Estimates are obtained for the number of singular points, which are not poles, lying on the unit circle of the complex plane of a class of meromorphic functions which are represented by C-fractions.
Before the introduction of the radius of curvature method in 1968, departures were computed along straight-line segments with the so-called tangential method. Since 1968 many variations of the curvature method have been developed. This paper extends available departure methods to a helical method that uses torsional as well as curvature information in the raw directional-survey data. Fortran routines have been written implementing this method. The algorithms presented here were used to implement these routines.station number, k, would be associated with its distinctive transformation T = T k .) __ Moreover, T is assumed to take the direction vector U k + 1 into a unit vec.tor (N x' Ny, N z ), with the inclination angle 0 defIned by the formula N z = cos O. The desired departure in the T frame of reference is then denoted by the vector (Ox' 0y' 0z)' which is developed as follows.Letting /l.0k be the length of the borehole between the k and the (k + 1) stations, then the radius r ck of the kth circular arc is r ck = ADk / 15 k , .
Abstract.Estimates are obtained for the number of singular points, which are not poles, lying on the unit circle of the complex plane of a class of meromorphic functions which are represented by C-fractions.
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