Related papers: Quaternion Analysis
The history of complementary observables and mutual unbiased bases is reviewed. A characterization is given in terms of conditional entropy of subalgebras. The concept of complementarity is extended to non-commutative subalgebras.…
Motivated by a model in quantum computation we study orthogonal sets of integral vectors of the same norm that can be extended with new vectors keeping the norm and the orthogonality. Our approach involves some arithmetic properties of the…
We study differential splitting fields of quaternion algebras with derivations. A quaternion algebra over a field $k$ is always split by a quadratic extension of $k$. However, a differential quaternion algebra need not be split over any…
A nonlinear dynamical modeling of interaction between automatic and conscious processes in the brain is described. Effects of sensations, emotions and reflections on the electromagnetic activity of the brain are represented in terms of…
We provide an algorithm that, given any order $O$ in a quaternion algebra over a global field, computes representatives of all right equivalence classes of right $O$-ideals, including the non-invertible ones. The theory is developed for a…
Quaternions, discovered by Sir William Rowan Hamilton in the 19th century, are a significant extension of complex numbers and a profound tool for understanding three-dimensional rotations. This work explores the quaternion's history,…
Algebraic and analytic aspects of self-adjoint operators of order four or more with polynomial coefficients are investigated. As a consequence, a systematic way of constructing such operators is given. The procedure is applied to obtain…
This dissertation is about The history of quaternions and their associated rotation groups as it relates to theoretical physics.
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…
Based on the full similarity in algebraic properties and differentiation rules between quaternionic (H-) holomorphic and complex (C-) holomorphic functions, we assume that there exists one holistic notion of a holomorphic function that has…
We develop observer design over hypercomplex quaternions in a characteristic-polynomial-free framework. Using the standard right-module convention, we derive a right observable companion form and companion polynomial that encode error…
The new approach to decays of heavy quarkonia, based on factorization and expansions in powers of the relative velocity of the valence quarks is reviewed.
Polar decompositions of quaternion matrices with respect to a given indefinite inner product are studied. Necessary and sufficient conditions for the existence of an $H$-polar decomposition are found. In the process an equivalent to Witt's…
In this study, a new form of quadratic spline is obtained, where the coefficients are determined explicitly by variational methods. Convergence is studied and parity conservation is demonstrated. Finally, the method is applied to solve…
In the paper I considered mappings of conjugation of quaternion algebra. I proved the theorem that there is unique expansion of R-linear mapping of quaternion algebra relative to the given set of mappings of conjugation.
We derive an appropriate definition of transpose for quaternionic matrices and give a new panoramic review of the quaternionic groups. We aim to analyse possible quaternionic groups for GUTs.
Quaternionic formulation of D=4 conformal group and of its associated twistors and their relation to harmonic analyticity is presented. Generalization of $SL(2,\cal{C})$ to the D=4 conformal group SO(5,1) and its covering group…
The ideas of instantaneous amplitude and phase are well understood for signals with real-valued samples, based on the analytic signal which is a complex signal with one-sided Fourier transform. We extend these ideas to signals with…
We study power series and analyticity in the quaternionic setting. We first consider a function f defined as the sum of a quaternionic power series centered at 0 in its domain of convergence (which is a ball B(0,R) centered at 0). At each…
Over the past few years, the applications of dual-quaternions have not only developed in many different directions but has also evolved in exciting ways in several areas. As dual-quaternions offer an efficient and compact symbolic form with…