Related papers: Quaternions in molecular modeling
The Quaternion Fourier transform (QFT) is one of the key tools in studying color image processing. Indeed, a deep understanding of the QFT has created the color images to be transformed as whole, rather than as color separated component. In…
We study matrix forms of quaternionic versions of the Fourier Transform and Convolution operations. Quaternions offer a powerful representation unit, however they are related to difficulties in their use that stem foremost from…
Dual quaternions have gained significant attention due to their wide applications in areas such as multi-agent formation control, 3D motion modeling, and robotics. A fundamental aspect in dual quaternion research involves the projection…
The article is devoted to affine and wrap algebras over quaternions and octonions. Residues of functions of quaternion and octonion variables are studied. They are used for construction of such algebras. Their structure is investigated.
This dissertation is about The history of quaternions and their associated rotation groups as it relates to theoretical physics.
The paper explains how a unit generalized quaternion is used to represent a rotation of a vector in 3-dimensional space. We review of some algebraic properties of generalized quaternions and operations between them and then show their…
Over the last decades quaternions have become a crucial and very successful tool for attitude representation in robotics and aerospace. However, there is a major problem that is continuously causing trouble in practice when it comes to…
We present in this paper some fundamental tools for developing matrix analysis over the complex quaternion algebra. As applications, we consider generalized inverses, eigenvalues and eigenvectors, similarity, determinants of complex…
In the QCD analysis, when quarks are expressed in quaternion basis, the product of quaternions are expressed by octonions and the octonion posesses the triality symmetry. Roles of triality in the gluon self energy calculation and finite…
More than 150 years after their invention by Hamilton, quaternions are now widely used in the aerospace and computer animation industries to track the paths of moving objects undergoing three-axis rotations. It is shown here that they…
The rotation of trapped molecules offers a promising platform for quantum technologies and quantum information processing. In parallel, quantum error correction codes that can protect quantum information encoded in rotational states of a…
The interior structure of arbitrary sets of quaternion units is analyzed using general methods of the theory of matrices. It is shown that the units are composed of quadratic combinations of fundamental objects having a dual mathematical…
Quaternions, split quaternions, and hybrid numbers are very well-known number systems. These number systems are used to make geometry in Euclidean and Lorentz spaces. These number systems can be obtained with the help of a quadratic form.…
Torque is ubiquitous in many molecular systems, including collisions, chemical reactions, vibrations, electronic excitations and especially rotor molecules. We present a straightforward theoretical method based on forces acting on atoms and…
It is known that quaternions represent rotations in 3D Euclidean and Minkowski spaces. However, product by a quaternion gives rotation in two independent planes at once and to obtain single-plane rotations one has to apply by half-angle…
A rotor system, having the symmetry afforded by the two-parameter quantum algebra Uqp(u(2)), is investigated in this communication. This system is useful in rotational spectroscopy of molecules and nuclei. In particular, it is shown to lead…
The applications of quaternion in physics are discussed with an emphasis on elementary particle symmetry and interaction. Three colours of the quark and the quantum chromodynamics (QCD) can be introduced directly from the invariance of…
This study investigates the theoretical and computational aspects of quaternion generalized inverses, focusing on outer inverses and {1,2}-inverses with prescribed range and/or null space constraints. In view of the non-commutative nature…
Quaternions often appear in wide areas of applied science and engineering such as wireless communications systems, mechanics, etc. It is known that are two types of non-isomorphic generalized quaternion algebras, namely: the algebra of…
A common problem in physics and engineering is determination of the orientation of an object given its angular velocity. When the direction of the angular velocity changes in time, this is a nontrivial problem involving coupled differential…