{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2022,3,30]],"date-time":"2022-03-30T03:53:05Z","timestamp":1648612385850},"reference-count":32,"publisher":"World Scientific Pub Co Pte Lt","issue":"06","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Wavelets Multiresolut Inf. Process."],"published-print":{"date-parts":[[2011,11]]},"abstract":"<jats:p> In this paper, a multifractal analysis of some non-self-similar functions based on the superposition of finite number of weighted quasi-self-similar ones \u2211<jats:sub>i<\/jats:sub>\u03c9<jats:sub>i<\/jats:sub>F<jats:sub>i<\/jats:sub> is developed. In general, such superpositions do not yield neither a self-similar nor a quasi-self-similar outcome. Furthermore, there are two main problems that appear. Firstly, a phenomenon of regularity compensation may exist. Secondly, the computation of the spectrum of singularities and therefore the validity of the multifractal formalism based on the possibility of constructing Gibbs measures fail. In this paper, we propose to study such problems by conducting a multifractal analysis of such combinations and to check the validity of the multifractal formalism in the case where there is no compensation of regularity. Furthermore, we compute the box dimension of the associated graphs and provide some examples. The paper in its full subject re-considers the results of Ref. 3 in the quasi-self-similar case. <\/jats:p>","DOI":"10.1142\/s0219691311004407","type":"journal-article","created":{"date-parts":[[2011,6,29]],"date-time":"2011-06-29T04:12:47Z","timestamp":1309320767000},"page":"965-987","source":"Crossref","is-referenced-by-count":2,"title":["MULTIFRACTAL ANALYSIS OF SOME WEIGHTED QUASI-SELF-SIMILAR FUNCTIONS"],"prefix":"10.1142","volume":"09","author":[{"given":"JAMIL","family":"AOUIDI","sequence":"first","affiliation":[{"name":"Department of Mathematics, Preparatory Institute for Military Academies, Avenue Marechal Tito, 4029 Sousse, Tunisia"},{"name":"Unit\u00e9 de Recherche Ondelettes et Fractales, D\u00e9partement de Math\u00e9matiques, Facult\u00e9 de Sciences, Monastir 5000, Tunisie"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"ANOUAR BEN","family":"MABROUK","sequence":"additional","affiliation":[{"name":"Computational Mathematical Laboratory, Department of Mathematics, Faculty of Sciences, 5000 Monastir, Tunisia"},{"name":"Department of Mathematics, Faculty of Sciences, Taibah University, Saudi Arab Kingdom"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"219","published-online":{"date-parts":[[2012,5,2]]},"reference":[{"key":"rf1","volume-title":"Th\u00e8se de Doctorat de la Facult\u00e9 des Sciences de Monastir","author":"Aouidi J.","year":"2002"},{"key":"rf2","doi-asserted-by":"publisher","DOI":"10.1023\/A:1015729908167"},{"key":"rf3","doi-asserted-by":"publisher","DOI":"10.1080\/10652460310001600645"},{"key":"rf4","first-page":"635","volume":"70","author":"Arneodo A.","journal-title":"J. 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