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Multicomponent Number Systems

100%

Majerník V.

Acta Physica Polonica A

1996

vol. 90

issue 3

491-498

We introduce three types of the four-component number systems which are constructed by joining the complex, binary and dual two-component numbers. We study their algebraic properties and rewrite the Euler and Moivre formulas for them. The most general multicomponent number system joining the complex, binary dual numbers is the eight-component number system, for which we determine the algebraic properties and the generalized Euler and Moivre formulas. Some applications of the multicomponent number systems in differential and integral calculus, which are of physical relevance, are also presented.

Basic Space-Time Transformations Expressed by Means of Two-Component Number Systems

63%

Majerník V.

Acta Physica Polonica A

1994

vol. 86

issue 3

291-295

We slow that the Lorentz and Galilei transformations can be expressed in the algebraic structures called the rings of two-component binary and dual number systems.

Galilean Transformation Expressed by the Dual Four-Component Numbers

63%

Majerník V.

Acta Physica Polonica A

1995

vol. 87

issue 6

919-923

We express the special Galilean transformation in the algebraic ring of the dual four-component numbers.

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Multicomponent Number Systems

Basic Space-Time Transformations Expressed by Means of Two-Component Number Systems

Galilean Transformation Expressed by the Dual Four-Component Numbers