{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,7,15]],"date-time":"2026-07-15T15:41:21Z","timestamp":1784130081323,"version":"3.55.0"},"reference-count":7,"publisher":"World Scientific Pub Co Pte Lt","issue":"01","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Wavelets Multiresolut Inf. Process."],"published-print":{"date-parts":[[2015,1]]},"abstract":"<jats:p> In this paper, a simple method is given in order to construct an area preserving mapping from a developable surface M to a plane. Based on the area preserving projection, we give some important formulas on M, and define a multi-resolution analysis on L<jats:sup>2<\/jats:sup>(M). We provide the conditions to further discuss the continuous wavelet transform and discrete wavelet transform on developable surface. At the same time, we derived two-scale equations that the scaling function and wavelet function on developable surface satisfied, we also define and discuss the orthogonality, and several important theorems are given. Finally, we construct the numerical examples. The focus of this paper is the area preserving mapping that from developable surface M to a plane, and the discrete wavelet transform on developable surface. <\/jats:p>","DOI":"10.1142\/s0219691315500071","type":"journal-article","created":{"date-parts":[[2015,1,20]],"date-time":"2015-01-20T22:18:26Z","timestamp":1421792306000},"page":"1550007","source":"Crossref","is-referenced-by-count":5,"title":["Wavelet analysis on developable surface base on area preserving projection"],"prefix":"10.1142","volume":"13","author":[{"given":"Bao Qin","family":"Wang","sequence":"first","affiliation":[{"name":"School of Mathematical Science, XinJiang Normal University, Urumqi, 830054, P. R. China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Gang","family":"Wang","sequence":"additional","affiliation":[{"name":"School of Mathematical Science, XinJiang Normal University, Urumqi, 830054, P. R. China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Xiao Hui","family":"Zhou","sequence":"additional","affiliation":[{"name":"School of Mathematical Science, XinJiang Normal University, Urumqi, 830054, P. R. China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Yu","family":"Su","sequence":"additional","affiliation":[{"name":"School of Mathematical Science, XinJiang Normal University, Urumqi, 830054, P. R. China"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"219","published-online":{"date-parts":[[2015,3,9]]},"reference":[{"key":"rf1","doi-asserted-by":"publisher","DOI":"10.1142\/S0219691308002288"},{"key":"rf2","doi-asserted-by":"publisher","DOI":"10.1016\/j.acha.2009.10.002"},{"key":"rf3","doi-asserted-by":"publisher","DOI":"10.1016\/j.acha.2007.01.003"},{"key":"rf5","series-title":"Fachbereich Mathematik und Infomatikder","volume-title":"Interpolating Scaling Vectors and Multiwavelets in Rd","author":"Koch K.","year":"2006"},{"key":"rf7","doi-asserted-by":"publisher","DOI":"10.1016\/j.acha.2010.09.008"},{"key":"rf8","doi-asserted-by":"publisher","DOI":"10.1142\/S0218001411008865"},{"key":"rf9","doi-asserted-by":"publisher","DOI":"10.1142\/S021969131250035X"}],"container-title":["International Journal of Wavelets, Multiresolution and Information Processing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S0219691315500071","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,8,6]],"date-time":"2019-08-06T15:05:01Z","timestamp":1565103901000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/abs\/10.1142\/S0219691315500071"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2015,1]]},"references-count":7,"journal-issue":{"issue":"01","published-online":{"date-parts":[[2015,3,9]]},"published-print":{"date-parts":[[2015,1]]}},"alternative-id":["10.1142\/S0219691315500071"],"URL":"https:\/\/doi.org\/10.1142\/s0219691315500071","relation":{},"ISSN":["0219-6913","1793-690X"],"issn-type":[{"value":"0219-6913","type":"print"},{"value":"1793-690X","type":"electronic"}],"subject":[],"published":{"date-parts":[[2015,1]]}}}