{"id":"https://openalex.org/W4417129289","doi":"https://doi.org/10.48550/arxiv.2510.09336","title":"Quantum Trigonometric B\u00e9zier Curves","display_name":"Quantum Trigonometric B\u00e9zier Curves","publication_year":2025,"publication_date":"2025-10-10","ids":{"openalex":"https://openalex.org/W4417129289","doi":"https://doi.org/10.48550/arxiv.2510.09336"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2510.09336","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2510.09336","pdf_url":"https://arxiv.org/pdf/2510.09336","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,"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":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"type":"preprint","indexed_in":["arxiv","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2510.09336","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5009733320","display_name":"\u00c7etin Di\u0307\u015fi\u0307b\u00fcy\u00fck","orcid":"https://orcid.org/0000-0001-5105-2255"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Di\u015fib\u00fcy\u00fck, \u00c7etin","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":["https://openalex.org/A5009733320"],"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/T11245","display_name":"Advanced Numerical Analysis Techniques","score":0.8885999917984009,"subfield":{"id":"https://openalex.org/subfields/2206","display_name":"Computational Mechanics"},"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/T11245","display_name":"Advanced Numerical Analysis Techniques","score":0.8885999917984009,"subfield":{"id":"https://openalex.org/subfields/2206","display_name":"Computational Mechanics"},"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/T11435","display_name":"Polynomial and algebraic computation","score":0.013100000098347664,"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"}},{"id":"https://openalex.org/T12661","display_name":"Iterative Methods for Nonlinear Equations","score":0.009499999694526196,"subfield":{"id":"https://openalex.org/subfields/2612","display_name":"Numerical Analysis"},"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/trigonometric-substitution","display_name":"Trigonometric substitution","score":0.7688999772071838},{"id":"https://openalex.org/keywords/differentiation-of-trigonometric-functions","display_name":"Differentiation of trigonometric functions","score":0.7174000144004822},{"id":"https://openalex.org/keywords/trigonometry","display_name":"Trigonometry","score":0.6933000087738037},{"id":"https://openalex.org/keywords/trigonometric-integral","display_name":"Trigonometric integral","score":0.6913999915122986},{"id":"https://openalex.org/keywords/integration-using-eulers-formula","display_name":"Integration using Euler's formula","score":0.6664000153541565},{"id":"https://openalex.org/keywords/pythagorean-trigonometric-identity","display_name":"Pythagorean trigonometric identity","score":0.6317999958992004},{"id":"https://openalex.org/keywords/quantum","display_name":"Quantum","score":0.5964000225067139},{"id":"https://openalex.org/keywords/trigonometric-functions","display_name":"Trigonometric functions","score":0.5432999730110168}],"concepts":[{"id":"https://openalex.org/C9317044","wikidata":"https://www.wikidata.org/wiki/Q1191963","display_name":"Trigonometric substitution","level":5,"score":0.7688999772071838},{"id":"https://openalex.org/C30786353","wikidata":"https://www.wikidata.org/wiki/Q3296857","display_name":"Differentiation of trigonometric functions","level":5,"score":0.7174000144004822},{"id":"https://openalex.org/C29001434","wikidata":"https://www.wikidata.org/wiki/Q8084","display_name":"Trigonometry","level":2,"score":0.6933000087738037},{"id":"https://openalex.org/C65692021","wikidata":"https://www.wikidata.org/wiki/Q1094282","display_name":"Trigonometric integral","level":3,"score":0.6913999915122986},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6784999966621399},{"id":"https://openalex.org/C65454745","wikidata":"https://www.wikidata.org/wiki/Q6043250","display_name":"Integration using Euler's formula","level":5,"score":0.6664000153541565},{"id":"https://openalex.org/C89507098","wikidata":"https://www.wikidata.org/wiki/Q2039117","display_name":"Pythagorean