Results 31 to 40 of about 18,831 (324)
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
Linear Algebra and its Applications, 1984 Let k be a field of characteristic not equal to 2, and let L be a finite field extension of k. Then a Lie algebra G is quaternionic if there is a quaternion division algebra Q over L such that G is isomorphic to the k- Lie-algebra \(Q^-/L1\). The main theorem of the paper gives equivalent conditions for a finite-dimensional Lie algebra over a perfect ...
openaire +2 more sources
Dual Quaternions for the Kinematic Description of a Fish–Like Propulsion System
International Journal of Applied Mathematics and Computer Science, 2023 This study discusses the use of quaternions and dual quaternions in the description of artificial fish kinematics. The investigation offered here illustrates quaternion and dual quaternion algebra, as well as its implementation in the software chosen ...
Kitowski Zygmunt +2 more
doaj +1 more source
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
, 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.
openaire +3 more sources
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
Convolution Theorems for Quaternion Fourier Transform: Properties and Applications
Abstract and Applied Analysis, 2013 General convolution theorems for two-dimensional quaternion Fourier transforms (QFTs) are presented. It is shown that these theorems are valid not only for real-valued functions but also for quaternion-valued functions. We describe some useful properties
Mawardi Bahri +2 more
doaj +1 more source
Quaternion based generalization of Chern–Simons theories in arbitrary dimensions
Physics Letters B, 2017 A generalization of Chern–Simons gauge theory is formulated in any dimension and arbitrary gauge group where gauge fields and gauge parameters are differential forms of any degree.
Alessandro D'Adda +3 more
doaj +1 more source
IEEE Access, 2021 For scenarios of coherent underwater sources at low signal-to-noise ratio (SNR), a novel quaternion-based DOA algorithm without eigendecomposition is proposed using a linear vector-hydrophone array.
Yi Lou +3 more
doaj +1 more source
Weighted Convolution for Quaternion Linear Canonical Cosine Transform and Its Application
AxiomsConvolution plays a pivotal role in the domains of signal processing and optics. This paper primarily focuses on studying the weighted convolution for quaternion linear canonical cosine transform (QLCcT) and its application in multiplicative filter ...
Rongbo Wang, Qiang Feng
doaj +1 more source