Zeros of a one-parameter family of rational harmonic trinomials

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2024-10-29 DOI:10.1016/j.jmaa.2024.128997

Linkui Gao , Junyang Gao , Gang Liu

引用次数: 0

Abstract

The number of zeros of a one-parameter family of rational harmonic trinomials is studied. It is considered to be as an analogue work on that of corresponding harmonic trinomials investigated recently by Brilleslyper et al. and Brooks et al. Note that their proofs rely on the Argument Principle for Harmonic Functions and involve finding the winding numbers about the origin of a hypocycloid. Our proof is similar by means of Poincaré index and the geometry of epicycloid.

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有理谐波三项式一参数族的零点

本文研究了有理调和三项式一参数族的零点个数。我们认为这是 Brilleslyper 等人和 Brooks 等人最近研究的相应谐波三项式的类比工作。需要注意的是，他们的证明依赖于谐函数的论证原理，并涉及寻找关于下环面原点的绕数。我们的证明与此类似，都是通过波恩卡莱指数和外接环面几何来实现的。

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

Accounts of Chemical Research 化学-化学综合

CiteScore

31.40

自引率

1.10%

发文量

312

审稿时长

2 months

期刊介绍： Accounts of Chemical Research presents short, concise and critical articles offering easy-to-read overviews of basic research and applications in all areas of chemistry and biochemistry. These short reviews focus on research from the author’s own laboratory and are designed to teach the reader about a research project. In addition, Accounts of Chemical Research publishes commentaries that give an informed opinion on a current research problem. Special Issues online are devoted to a single topic of unusual activity and significance. Accounts of Chemical Research replaces the traditional article abstract with an article "Conspectus." These entries synopsize the research affording the reader a closer look at the content and significance of an article. Through this provision of a more detailed description of the article contents, the Conspectus enhances the article's discoverability by search engines and the exposure for the research.