{"id":"https://openalex.org/W4416627253","doi":"https://doi.org/10.9734/arjom/2025/v21i121019","title":"Hyperbolic Extensions of Generalized Pandita Numbers","display_name":"Hyperbolic Extensions of Generalized Pandita Numbers","publication_year":2025,"publication_date":"2025-11-25","ids":{"openalex":"https://openalex.org/W4416627253","doi":"https://doi.org/10.9734/arjom/2025/v21i121019"},"language":"en","primary_location":{"id":"doi:10.9734/arjom/2025/v21i121019","doi":"https://doi.org/10.9734/arjom/2025/v21i121019","is_oa":true,"landing_page_url":"https://doi.org/10.9734/arjom/2025/v21i121019","pdf_url":null,"source":{"id":"https://openalex.org/S4210207970","display_name":"Asian Research Journal of Mathematics","issn_l":"2456-477X","issn":["2456-477X"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/P4310320855","host_organization_name":"Sciencedomain International","host_organization_lineage":["https://openalex.org/P4310320855"],"host_organization_lineage_names":["Sciencedomain International"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Asian Research Journal of Mathematics","raw_type":"journal-article"},"volume":null,"type":"article","is_traditional":true,"indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"diamond","oa_url":"https://doi.org/10.9734/arjom/2025/v21i121019","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5118800663","display_name":"Fatih Zahid KALCA","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I3017902709","display_name":"Zonguldak B\u00fclent Ecevit University","ror":"https://ror.org/01dvabv26","country_code":"TR","type":"education","lineage":["https://openalex.org/I3017902709"]}],"countries":["TR"],"is_corresponding":false,"raw_author_name":"Fatih Zahid Kalca","raw_affiliation_strings":["Department of Mathematics, Art and Science Faculty, Zonguldak B\u00a8ulent Ecevit University, 67100, Zonguldak, Turkey"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Art and Science Faculty, Zonguldak B\u00a8ulent Ecevit University, 67100, Zonguldak, Turkey","institution_ids":["https://openalex.org/I3017902709"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5066232761","display_name":"Y\u00fcksel Soykan","orcid":"https://orcid.org/0000-0002-1895-211X","observed_orcids":["https://orcid.org/0000-0002-1895-211X"]},"institutions":[{"id":"https://openalex.org/I3017902709","display_name":"Zonguldak B\u00fclent Ecevit University","ror":"https://ror.org/01dvabv26","country_code":"TR","type":"education","lineage":["https://openalex.org/I3017902709"]}],"countries":["TR"],"is_corresponding":false,"raw_author_name":"Yuksel Soykan","raw_affiliation_strings":["Department of Mathematics, Art and Science Faculty, Zonguldak B\u00a8ulent Ecevit University, 67100, Zonguldak, Turkey"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Art and Science Faculty, Zonguldak B\u00a8ulent Ecevit University, 67100, Zonguldak, Turkey","institution_ids":["https://openalex.org/I3017902709"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I3017902709"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.0,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"21","issue":"12","first_page":"13","last_page":"39"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12516","display_name":"Advanced Mathematical Theories and Applications","score":0.7300000190734863,"subfield":{"id":"https://openalex.org/subfields/3109","display_name":"Statistical and Nonlinear Physics"},"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/T12516","display_name":"Advanced Mathematical Theories and Applications","score":0.7300000190734863,"subfield":{"id":"https://openalex.org/subfields/3109","display_name":"Statistical and Nonlinear Physics"},"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/T12037","display_name":"Algebraic and Geometric Analysis","score":0.22030000388622284,"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/T10948","display_name":"Advanced Combinatorial Mathematics","score":0.01640000008046627,"subfield":{"id":"https://openalex.org/subfields/2607","display_name":"Discrete Mathematics and Combinatorics"},"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/hyperbolic-numbers","display_name":"hyperbolic numbers","score":0.9490000009536743},{"id":"https://openalex.org/keywords/generating-functions","display_name":"generating functions","score":0.8320000171661377},{"id":"https://openalex.org/keywords/closed-form-expressions","display_name":"closed-form expressions","score":0.6790000200271606},{"id":"https://openalex.org/keywords/summation-formulas","display_name":"summation formulas","score":0.8820000290870667},{"id":"https://openalex.org/keywords/matrix-representation","display_name":"matrix representation","score":0.7350000143051147},{"id":"https://openalex.org/keywords/recurrence-sequences","display_name":"recursive