Results 21 to 30 of about 57,815 (333)
Machines, 2022 This study derives a learning algorithm for a quaternion neural network using the steepest descent method extended to quaternion numbers. This applies the generalised Hamiltonian–Real calculus to obtain derivatives of a real–valued cost function ...
Kazuhiko Takahashi +2 more
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Quaternion-Type Catalan Transforms of the ρ-Fibonacci and ρ-Lucas Numbers
Journal of Mathematics, 2023 In this paper, we define a new sequence called the quaternion-type Catalan sequence and give generating function, exponential representation, quaternionic Catalan matrix and its some properties.
Kübra Gül
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Quaternion lattices and quaternion fields
Archiv der Mathematik, 2023 AbstractLet $$Q_8$$ Q 8 be the quaternion group of order 8 and $${\chi }$$ χ its faithful irreducible character. Then $${\chi }$$ χ can be realized over certain imaginary quadratic number ...
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IEEE Access, 2022 We propose a novel neural network architecture based on dual quaternions which allow for a compact representation of information with a main focus on describing rigid body movements.
Johannes Poppelbaum, Andreas Schwung
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Eigenvalues of the basic Dirac operator on quaternion-Kahler foliations [PDF]
, 2006 In this paper, we give an optimal lower bound for the eigenvalues of the basic Dirac operator on a quaternion-Kahler foliation. The limiting case is characterized by the existence of quaternion-Kahler Killing spinors.
Habib, Georges
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Quaternion Approach to the Measurement of the Local Birefringence Distribution in Optical Fibers
IEEE Photonics Journal, 2015 A method to structure the Jones quaternion utilizing Pauli matrices is proposed, improving the quaternion theory of polarization optics. It is proved that the Stokes quaternion is the double product of the Jones quaternion and its Hermitian transpose and
Lanlan Liu +4 more
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Quaternion Hermitian Planes [PDF]
Results in Mathematics, 1993 The quaternion hermitian planes are defined, and are characterized by certain groups of automorphisms. For this purpose, characterizations of locally compact connected translation planes (in the context of stable planes) and compact connected projective desarguesian planes are given.
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Rotacija z enotskim kvaternionom ( = Rotation with unit quaternion) [PDF]
Geodetski Vestnik, 2014 A quaternion is a hyper-complex number. A rule for quaternion multiplications allows us to use it as a rotation in three-dimensional space. The aim of this article is to present quaternion rotations to the Slovene professional geodetic public ...
Klemen Kregar +2 more
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Quaternionic wave function [PDF]
International Journal of Modern Physics A, 2019 We argue that quaternions form a natural language for the description of quantum-mechanical wave functions with spin. We use the quaternionic spinor formalism which is in one-to-one correspondence with the usual spinor language. No unphysical degrees of freedom are admitted, in contrast to the majority of literature on quaternions.
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Quaternion Algebras and Generalized Fibonacci–Lucas Quaternions [PDF]
Advances in Applied Clifford Algebras, 2015 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Flaut, Cristina, Savin, Diana
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