Title :
Non-classical structural mathematical means and optic
Author :
Sorokin, V.K. ; Lobanova, L.S.
Author_Institution :
Ukrainian Eng.-Pedagogical Acad., Kharkiv, Ukraine
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;
Conference_Titel :
Mathematical Methods in Electromagnetic Theory, 2000. MMET 2000. International Conference on
Conference_Location :
Kharkov
Print_ISBN :
0-7803-6347-7
DOI :
10.1109/MMET.2000.890540