sequences","score":0.6899999976158142},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"discrete mathematics","score":0.335999995470047}],"concepts":[{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.6514999866485596},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5976999998092651},{"id":"https://openalex.org/C9376300","wikidata":"https://www.wikidata.org/wiki/Q168817","display_name":"Algebraic number","level":2,"score":0.5432000160217285},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.4799000024795532},{"id":"https://openalex.org/C36503486","wikidata":"https://www.wikidata.org/wiki/Q11235244","display_name":"Domain (mathematical analysis)","level":2,"score":0.4717999994754791},{"id":"https://openalex.org/C2780801425","wikidata":"https://www.wikidata.org/wiki/Q5164392","display_name":"Construct (python library)","level":2,"score":0.44670000672340393},{"id":"https://openalex.org/C178489894","wikidata":"https://www.wikidata.org/wiki/Q8789","display_name":"Cryptography","level":2,"score":0.44589999318122864},{"id":"https://openalex.org/C110812573","wikidata":"https://www.wikidata.org/wiki/Q175515","display_name":"Symbolic computation","level":2,"score":0.43050000071525574},{"id":"https://openalex.org/C2778112365","wikidata":"https://www.wikidata.org/wiki/Q3511065","display_name":"Sequence (biology)","level":2,"score":0.4194999933242798},{"id":"https://openalex.org/C182419690","wikidata":"https://www.wikidata.org/wiki/Q205464","display_name":"Algebraic structure","level":2,"score":0.4187000095844269},{"id":"https://openalex.org/C45374587","wikidata":"https://www.wikidata.org/wiki/Q12525525","display_name":"Computation","level":2,"score":0.39969998598098755},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.3720000088214874},{"id":"https://openalex.org/C92047909","wikidata":"https://www.wikidata.org/wiki/Q204034","display_name":"Hyperbolic function","level":2,"score":0.362199991941452},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.3580999970436096},{"id":"https://openalex.org/C70984080","wikidata":"https://www.wikidata.org/wiki/Q2619102","display_name":"Hyperbolic manifold","level":3,"score":0.3393999934196472},{"id":"https://openalex.org/C55862258","wikidata":"https://www.wikidata.org/wiki/Q1017238","display_name":"Hyperbolic coordinates","level":5,"score":0.3068000078201294},{"id":"https://openalex.org/C96469262","wikidata":"https://www.wikidata.org/wiki/Q1324364","display_name":"Homogeneous space","level":2,"score":0.3027999997138977},{"id":"https://openalex.org/C188971069","wikidata":"https://www.wikidata.org/wiki/Q1636734","display_name":"Universal algebra","level":3,"score":0.29919999837875366},{"id":"https://openalex.org/C40020168","wikidata":"https://www.wikidata.org/wiki/Q7310818","display_name":"Relatively hyperbolic group","level":4,"score":0.28700000047683716},{"id":"https://openalex.org/C185701065","wikidata":"https://www.wikidata.org/wiki/Q159943","display_name":"Abstract algebra","level":3,"score":0.2761000096797943},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.27320000529289246},{"id":"https://openalex.org/C68363185","wikidata":"https://www.wikidata.org/wiki/Q180969","display_name":"Algebraic geometry","level":2,"score":0.26980000734329224},{"id":"https://openalex.org/C163258240","wikidata":"https://www.wikidata.org/wiki/Q25342","display_name":"Power (physics)","level":2,"score":0.2547999918460846}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.9734/arjom/2025/v21i121019","doi":"https://doi.org/10.9734/arjom/2025/v21i121019","is_oa":true,"landing_page_url":"https://doi.org/10.9734/arjom/2025/v21i121019","pdf_url":null,"source":{"id":"https://openalex.org/S4210207970","display_name":"Asian Research Journal of Mathematics","issn_l":"2456-477X","issn":["2456-477X"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/P4310320855","host_organization_name":"Sciencedomain International","host_organization_lineage":["https://openalex.org/P4310320855"],"host_organization_lineage_names":["Sciencedomain International"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Asian Research Journal of Mathematics","raw_type":"journal-article"},{"id":"pmh:oai:journalarjom.com:article/1019","doi":null,"is_oa":true,"landing_page_url":"https://journalarjom.com/index.php/ARJOM/article/view/1019","pdf_url":null,"source":{"id":"https://openalex.org/S4210207970","display_name":"Asian Research Journal of Mathematics","issn_l":"2456-477X","issn":["2456-477X"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/P4310320855","host_organization_name":"Sciencedomain International","host_organization_lineage":["https://openalex.org/P4310320855"],"host_organization_lineage_names":["Sciencedomain