Results 11 to 20 of about 12,646 (309)
Quaternion CR-submanifolds of a quaternion Kaehler manifold [PDF]
International Journal of Mathematics and Mathematical Sciences, 2001 We study the quaternion CR-submanifolds of a quaternion Kaehler manifold. More specifically we study the properties of the canonical structures and the geometry of the canonical foliations by using the Bott connection and the index of a quaternion CR ...
Bassil J. Papantoniou, M. Hasan Shahid
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CoRR, 2022 Quaternion valued neural networks experienced rising popularity and interest from researchers in the last years, whereby the derivatives with respect to quaternions needed for optimization are calculated as the sum of the partial derivatives with respect to the real and imaginary parts.
Johannes Pöppelbaum, Andreas Schwung
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Quaternion Matrix Factorization for Low-Rank Quaternion Matrix Completion
Mathematics, 2023 The main aim of this paper is to study quaternion matrix factorization for low-rank quaternion matrix completion and its applications in color image processing.
Jiang-Feng Chen +3 more
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Quaternion Statistical Submanifolds and Submersions
MathematicsThis paper aims to develop a general theory of quaternion Kahlerian statistical manifolds and to study quaternion CR-statistical submanifolds in such ambient manifolds.
Aliya Naaz Siddiqui, Fatimah Alghamdi
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Visualizing Quaternion Multiplication [PDF]
IEEE Access, 2017 Quaternion rotation is a powerful tool for rotating vectors in 3-D; as a result, it has been used in various engineering fields, such as navigations, robotics, and computer graphics. However, understanding it geometrically remains challenging, because it
Jongchan Baek +3 more
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Dual quaternions and dual quaternionic curves [PDF]
Filomat, 2019 After a brief review of the different types of quaternions, we develop a new perspective for dual quaternions with dividing two parts. Due to this new perspective, we will define the isotropic and nonisotropic dual quaternions. Then we will also give the basic algebraic concepts about the dual quaternions. Moreover, we define isotropic dual
Dagdeviren, Ali, Yuce, Salim
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A quaternionic Nullstellensatz [PDF]
Journal of Pure and Applied Algebra, 2021 We prove a Nullstellensatz for the ring of polynomial functions in n non-commuting variables over Hamilton's ring of real quaternions. We also characterize the generalized polynomial identities in n variables which hold over the quaternions, and more generally, over any division algebra.
Alon, Gil, Paran, Elad
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Quaternions: A Mathematica Package for Quaternionic Analysis [PDF]
, 2011 This paper describes new issues of theMathematica standard package Quaternions for implementing Hamilton's Quaternion Algebra. This work attempts to endow the original package with the ability to perform operations on symbolic expressions involving quaternion-valued functions.
M. Irene Falcão, Fernando Miranda
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, 2023 Based on the framework of differential inclusion, we design a quaternion-valued neural network (QVNN) to solve a class of nonsmooth nonconvex optimization problems with equality, bounded and inequality constraints in quaternion domain.
Liu, J, Liao, X, Dong, JS
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On Pell Quaternions and Pell-Lucas Quaternions
Advances in Applied Clifford Algebras, 2015 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Cimen, Cennet Bolat, Ipek, Ahmet
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