{"id":"https://openalex.org/W4399860508","doi":"https://doi.org/10.3390/sym16060771","title":"Statistical Warped Product Immersions into Statistical Manifolds of (Quasi-)Constant Curvature","display_name":"Statistical Warped Product Immersions into Statistical Manifolds of (Quasi-)Constant Curvature","publication_year":2024,"publication_date":"2024-06-19","ids":{"openalex":"https://openalex.org/W4399860508","doi":"https://doi.org/10.3390/sym16060771"},"language":"en","primary_location":{"id":"doi:10.3390/sym16060771","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym16060771","pdf_url":"https://www.mdpi.com/2073-8994/16/6/771/pdf?version=1718797981","source":{"id":"https://openalex.org/S190787756","display_name":"Symmetry","issn_l":"2073-8994","issn":["2073-8994"],"is_oa":true,"is_in_doaj":false,"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":"Symmetry","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://www.mdpi.com/2073-8994/16/6/771/pdf?version=1718797981","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5034019750","display_name":"Aliya Naaz S\u0131dd\u0131qu\u0131","orcid":"https://orcid.org/0000-0003-3895-7548"},"institutions":[{"id":"https://openalex.org/I155125381","display_name":"Galgotias University","ror":"https://ror.org/02w8ba206","country_code":"IN","type":"education","lineage":["https://openalex.org/I155125381"]}],"countries":["IN"],"is_corresponding":false,"raw_author_name":"Aliya Naaz Siddiqui","raw_affiliation_strings":["Division of Mathematics, School of Basic Sciences, Galgotias University, Greater Noida 203201, Uttar Pradesh, India"],"raw_orcid":"https://orcid.org/0000-0003-3895-7548","affiliations":[{"raw_affiliation_string":"Division of Mathematics, School of Basic Sciences, Galgotias University, Greater Noida 203201, Uttar Pradesh, India","institution_ids":["https://openalex.org/I155125381"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5030826658","display_name":"Meraj Ali Khan","orcid":"https://orcid.org/0000-0001-6554-1228"},"institutions":[{"id":"https://openalex.org/I240666556","display_name":"Imam Mohammad ibn Saud Islamic University","ror":"https://ror.org/05gxjyb39","country_code":"SA","type":"education","lineage":["https://openalex.org/I240666556"]}],"countries":["SA"],"is_corresponding":true,"raw_author_name":"Meraj Ali Khan","raw_affiliation_strings":["Department of Mathematics and Statistics, College of Science, Imam Mohammad Ibn Saud Islamic University (IMSIU), P.O. Box 65892, Riyadh 11566, Saudi Arabia"],"raw_orcid":"https://orcid.org/0000-0001-6554-1228","affiliations":[{"raw_affiliation_string":"Department of Mathematics and Statistics, College of Science, Imam Mohammad Ibn Saud Islamic University (IMSIU), P.O. Box 65892, Riyadh 11566, Saudi Arabia","institution_ids":["https://openalex.org/I240666556"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5039657075","display_name":"Sudhakar Kumar Chaubey","orcid":"https://orcid.org/0000-0002-3882-4596"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Sudhakar Kumar Chaubey","raw_affiliation_strings":["Department of Information Technology, University of Technology and Applied Sciences, P.O. Box 77, Shinas 324, Oman"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Information Technology, University of Technology and Applied Sciences, P.O. Box 77, Shinas 324, Oman","institution_ids":[]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5030826658"],"corresponding_institution_ids":["https://openalex.org/I240666556"],"apc_list":{"value":2000,"currency":"CHF","value_usd":2165},"apc_paid":{"value":2000,"currency":"CHF","value_usd":2165},"fwci":0.8694,"has_fulltext":false,"cited_by_count":1,"citation_normalized_percentile":{"value":0.68674341,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":94,"max":97},"biblio":{"volume":"16","issue":"6","first_page":"771","last_page":"771"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12417","display_name":"Morphological variations and asymmetry","score":0.996999979019165,"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"}},"topics":[{"id":"https://openalex.org/T12417","display_name":"Morphological variations and asymmetry","score":0.996999979019165,"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":0.9889000058174133,"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/T10229","display_name":"Geometric