The availabilities of light and soil water resources usually spatially co-vary in natural habitats, and the spatial pattern of such co-variation may affect the benefits of physiological integration between connected ramets of clonal plants. In a greenhouse experiment, we grew connected or disconnected ramet pairs [consisting of a proximal (relatively old) and a distal (relative young) ramet] of...

This paper is a survey of our work based on the stratified Morse theory of Goresky and MacPherson. First we discuss the Morse theory of Euclidean space stratified by an arrangement. This is used to show that the complement of a complex hyperplane arrangement admits a minimal cell decomposition. Next we review the construction of a cochain complex whose cohomology computes the local system cohom...

These notes provide a self-contained account of the combinatorial theory of intrinsic volumes for polyhedral cones. Streamlined derivations of the General Steiner formula, the conic analogues of the Brianchon-Gram-Euler and the Gauss-Bonnet relations, and the Principal Kinematic Formula are given. In addition, a connection between the characteristic polynomial of a hyperplane arrangement and th...

We report on the definition and characteristics of nodes in the chaotic region of bifurcation diagrams in the case of 1D mono-parametrical and S-unimodal maps, using as guiding example the logistic map. We examine the arrangement of critical curves, the identification and arrangement of nodes, and the connection between the periodic windows and nodes in the chaotic zone. We finally present seve...

Introduction. A pseudoline is formed from a line by stretching the plane without tearing: it is the image of a line under a homeomorphism of the plane [13]. In arrangements of pseudolines, pairs of pseudolines intersect at most once and cross at their intersections. Pseudoline arrangements can be used to model sorting networks [1], tilings of convex polygons by rhombi [4], and graphs that have ...

We generalize the Hadwiger theorem on line transversals to collections of compact convex sets in the plane to the case where the sets are connected and the transversals form an arrangement of pseudolines. The proof uses the embeddability of pseudoline arrangements in topological affine planes. In 1940 Santaló showed [8], by an example, that Vincensini’s proof [9] of an extension of Helly’s theo...

Let G be a graph embedded in the plane and let A be an arrangement of pseudolines intersecting the drawing of G. An aligned drawing of G and A is a planar polyline drawing Γ of G with an arrangement A of lines so that Γ and A are homeomorphic to G and A. We show that if A is stretchable and every edge e either entirely lies on a pseudoline or intersects at most one pseudoline, then G and A have...

With growth the construction technologies, Cold-Formed Steel, CFS, sections are widely used in ordinary steel buildings because of some advantages such as light weight, ease of installation, decrease in cost, and increase in speed of operation. Using the bolted connections for CFS joist is one of the best details for steel structures. The main objective of this study is to conduct an experiment...

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...