1. Conjunts numèrics

2022/202

Fonaments matemàtics : àlgebra i Càlcul

2013/201

Introducció a la lògica

2013/201

Estadística : problemes resolts

Contingut:1 Probabilitat 2 Combinatòria 3 Models de probabilitat discrets 4 Models de probabilitat continus 5 Mostreig 6 Estimadors 7 Intervals de confiança 8 Contrast d'Hipòtesi 9 Exàmens 10 Bibliografia2016/201

GD Geometria per al disseny. Pràctiques

2022/202

Point set stratification and minimum weight structures

Three different concepts of depth in a point set are considered and compared: Convex depth, location depth and Delaunay depth. As a notion of weight is naturally associated to each depth definition, we also present results on minimum weight structures (like spanning trees, poligonizations and triangulations) with respect to the three variations.DURSYMinisterio de Ciencia y Tecnologí

Metric dimension of maximal outerplanar graphs

In this paper, we study the metric dimension problem in maximal outerplanar graphs. Concretely, if ß(G) denotes the metric dimension of a maximal outerplanar graph G of order n, we prove that 2=ß(G)=¿2n5¿ and that the bounds are tight. We also provide linear algorithms to decide whether the metric dimension of G is 2 and to build a resolving set S of size ¿2n5¿ for G. Moreover, we characterize all maximal outerplanar graphs with metric dimension 2.Peer ReviewedPostprint (author's final draft

Properties for Voronoi diagrams of arbitrary order on the sphere

For a given set of points U on a sphere S, the order k spherical Voronoi diagram SV_k(U) decomposes the surface of S into regions whose points have the same k nearest points of U. We study properties for SV_k(U), using different tools: the geometry of the sphere, a labeling for the edges of SV_k(U), and the inversion transformation. Hyeon-Suk Na, Chung-Nim Lee, and Otfried Cheong (Comput. Geom., 2002) applied inversions to construct SV_1(U). We generalize their construction for spherical Voronoi diagrams from order 1 to any order k. We use that construction to prove formulas for the numbers of vertices, edges, and faces in SV_k(U). Among the properties of SV_k(U), we also show that SV_k(U) has a small orientable cycle double cover.Postprint (published version

Paired and semipaired domination in near-triangulations

A dominating set of a graph G is a subset D of vertices such that every vertex not in D is adjacent to at least one vertex in D. A dominating set D is paired if the subgraph induced by its vertices has a perfect matching, and semipaired if every vertex in D is paired with exactly one other vertex in D that is within distance 2 from it. The paired domination number, denoted by ¿pr(G), is the minimum cardinality of a paired dominating set of G, and the semipaired domination number, denoted by ¿pr2(G), is the minimum cardinality of a semipaired dominating set of G. A near-triangulation is a biconnected planar graph that admits a plane embedding such that all of its faces are triangles except possibly the outer face. We show in this paper that ¿pr(G) = 2b n 4 c for any neartriangulation G of order n = 4, and that with some exceptions, ¿pr2(G) = b 2n 5 c for any near-triangulation G of order n = 5.Peer ReviewedPreprin