trigonometric identity","level":5,"score":0.6317999958992004},{"id":"https://openalex.org/C84114770","wikidata":"https://www.wikidata.org/wiki/Q46344","display_name":"Quantum","level":2,"score":0.5964000225067139},{"id":"https://openalex.org/C178009071","wikidata":"https://www.wikidata.org/wiki/Q93344","display_name":"Trigonometric functions","level":2,"score":0.5432999730110168},{"id":"https://openalex.org/C156760230","wikidata":"https://www.wikidata.org/wiki/Q1969650","display_name":"Trigonometric polynomial","level":3,"score":0.510699987411499},{"id":"https://openalex.org/C164897557","wikidata":"https://www.wikidata.org/wiki/Q7250037","display_name":"Proofs of trigonometric identities","level":5,"score":0.48750001192092896},{"id":"https://openalex.org/C12426560","wikidata":"https://www.wikidata.org/wiki/Q189569","display_name":"Basis (linear algebra)","level":2,"score":0.48030000925064087},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.367000013589859},{"id":"https://openalex.org/C137019171","wikidata":"https://www.wikidata.org/wiki/Q2623817","display_name":"Quantum algorithm","level":3,"score":0.3538999855518341},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.3513000011444092},{"id":"https://openalex.org/C28537468","wikidata":"https://www.wikidata.org/wiki/Q464356","display_name":"Trigonometric interpolation","level":5,"score":0.3386000096797943},{"id":"https://openalex.org/C2780801425","wikidata":"https://www.wikidata.org/wiki/Q5164392","display_name":"Construct (python library)","level":2,"score":0.2976999878883362},{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.29409998655319214},{"id":"https://openalex.org/C75190567","wikidata":"https://www.wikidata.org/wiki/Q41237","display_name":"Rational function","level":2,"score":0.28929999470710754},{"id":"https://openalex.org/C120362076","wikidata":"https://www.wikidata.org/wiki/Q1149336","display_name":"Trigonometric series","level":2,"score":0.27309998869895935},{"id":"https://openalex.org/C43682372","wikidata":"https://www.wikidata.org/wiki/Q7269080","display_name":"Quantum operation","level":4,"score":0.27090001106262207},{"id":"https://openalex.org/C192122513","wikidata":"https://www.wikidata.org/wiki/Q2835770","display_name":"Quantum phase estimation algorithm","level":5,"score":0.2547999918460846}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2510.09336","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2510.09336","pdf_url":"https://arxiv.org/pdf/2510.09336","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,"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":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},{"id":"doi:10.48550/arxiv.2510.09336","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2510.09336","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,"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":null,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2510.09336","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2510.09336","pdf_url":"https://arxiv.org/pdf/2510.09336","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,"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":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":[],"abstract_inverted_index":{"In":[0],"order":[1],"to":[2,30],"construct":[3],"quantum":[4,38,46,66,75],"trigonometric":[5,15,39,47,67,76],"B\u00e9zier":[6,40,48,68,77],"curves":[7,49,69,78],"with":[8],"shape":[9,33,81],"parameter,":[10],"one":[11],"parameter":[12],"family":[13],"of":[14,26,36,65],"Bernstein":[16],"basis":[17,28],"functions":[18,29],"are":[19],"introduced.":[20],"We":[21,42],"study":[22],"the":[23,27,32,37,73],"total":[24],"positivity":[25],"analyze":[31],"preserving":[34,82],"properties":[35],"curves.":[41],"also":[43],"showed":[44],"that":[45,72],"can":[50],"be":[51],"evaluated":[52],"by":[53],"two":[54],"different":[55],"recursive":[56],"evaluation":[57],"algorithms.":[58],"Finally,":[59],"we":[60],"have":[61],"defined":[62],"rational":[63,74],"counterpart":[64],"and":[70],"show":[71],"posses":[79],"nice":[80],"properties.":[83]},"counts_by_year":[],"updated_date":"2026-08-05T07:39:15.569665","created_date":"2025-10-14T00:00:00"}