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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Existence of Split Property in Quaternion Algebra Over Composite of Quadratic Fields [PDF]
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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PERIOD IDENTITIES OF CM FORMS ON QUATERNION ALGEBRAS [PDF]
Forum of Mathematics, Sigma, 2020 Waldspurger’s formula gives an identity between the norm of a torus period and an $L$-function of the twist of an automorphic representation on GL(2).
CHARLOTTE CHAN
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Selectivity in Quaternion Algebras [PDF]
Journal of Number Theory, 2010 We prove an integral version of the classical Albert-Brauer-Hasse-Noether theorem regarding quaternion algebras over number fields. Let $\mathfrak A$ be a quaternion algebra over a number field $K$ and assume that $\mathfrak A$ satisfies the Eichler condition; that is, there exists an archimedean prime of $K$ which does not ramify in $\mathfrak A$. Let
Benjamin Linowitz
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Explicit isomorphisms of quaternion algebras over quadratic global fields [PDF]
Research in Number Theory, 2020 Let L be a separable quadratic extension of either Q\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength ...
Tímea Csahók +3 more
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About special elements in quaternion algebras over finite fields [PDF]
, 2016 In this paper we study special Fibonacci quaternions and special generalized Fibonacci-Lucas quaternions in quaternion algebras over finite fields.Comment: This is a preliminary form of the ...
Savin, Diana
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An algorithm for the principal ideal problem in indefinite quaternion algebras [PDF]
LMS J. Comput. Math., 2014 Deciding whether an ideal of a number field is principal and finding a generator is a fundamental problem with many applications in computational number theory.
Aurel Page
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Fascinating Number Sequences from Fourth Order Difference Equation Via Quaternion Algebras
Discussiones Mathematicae - General Algebra and Applications, 2021 The balancing and Lucas-balancing numbers are solutions of second order recurrence relations. A linear combination of these numbers can also be obtained as solutions of a fourth order recurrence relation.
Patra Asim
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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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Quaternion Algebras and Generalized Fibonacci–Lucas Quaternions [PDF]
Advances in Applied Clifford Algebras, 2015 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Flaut, Cristina, Savin, Diana
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