Functional Calculus for Dual Quaternions

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2023-05-24 DOI:10.1007/s00006-023-01282-y

Stephen Montgomery-Smith

引用次数: 2

Abstract

We give a formula for \(f(\eta ),\) where \(f:{\mathbb {C}} \rightarrow {\mathbb {C}}\) is a continuously differentiable function satisfying \(f(\bar{z}) = \overline{f(z)},\) and \(\eta \) is a dual quaternion. Note this formula is straightforward or well known if \(\eta \) is merely a dual number or a quaternion. If one is willing to prove the result only when f is a polynomial, then the methods of this paper are elementary.

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对偶四元数的泛函微积分

我们给出了\（f（\eta），\）的一个公式，其中\（f:｛\mathbb｛C｝｝\rightarrow｛\math bb｛C｝）是一个连续可微函数，满足\（f｛z｝）=\overline｛f（z）｝，\），\（\eta\）是对偶四元数。注意，如果\（\eta\）只是一个对偶数或四元数，则该公式是直接的或众所周知的。如果仅当f是多项式时才愿意证明结果，则本文的方法是初等的。

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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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

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