Refer to Figure 1. A monotone matching is a set of n segments, each the portion of a unique pseudoline, and each spanning a unique slab, such that the left endpoint of each segment is above the right endpoint of the segment in the previous slab. In addition, the point on the first vertical line is below the left endpoint of the first segment, and the point on the last vertical line is above the...

This thesis explores two specific topics of discrete geometry, the multitriangulations and the polytopal realizations of products, whose connection is the problem of finding polytopal realizations of a given combinatorial structure. A k-triangulation is a maximal set of chords of the convex n-gon such that no k+1 of them mutually cross. We propose a combinatorial and geometric study of multitri...

BACKGROUND Sensitizing events may trigger and stimulate discursive renewal. From a discursive institutional perspective, changing discourses are the driving force behind the institutional dynamics of policy domains. Theoretically informed by discursive institutionalism, this article assesses the impact of a series of four sensitizing events that triggered serious environmental health concerns i...

this paper presents participation of faculties and heads of department (hods) in environmental education. for this purpose 60 hods/faculties from polytechnic colleges of tamilnadu, india and 100 hods/ faculties from associate degree level technical institutions in iran from civil engineering branch were selected. several hypotheses were formulated to achieve certain objectives of the study. th...

4 A drawing of a graph is pseudolinear if there is a pseudoline arrangement such that 5 each pseudoline contains exactly one edge of the drawing. The pseudolinear crossing 6 number c̃r(G) of a graph G is the minimum number of pairwise crossings of edges in 7 a pseudolinear drawing of G. We establish several facts on the pseudolinear crossing 8 number, including its computational complexity and i...

Fish and other aquatic vertebrates use their mechanosensory lateral line to detect objects and motion in their immediate environment. Differences in lateral line morphology have been extensively characterized among species; however, intraspecific variation remains largely unexplored. In addition, little is known about how environmental factors modify development of lateral line morphology. Pred...

This paper is about two arrangements of hyperplanes. The first — the Shi arrangement — was introduced by Jian-Yi Shi to describe the Kazhdan-Lusztig cells in the affine Weyl group of type A. The second — the Ish arrangement — was recently defined by the first author who used the two arrangements together to give a new interpretation of the q, t-Catalan numbers of Garsia and Haiman. In the prese...