控制论的数论部分

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2022-01-01 DOI:10.1070/RM10050

Aleksandr Iosifovich Ovseevich

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引用次数: 0

摘要

Q的重要性主要是由于它为两个稳定矩阵M = - diag(1,2，…)定义了一个公共Lyapunov函数。， N)和A + BC，其中对于i = 1, Aei =−iei+1，…， N, B = e1，且C =−(1/2)B * Q。这里是ei, i = 1，…， N，构成R和eN+1 = 0的标准基。[6]中证明了Q是一个偶数矩阵，即Qij∈2Z，并推测了矩阵的所有元素都可以被N(N + 1)整除。[6]中的证明是基于考虑正交多项式的。这里我们用类似的方法证明了这个猜想。

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A number-theoretic part of control theory

The importance of Q is primarily due to the fact that it defines a common Lyapunov function for the two stable matrices M = −diag(1, 2, . . . , N) and A + BC, where Aei = −iei+1 for i = 1, . . . , N , B = e1, and C = −(1/2)B∗Q. Here the ei, i = 1, . . . , N , form the standard basis of R and eN+1 = 0. In [6] it was shown that Q is an even integer matrix, that is, Qij ∈ 2Z, and it was conjectured that all elements of the matrix are divisible by N(N + 1). The proofs in [6] were based on considering orthogonal polynomials. Here we prove this conjecture using similar methods.

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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.