Results 31 to 40 of about 19,319 (303)
IEEE Access, 2022 We propose a novel neural network architecture based on dual quaternions which allow for a compact representation of information with a main focus on describing rigid body movements.
Johannes Poppelbaum, Andreas Schwung
doaj +1 more source
Quaternion group algebra and representations of the quaternions [PDF]
Communications in Algebra, 2019 AbstractIn this paper, we provide a concrete and explicit decomposition of the quaternion group algebra through a suitable basis of the algebra.
openaire +2 more sources
Hopf algebra structures on generalized quaternion algebras
Electronic Research ArchiveIn this paper, we use elementary linear algebra methods to explore possible Hopf algebra structures within the generalized quaternion algebra. The sufficient and necessary conditions that make the generalized quaternion algebra a Hopf algebra are given ...
Quanguo Chen , Yong Deng
doaj +1 more source
Partial Differential Equations in Applied Mathematics, 2023 This paper is devoted to the study of the quaternion Laplace transform, which is a natural generalization of the classical Laplace transform using the quaternion algebra. We find that some of its properties such as derivative, convolution and correlation
Muhammad Afdal Bau +4 more
doaj
Cauchy matrix and Liouville formula of quaternion impulsive dynamic equations on time scales
Open Mathematics, 2020 In this study, we obtain the scalar and matrix exponential functions through a series of quaternion-valued functions on time scales. A sufficient and necessary condition is established to guarantee that the induced matrix is real-valued for the complex ...
Li Zhien, Wang Chao
doaj +1 more source
Selectivity in quaternion algebras
Journal of Number Theory, 2012 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
openaire +3 more sources
Quaternions and the Algebra of Vectors [PDF]
Nature, 1893 IN a recent number of this Journal (p. 151) Mr. McAulay puts certain questions to Mr. Heaviside and to me, relating to a subject of such importance as to justify an answer somewhat at length. I cannot of course speak for Mr. Heaviside, although I suppose that his views are not very different from mine on the most essential points, but even if he shall ...
openaire +2 more sources
On generalized quaternion algebras [PDF]
International Journal of Mathematics and Mathematical Sciences, 1979 Let B be a commutative ring with 1, and G( = {σ}) an automorphism group of B of order 2. The generalized quaternion ring extension B[j] over B is defined by S. Parimala and R. Sridharan such that (1) B[j] is a free B‐module with a basis {1, j}, and (2) j2 = −1 and jb = σ(b)j for each b in B. The purpose of this paper is to study the separability of B[j]
openaire +2 more sources
A Clifford algebra associated to generalized Fibonacci quaternions
, 2014 In this paper we find a Clifford algebra associated to generalized Fibonacci quaternions. In this way, we provide a nice algorithm to obtain a division quaternion algebra starting from a quaternion non-division algebra and vice ...
Flaut, Cristina
core +1 more source
Quad-Quaternion MUSIC for DOA Estimation Using Electromagnetic Vector Sensors
EURASIP Journal on Advances in Signal Processing, 2008 A new quad-quaternion model is herein established for an electromagnetic vector-sensor array, under which a multidimensional algebra-based direction-of-arrival (DOA) estimation algorithm, termed as quad-quaternion MUSIC (QQ-MUSIC), is proposed.
Xiaofeng Gong, Zhiwen Liu, Yougen Xu
doaj +1 more source