Search results for "Polyhedra"
showing 10 items of 43 documents
Controlled polyhedral sweeping processes: existence, stability, and optimality conditions
2021
This paper is mainly devoted to the study of controlled sweeping processes with polyhedral moving sets in Hilbert spaces. Based on a detailed analysis of truncated Hausdorff distances between moving polyhedra, we derive new existence and uniqueness theorems for sweeping trajectories corresponding to various classes of control functions acting in moving sets. Then we establish quantitative stability results, which provide efficient estimates on the sweeping trajectory dependence on controls and initial values. Our final topic, accomplished in finite-dimensional state spaces, is deriving new necessary optimality and suboptimality conditions for sweeping control systems with endpoint constrain…
The Windy clustered prize-collecting arc-routing problem
2011
This paper introduces the windy clustered prize-collecting arc-routing problem. It is an arc-routing problem where each demand edge is associated with a profit that is collected once if the edge is serviced, independent of the number of times the edge is traversed. It is further required that if a demand edge is serviced, then all the demand edges of its component are also serviced. A mathematical programming formulation is given and some polyhedral results including several facet-defining and valid inequalities are presented. The separation problem for the different families of inequalities is studied. Numerical results from computational experiments are analyzed. © 2011 INFORMS.
Historical Notes on Star Geometry in Mathematics, Art and Nature
2018
Gamma: “I can. Look at this Counterexample 3: a star-polyhedron I shall call it urchin. This consists of 12 star-pentagons. It has 12 vertices, 30 edges, and 12 pentagonal faces-you may check it if you like by counting. Thus the Descartes-Euler thesis is not true at all, since for this polyhedron \(V - E + F = - 6\)”. Delta: “Why do you think that your ‘urchin’ is a polyhedron?” Gamma: “Do you not see? This is a polyhedron, whose faces are the twelve star-pentagons”. Delta: “But then you do not even know what a polygon is! A star-pentagon is certainly not a polygon!”
Computational Homogenization of Heterogeneous Materials by a Novel Hybrid Numerical Scheme
2020
The Virtual Element Method (VEM) is a recent numerical technique capable of dealing with very general polygonal and polyhedral mesh elements, including irregular or non-convex ones. Because of this feature, the VEM ensures noticeable simplification in the data preparation stage of the analysis, especially for problems whose analysis domain features complex geometries, as in the case of computational micro-mechanics problems. The Boundary Element Method (BEM) is a well known, extensively used and effective numerical technique for the solution of several classes of problems in science and engineering. Due to its underlying formulation, the BEM allows reducing the dimensionality of the proble…
Novel Imidazolium Based Catalyst for the Chemical Fixation of Carbon Dioxide
2015
The project scheduling polyhedron: Dimension, facets and lifting theorems
1993
Abstract The Project scheduling with resource constraints can be formulated as follows: given a graph G with node set N, a set H of directed arcs corresponding to precedence relations, and a set H′ of disjunctive arcs reflecting the resource incompatibilities, find among the subsets of H′ satisfying the resource constraints the set S that minimizes the longest path in graph (N, H ∪ S). We define the project scheduling polyhedron Qs as the convex hull of the feasible solutions. We investigate several classes of inequalities with respect to their facet-defining properties for the associated polyhedron. The dimension of Qs is calculated and several inequalities are shown to define facets. For …
Reinforced cyclam derivatives functionalized on the bridging unit
2016
International audience; A new synthetic method has been developed for the preparation of reinforced cyclams (1,4,8,11-tetraazacyclotetradecane) C-functionalized on the bridging unit, by using a "one pot" reaction starting from the appropriate bis-aminal cyclam intermediate. The high reactivity of quaternized aminal moiety toward nucleophilic agent has been used to elaborate a new class of cross-bridged and side-bridged cyclam derivatives containing cyanide group on the ethylene bridge. Several chelators and corresponding copper(II) complexes have been prepared and characterized by X-ray diffraction. These new constrained polyazamacrocycles are valuable precursors of bifunctional chelating a…
The mixed general routing polyhedron
2003
[EN] In Arc Routing Problems, ARPs, the aim is to find on a graph a minimum cost traversal satisfying some conditions related to the links of the graph. Due to restrictions to traverse some streets in a specified way, most applications of ARPs must be modeled with a mixed graph. Although several exact algorithms have been proposed, no polyhedral investigations have been done for ARPs on a mixed graph. In this paper we deal with the Mixed General Routing Problem which consists of finding a minimum cost traversal of a given link subset and a given vertex subset of a mixed graph. A formulation is given that uses only one variable for each link (edge or arc) of the graph. Some properties of the…
Characterizing extreme points of polyhedra an extension of a result by Wolfgang Bühler
1982
This paper reconsiders the characterization given by Buhler admitting convex polyhedra of probability distributions on a finite or countable set which are given by systems of linear inequalities more complex than those considered before.