Results 41 to 50 of about 653,122 (340)
Enabling quaternion derivatives: the generalized HR calculus [PDF]
Royal Society Open Science, 2015 Quaternion derivatives exist only for a very restricted class of analytic (regular) functions; however, in many applications, functions of interest are real-valued and hence not analytic, a typical case being the standard real mean square error objective
Dongpo Xu +3 more
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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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Cauchy matrix and Liouville formula of quaternion impulsive dynamic equations on time scales
Open Mathematics, 2020 In this study, we obtain the scalar and matrix exponential functions through a series of quaternion-valued functions on time scales. A sufficient and necessary condition is established to guarantee that the induced matrix is real-valued for the complex ...
Li Zhien, Wang Chao
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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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Dual Quaternions for the Kinematic Description of a Fish–Like Propulsion System
International Journal of Applied Mathematics and Computer Science, 2023 This study discusses the use of quaternions and dual quaternions in the description of artificial fish kinematics. The investigation offered here illustrates quaternion and dual quaternion algebra, as well as its implementation in the software chosen ...
Kitowski Zygmunt +2 more
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Free integro-differential algebras and Groebner-Shirshov bases [PDF]
, 2014 The notion of commutative integro-differential algebra was introduced for the algebraic study of boundary problems for linear ordinary differential equations. Its noncommutative analog achieves a similar purpose for linear systems of such equations.
Guo, Li +5 more
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Bounds on the levels of composition algebras
, 2010 Certain families of quaternion and octonion algebras are conjectured to be of level and sublevel n. A proof of this conjecture is offered in the case where n is a power of two. Hoffmann's proof of the existence of infinitely many new values for the level
James O'Shea +2 more
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Minimal rings related to generalized quaternion rings [PDF]
, 2023 The family of rings of the form Z4 〈x, y〉〈x2 − a, y2 − b, yx − xy − 2(c + dx + ey + f xy)〉 is investigated which contains the generalized Hamilton quaternions over Z4. These rings are local rings of order 256.
Jose Maria GRAU +8 more
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Color Edge Detection Hardware based on Geometric Algebra.
, 2006 Modern techniques treat color images as separate monochrome images for processing. Partly, because there is no straightforward generalization of linear filters available for color.
B. Mishra +5 more
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Levels and sublevels of composition algebras
, 2007 Lewis' and Leep's bounds on the level and sublevel of quaternion algebras are extended to the class of composition algebras. Some simple constructions of composition algebras of known level values are given.
O'Shea, James
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