By Peter Henrici

ISBN-10: 0471372447

ISBN-13: 9780471372448

Offers functions in addition to the fundamental conception of analytic features of 1 or a number of advanced variables. the 1st quantity discusses purposes and simple idea of conformal mapping and the answer of algebraic and transcendental equations. quantity covers issues commonly hooked up with traditional differental equations: detailed services, vital transforms, asymptotics and endured fractions. quantity 3 information discrete fourier research, cauchy integrals, building of conformal maps, univalent features, power idea within the aircraft and polynomial expansions.

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**Extra info for Applied and Computational Complex Analysis. Vol. 1: Power Series, Integration, Conformal Mapping, Location of Zeros**

**Example text**

OPEN PROBLEM 5. Obtain a tight bound on the number of changes in the Delaunay triangulation of a set of moving points, each of which is moving with a fixed velocity. 6. Hausdorff distance and Voronoi surfaces Let iS be a set of points in R^. The Voronoi surface of S is defined as the bivariate function 7r(x) = min^e^ p(^, x), for x G M^, where p(-, •) is the distance function in M^, which we will assume to be some fixed Lp metric. By definition, the orthogonal projection of the graph of 7t onto the xj-plane is the Voronoi diagram of S under the metric p.

A line that intersects all sets of S is called a transversal (or a stabber) of S. Note that a line intersects a set if and only if it intersects its convex hull, so convexity is usually not a real restriction. For each set Si e S, let S* denote the set of points dual to the lines that intersect St, using a standard duality transform [54]. Sf is bounded from above by a convex x-monotone curve Ai and from below by a concave x-monotone curve Bf; see Figure 9. The stabbing region of S (or the space of all transversals) is the intersection 5* = 0/^=1 ^f- ^ ^ definition, ~~
~~

On the other hand, if pairs of curves in F can intersect in four or more points, then dK may contain Q{n^) intersection points in the worst case. This raises the question of what happens if any two curves in F intersect in at most three points. Using DS(n, 3)-sequences, Edelsbrunner et al. [55] have shown that the maximum combinatorial complexity of the union K is S{na(n)) (here we need to assume that the curves in F are unbounded, because two closed Jordan curves, in general position, cannot intersect in three points).

### Applied and Computational Complex Analysis. Vol. 1: Power Series, Integration, Conformal Mapping, Location of Zeros by Peter Henrici

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