a refrigeration cycle is a chain of various pieces of equipment including compressors, condensers, evaporators, and expansion devices each of which takes on a particular thermodynamic process duty in the cycle that eventually results in the production of the required refrigeration. the results of optimized mixed refrigerant cycles (mrcs) in part i show that the configuration of mrc is an effect...

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.