相关论文: Quaternions in mathematical physics (2): Analytica…

This book intends to give the main definitions and theorems in mathematics which could be useful for workers in theoretical physics. It gives an extensive and precise coverage of the subjects which are addressed, in a consistent and…

Rotations on the 3-dimensional Euclidean vector-space can be represented by real quaternions, as was shown by Hamilton. Introducing complex quaternions allows us to extend the result to elliptic and hyperbolic rotations on the Minkowski…

150 years after the discovery of quaternions, Hamilton's conjecture that quaternions are a fundamental language for physics is reevaluated and shown to be essentially correct, provided one admits complex numbers in both classical 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…

In the 6th Int. Symposium on OPSFA there were several communications dealing with concrete applications of orthogonal polynomials to experimental and theoretical physics, chemistry, biology and statistics. Here I make suggestions concerning…

The satisfactory development of Quaternionic Analysis has indicated new solutions for physical and mathematical problems. It is worth mentioning the fact that quaternions possess four dimensions, and in this way they may be considered as…

We give a simple and self contained introduction to quaternions and their practical usage in dynamics. The rigid body dynamics are presented in full details. In the appendix, some more exotic relations are given that allow to write more…

Regarding quaternions as normal matrices, we first characterize the $2\times 2$ matrix-valued functions, defined on subsets of quaternions, whose values are quaternions. Then we investigate the regularity of quaternionic-valued functions,…

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 paper shows how to write Maxwell's Equations in Hamilton's Quaternions. The fact that the quaternion product is non-commuting leads to distinct left and right derivatives which must both be included in the theory. A new field component…

Most of theoretical physics is based on the mathematics of functions of a real or a complex variable; yet we frequently are drawn to try extending our reach to include quaternions. The non-commutativity of the quaternion algebra poses…

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…

In this paper, we present a further generalization of the bi- periodic Fibonacci quaternions and octonions. We give the generating function, the Binet formula, and some basic properties of these quaternions and octonions. The results of…

In this study, we define the dual Fibonacci quaternion and the dual Lucas quternion. We derive the relations between the dual Fibonacci and the dual Lucas quaternion which connected the Fibonacci and the Lucas numbers. Furthermore, we give…

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…

It is known that the groups of Euclidean rotations in dimension 3 (isometries of $S^2$), general Lorentz transformations in dimension 4 (Hyperbolic isometries in dimension 3), and screw motions in dimension 3 can be represented by the…

In this paper we study special Fibonacci quaternions and special generalized Fibonacci-Lucas quaternions in quaternion algebras over finite fields.

In this article, we give the most genaral form of the quaternions algebra depending on 3-parameters. We define 3-parameter generalized quaternions (3PGQs) and study on various properties and applications. Firstly we present the definiton,…

Some comments are made on the matrices which serve as the basis of a quaternionic algebra. We show that these matrices are related with the quaternionic action of the imaginary units from the left and from the right.

The duality triads were defined in the preceding paper.(ArXiv: math.GM/0402260 v 1 Feb. 2004). Notation, enumeration of formulas and references is therefore to be continued hereby. In this paper Fibonomial triangle and further Pascal-like…