关于多项式和指数和的实根的期望个数

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2023-06-01 DOI:10.1016/j.jco.2022.101720

Gregorio Malajovich

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引用次数: 3

摘要

已知正交不变随机齐次实数多项式系统的实数投影根的期望值等于bsamzout数的平方根。一个类似的结果是已知的随机多齐次系统，通过正交群的乘积不变。在这篇笔记中，这些结果被推广到某些稀疏多项式系统族，不假设正交不变性。

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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On the expected number of real roots of polynomials and exponential sums

The expected number of real projective roots of orthogonally invariant random homogeneous real polynomial systems is known to be equal to the square root of the Bézout number. A similar result is known for random multi-homogeneous systems, invariant through a product of orthogonal groups. In this note, those results are generalized to certain families of sparse polynomial systems, with no orthogonal invariance assumed.

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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.