{"id":"https://openalex.org/W7203718356","doi":"https://doi.org/10.48550/arxiv.2608.15158","title":"A Continuous digit projector from binary representations of numbers onto $A_2$-representation","display_name":"A Continuous digit projector from binary representations of numbers onto $A_2$-representation","publication_year":2026,"publication_date":"2026-08-15","ids":{"openalex":"https://openalex.org/W7203718356","doi":"https://doi.org/10.48550/arxiv.2608.15158"},"language":"en","primary_location":{"id":"doi:10.48550/arxiv.2608.15158","doi":"https://doi.org/10.48550/arxiv.2608.15158","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2608.15158","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"},"volume":null,"type":"preprint","is_traditional":true,"indexed_in":["datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://doi.org/10.48550/arxiv.2608.15158","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5147416995","display_name":"O. O. Nikorak","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I190444043","display_name":"Institute of Mathematics","ror":"https://ror.org/04q3mp532","country_code":"UA","type":"facility","lineage":["https://openalex.org/I149851306","https://openalex.org/I190444043"]}],"countries":["UA"],"is_corresponding":false,"raw_author_name":"Nikorak, O. O.","raw_affiliation_strings":["Institute of Mathematics of NASU , Kyiv , Ukraine"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Institute of Mathematics of NASU , Kyiv , Ukraine","institution_ids":["https://openalex.org/I190444043"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5123981198","display_name":"S. P. Ratushniak","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I190444043","display_name":"Institute of Mathematics","ror":"https://ror.org/04q3mp532","country_code":"UA","type":"facility","lineage":["https://openalex.org/I149851306","https://openalex.org/I190444043"]},{"id":"https://openalex.org/I3131271221","display_name":"Dragomanov Ukrainian State University","ror":"https://ror.org/00batt813","country_code":"UA","type":"education","lineage":["https://openalex.org/I3131271221"]}],"countries":["UA"],"is_corresponding":false,"raw_author_name":"Ratushniak, S. P.","raw_affiliation_strings":["Institute of Mathematics of NASU , Dragomanov Ukrainian State University , Kyiv , Ukraine"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Institute of Mathematics of NASU , Dragomanov Ukrainian State University , Kyiv , Ukraine","institution_ids":["https://openalex.org/I190444043","https://openalex.org/I3131271221"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":null,"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10588","display_name":"Mathematical Dynamics and Fractals","score":0.49459999799728394,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"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/T10588","display_name":"Mathematical Dynamics and Fractals","score":0.49459999799728394,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"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/T13234","display_name":"p-Adic Analysis and Mathematical Physics","score":0.34450000524520874,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"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/T13400","display_name":"Mathematical and Theoretical Analysis","score":0.022600000724196434,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"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/binary-representation","display_name":"binary representation","score":0.7020000219345093},{"id":"https://openalex.org/keywords/continued-fractions","display_name":"continued fractions","score":0.5789999961853027},{"id":"https://openalex.org/keywords/normal-numbers","display_name":"normal numbers","score":0.38600000739097595}],"concepts":[{"id":"https://openalex.org/C2776865275","wikidata":"https://www.wikidata.org/wiki/Q311666","display_name":"Projector","level":2,"score":0.8011000156402588},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7968000173568726},{"id":"https://openalex.org/C2776359362","wikidata":"https://www.wikidata.org/wiki/Q2145286","display_name":"Representation (politics)","level":3,"score":0.6647999882698059},{"id":"https://openalex.org/C48372109","wikidata":"https://www.wikidata.org/wiki/Q3913","display_name":"Binary number","level":2,"score":0.6021999716758728},{"id":"https://openalex.org/C16171025","wikidata":"https://www.wikidata.org/wiki/Q863349","display_name":"Singularity","level":2,"score":0.5541999936103821},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.534600019454956},{"id":"https://openalex.org/C2834757","wikidata":"https://www.wikidata.org/wiki/Q4925424","display_name":"Monotone