Newton’s laws for a biquaternionic model of the electro-gravimagnetic field, charges, currents, and their interactions

In the present paper, a biquaternionic model of the electro-gravimagnetic (EGM) field is considered, which is called energetic. For this, a complex Hamiltonian form of Maxwell equations (MEs) is used, which allows to get the biquaternionic form of these equations. Note that Maxwell gave his equations in quaternionic form, but the modern form belongs to Heaviside. 

Quaternionic forms of MEs were used by some authors for their solving. Kassandrov applied similar forms for building a unified field model. Here we use the scalar-vector form of biquaternion, which is very impressive and can be adapted for writing the physical variables and equations. Based on Newton’s laws, the biquaternionic transformation equations of charges and currents at the presence of the EGM fields are constructed. The relation of these equations to hydrodynamics equations is considered. The energy conservation law at the presence of the field interaction is found.

In search of a Mathematical Theory Using Space-Time

Two types of matter namely observable subluminal matter called tardyon (locality) and the unobservable superluminal matter called tachyon (non-locality) co-exist in a motion. While the Tardyon can be converted as Tachyon, Tachyon alters itself as Tardyon.  The Tardyonic rotating motion produces the centrifugal force, and tachyonic rotating motion produces the centripetal force, that is gravity. By applying the tardyonic and tachyonic coexistence principle, this study tries to prepare a new gravitational formula to establish the mathematical theory of Space Time.

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On Discretizations of the Generalized Boole Type Transformations and their Ergodicity

The Frobenius-Perron Operator and Its Discretization:

We consider an m-dimensional; not necessary compact; C1- manifold Mm, endowed with a Lebesgue measure μ determined on the σ-algebra of Borel subsets of Mm and ϕ: Mm→Mm being an almost everywhere smooth mapping. The related Frobenius-Perron operator

is defined by means of the integral relationship

for any and all μ-measurable subsets A⊂M^m Equivalently it can be defined as a mapping on the measure space (M^m)

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