Difference Equations and Julia Sets of Several Functions for Degenerate q-Sigmoid Polynomials

IF 3.6 2区数学 Q1 MATHEMATICS, INTERDISCIPLINARY APPLICATIONS

Fractal and Fractional Pub Date : 2023-10-30 DOI:10.3390/fractalfract7110791

Jung-Yoog Kang, Cheon-Seoung Ryoo

引用次数: 0

Abstract

In this article, we construct a new type of degenerate q-sigmoid (DQS) polynomial for sigmoid functions containing quantum numbers and find several difference equations related to it. We check how each point moves by iteratively synthesizing a quartic degenerate q-sigmoid (DQS) polynomial that appears differently depending on q in the space of a complex structure. We also construct Julia sets associated with quartic DQS polynomials and find their features. Based on this, we make some conjectures.

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退化q-Sigmoid多项式的差分方程和若干函数的Julia集

本文构造了含有量子数的sigmoid函数的一类新的退化q-sigmoid (DQS)多项式，并得到了与之相关的几个差分方程。我们通过迭代合成一个四次退化q-sigmoid (DQS)多项式来检查每个点如何移动，该多项式在复杂结构的空间中随q的不同而不同。我们还构造了与四次DQS多项式相关的Julia集，并找到了它们的特征。在此基础上，我们做了一些推测。

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

Fractal and Fractional MATHEMATICS, INTERDISCIPLINARY APPLICATIONS-

CiteScore

4.60

自引率

18.50%

发文量

632

审稿时长

11 weeks

期刊介绍： Fractal and Fractional is an international, scientific, peer-reviewed, open access journal that focuses on the study of fractals and fractional calculus, as well as their applications across various fields of science and engineering. It is published monthly online by MDPI and offers a cutting-edge platform for research papers, reviews, and short notes in this specialized area. The journal, identified by ISSN 2504-3110, encourages scientists to submit their experimental and theoretical findings in great detail, with no limits on the length of manuscripts to ensure reproducibility. A key objective is to facilitate the publication of detailed research, including experimental procedures and calculations. "Fractal and Fractional" also stands out for its unique offerings: it warmly welcomes manuscripts related to research proposals and innovative ideas, and allows for the deposition of electronic files containing detailed calculations and experimental protocols as supplementary material.