Analysis and Curvature Flows","score":0.9884999990463257,"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/constant-curvature","display_name":"Constant curvature","score":0.6453272700309753},{"id":"https://openalex.org/keywords/image-warping","display_name":"Image warping","score":0.6119910478591919},{"id":"https://openalex.org/keywords/constant","display_name":"Constant (computer programming)","score":0.5972083210945129},{"id":"https://openalex.org/keywords/curvature","display_name":"Curvature","score":0.5907992720603943},{"id":"https://openalex.org/keywords/submanifold","display_name":"Submanifold","score":0.5884254574775696},{"id":"https://openalex.org/keywords/context","display_name":"Context (archaeology)","score":0.5752434134483337},{"id":"https://openalex.org/keywords/product","display_name":"Product (mathematics)","score":0.5739148855209351},{"id":"https://openalex.org/keywords/manifold","display_name":"Manifold (fluid mechanics)","score":0.5157395005226135},{"id":"https://openalex.org/keywords/range","display_name":"Range (aeronautics)","score":0.49467942118644714},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.4857066571712494},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.47306835651397705},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.469374418258667},{"id":"https://openalex.org/keywords/mean-curvature","display_name":"Mean curvature","score":0.44237205386161804},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.32021772861480713},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.23473763465881348},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.16805779933929443},{"id":"https://openalex.org/keywords/geology","display_name":"Geology","score":0.06277549266815186},{"id":"https://openalex.org/keywords/engineering","display_name":"Engineering","score":0.06167909502983093}],"concepts":[{"id":"https://openalex.org/C2779668893","wikidata":"https://www.wikidata.org/wiki/Q2250422","display_name":"Constant curvature","level":3,"score":0.6453272700309753},{"id":"https://openalex.org/C157202957","wikidata":"https://www.wikidata.org/wiki/Q1659609","display_name":"Image warping","level":2,"score":0.6119910478591919},{"id":"https://openalex.org/C2777027219","wikidata":"https://www.wikidata.org/wiki/Q1284190","display_name":"Constant (computer programming)","level":2,"score":0.5972083210945129},{"id":"https://openalex.org/C195065555","wikidata":"https://www.wikidata.org/wiki/Q214881","display_name":"Curvature","level":2,"score":0.5907992720603943},{"id":"https://openalex.org/C151300846","wikidata":"https://www.wikidata.org/wiki/Q125539","display_name":"Submanifold","level":2,"score":0.5884254574775696},{"id":"https://openalex.org/C2779343474","wikidata":"https://www.wikidata.org/wiki/Q3109175","display_name":"Context (archaeology)","level":2,"score":0.5752434134483337},{"id":"https://openalex.org/C90673727","wikidata":"https://www.wikidata.org/wiki/Q901718","display_name":"Product (mathematics)","level":2,"score":0.5739148855209351},{"id":"https://openalex.org/C529865628","wikidata":"https://www.wikidata.org/wiki/Q1790740","display_name":"Manifold (fluid mechanics)","level":2,"score":0.5157395005226135},{"id":"https://openalex.org/C204323151","wikidata":"https://www.wikidata.org/wiki/Q905424","display_name":"Range (aeronautics)","level":2,"score":0.49467942118644714},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.4857066571712494},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.47306835651397705},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.469374418258667},{"id":"https://openalex.org/C175017881","wikidata":"https://www.wikidata.org/wiki/Q1318998","display_name":"Mean curvature","level":3,"score":0.44237205386161804},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.32021772861480713},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.23473763465881348},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.16805779933929443},{"id":"https://openalex.org/C127313418","wikidata":"https://www.wikidata.org/wiki/Q1069","display_name":"Geology","level":0,"score":0.06277549266815186},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.06167909502983093},{"id":"https://openalex.org/C146978453","wikidata":"https://www.wikidata.org/wiki/Q3798668","display_name":"Aerospace