International"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2456-477X","raw_type":"info:eu-repo/semantics/article"},{"id":"pmh:oai:HAL:hal-05382712v1","doi":null,"is_oa":false,"landing_page_url":"https://hal.science/hal-05382712","pdf_url":null,"source":{"id":"https://openalex.org/S4306402512","display_name":"HAL","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I4405252976","host_organization_name":"Centre pour la Communication Scientifique Directe","host_organization_lineage":["https://openalex.org/I4405252976"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Asian Research Journal of Mathematics, 2025, 21 (12), pp.13-39","raw_type":"info:eu-repo/semantics/article"},{"id":"pmh:oai:acikarsiv.beun.edu.tr:20.500.12628/29809","doi":null,"is_oa":false,"landing_page_url":"https://hdl.handle.net/20.500.12628/29809","pdf_url":null,"source":{"id":"https://openalex.org/S7407055168","display_name":"Zonguldak B\u00fclent Ecevit University Institutional Repository","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"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":null,"raw_type":"Article"}],"best_oa_location":{"id":"doi:10.9734/arjom/2025/v21i121019","doi":"https://doi.org/10.9734/arjom/2025/v21i121019","is_oa":true,"landing_page_url":"https://doi.org/10.9734/arjom/2025/v21i121019","pdf_url":null,"source":{"id":"https://openalex.org/S4210207970","display_name":"Asian Research Journal of Mathematics","issn_l":"2456-477X","issn":["2456-477X"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/P4310320855","host_organization_name":"Sciencedomain International","host_organization_lineage":["https://openalex.org/P4310320855"],"host_organization_lineage_names":["Sciencedomain International"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Asian Research Journal of Mathematics","raw_type":"journal-article"},"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W4413131001","https://openalex.org/W7127413179","https://openalex.org/W4416169772","https://openalex.org/W3108427825","https://openalex.org/W4210522330","https://openalex.org/W4417432341","https://openalex.org/W4415614621","https://openalex.org/W4283732858","https://openalex.org/W4390880344","https://openalex.org/W4415570269"],"abstract_inverted_index":{"This":[0],"paper":[1],"introduces":[2],"the":[3,12,27,35,43,63,127,146,153,166],"framework":[4],"of":[5,16,23,30,37,130,148,155],"generalized":[6],"hyperbolic":[7,17,38,64,67],"Pandita":[8,65],"numbers":[9],"constructed":[10],"over":[11],"bidimensional":[13],"Clifford":[14],"algebra":[15],"numbers,":[18,69],"contributing":[19],"a":[20],"novel":[21],"class":[22],"structured":[24],"sequences":[25],"to":[26,59,108],"expanding":[28],"domain":[29],"number":[31],"theory.":[32],"Anchored":[33],"in":[34,141,145,178],"principles":[36],"systems,":[39,150],"these":[40],"constructs":[41],"pave":[42],"way":[44],"for":[45,168],"exploring":[46],"algebraic":[47,111],"symmetries":[48],"and":[49,66,78,96,120,133,158,175],"recursive":[50],"behaviors":[51],"beyond":[52],"classical":[53],"formulations.":[54],"Special":[55],"attention":[56],"is":[57],"devoted":[58],"notable":[60],"cases,":[61],"including":[62],"Pandita-Lucas":[68],"whose":[70],"properties":[71],"are":[72,106],"meticulously":[73],"examined.":[74],"To":[75],"deepen":[76],"understanding":[77],"facilitate":[79],"computation,":[80],"we":[81],"derive":[82],"explicit":[83],"closed-form":[84],"representations":[85,105],"using":[86],"Binet-type":[87],"formulas,":[88],"construct":[89],"generating":[90],"functions":[91],"through":[92,113],"formal":[93],"power":[94],"series,":[95],"establish":[97],"summation":[98],"expressions":[99],"with":[100],"broad":[101],"applicability.":[102],"Additionally,":[103],"matrix-based":[104],"developed":[107],"offer":[109],"an":[110],"lens":[112],"which":[114],"structural":[115],"dynamics":[116],"can":[117],"be":[118],"modeled":[119],"analyzed.":[121],"These":[122],"formulations":[123],"not":[124],"only":[125],"enrich":[126],"theoretical":[128],"foundations":[129],"discrete":[131],"mathematics":[132],"symbolic":[134],"computation":[135],"but":[136],"also":[137],"highlight":[138],"promising":[139],"applications":[140],"engineering":[142],"disciplines\u2014":[143],"particularly":[144],"modeling":[147],"iterative":[149],"signal":[151],"transformations,":[152],"analysis":[154],"complex":[156],"networks,":[157],"cryptographic":[159],"systems.":[160],"The":[161],"insights":[162],"presented":[163],"herein":[164],"lay":[165],"groundwork":[167],"future":[169],"exploration":[170],"into":[171],"hybrid":[172],"sequence":[173],"systems":[174],"their":[176],"role":[177],"interdisciplinary":[179],"problem":[180],"solving.":[181]},"counts_by_year":[],"updated_date":"2026-10-25T09:29:13.331239","created_date":"2025-11-25T00:00:00"}