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The functional space of biquaternions is considered on Minkovskiy space. The scalar-vector biquaternions representation is used which was offered by W. Hamilton for quaternions. With introduction of differential operator - a mutual complex…
Fractals are self-repeating patterns which have dimensions given by fractions rather than integers. While the dimension of a system unambiguously defines its properties, a fractional dimensional system can exhibit interesting properties.…
The paper aims to apply the octonions to explore the contribution of some influence factors to magnetic moments, revealing the connection among the influence factors and spin texture. J. C. Maxwell was the first to introduce the quaternions…
The purpose of this effort is to investigate if the use of quaternion mathematics can be used to better model and simulate the electromagnetic fields that occur from moving electromagnetic charges. One observed deficiency with the commonly…
QCD is the fundamental theory to describe the strong interaction, where quarks and gluons have the color degrees of freedom. However, a single quark or gluon can not be separated out and all observable particles are color singlet states.…
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,…
Neural networks in the real domain have been studied for a long time and achieved promising results in many vision tasks for recent years. However, the extensions of the neural network models in other number fields and their potential…
Colour vision has long fascinated scientists, who have sought to understand both the physiology of the mechanics of colour vision and the psychophysics of colour perception. We consider representations of colour in anatomically constrained…
This paper describes the passage of light through a system of waveplates mathematically in terms of quaternions, an extension of the complex numbers, instead of the more usual Jones vectors and Jones matrices. Both the light beam and the…
The vacuum of QCD is characterized by the Higgs mechanism. Color is ``spontaneously broken'' by a quark-antiquark condensate in the octet representation. The massive gluons carry integer electric charges and are identified with the vector…
A general method is presented which allows one to determine from the local gauge invariant observables of a quantum field theory the underlying particle and symmetry structures appearing at the lower (ultraviolet) end of the…
Electron pairing at low temperatures leads to superconductivity. A fundamental question is whether more complex states - characterized by order in four-electron composite objects, termed electron quadrupling or composite order - can exist…
Quaternions were appeared through Lagrangian formulation of mechanics in Symplectic vector space. Its general form was obtained from the Clifford algebra, and Frobenius' theorem, which says that "the only finite-dimensional real division…
In the past few years, we have presented a new way of considering quark confinement. Through a careful choice of a Cho-Duan-Ge Abelian Decomposition, we can construct the QCD Wilson Loop in terms of an Abelian restricted field. The…
The basic properties of the confinement mechanism in QCD -- the temperature dependence of the spatial and temporal string tensions ($\sigma_s(T)$ and $\sigma_E(T)$) -- are studied in the framework of the Field Correlator Method (FCM). It is…
Functional defects in periodic media confine waves - acoustic, electromagnetic, electronic, spin, etc. - in various dimensions, depending on the structure of the defect. While defects are usually modelled by a superlattice with a typical…
The paper aims to apply the algebra of octonions to explore the contributions of external derivative of electric moments and so forth on the induced electric currents, revealing a few major influencing factors relevant to the direct and…
An attempt is made to describe from first principles the large-scale structure of the confining vacuum in quantum chromodynamics. Starting from our previous variational studies of the SU(2) pure gauge theory in an external Abelian…
The symmetry studies of Maxwell equations gave new insight on the nature of electromagnetic (EM) field. It has in general case quaternion single structure, consisting of four independent field constituents, which differ with each other by…
The paper aims to explore the physical quantities of several invariants, including the basic postulates of some types of crucial coordinate transformations, conservation laws and continuity equations, in the electromagnetic and…