms","issn_l":"2075-1680","issn":["2075-1680"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Axioms","raw_type":"journal-article"},{"id":"pmh:oai:doaj.org/article:43787f393dae4221944b9cd0edee2224","is_oa":true,"landing_page_url":"https://doaj.org/article/43787f393dae4221944b9cd0edee2224","pdf_url":null,"source":{"id":"https://openalex.org/S112646816","display_name":"SHILAP Revista de lepidopterolog\u00eda","issn_l":"0300-5267","issn":["0300-5267","2340-4078"],"is_oa":true,"is_in_doaj":true,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Axioms, Vol 14, Iss 8, p 591 (2025)","raw_type":"article"}],"best_oa_location":{"id":"doi:10.3390/axioms14080591","is_oa":true,"landing_page_url":"https://doi.org/10.3390/axioms14080591","pdf_url":null,"source":{"id":"https://openalex.org/S4210173132","display_name":"Axioms","issn_l":"2075-1680","issn":["2075-1680"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Axioms","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G3762746986","display_name":null,"funder_award_id":"EGP2024-125635NB-I02","funder_id":"https://openalex.org/F4320324798","funder_display_name":"Tanta University"}],"funders":[{"id":"https://openalex.org/F4320324798","display_name":"Tanta University","ror":"https://ror.org/016jp5b92"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":17,"referenced_works":["https://openalex.org/W577242143","https://openalex.org/W1518877246","https://openalex.org/W1969882757","https://openalex.org/W2056358560","https://openalex.org/W2059473956","https://openalex.org/W2066763967","https://openalex.org/W2072331245","https://openalex.org/W2089013457","https://openalex.org/W2097403045","https://openalex.org/W2962823414","https://openalex.org/W3141359286","https://openalex.org/W3195756446","https://openalex.org/W4206311976","https://openalex.org/W4211007335","https://openalex.org/W4252558075","https://openalex.org/W4366690262","https://openalex.org/W4405795084"],"related_works":["https://openalex.org/W4391375266","https://openalex.org/W2935759653","https://openalex.org/W2064273847","https://openalex.org/W2296071024","https://openalex.org/W4200159216","https://openalex.org/W2091775113","https://openalex.org/W2342571225","https://openalex.org/W2049348035","https://openalex.org/W2030101063","https://openalex.org/W2082564304"],"abstract_inverted_index":{"We":[0],"obtain":[1],"different":[2],"categories":[3],"of":[4,6,19,29,47,56,62,65,70,77],"singularities":[5,82],"fuzzy":[7,9,13,16,21,26,30,39,44,49,54,63,67,80],"retracts,":[8,11],"deformation":[10],"and":[12,51],"foldings":[14,55],"on":[15],"fundamental":[17,27,45],"groups":[18,28,46],"the":[20,43,48,52,75],"Friedmann\u2013Lema\u00eetre\u2013Robertson\u2013Walker":[22],"Space":[23],"W\u02dc4.":[24],"The":[25],"submanifolds":[31],"in":[32],"W\u02dc4":[33,57,71],"are":[34,58,72,83],"characterized":[35],"combinatorially":[36],"using":[37],"these":[38],"geometrical":[40,68],"transformations.":[41],"Also,":[42],"geodesics":[50],"limit":[53],"described.":[59],"New":[60],"types":[61],"singularity":[64],"some":[66,78],"transformations":[69],"obtained.":[73],"Finally,":[74],"regularity":[76],"other":[79],"retract":[81],"discussed.":[84]},"counts_by_year":[{"year":2026,"cited_by_count":1}],"updated_date":"2026-04-04T08:04:53.788161","created_date":"2025-10-10T00:00:00"}
