Results 31 to 40 of about 56,344 (329)
Applied Mathematics Letters, 2003 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
S. DE LEO, ROTELLI, Pietro
openaire +3 more sources
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
doaj +1 more source
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
core +4 more sources
On balancing quaternions and Lucas-balancing quaternions
Discussiones Mathematicae - General Algebra and Applications, 2021 In this paper we define and study balancing quaternions and Lucas-balancing quaternions. We give the generating functions, matrix generators and Binet formulas for these numbers. Moreover, the well-known properties e.g. Catalan, d’ Ocagne identities have been obtained for these quaternions.
openaire +2 more sources
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
doaj +1 more source
Quaternions and matrices of quaternions
Linear Algebra and its Applications, 1997 The author gives a useful survey on quaternions and matrices of quaternions. He recalls standard facts going back to Rowan Hamilton as well as new results motivated by applications in physical theories. The main research problem presented in the paper is to extend the classical matrix theory from complex to the quaternion matrices.
openaire +4 more sources
Quaternion Hankel Transform and its Generalization [PDF]
Sahand Communications in Mathematical AnalysisIn this study, the quaternion Hankel transform is developed. Basic operational properties and inversion formula of quaternion Hankel transform are derived. Parseval’s relation for this transform is also established.
Khinal Parmar, V. R. Lakshmi Gorty
doaj +1 more source
Partial Differential Equations in Applied Mathematics, 2023 This paper is devoted to the study of the quaternion Laplace transform, which is a natural generalization of the classical Laplace transform using the quaternion algebra. We find that some of its properties such as derivative, convolution and correlation
Muhammad Afdal Bau +4 more
doaj +1 more source
Some Equivalence Relations and Results over the Commutative Quaternions and Their Matrices
Analele Stiintifice ale Universitatii Ovidius Constanta: Seria Matematica, 2017 In this paper, we give some equivalence relations and results over the commutative quaternions and their matrices. In this sense, consimilarity, semisimilarity, and consemisimilarity over the commutative quaternion algebra and commutative quaternion ...
Kosal Hidayet Huda, Tosun Murat
doaj +1 more source
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
doaj +1 more source