Results 31 to 40 of about 609,367 (341)

Hyperquaternions and physics

SciPost Physics Proceedings, 2023
The paper develops, within a new representation of Clifford algebras in terms of tensor products of quaternions called hyperquaternions, several applications.
Patrick R. Girard, Romaric Pujol, Patrick Clarysse, Philippe Delachartre
doaj   +1 more source

Quaternion algebras and quaternion orders

, 2012
Montserrat Alsina, P. Bayer
openaire   +2 more sources

About Some Split Central Simple Algebras

Analele Stiintifice ale Universitatii Ovidius Constanta: Seria Matematica, 2014
In this paper we study certain quaternion algebras and symbol algebras which split.
Savin Diana
doaj   +1 more source

Contractions on ranks and quaternion types in clifford algebras

Vestnik Samarskogo Gosudarstvennogo Tehničeskogo Universiteta. Seriâ: Fiziko-Matematičeskie Nauki, 2015
In this paper we consider expressions in real and complex Clifford algebras, which we call contractions or averaging. We consider contractions of arbitrary Clifford algebra element.
Dmitry S Shirokov
doaj   +1 more source

On split quaternion equivalents for Quaternaccis, shortly Split Quaternaccis

Open Mathematics, 2021
In this paper, we introduce generalizations of Quaternacci sequences (Quaternaccis), called Split Quaternacci sequences, which arose on a base of split quaternion algebras.
Bajorska-Harapińska Beata, Ludew Jakub Jan, Smoleń-Duda Barbara, Wituła Roman   +3 more
doaj   +1 more source

Complex and Hypercomplex Discrete Fourier Transforms Based on Matrix Exponential Form of Euler's Formula [PDF]

, 2011
We show that the discrete complex, and numerous hypercomplex, Fourier transforms defined and used so far by a number of researchers can be unified into a single framework based on a matrix exponential version of Euler's formula $e^{j\theta}=\cos\theta+j ...
Ell, Todd A., Sangwine, Stephen J.
core   +2 more sources

The Breuil--Mezard conjecture for quaternion algebras [PDF]

, 2013
We formulate a version of the Breuil--Mezard conjecture for quaternion algebras, and show that it follows from the Breuil--Mezard conjecture for GL_2. In the course of the proof we establish a mod p analogue of the Jacquet--Langlands correspondence for ...
Toby Gee, D. Geraghty
semanticscholar   +1 more source

Superderivations and Jordan superderivations of generalized quaternion algebras [PDF]

Journal of Mahani Mathematical Research
Let $H_{\alpha,\beta}$ be the generalized quaternion algebra over a unitary commutative ring. This paper aims to consider superderivations and Jordan superderivations of $H_{\alpha,\beta}$ and hence to obtain the superalgebra $Der_{s} (H_{\alpha,\beta})$
Leila Heidari Zadeh
doaj   +1 more source

Counting zeros in quaternion algebras using Jacobi forms

Transactions of the American Mathematical Society, 2018
We use the theory of Jacobi forms to study the number of elements in a maximal order of a definite quaternion algebra over the field of rational numbers whose characteristic polynomial equals a given polynomial. A certain weighted average of such numbers
H. Boylan, N. Skoruppa, Haigang Zhou
semanticscholar   +1 more source

Asymptotic and Mittag–Leffler Synchronization of Fractional-Order Octonion-Valued Neural Networks with Neutral-Type and Mixed Delays

Fractal and Fractional, 2023
Very recently, a different generalization of real-valued neural networks (RVNNs) to multidimensional domains beside the complex-valued neural networks (CVNNs), quaternion-valued neural networks (QVNNs), and Clifford-valued neural networks (ClVNNs) has ...
Călin-Adrian Popa
doaj   +1 more source