On a Generalized Superellipse: From Models to Applications

IF 2.1 3区数学 Q1 MATHEMATICS, APPLIED

Mathematical Methods in the Applied Sciences Pub Date : 2025-02-14 DOI:10.1002/mma.10795

Ivana Kovacic

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.

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广义超椭圆：从模型到应用

本文研究了一个幂型泛函方程及其在直角坐标系和极坐标下的各种形式。本文概述了相关贡献，并根据它们可以产生的形状进行了说明，从而通过展示在非线性科学的不同领域中相同的数学模型的应用，建立了跨学科的现象学联系，标志着在这种情况下的一种新方法。最后，从函数方程和哈密顿函数两方面阐述了该方程的解析解。并给出了用三角函数或广义三角函数表示的原始解。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Mathematical Methods in the Applied Sciences 数学-应用数学

CiteScore

4.90

自引率

6.90%

发文量

798

审稿时长

6 months

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.