Compared to quaternions, reduced biquaternions satisfy the multiplication commutative rule and are widely employed in applications such as image processing, fuzzy recognition, image compression, and digital signal processing. However, there is little...
The quaternion windowed linear canonical transform is a tool for processing multidimensional data and enhancing the quality and efficiency of signal and image processing; however, it has disadvantages due to the noncommutativity of quaternion multipl...
Quaternion and biquaternion symmetry transformations have been applied to non-Cartesian reference systems of direct and reciprocal crystal lattices. The transformations performed directly in the sets of crystal reference axes simplify the calculation...
This paper begins with the introduction of biquaternion algebra and its properties in compact, profound and comprehensible approach. The Schrödinger equation including both the scalar Aharonov-Bohm(sAB) and Aharonov-Casher(AC) effects, that are curre...
Reduced biquaternion (RB) matrices provide a commutative algebraic framework for coupled multicomponent data, but their factorizations are usually formulated through complex or real representation matrices. The aim of this study is to develop and val...
Higher-dimensional hypercomplex fractal sets are getting more and more attention because of the discovery of more and more interesting properties and visual aesthetics. In this study, the attention was focused on generalized biquaternionic Julia sets...
A biquaternionic version of the Dirac Equation is introduced, with a procedure for converting four-component spinors to elements of the Pauli algebra. In this version, mass appears as a coefficient between the 4-gradient of a spinor and its image und...
Mathematics is the wide-ranging solid foundation of the engineering sciences which ensures their progress by providing them with its unique toolkit of rules, methods, algorithms and numerical systems. In this paper, an overview of the numerical syste...
This paper examines the possibility of controlling the outcome of measured (flat space-time) relativistic effects, such as time dilation or length contractions, using pure rotations and their nontrivial interactions with Lorentz boosts in the isometr...
We briefly present our version of noncommutative analysis over matrix algebras, the algebra of biquaternions (
This work addresses a significant gap in the existing literature by developing integral representation formulas for extended quaternion-valued functions within the framework of Clifford analysis. While classical Cauchy-type and Borel–Pompeiu fo...
We present a spectral-action framework for connecting generalized trace dynamics (GTD) to the structural form of the low-energy action of the observed Universe. The fundamental single-STM-atom Lagrangian is decomposed exactly into a purely bosonic se...