有理谐波三项式一参数族的零点

IF 1.2 3区数学 Q1 MATHEMATICS Journal of Mathematical Analysis and Applications Pub Date : 2025-03-15 Epub Date: 2024-10-29 DOI:10.1016/j.jmaa.2024.128997

Linkui Gao , Junyang Gao , Gang Liu

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引用次数: 0

摘要

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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Zeros of a one-parameter family of rational harmonic trinomials

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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来源期刊

Journal of Mathematical Analysis and Applications 数学-数学

CiteScore

2.50

自引率

7.70%

发文量

790

审稿时长

6 months

期刊介绍： The Journal of Mathematical Analysis and Applications presents papers that treat mathematical analysis and its numerous applications. The journal emphasizes articles devoted to the mathematical treatment of questions arising in physics, chemistry, biology, and engineering, particularly those that stress analytical aspects and novel problems and their solutions. Papers are sought which employ one or more of the following areas of classical analysis: • Analytic number theory • Functional analysis and operator theory • Real and harmonic analysis • Complex analysis • Numerical analysis • Applied mathematics • Partial differential equations • Dynamical systems • Control and Optimization • Probability • Mathematical biology • Combinatorics • Mathematical physics.