polygon","level":2,"score":0.490200012922287},{"id":"https://openalex.org/C105462591","wikidata":"https://www.wikidata.org/wiki/Q3737844","display_name":"Binary function","level":3,"score":0.4627000093460083},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.45660001039505005},{"id":"https://openalex.org/C167528306","wikidata":"https://www.wikidata.org/wiki/Q5508776","display_name":"Function representation","level":3,"score":0.4431000053882599},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.41499999165534973},{"id":"https://openalex.org/C17020691","wikidata":"https://www.wikidata.org/wiki/Q139677","display_name":"Operator (biology)","level":5,"score":0.40799999237060547},{"id":"https://openalex.org/C94957134","wikidata":"https://www.wikidata.org/wiki/Q82990","display_name":"Numerical digit","level":2,"score":0.3756999969482422},{"id":"https://openalex.org/C94375191","wikidata":"https://www.wikidata.org/wiki/Q11205","display_name":"Arithmetic","level":1,"score":0.3465000092983246},{"id":"https://openalex.org/C185529760","wikidata":"https://www.wikidata.org/wiki/Q164307","display_name":"Binary operation","level":2,"score":0.3124000132083893},{"id":"https://openalex.org/C2780813799","wikidata":"https://www.wikidata.org/wiki/Q3274237","display_name":"Zero (linguistics)","level":2,"score":0.3077999949455261},{"id":"https://openalex.org/C204911207","wikidata":"https://www.wikidata.org/wiki/Q860609","display_name":"Generating function","level":2,"score":0.27549999952316284},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.2750999927520752},{"id":"https://openalex.org/C2778199601","wikidata":"https://www.wikidata.org/wiki/Q5165476","display_name":"Continuous function (set theory)","level":3,"score":0.26820001006126404},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.2662999927997589},{"id":"https://openalex.org/C94020503","wikidata":"https://www.wikidata.org/wiki/Q12916","display_name":"Real number","level":2,"score":0.26570001244544983}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.48550/arxiv.2608.15158","doi":"https://doi.org/10.48550/arxiv.2608.15158","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2608.15158","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"doi:10.48550/arxiv.2608.15158","doi":"https://doi.org/10.48550/arxiv.2608.15158","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2608.15158","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"},"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/W7105997865","https://openalex.org/W4308006830","https://openalex.org/W4387131820","https://openalex.org/W4405844789","https://openalex.org/W4312757007","https://openalex.org/W2344493711","https://openalex.org/W7129666179","https://openalex.org/W3134916895","https://openalex.org/W2900317681","https://openalex.org/W4417507901"],"abstract_inverted_index":{"As":[0],"is":[1,8,24,74,80,120,148],"known,":[2],"the":[3,13,18,42,46,53,56,66,77,86,101,114,117,129,132,138,141,153,156],"$A_2$-continued":[4,57],"representation":[5,49,58,96,143],"of":[6,21,41,45,50,55,65,89,103,116,140,144,155],"numbers":[7,51,90],"not":[9],"topologically":[10],"equivalent":[11],"to":[12,93,151],"classical":[14,47],"binary":[15,48,95],"representation;":[16],"therefore,":[17],"digit":[19,43],"projector":[20,44],"such":[22],"representations":[23],"a":[25,33,63,104,108,126],"discontinuous":[26],"function.":[27],"In":[28],"this":[29],"paper,":[30],"we":[31],"introduce":[32],"continuous":[34,109],"function":[35,64,78,111,118],"that":[36,76],"serves":[37],"as":[38],"an":[39],"analogue":[40],"into":[52],"digits":[54],"with":[59,91],"zero":[60],"redundancy,":[61],"namely":[62],"form":[67],"\\[f(\u0394^2_{\u03b1_1\u03b1_2...\u03b1_{2n-1}\u03b1_{2n}...})=":[68],"\u0394^{A_2}_{(\\frac{1}{2})^{1-\u03b1_1}(\\frac{1}{2})^{\u03b1_2}...":[69],"(\\frac{1}{2})^{1-\u03b1_{2n-1}}(\\frac{1}{2})^{\u03b1_{2n}}...},":[70],"\u03b1_n\\in":[71],"\\{0,1\\}.\\]":[72],"It":[73],"proved":[75],"$f$":[79,119],"well-defined,":[81],"continuous,":[82],"and":[83,97,137],"monotone.":[84],"Using":[85],"normal":[87],"properties":[88],"respect":[92],"their":[94],"Lebesgue's":[98],"theorem":[99],"asserting":[100],"existence":[102],"finite":[105],"derivative":[106],"for":[107],"monotone":[110],"almost":[112],"everywhere,":[113],"singularity":[115,154],"established.":[121],"The":[122],"paper":[123],"also":[124],"establishes":[125],"relationship":[127,147],"between":[128],"considered":[130],"function,":[131],"right-shift":[133],"operator":[134],"on":[135],"digits,":[136],"inversor":[139],"continued":[142],"numbers.":[145],"This":[146],"then":[149],"used":[150],"establish":[152],"inversor.":[157]},"counts_by_year":[],"updated_date":"2026-11-04T10:54:05.112534","created_date":"2026-08-19T00:00:00"}
