Search results for "Polyhedra"

Copolymers of ethylene with monoalkenyl- and monoalkenyl(siloxy)silsesquioxane (POSS) comonomers – Synthesis and characterization

2017

Abstract The hybrid ethylene/POSS copolymers were obtained using the rac -Et(Ind) 2 ZrCl 2 catalyst activated by MAO. A series of monoalkenyl- and monoalkenyl(siloxy)silsesquioxanes derivatives with different structures of reactive alkenyl substituent and types of non-reactive groups attached to the T 8 POSS cage was used as comonomers. The kind and concentration of the POSS comonomer in the reaction feed as well as extended reaction time were found to strongly influence the catalyst efficiency and incorporation of POSS units into polymer chains. The comonomer reactivity was significantly dependent on the length of the alkenyl reactive substituent in the POSS molecule and it was highest for…

An exact algorithm for the min-cost network containment problem

2004

A network design problem which arises in the distribution of a public utility provided by several competitive suppliers is studied. The problem addressed is that of determining minimum-cost (generalized) arc capacities in order to accommodate any demand between given source–sink pairs of nodes, where demands are assumed to fall within predetermined ranges. Feasible flows are initially considered as simply bounded by the usual arc capacity constraints. Then, more general linear constraints are introduced which may limit the weighted sum of the flows on some subsets of arcs. An exact cutting plane algorithm is presented for solving both of the above cases and some computational results are re…

New Results on the Mixed General Routing Problem

2005

[EN] In this paper, we deal with the polyhedral description and the resolution of the Mixed General Routing Problem. This problem, in which the service activity occurs both at some of the nodes and at some of the arcs and edges of a mixed graph, contains a large number of important arc and node routing problems as special cases. Here, a large family of facet-defining inequalities, the Honeycomb inequalities, is described. Furthermore, a cutting-plane algorithm for this problem that incorporates new separation procedures for the K-C, Regular Path-Bridge, and Honeycomb inequalities is presented. Branch and bound is invoked when the final solution of the cutting-plane procedure is fractional. …

Wolfe's theorem for weakly differentiable cochains

2014

Abstract A fundamental theorem of Wolfe isometrically identifies the space of flat differential forms of dimension m in R n with the space of flat m -cochains, that is, the dual space of flat chains of dimension m in R n . The main purpose of the present paper is to generalize Wolfe's theorem to the setting of Sobolev differential forms and Sobolev cochains in R n . A suitable theory of Sobolev cochains has recently been initiated by the second and third author. It is based on the concept of upper norm and upper gradient of a cochain, introduced in analogy with Heinonen–Koskela's concept of upper gradient of a function.

An exact algorithm for the solution of a network design problem

2004

Self-assembly of catalytically-active supramolecular coordination compounds within metal-organic frameworks

2019

[EN] Supramolecular coordination compounds (SCCs) represent the power of coordination chemistry methodologies to self-assemble discrete architectures with targeted properties. SCCs are generally synthesized in solution, with isolated fully coordinated metal atoms as structural nodes, thus severely limited as metal-based catalysts. Metal-organic frameworks (MOFs) show unique features to act as chemical nanoreactors for the in situ synthesis and stabilization of otherwise not accessible functional species. Here, we present the self-assembly of Pd-II SCCs within the confined space of a pre-formed MOF (SCCs@MOF) and its post-assembly metalation to give a Pd-II-Au-III supra molecular assembly, c…

One-step reactive processing of low density polyethylene and octavinyl polyhedral oligomeric silsesquioxane

2015

Polyhedral oligomeric silsesquioxane (POSS) are an innovative class of organosilicon compounds suitable for formulation of advanced organic-inorganic hybrid materials. Nanocomposites based POSS found application mostly in high-temperature resistance and fire-resistance materials. POSS are characterized by a three dimensional cage-like structure, made of Si-O bonds, with different organic groups directly linked to the Si atoms of the cage structure. The organic groups can be designed to facilitate the dispersion of the nanoparticle itself in the polymer matrix or also to react with the polymer chain. This work focuses on the possibility to obtain crosslinking of polyethylene using octavinyl-…

Multi-Alkenylsilsesquioxanes as Comonomers and Active Species Modifiers of Metallocene Catalyst in Copolymerization with Ethylene.

2018

The copolymers of ethylene (E) with open-caged iso-butyl-substituted tri-alkenyl-silsesquioxanes (POSS-6-3 and POSS-10-3) and phenyl-substituted tetra-alkenyl-silsesquioxane (POSS-10-4) were synthesized by copolymerization over the ansa-metallocene catalyst. The influence of the kind of silsesquioxane and of the copolymerization conditions on the reaction performance and on the properties of the copolymers was studied. In the case of copolymerization of E/POSS-6-3, the positive comonomer effect was observed, which was associated with the influence of POSS-6-3 on transformation of the bimetallic ion pair to the active catalytic species. Functionality of silsesquioxanes and polymerization par…

Study of thermal properties of polyethylene and polypropylene nanocomposites with long alkyl chain-substituted POSS fillers

2016

The effect of incorporation of octakis({alkyl}dimethylsiloxy)octasilsesquioxanes molecules with n-octyl, n-octadecyl and 4-methyl-hexyl substituents on thermal properties of polypropylene (PP), low-density polyethylene (LDPE) and high-density polyethylene (HDPE) was investigated. Thermal properties of those composite materials were evaluated by means of the differential scanning calorimetry (DSC) and thermogravimetric analysis (TG) methods. The type and mass% content of POSS nanofillers influenced the crystallization and melting properties as well as thermal stability of the obtained polyolefin nanocomposites. The incorporated POSS particles—acting as nucleating agents—improved the crystall…

Formulations and valid inequalities for the capacitated dispersion problem

2023

This work focuses on the capacitated dispersion problem for which we study several mathematical formulations in different spaces using variables associated with nodes, edges, and costs. The relationships among the presented formulations are investigated by comparing the projections of the feasible sets of the LP relaxations onto the subspace of natural variables. These formulations are then strengthened with families of valid inequalities and variable-fixing procedures. The separation problems associated with the valid inequalities that are exponential in number are shown to be polynomially solvable by reducing them to longest path problems in acyclic graphs. The dual bounds obtained from s…