Results 71 to 80 of about 245,475 (190)
, 1989 The authors define and study the arithmetic of special orders in quaternion division algebras over number fields. Special orders are analogous to orders of the form \(\left( \begin{matrix} Z\\ NZ\end{matrix} \begin{matrix} Z\\ Z\end{matrix} \right)\) in \(Mat(2,{\mathbb{Q}}_ p)\) and include maximal and Eichler orders as special cases.
Hijikata, H., Pizer, A., Shemanske, T.
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In this paper, we derive some practical necessary and sufficient conditions for the existence of a solution to a new system of coupled two-sided Sylvester-like matrix equations with arbitrary number of equations and unknowns over the quaternion algebra ...
He, Zhuo Heng, +4 more
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Curvilinear Integral Theorem for G-Monogenic Mappings in the Algebra of Complex Quaternion [PDF]
, 2016 For G-monogenic mappings taking values in the algebra of complex quaternion we prove a curvilinear analogue of the Cauchy integral theorem in the case where a curve of integration lies on the boundary of a domain of G ...
Kuzmenko T. S.
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On free ring extensions of degree n
International Journal of Mathematics and Mathematical Sciences, 1981 Nagahara and Kishimoto [1] studied free ring extensions B(x) of degree n for some integer n over a ring B with 1, where xn=b, cx=xρ(c) for all c and some b in B(ρ=automophism of B), and {1,x…,xn−1} is a basis.
George Szeto
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Research on splitting quaternions with generalized Tribonacci hybrid number components [PDF]
Notes on Number Theory and Discrete MathematicsThis paper introduces the Generalized Tribonacci Hybrid Split Quaternion (GTHSQ), a novel split quaternion with coefficients derived from generalized Tribonacci hybrid numbers.
Yanni Yang, Yong Deng
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Free Subgroups of Quaternion Algebras [PDF]
Proceedings of the American Mathematical Society, 1993 Using the theory of group actions on trees, we shall prove that if a quaternion algebra over Laurant polynomials is not split then a certain congruence subgroup of the group of norm one elements is a free group. This generalizes and gives an easy, conceptually simpler proof than that given by Pollen for the field of real numbers.
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ComputersIn this paper, we describe the associative and commutative algebra or the (2,2)-model of quaternions with application in color image enhancement. The method of alpha-rooting, which is based on the 2D quaternion discrete Fourier transform (QDFT) is ...
Artyom M. Grigoryan, Alexis A. Gomez
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Linked triples of quaternion algebras [PDF]
Pacific Journal of Mathematics, 2014 Let \(F\) be a field of characteristic not \(2\). A collection \(Q_1,\ldots,Q_n\) (\(n\geq 2\)) of quaternion algebras over \(F\) is said to have a common slot if there exist \(a,b_i\in F^*\) with \(Q_i\cong (a,b_i)\), \(1\leq i\leq n\). This collection is said to be linked if any pair \(Q_i,Q_j\) has a common slot. \textit{E. Peyre} [Proc. Symp.
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CORRELATION THEOREMS FOR TYPE II QUATERNION FOURIER TRANSFORM
, 2013 We present the correlation within the framework of the quaternion algebra. We establish the correlation theorem for type II quaternion Fourier transform (QFT) and obtain some important properties of the relationship between the quaternion correlation and
Ryuichi Ashino +3 more
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Nonlinear AnalysisThis paper investigates the stochastic stability problem of fractional-order quaternion-valued neural networks (FOQVNNs) on time scales with general probabilistic bounded Markovian switching and neutral delays.
Cheng Huang, Qiankun Song
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