02-158 S.B. Karavashkin and O.N. Karavashkina

On complex functions analyticity (197K, Postscript) Mar 28, 02

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Abstract. We analyse here the conventional definitions of analyticity and differentiability of functions of complex variable. We reveal the possibility to extend the conditions of analyticity and differentiability to the functions implementing the non-conformal mapping. On this basis we formulate more general definitions of analyticity and differentiability covering those conventional. We present some examples of such functions. By the example of a horizontal belt on a plane Z mapped non-conformally onto a crater-like harmonic vortex, we study the pattern of trajectory variation of a body motion in such field in case of field power function varying in time. We present the technique to solve the problems of such type with the help of dynamical functions of complex variable implementing the analytical non-conformal mapping

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