The Nevanlinna defect relation and other results on the Nevanlinna theory assert that each meromorphic mapping f of C into P(C) has few deficient hyperplanes in P(C) . However, it seems to me that meromorphic mappings with a deficient hyperplane must be very few. In this paper, we show that for an arbitrary given transcendental meromorphic mapping f (which may be linearly degenerate), we can el...

The paper is devoted to computation of the cohomology of the complex of logarithmic differential forms with coefficients in rational functions whose poles are located on the union of several hyperplanes of a linear space over a field of characteristic zero. The main result asserts that for a vast class of hyperplane arrangements, including all free and generic arrangements, the cohomology algeb...

The production possibility set (PPS) is defined as the set of all inputs and outputs of a system in which inputs can produce outputs. In data envelopment analysis (DEA), identification of the strong defining hyperplanes of the empirical production possibility set (PPS) is important, because they can be used for determining rates of change of outputs with change in inputs. Also, efficient hyperp...

We study an NP-complete geometric covering problem called d-Dimensional Rectangle Stabbing, where, given a set of axis-parallel d-dimensional hyperrectangles, a set of axis-parallel (d − 1)-dimensional hyperplanes and a positive integer k, the question is whether one can select at most k of the hyperplanes such that every hyperrectangle is intersected by at least one of these hyperplanes. This ...

By introducing redundant Klee-Minty examples, we have previously shown that the central path can be bent along the edges of the Klee-Minty cubes, thus having 2n − 2 sharp turns in dimension n. In those constructions the redundant hyperplanes were placed parallel with the facets active at the optimal solution. In this paper we present a simpler and more powerful construction, where the redundant...

Let A be a real arrangement of hyperplanes. Let B = B(q) be Varchenko’s quantum bilinear form of A, introduced [15], specialized so that all hyperplanes have weight q . B(q) is nonsingular for all complex q except certain roots of unity. Here, we examine the kernel of B at roots of unity in relation to the topology of the hyperplane singularity. We use Varchenko’s work [16] to relate B(q) to a ...

We prove a new, tight upper bound on the number of incidences between points and hyperplanes in Euclidean d-space. Given n points, of which k are colored red, there are Od(m 2/3 k 2/3 n +kn+m) incidences between the k red points and m hyperplanes spanned by all n points provided that m = Ω(n). For the monochromatic case k = n, this was proved by Agarwal and Aronov [1]. We use this incidence bou...

A method is described for finding decision boundaries, approximated by piecewise linear segments, for classifying patterns in R(N),N>/=2, using an elitist model of genetic algorithms. It involves generation and placement of a set of hyperplanes (represented by strings) in the feature space that yields minimum misclassification. A scheme for the automatic deletion of redundant hyperplanes is als...

In this paper we present some theoretical results on two forms of multi-point crossover: n-point crossover and uniform crossover. This analysis extends the work from De long's thesis, which dealt with dis~ption of n-point crossover on 2nd order hyperplanes. We present various extensions to this theory, including 1) an analysis of the disruption of n-point crossover on kth order hyperplanes: 2) ...