Given a set S of n disjoint convex polygons {Pi | 1 i n} in a plane, each with ki vertices, the transversal problem is to find, if there exists one, a straight line that goes through every polygon in S. We show that the transversal problem can be solved in O(N + n logn) time, where N = ni=1 ki is the total number of vertices of the polygons.  2002 Elsevier Science B.V. All rights reserved.

A center-transversal line for two finite point sets in R is a line with the property that any closed halfspace that contains it also contains at least one third of each point set. It is known that a center-transversal line always exists,but the best known algorithm for finding such a line takes roughly n time. We propose an algorithm that finds a center-transversal line in O(nκ(n)) worst-case t...

The authors present a review on the recent approaches proposed to implement transversal RF filters. Different tunable transversal filters consisting of wavelength tunable optical taps and those employing the tunability of dispersive devices are presented showing their high-performance characteristics. A comprehensive review of the fundamentals and a discussion on the main limitation of these st...

In this paper, we study half-lightlike submanifolds of a semi-Riemannian manifold such that the shape operator of screen distribution is conformal to the shape operator of screen transversal distribution. We mainly obtain some results concerning the induced Ricci curvature tensor and the null sectional curvature of screen transversal conformal half-lightlike submanifolds. 2010 Mathematics Subje...

We establish some inequalities about the Khovanov-Rozansky cohomologies of braids. These give new upper bounds of the self-linking numbers of transversal knots in standard contact S which is sharper than the well known bound given by the HOMFLY polynomial. We also introduce a sequence of transversal knot invariants, and discuss some of their properties.

In this paper, the principal tool to describe transversal polymatroids with Gorenstein base ring is polyhedral geometry, especially the Danilov−Stanley theorem for the characterization of canonical module. Also, we compute the a − invariant and the Hilbert series of base ring associated to this class of transversal polymatroids.

Let H,K be subgroups of G. We investigate the intersection properties of left and right cosets of these subgroups. If H and K are subgroups of G, then G can be partitioned as the disjoint union of all left cosets of H, as well as the disjoint union of all right cosets of K. But how do these two partitions of G intersect each other? Definition 1. Let G be a group, and H a subgroup of G. A left t...