{"title":"On a Generalized Superellipse: From Models to Applications","authors":"Ivana Kovacic","doi":"10.1002/mma.10795","DOIUrl":null,"url":null,"abstract":"<div>\n \n <p>This study is concerned with a power-form functional equation and its various forms in Cartesian and polar coordinates. An overview of the related contributions is presented and illustrated in terms of the shapes that they can yield, thereby establishing cross-disciplinary phenomenological links by demonstrating the application of identical mathematical models across diverse fields within nonlinear science, marking a novel approach in this context. Finally, an analytical solution of this equation is elaborated both with respect to its form as a functional equation and as a Hamiltonian function. The original solutions in terms of trigonometric or generalized trigonometric functions are presented as well.</p>\n </div>","PeriodicalId":49865,"journal":{"name":"Mathematical Methods in the Applied Sciences","volume":"48 8","pages":"9344-9349"},"PeriodicalIF":1.8000,"publicationDate":"2025-02-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Mathematical Methods in the Applied Sciences","FirstCategoryId":"100","ListUrlMain":"https://onlinelibrary.wiley.com/doi/10.1002/mma.10795","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}
引用次数: 0
Abstract
This study is concerned with a power-form functional equation and its various forms in Cartesian and polar coordinates. An overview of the related contributions is presented and illustrated in terms of the shapes that they can yield, thereby establishing cross-disciplinary phenomenological links by demonstrating the application of identical mathematical models across diverse fields within nonlinear science, marking a novel approach in this context. Finally, an analytical solution of this equation is elaborated both with respect to its form as a functional equation and as a Hamiltonian function. The original solutions in terms of trigonometric or generalized trigonometric functions are presented as well.
期刊介绍：
Mathematical Methods in the Applied Sciences publishes papers dealing with new mathematical methods for the consideration of linear and non-linear, direct and inverse problems for physical relevant processes over time- and space- varying media under certain initial, boundary, transition conditions etc. Papers dealing with biomathematical content, population dynamics and network problems are most welcome.
Mathematical Methods in the Applied Sciences is an interdisciplinary journal: therefore, all manuscripts must be written to be accessible to a broad scientific but mathematically advanced audience. All papers must contain carefully written introduction and conclusion sections, which should include a clear exposition of the underlying scientific problem, a summary of the mathematical results and the tools used in deriving the results. Furthermore, the scientific importance of the manuscript and its conclusions should be made clear. Papers dealing with numerical processes or which contain only the application of well established methods will not be accepted.
Because of the broad scope of the journal, authors should minimize the use of technical jargon from their subfield in order to increase the accessibility of their paper and appeal to a wider readership. If technical terms are necessary, authors should define them clearly so that the main ideas are understandable also to readers not working in the same subfield.
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