We demonstrate an infinite family of pseudoline arrangements, in which an arrangement of n pseudolines has no member incident to more than 4n/9 points of intersection. (This shows the “Strong Dirac” conjecture to be false for pseudolines.) We also prove non-trivial lower bounds on the maximum number of intersection points on any curve in an arrangement of curves in the plane, for various classe...

Among the many ways to view oriented matroids as geometrical objects, we consider two that have special properties: • Bland’s analysis of complementary subspaces in IRn [2] has the special feature that it simultaneously and symmetrically represents a realizable oriented matroid and its dual; • Lawrence’s topological representation of oriented matroids by arrangements of pseudospheres [4] has th...

We study two kinds of segment orders, using definitions first proposed by Farhad Shahrokhi. Although the two kinds of segment orders appear to be quite different, we prove several results suggesting that the are very much the same. For example, we show that the following classes belong to both kinds of segment orders: (1) all posets having dimension at most 3; (2) interval orders; and for n ≥ 3...

We describe an incremental algorithm to enumerate the isomorphism classes of double pseudoline arrangements. The correction of our algorithm is based on the connectedness under mutations of the spaces of one-extensions of double pseudoline arrangements, proved in this paper. Counting results derived from an implementation of our algorithm are also reported.

Let GH(S; H) be the bipartite graph with partition sets S and H , the set of simplices and hyperplanes of H, where simplex s∈ S is adjacent to hyperplane h∈H if one facet of s lies on h. In this paper, we give a complete characterization of GH(S; H) when H is a -arrangement. We also study GH(S; H) when H is a pseudoline arrangement. c © 2001 Elsevier Science B.V. All rights reserved.

The single-phase flow and thermal performance of a double pipe heat exchanger are examined by experimental methods. The working fluid is water at atmospheric pressure. Temperature measurements at the inlet and outlet of the two streams and also at an intermediate point half way between the inlet and outlet is made, using copper-constantan thermocouple wires. Mass flow rates for each stream are ...

Any finite set of lines in the real projective plane determines a cell complex; these complexes and their combinatorial properties have been a subject of study at least since 1826 [9]. More recently, Levi [6] considered a topological generalization of this notion, defined as follows: Consider a simple closed curve in RP2 which does not separate RP2; this is called a pseudoline. (It is clear tha...

During cross flow in a heat exchanger, heat transfer in the front portion of the tube is more compared to back portion of the tube. This is due to less formation of vortices at the backside of the tube. For uniform heat transfer to take place throughout the tube, it is necessary to increase the vortex formation at the rear side of the tube. The aim of this study is to explore the possibilities ...