THE THEORY OF FUNCTIONS OF A COMPLEX VARIABLE UNDER DIRAC—PAULI REPRESENTATION AND ITS APPLICATION IN FLUID DYNAMICS(Ⅰ)

Abstract

Abstract: In this paper:(A) We cast aside the traditional quaternion theory and build up the theory of functions of a complex variable under Dirac-Pauli representation. Thus the multivariate and multidimensional problems become rather simple problems.(B) We simplify the Navier-Stokes equation of incompressible viscous fluid dynamics and the equations group ofisentropic aerodynamics by theory of functions of a complex variable under Dirac-Pauli representation. And the above-equations, as central problems of fluid dynamics, are classified as the nonlinear equation with only one complex unknown function.So the changes are the Great Pole, and give birth to the Two Bearings; the Two Bearings give birth to the Four Quadrants, ’and the Four Quadrants give birth to the Eight Diagrams.——Commentaries on Changes,Copula (I)

Key words: eigenstrain, Eshelby tensor, boundary integral equation (BIE), polynomial, inhomogeneity

Shen Hui-chuan . THE THEORY OF FUNCTIONS OF A COMPLEX VARIABLE UNDER DIRAC—PAULI REPRESENTATION AND ITS APPLICATION IN FLUID DYNAMICS(Ⅰ). Applied Mathematics and Mechanics (English Edition), 1986, 7(4): 391-411.

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