Results 21 to 30 of about 609,367 (341)
Quaternion-based machine learning on topological quantum systems
Machine Learning: Science and Technology, 2023 Topological phase classifications have been intensively studied via machine-learning techniques where different forms of the training data are proposed in order to maximize the information extracted from the systems of interests. Due to the complexity in
Min-Ruei Lin, Wan-Ju Li, Shin-Ming Huang
doaj +1 more source
Some properties of orders of quaternion algebras with regard to the discrete norm [PDF]
Mathematica Bohemica, 2016 Quaternion algebras $(\frac{-1,b}{\mathbb{Q}})$ are investigated and isomorphisms between them are described. Furthermore, the orders of these algebras are presented and the uniqueness of the discrete norm for such orders is proved.
Jan Horníček +2 more
doaj +1 more source
Mathematics, 2022 Due to the computational aspects which appear in the study of algebras obtained by the Cayley–Dickson process, it is difficult to obtain nice properties for these algebras. For this reason, finding some identities in such algebras plays an important role
Cristina Flaut, Geanina Zaharia
doaj +1 more source
Some modern developments in the theory of real division algebras; pp. 53–59 [PDF]
Proceedings of the Estonian Academy of Sciences, 2010 The study of real division algebras was initiated by the construction of the quaternion and the octonion algebras in the mid-19th century. In spite of its long history, the problem of classifying all finite-dimensional real division algebras is still ...
Erik Darpö
doaj +1 more source
Exponential and logarithm of multivector in low-dimensional (n = p + q < 3) Clifford algebras
Nonlinear Analysis, 2022 The aim of the paper is to give a uniform picture of complex, hyperbolic, and quaternion algebras from a perspective of the applied Clifford geometric algebra.
Adolfas Dargys, Artūras Acus
doaj +1 more source
Unit groups of maximal orders in totally definite quaternion algebras over real quadratic fields [PDF]
Transactions of the American Mathematical Society, 2018 We study a form of refined class number formula (resp. type number formula) for maximal orders in totally definite quaternion algebras over real quadratic fields, by taking into consideration the automorphism groups of right ideal classes (resp.
Qun Li, Jiangwei Xue, Chia-Fu Yu
semanticscholar +1 more source
On numerical/non-numerical algebra: Semi-tensor product method
Mathematical Modelling and Control, 2021 A kind of algebra, called numerical algebra, is proposed and investigated. As its opponent, non-numerical algebra is also defined. The numeralization and dis-numeralization, which convert non-numerical algebra to numerical algebra and vise versa, are ...
Daizhan Cheng +3 more
doaj +1 more source
Proper ARMA Modeling and Forecasting in the Generalized Segre’s Quaternions Domain
Mathematics, 2022 The analysis of time series in 4D commutative hypercomplex algebras is introduced. Firstly, generalized Segre’s quaternion (GSQ) random variables and signals are studied.
Jesús Navarro-Moreno +2 more
doaj +1 more source
On quaternionic functional analysis [PDF]
, 2006 In this article, we will show that the category of quaternion vector spaces, the category of (both one-sided and two sided) quaternion Hilbert spaces and the category of quaternion $B^*$-algebras are equivalent to the category of real vector spaces, the ...
Agrawal +17 more
core +2 more sources
Shorter quantum circuits via single-qubit gate approximation [PDF]
Quantum, 2023 We give a novel procedure for approximating general single-qubit unitaries from a finite universal gate set by reducing the problem to a novel magnitude approximation problem, achieving an immediate improvement in sequence length by a factor of 7/9 ...
Vadym Kliuchnikov +4 more
doaj +1 more source