Non-classical structural mathematical means and optic

Author

Sorokin, V.K. ; Lobanova, L.S.

Author_Institution

Ukrainian Eng.-Pedagogical Acad., Kharkiv, Ukraine

Volume

2

fYear

2000

fDate

2000

Firstpage

697

Abstract

Rvachev (1991, 1995) has shown that, for a body velocity comparable with the light velocity, the Archimedean axiom and the Archimedean arithmetic calculus rules (+,-,x,/) are not correct, if it is applied to the calculations in the mathematical methods in electromagnetic theory and optics. NonArchimedean arithmetic rules and functions are nonclassical structural mathematical means and must be used for calculations in the mathematical methods in electromagnetic theory. It is shown that a two-dimensional model can be constructed. This model allows one to derive on numerous occasions the algebraic expressions of the nonArchimedean arithmetic rules, the nonArchimedean functions and algebraic expressions of the optical laws, for example, the optical laws for the light propagation and reflection on the two optical mediums boundary

Keywords

calculus; light propagation; light reflection; light velocity; Archimedean arithmetic calculus rules; Archimedean axiom; algebraic expressions; body velocity; electromagnetic theory; light propagation; light reflection; light velocity; mathematical methods; nonArchimedean arithmetic rules; nonclassical structural mathematics; optical laws; optical mediums boundary; optics; two-dimensional model; Analytical models; Arithmetic; Mathematical model; Optical propagation; Optical reflection; Optical refraction; Spirals;

fLanguage

English

Publisher

ieee

Conference_Titel

Mathematical Methods in Electromagnetic Theory, 2000. MMET 2000. International Conference on

Conference_Location

Kharkov

ISSN

1

Print_ISBN

0-7803-6347-7

Type

conf

DOI

10.1109/MMET.2000.890540

Filename

890540