Sep 10, 1997 - Section 2 contains a number of preliminary results that are needed for ... the half-plane (see, e.g., [16, pp. ... and let a and b denote, respectively, the points where γ intersects ... Rm(Q) := {w : 0 < w < m(Q), 0 < w < 1} are straight lines parallel to .... and the monotonicity result of [6, Theorem 4]; see also [18, p.
The Asymptotic Behavior of Conformal Modules of Quadrilaterals with Applications to the Estimation of Resistance Values N. Papamichael and N. S. Stylianopoulos Dedicated to Professor Dieter Gaier on the occasion of his 70th birthday Abstract. We consider the conformal mapping of “strip-like” domains and derive a number of asymptotic results for computing the conformal modules of an associated class of quadrilaterals. These results are then used for the following two purposes: (a) to estimate the error of certain engineering formulas for measuring resistance values of integrated circuit networks; and (b) to compute the modules of complicated quadrilaterals of the type that occur frequently in engineering applications.
1. Introduction The conformal module m(Q) of a quadrilateral Q := {Ä; z 1 , z 2 , z 3 , z 4 }, consisting of a Jordan domain Ä and four points z 1 , z 2 , z 3 , z 4 in counterclockwise order on ∂Ä, is defined as follows: Let R L denote a rectangle of length L and height 1 of the form R L := {w : 0 <
