Detecting intersecting surfaces and computing their intersection curves is one of the fundamental problems in solid modeling algebra. This paper introduces a new strategy to classify surfaces against their intersection status, where exact geometric entities are replaced by fuzzy geometric ones. Intersecting surfaces are thus replaced by fuzzy intersecting faces and a fuzzy intersection algorith...

This article follows the paper of Griffiths and Harris, "On the variety of special linear systems on a general algebraic curve." 1. WARMUP ON DEGENERATIONS The classic first problem in Schubert calculus is: how many lines intersect four general lines in P 3 ? First, what does this numerology come from? The space of lines in P 3 is G(1, 3) which has dimension 2 × 2 = 4. The locus of lines inters...

Efforts to involve data science in policy analysis can be traced back decades but transforming analytic findings into decisions is still far from straightforward task. Data-driven decision-making requires understanding approaches, practices, and research results many disciplines, which makes it interesting investigate whether are moving parallel or their pathways have intersected. Our investiga...

Numerical models based on linear elasticity theory predict asymmetric slip distribution with a steep slip gradient near the line of intersection of intersecting normal faults. They also predict a discrepancy between the direction of slip on the fault plane and the direction of resolved shear stress. Both variations in slip magnitude and direction are due to mechanical interaction between the fa...

In this paper we present a simple unifying approach to prove several statements about intersecting and cross-intersecting families, including the Erdős–Ko–Rado theorem, the Hilton–Milner theorem, a theorem due to Frankl concerning the size of intersecting families with bounded maximal degree, and versions of results on the sum of sizes of non-empty cross-intersecting families due to Frankl and ...

It is well known that an intersecting family of subsets of an nelement set can contain at most 2n−1 sets. It is natural to wonder how ‘close’ to intersecting a family of size greater than 2n−1 can be. Katona, Katona and Katona introduced the idea of a ‘most probably intersecting family.’ Suppose that A is a family and that 0 < p < 1. Let A(p) be the (random) family formed by selecting each set ...

Given a tree and a set P of non-trivial simple paths on it, Vpt(P) is the VPT graph (i.e. the vertex intersection graph) of the paths P of the tree T , and Ept(P) is the EPT graph (i.e. the edge intersection graph) of P. These graphs have been extensively studied in the literature. Given two (edge) intersecting paths in a graph, their split vertices is the set of vertices having degree at least...