engineering","level":1,"score":0.0},{"id":"https://openalex.org/C151730666","wikidata":"https://www.wikidata.org/wiki/Q7205","display_name":"Paleontology","level":1,"score":0.0},{"id":"https://openalex.org/C78519656","wikidata":"https://www.wikidata.org/wiki/Q101333","display_name":"Mechanical engineering","level":1,"score":0.0},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.3390/sym16060771","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym16060771","pdf_url":"https://www.mdpi.com/2073-8994/16/6/771/pdf?version=1718797981","source":{"id":"https://openalex.org/S190787756","display_name":"Symmetry","issn_l":"2073-8994","issn":["2073-8994"],"is_oa":true,"is_in_doaj":false,"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":"Symmetry","raw_type":"journal-article"},{"id":"pmh:oai:doaj.org/article:14eba223593a4047bd76adc09fa214b4","is_oa":false,"landing_page_url":"https://doaj.org/article/14eba223593a4047bd76adc09fa214b4","pdf_url":null,"source":{"id":"https://openalex.org/S4306401280","display_name":"DOAJ (DOAJ: Directory of Open Access Journals)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Symmetry, Vol 16, Iss 6, p 771 (2024)","raw_type":"article"}],"best_oa_location":{"id":"doi:10.3390/sym16060771","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym16060771","pdf_url":"https://www.mdpi.com/2073-8994/16/6/771/pdf?version=1718797981","source":{"id":"https://openalex.org/S190787756","display_name":"Symmetry","issn_l":"2073-8994","issn":["2073-8994"],"is_oa":true,"is_in_doaj":false,"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":"Symmetry","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4399860508.pdf"},"referenced_works_count":22,"referenced_works":["https://openalex.org/W1520168181","https://openalex.org/W1598279643","https://openalex.org/W2009872511","https://openalex.org/W2031917130","https://openalex.org/W2057521929","https://openalex.org/W2062346296","https://openalex.org/W2069638163","https://openalex.org/W2072793777","https://openalex.org/W2275930313","https://openalex.org/W2757704141","https://openalex.org/W2802774444","https://openalex.org/W2899016568","https://openalex.org/W2941814768","https://openalex.org/W2970690066","https://openalex.org/W3016011518","https://openalex.org/W3083675169","https://openalex.org/W3159004522","https://openalex.org/W3192921199","https://openalex.org/W4240085759","https://openalex.org/W4362572889","https://openalex.org/W4396636763","https://openalex.org/W6634556549"],"related_works":["https://openalex.org/W2964267756","https://openalex.org/W4297825487","https://openalex.org/W2508030851","https://openalex.org/W2244708326","https://openalex.org/W1597471746","https://openalex.org/W3119140586","https://openalex.org/W2593232824","https://openalex.org/W4302324255","https://openalex.org/W1486895930","https://openalex.org/W2893392424"],"abstract_inverted_index":{"Warped":[0],"products":[1],"provide":[2],"an":[3],"elegant":[4],"and":[5,10,32,47,72],"versatile":[6],"framework":[7],"for":[8,75],"exploring":[9],"understanding":[11],"a":[12,26,30,40,76,82,86],"wide":[13],"range":[14],"of":[15,35,64,85],"geometric":[16],"structures.":[17],"Their":[18],"ability":[19],"to":[20,57],"combine":[21],"two":[22,70],"distinct":[23,73],"manifolds":[24],"through":[25],"warping":[27],"function":[28],"introduces":[29],"rich":[31],"diverse":[33],"set":[34],"geometries,":[36],"thus":[37],"making":[38],"them":[39],"powerful":[41],"tool":[42],"in":[43,61,81],"various":[44],"mathematical,":[45],"physical,":[46],"computational":[48],"applications.":[49],"This":[50,90],"article":[51,91],"addresses":[52],"the":[53,62],"central":[54],"query":[55],"related":[56],"warped":[58,78],"product":[59,79],"submanifolds":[60],"context":[63],"statistics.":[65],"It":[66],"focuses":[67],"on":[68],"deriving":[69],"new":[71],"inequalities":[74],"statistical":[77,83],"submanifold":[80],"manifold":[84],"constant":[87],"(quasi-constant)":[88],"curvature.":[89],"then":[92],"finishes":[93],"with":[94],"some":[95],"concluding":[96],"remarks.":[97]},"counts_by_year":[{"year":2026,"cited_by_count":1}],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}