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One-Dimensional Quaternionic Special Affine Fourier Transform
We extend the special affine Fourier transform in the context of quaternion valued functions and study its properties including an uncertainty...
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Uncertainty Principles For The Continuous Quaternion Shearlet Transform
In this paper, we present some new elements of harmonic analysis related to the continuous quaternion shearlet transform .The main objective of this...
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A 1d Up Approach to Conformal Geometric Algebra: Applications in Line Fitting and Quantum Mechanics
We discuss an alternative approach to the conformal geometric algebra (CGA) in which just a single extra dimension is necessary, as compared to the...
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Quaternion Algebra on 4D Superfluid Quantum Space-Time: Gravitomagnetism
Gravitomagnetic equations result from applying quaternionic differential operators to the energy–momentum tensor. These equations are similar to the...
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On SVD and Polar Decomposition in Real and Complexified Clifford Algebras
In this paper, we present a natural implementation of singular value decomposition (SVD) and polar decomposition of an arbitrary multivector in...
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On the Problem of Choosing Subgroups of Clifford Algebras for Applications in Fundamental Physics
Clifford algebras are used for constructing spin groups, and are therefore of particular importance in the theory of quantum mechanics. An...
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Polar Decomposition of Complexified Quaternions and Octonions
We present a hitherto unknown polar representation of complexified quaternions (also known as biquaternions), also applicable to complexified...
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A kinematic model of the Rytov’s law in the optical fiber via split quaternions: application to electromagnetic theory
In this paper, we analyze the homothetic motion of the polarization plane traveling along the linearly polarized light wave ((LPL)-wave) in the...
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Fusion category symmetry. Part I. Anomaly in-flow and gapped phases
We study generalized discrete symmetries of quantum field theories in 1+1D generated by topological defect lines with no inverse. In particular, we...
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Quantum gravity effects in the infrared: a theoretical derivation of the low-energy fine structure constant and mass ratios of elementary particles
We have recently proposed a pre-quantum, pre-spacetime theory as a matrix-valued Lagrangian dynamics on an octonionic spacetime. This theory offers...
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An Ontological Basis for the Diffusion Theory
Fick’s diffusion equation represents physical reality that has been interpreted by Einstein and Smoluchowski. In this way, the question of...
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B-Spline Pythagorean Hodograph Curves in Clifford Algebras
In several recent publications B-spline functions appeared with control points from abstract algebras, e.g. complex numbers, quaternions or Clifford...
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\(\mathscr {N}\,{=}\,2\) Supergravities in Harmonic Superspace
Basics of \(\mathscr {N}\,{=}\,2, 4D\) conformal and Einstein supergravities in the harmonic superspace approach...
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Inertial Navigation in Space Using the Regular Quaternion Equations of Astrodynamics
Quaternion equations are proposed for the ideal operation of spatial inertial navigation systems with an azimuthally stabilized platform and a...
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Some New Quaternionic Quadratics with Zeros in Terms of Second Order Quaternion Recurrences
In this paper a comprehensive analysis of the Horadam quaternion zeros for some new types of bivariate quadratic quaternion polynomial equations is...
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Formulation of the Snell–Descartes Laws in Terms of Geometric Algebra
A formulation of the laws of reflection and refraction of optical rays by the interface of two isotropic media using the mathematical apparatus of...
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Dual Hyperquaternion Poincaré Groups
A new representation of the Poincaré groups in n dimensions via dual hyperquaternions is developed, hyperquaternions being defined as a tensor...
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Quaternion-Valued Smooth Compactly Supported Orthogonal Wavelets with Symmetry
We construct two novel quaternion-valued smooth compactly supported symmetric orthogonal wavelet (QSCSW) filters of length greater than existing...
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Two-Component Spinorial Formalism Using Quaternions for Six-Dimensional Spacetimes
In this article we construct and discuss several aspects of the two-component spinorial formalism for six-dimensional spacetimes, in which chiral...