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Based on Maxwellian quaternionic electromagnetic theory, the electromagnetic interaction, gravitational interaction and their coupling influence with the dark matter field in octonionic space are discussed. The research results disclose the…
The paper focuses on considering some special precessional motions as the spin motions, separating the octonion angular momentum of a proton into six components, elucidating the proton angular momentum in the proton spin puzzle, especially…
The sedenion compounding fields and their quantum interplays can be presented by analogy with the octonionic electromagnetic, gravitational, strong and weak interactions. In sedenion fields which are associated with electromagnetic,…
The paper aims to apply the trigintaduonion spaces to explore the physical properties of four interactions simultaneously, including the electromagnetic fields, gravitational fields, weak nuclear fields, and strong nuclear fields. J. C.…
The paper aims to apply the complex octonion to explore the influence of the energy gradient on the Eotvos experiment, impacting the gravitational mass in the ultra-strong magnetic fields. Until now the Eotvos experiment has never been…
The paper aims to apply the complex-sedenions to explore the field equations of four fundamental interactions, which are relevant to the classical mechanics and quantum mechanics, in the curved spaces. J. C. Maxwell was the first to utilize…
The paper studies the validity of Maxwell equation in the case for coexistence of electromagnetic field and gravitational field. With the algebra of quaternions, the Newton's law of gravitation is the same as that in classical theory of…
An attempt has been made to analyse the the role of octonions in various unified field theories associated with dyons and the dark matter. Starting with the split octonion al- gebra and its properties, we have discussed the octonionic…
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…
In the realm of Continuum Physics, material bodies are realized as continous media and so-called extensive quantities, such as mass, momentum and energy, are monitored through the fields of their densities, which are related by balance laws…
Using octonions, more specifically, using a 4 x 4 matrix representation of octonions obtained with the help of algebraic properties of quaternions, we obtain the fully symmetric Maxwell's equations (Maxwell's equations with electric and…
The paper aims to consider the strength gradient force as the dynamic of astrophysical jets, explaining the movement phenomena of astrophysical jets. J. C. Maxwell applied the quaternion analysis to describe the electromagnetic theory. This…
In this paper we present eight-component values "octons", generating associative noncommutative algebra. It is shown that the electromagnetic field in a vacuum can be described by a generalized octonic equation, which leads both to the wave…
The review of modern study of algebraic, geometric and differential properties of quaternionic (Q) numbers with their applications. Traditional and "tensor" formulation of Q-units with their possible representations are discussed and groups…
In this paper, we present some applications of quaternions and octonions. We present the real matrix representations for complex octonions and some of their properties which can be used in computations where these elements are involved.…
Based on Maxwellian quaternionic electromagnetic theory, the octonionic hyper-strong field, hyper-weak field and the quantum interplays can be presented by analogy with octonionic electromagnetic, gravitational, strong and weak…
As an expansion of complex numbers, the quaternions show close relations to numerous physically fundamental concepts. In spite of that, the didactic potential provided by quaternion interrelationships in formulating physical laws are hardly…
The paper discusses the influences of velocity curl and field strength on some theorems in the electromagnetic field and gravitational field. With the characteristics of the algebra of quaternions, the theorem of linear momentum,…
Based on the electromagnetic interaction and gravitational interaction, the quantum interplays of the ordinary matter and the dark matter in the octonion space are discussed. The paper presents the quantization of the particles of ordinary…
The paper discusses the impact of adjoint fields on the conservation laws in the gravitational field and electromagnetic field, by means of the characteristics of octonions. When the adjoint field can not be neglected, it will cause the…