Related papers: An introduction to using dual quaternions to study…
In the paper, we define the $q$-Fibonacci bicomplex quaternions and the $q$-Lucas bicomplex quaternions, respectively. Then, we give some algebraic properties of $q$-Fibonacci bicomplex quaternions and the $q$-Lucas bicomplex quaternions.
Just like the well-established Euler angles representation, fused angles are a convenient parameterisation for rotations in three-dimensional Euclidean space. They were developed in the context of balancing bodies, most specifically walking…
We study the general form of the possible kinetic terms for 2-form fields in four dimensions, under the restriction that they have a semibounded energy density. This is done by using covariant symplectic techniques and generalizes previous…
We point out a possible complementation of the basic equations of quantum mechanics in the presence of gravity. This complementation is suggested by the well-known fact that quantum mechanics can be equivalently formulated in the position…
Two-, three- and four-dimensional representations of Penrose tilings of the plane are described. The vertices that occur in these representations lie on lattices. Symmetries and methods of visualizing these representations are discussed.…
As a promising branch of robotics, imitation learning emerges as an important way to transfer human skills to robots, where human demonstrations represented in Cartesian or joint spaces are utilized to estimate task/skill models that can be…
The goal of this note is to give a characterization of generalized quaternion $2$-groups by using their posets of cyclic subgroups.
A discrete complexified quaternion Fourier transform is introduced. This is a generalization of the discrete quaternion Fourier transform to the case where either or both of the signal/image and the transform kernel are complex…
On base of differential biquaternions algebra and generalized functions theory the biquaternionic wave equation is considered under vector representation of its structural coefficient. Its generalized solutions are constructed, which…
This is a follow-up tutorial article of our previous article entitled "Robot Basics: Representation, Rotation and Velocity". For better understanding of the topics covered in this articles, we recommend the readers to first read our…
Within the framework of the theory of the column and row determinants, we obtain new determinantal representations of the W-weighted Drazin inverse over the quaternion skew field. We give determinantal representations of the W-weighted…
Double field theory was developed by theoretical physicists as a way to encompass $T$-duality. In this paper, we express the basic notions of the theory in differential-geometric invariant terms, in the framework of para-Kaehler manifolds.…
In this work, we use real quaternions and the basic concept of the final speed of light in an attempt to enhance the standard description of special relativity. First, we demonstrate that it is possible to introduce a quaternion time domain…
Lie symmetries of various geometrical and physical quantities in general relativity play an important role in understanding the curvature structure of manifolds. The Riemann curvature and Weyl tensors are two fourth-rank tensors in the…
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.…
In this paper, we give some properties of the Tribonacci and Tribonacci-Lucas quaternions and obtain some identities for them.
Multidimensional quaternion arrays (often referred to as "quaternion tensors") and their decompositions have recently gained increasing attention in various fields such as color and polarimetric imaging or video processing. Despite this…
Linear algebra is usually defined over a field such as the reals or complex numbers. It is possible to extend this to skew fields such as the quaternions. However, to the authors' knowledge there is no commonly accepted notation of linear…
During the process of teaching the concept of derivative, it is common and natural to refer to geometric interpretations, such as the use of the tangent line and the maximum and minimum points of a function, to illustrate the scope of the…
In this paper, we present a novel algorithm to extract a quaternion from a two dimensional camera frame for estimating a contained human skeletal pose. The problem of pose estimation is usually tackled through the usage of stereo cameras…