分裂列奥纳多四元数的一种新的极表示和恒等式

IF 2.1 3区数学 Q1 MATHEMATICS, APPLIED

Mathematical Methods in the Applied Sciences Pub Date : 2025-02-20 DOI:10.1002/mma.10830

Ali Atasoy

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引用次数: 0

摘要

在本研究中，我们定义了包含列奥纳多数的分裂列奥纳多四元数序列。我们给出了与分裂列奥纳多四元数相关的基本性质和恒等式，如比奈公式，以及加泰罗尼亚、卡西尼和d'Ocagne的恒等式。此外，我们还引入了一个创新的概念：使用Cayley Dickson符号对这些分裂四元数进行极坐标表示。这种替代表示提供了分裂莱昂纳多四元数结构的新视角，并对其几何解释和转换有了更深入的理解。

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A New Polar Representation and Identities for Split Leonardo Quaternions

In this study, we define split Leonardo quaternion sequences with components involving Leonardo numbers. We give fundamental properties and identities associated with split Leonardo quaternions, such as Binet's formula, as well as identities attributed to Catalan, Cassini, and d'Ocagne. Furthermore, we introduce an innovative concept: polar representation for these split quaternions using Cayley Dickson's notation. This alternative representation provides a new perspective on the structure of split Leonardo quaternions and give a deeper understanding of their geometric interpretations and transformations.

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来源期刊

Mathematical Methods in the Applied Sciences 数学-应用数学

CiteScore

4.90

自引率

6.90%

发文量

798

审稿时长

6 months

期刊介绍： Mathematical Methods in the Applied Sciences publishes papers dealing with new mathematical methods for the consideration of linear and non-linear, direct and inverse problems for physical relevant processes over time- and space- varying media under certain initial, boundary, transition conditions etc. Papers dealing with biomathematical content, population dynamics and network problems are most welcome. Mathematical Methods in the Applied Sciences is an interdisciplinary journal: therefore, all manuscripts must be written to be accessible to a broad scientific but mathematically advanced audience. All papers must contain carefully written introduction and conclusion sections, which should include a clear exposition of the underlying scientific problem, a summary of the mathematical results and the tools used in deriving the results. Furthermore, the scientific importance of the manuscript and its conclusions should be made clear. Papers dealing with numerical processes or which contain only the application of well established methods will not be accepted. Because of the broad scope of the journal, authors should minimize the use of technical jargon from their subfield in order to increase the accessibility of their paper and appeal to a wider readership. If technical terms are necessary, authors should define them clearly so that the main ideas are understandable also to readers not working in the same subfield.