涉及单位和的正数倒数之和与积的不等式的最佳常数

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2024-03-01 DOI:10.1186/s13660-024-03107-3

Yagub N. Aliyev

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引用次数: 0

摘要

本文研究了一个特殊的代数不等式，该不等式包含一个参数、倒数之和以及和为 1 的正实数的乘积，并利用新的优化论证确定了参数的最佳值。在三个数的情况下，这个代数不等式有一些有趣的几何应用，涉及欧拉不等式关于三角形外接圆和内接圆半径之比的推广。

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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The best constant for inequality involving the sum of the reciprocals and product of positive numbers with unit sum

In this paper, we study a special algebraic inequality containing a parameter, the sum of reciprocals and the product of positive real numbers whose sum is 1. Using a new optimization argument the best values of the parameter are determined. In the case of three numbers the algebraic inequality has some interesting geometric applications involving a generalization of Euler’s inequality about the ratio of radii of circumscribed and inscribed circles of a triangle.

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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.