{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,25]],"date-time":"2026-03-25T11:14:14Z","timestamp":1774437254230,"version":"3.50.1"},"reference-count":9,"publisher":"Wiley","license":[{"start":{"date-parts":[[2019,9,10]],"date-time":"2019-09-10T00:00:00Z","timestamp":1568073600000},"content-version":"unspecified","delay-in-days":0,"URL":"http:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["International Journal of Mathematics and Mathematical Sciences"],"published-print":{"date-parts":[[2019,9,10]]},"abstract":"<jats:p>In this work, we obtained a nonmatrix analytic expression for the generator of the Peano curve. Applying the iteration method of fractal, we established a simple arithmetic-analytic representation of the Peano curve as a function of ternary numbers. We proved that the curve passes each point in a unit square and that the coordinate functions satisfy a H\u00f6lder inequality with index <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M1\"><mml:mrow><mml:mi>\u03b1<\/mml:mi><mml:mo>=<\/mml:mo><mml:mrow><mml:mn>1<\/mml:mn><mml:mo>\/<\/mml:mo><mml:mn>2<\/mml:mn><\/mml:mrow><\/mml:mrow><\/mml:math>, which implies that the curve is everywhere continuous and nowhere differentiable.<\/jats:p>","DOI":"10.1155\/2019\/6745202","type":"journal-article","created":{"date-parts":[[2019,9,10]],"date-time":"2019-09-10T19:31:02Z","timestamp":1568143862000},"page":"1-7","source":"Crossref","is-referenced-by-count":1,"title":["Arithmetic-Analytic Representation of Peano Curve"],"prefix":"10.1155","volume":"2019","author":[{"given":"Guangjun","family":"Yang","sequence":"first","affiliation":[{"name":"College of Mathematics and Statistics, Yunnan University, Kunming 650091, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Xiaoling","family":"Yang","sequence":"additional","affiliation":[{"name":"College of Mathematics and Statistics, Yunnan University of Finance and Economy, Kunming 650221, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-1952-0076","authenticated-orcid":true,"given":"Ping","family":"Wang","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Penn State University, Schuylkill Haven, PA 17972, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"311","reference":[{"key":"3","year":"2015","journal-title":"Mathematics and Computer Science"},{"key":"4","year":"2013"},{"key":"5","doi-asserted-by":"publisher","DOI":"10.1007\/bf01199438"},{"key":"6","doi-asserted-by":"publisher","DOI":"10.1090\/s0002-9947-1900-1500526-4"},{"key":"7","doi-asserted-by":"publisher","DOI":"10.1016\/0001-8708(80)90045-6"},{"key":"8","year":"1994"},{"key":"9","doi-asserted-by":"publisher","DOI":"10.1016\/j.acha.2008.04.002"},{"key":"10","volume-title":"Recent developments in fractals and related fields","year":"2010"},{"key":"11","doi-asserted-by":"publisher","DOI":"10.1090\/spmj\/1441"}],"container-title":["International Journal of Mathematics and Mathematical Sciences"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/downloads.hindawi.com\/journals\/ijmms\/2019\/6745202.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/downloads.hindawi.com\/journals\/ijmms\/2019\/6745202.xml","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/downloads.hindawi.com\/journals\/ijmms\/2019\/6745202.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,9,10]],"date-time":"2019-09-10T19:31:04Z","timestamp":1568143864000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.hindawi.com\/journals\/ijmms\/2019\/6745202\/"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2019,9,10]]},"references-count":9,"alternative-id":["6745202","6745202"],"URL":"https:\/\/doi.org\/10.1155\/2019\/6745202","relation":{},"ISSN":["0161-1712","1687-0425"],"issn-type":[{"value":"0161-1712","type":"print"},{"value":"1687-0425","type":"electronic"}],"subject":[],"published":{"date-parts":[[2019,9,10]]}}}