Results 1 to 10 of about 172 (148)
Smoothing method for unit quaternion time series in a classification problem: an application to motion data [PDF]
Scientific Reports, 2023 Smoothing orientation data is a fundamental task in different fields of research. Different methods of smoothing time series in quaternion algebras have been described in the literature, but their application is still an open point. This paper develops a
Elena Ballante +4 more
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Graduate Texts in Mathematics, 2021 This open access textbook presents a comprehensive treatment of the arithmetic theory of quaternion algebras and orders, a subject with applications in diverse areas of mathematics. Written to be accessible and approachable to the graduate student reader, this text collects and synthesizes results from across the literature.
John Voight
exaly +4 more sources
Hypercomplex neural networks: Exploring quaternion, octonion, and beyond in deep learning [PDF]
MethodsXHypercomplex Neural Networks (HNNs) represent the next frontier in deep learning, building on the mathematical theory of quaternions, octonions, and higher-dimensional algebras to generalize conventional neural architectures.
Raghavendra M Devadas +5 more
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Existence of Split Property in Quaternion Algebra Over Composite of Quadratic Fields
Cauchy: Jurnal Matematika Murni dan Aplikasi, 2023 Quaternions are extensions of complex numbers that are four-dimensional objects. Quaternion consists of one real number and three complex numbers, commonly denoted by the standard vectors and .
Muhammad Faldiyan +2 more
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Quaternion-based machine learning on topological quantum systems
Machine Learning: Science and Technology, 2023 Topological phase classifications have been intensively studied via machine-learning techniques where different forms of the training data are proposed in order to maximize the information extracted from the systems of interests. Due to the complexity in
Min-Ruei Lin, Wan-Ju Li, Shin-Ming Huang
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Some properties of orders of quaternion algebras with regard to the discrete norm [PDF]
Mathematica Bohemica, 2016 Quaternion algebras $(\frac{-1,b}{\mathbb{Q}})$ are investigated and isomorphisms between them are described. Furthermore, the orders of these algebras are presented and the uniqueness of the discrete norm for such orders is proved.
Jan Horníček +2 more
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Some modern developments in the theory of real division algebras; pp. 53–59 [PDF]
Proceedings of the Estonian Academy of Sciences, 2010 The study of real division algebras was initiated by the construction of the quaternion and the octonion algebras in the mid-19th century. In spite of its long history, the problem of classifying all finite-dimensional real division algebras is still ...
Erik Darpö
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Mathematics, 2022 Due to the computational aspects which appear in the study of algebras obtained by the Cayley–Dickson process, it is difficult to obtain nice properties for these algebras. For this reason, finding some identities in such algebras plays an important role
Cristina Flaut, Geanina Zaharia
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Exponential and logarithm of multivector in low-dimensional (n = p + q < 3) Clifford algebras
Nonlinear Analysis, 2022 The aim of the paper is to give a uniform picture of complex, hyperbolic, and quaternion algebras from a perspective of the applied Clifford geometric algebra.
Adolfas Dargys, Artūras Acus
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Wiener Algebra for the Quaternions [PDF]
Mediterranean Journal of Mathematics, 2015 We define and study the counterpart of the Wiener algebra in the quaternionic setting, both for the discrete and continuous case. We prove a Wiener-Lévy type theorem and a factorization theorem. We give applications to Toeplitz and Wiener-Hopf operators.
Alpay, Daniel +3 more
openaire +3 more sources