具有一般复数系数的舒尔稳定三项式的稳定区域

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2023-12-16 DOI:10.1007/s10884-023-10331-w

Gerardo Barrera, Waldemar Barrera, Juan Pablo Navarrete

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引用次数: 0

摘要

在本文中，我们描述了形式为 \(f(\zeta ):=a\zeta ^n + b\zeta ^m +c\), \(\zeta \in \mathbb {C}\) 的三项式的稳定区域，其中 a、b 和 c 都是非零复数，并且 \(n,m\in \mathbb {N}\) 具有 \(n>m\)。更确切地说，我们提供了系数 a、b 和 c 的必要条件和充分条件，以使三项式 f 的所有根都属于复平面上的开放单位圆盘。证明基于 1908 年提出的波尔定理（Bohl in Math Ann 65(4):556-566, 1908）。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

The Stability Region for Schur Stable Trinomials with General Complex Coefficients

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The Stability Region for Schur Stable Trinomials with General Complex Coefficients

In this paper, we characterize the stability region for trinomials of the form \(f(\zeta ):=a\zeta ^n + b\zeta ^m +c\), \(\zeta \in \mathbb {C}\), where a, b and c are non-zero complex numbers and \(n,m\in \mathbb {N}\) with \(n>m\). More precisely, we provide necessary and sufficient conditions on the coefficients a, b and c in order that all the roots of the trinomial f belongs to the open unit disc in the complex plane. The proof is based on Bohl’s Theorem (Bohl in Math Ann 65(4):556–566, 1908) introduced in 1908.

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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.