A sufficient condition for kernel perfectness of a digraph in terms of semikernels modulo F

A kernel of a directed graph is a set of vertices which is both independent and absorbent. And a digraph is said to be kernel perfect if and only if any induced subdigraph has a kernel. Given a set of arcs F , a semikernel S modulo F is an independent set such that if some Sz-arc is not in F , then there exists a zS-arc. A sufficient condition on the digraph is given in terms of semikernel modulo F in order to guarantee that a digraph is kernel perfect. To do that we give a characterization of kernel perfectness which is a generalization of a previous result given by Neumann-Lara [Seminúcleos de una digrfica. Anales del Instituto de Matemticas 2, Universidad Nacional Autónoma de México, 1971]. And moreover, we show by means of an example that our result is independent of previous known sufficient conditions.     

On second order degree of graphs

Given a vertex v of a graph G the second order degree of v denoted as d 2(v) is defined as the number of vertices at distance 2 from v.In this paper we address the following question:What are the sufficient conditions for a graph to have a vertex v such that d2(v) ≥ d(v),where d(v) denotes the degree of v? Among other results,every graph of minimum degree exactly 2,except four graphs,is shown to have a vertex of second order degree as large as its own degree.Moreover,every K-4-free graph or every maximal planar graph is shown to have a vertex v such that d2(v) ≥ d(v).Other sufficient conditions on graphs for guaranteeing this property are also proved.     

Study of the mechanism of intumescence in fire retardant polymers: Part II—Mechanism of action in polypropylene-ammonium polyphosphate-pentaerythritol mixtures

It is shown that, by the addition of a typical intumescent mixture of ammonium polyphosphate and pentaerythritol to polypropylene, the mechanism of intumescence which develops on heating is not significantly affected by dispersion of the intumescent mixture in the polymer. On the other hand, in these mixtures, polypropylene seems to evolve, by thermal degradation, a smaller amount of flammable products than when it is heated alone. The ammonium polyphosphate-pentaerythritol additive is shown to induce fire retardant characteristics in polypropylene by means of a ‘condensed phase’ mechanism.     

Diameter vulnerability of GC graphs

Concern over fault tolerance in the design of interconnection networks has stimulated interest in finding large graphs with maximum degree Δ and diameter D such that the subgraphs obtained by deleting any set of s vertices have diameter at most D′, this value being close to D or even equal to it. This is the so-called (Δ,D,D′,s)-problem. The purpose of this work has been to study this problem for s=1 on some families of generalized compound graphs. These graphs were designed by Gómez (Ars Combin. 29-B (1990) 33) as a contribution to the (Δ,D)-problem, that is, to the construction of graphs having maximum degree Δ, diameter D and an order large enough. When approaching the mentioned problem in these graphs, we realized that each of them could be redefined as a compound graph, the main graph being the underlying graph of a certain iterated line digraph. In fact, this new characterization has been the key point to prove in a suitable way that the graphs belonging to these families are solutions to the (Δ,D,D+1,1)-problem.     

Ab initio molecular dynamics simulations of the oxygen reduction reaction on a Pt(111) surface in the presence of hydrated hydronium (H3O)(+)(H2O)2: direct or series pathway?

Car-Parrinello molecular dynamics simulations have been performed to investigate the oxygen reduction reaction (ORR) on a Pt(111) surface at 350 K. By progressive loading of (H3O)(+)(H2O)(2,3) + e- into a simulation cell containing a Pt slab and O2 for the first reduction step, and either products or intermediate species for the subsequent reduction steps, the detailed mechanisms of the ORR are well illustrated via monitoring MD trajectories and analyzing Kohn-Sham electronic energies. A proton transfer is found to be involved in the first reduction step; depending on the initial proton-oxygen distance, on the degree of proton hydration, and on the surface charge, such transfer may take place either earlier or later than the O2 chemisorption, in all cases forming an adsorbed end-on complex H-O-O*. Decomposition of H-O-O* takes place with a rather small barrier, after a short lifetime of approximately 0.15 ps, yielding coadsorbed oxygen and hydroxyl (O + HO*). Formation of the one-end adsorbed hydrogen peroxide, HOO*H, is observed via the reduction of H-O-O*, which suggests that the ORR may also proceed via HOO*H, i.e., a series pathway. However, HOO*H readily dissociates homolytically into two coadsorbed hydroxyls (HO* + HO*) rather than forming a dual adsorbed HOOH. Along the direct pathway, the reduction of H-O* + O* yields two possible products, O* + H2O* and HO* + HO*. Of the three intermediates from the second electron-transfer step, HOO*H from the series pathway has the highest energy, followed by O* + H2O* and HO* + HO* from the direct pathway. It is therefore theoretically validated that the O2 reduction on a Pt surface may proceed via a parallel pathway, the direct and series occurring simultaneously, with the direct as the dominant step.     

Mechanism of action of a fire retardant chloroparaffin

The mechanism by which a typical fire retardant chloroparaffin imparts fire retardant characteristics to high density polyethylene, polypropylene and polystyrene is studied by comparing the oxygen indices of these mixtures measured before and after dehydrochlorination. It is shown that flame poisoning by HCl evolved from the chloroparaffin is negligible in polystyrene and high density polyethylene, whereas it is noticeable in polypropylene. The results obtained are related to previous data on the thermal degradation of these mixtures. It is concluded that the chloroparaffin acts mainly by modifying the mechanism of pyrolysis of these polymers in the burning process. Only in the case of polypropylene is there an appreciable contribution by flame poisoning.     

Intercalation ofn-alkylamines into α-titanium phosphate from aqueous solutions

Journal of Inclusion Phenomena and Macrocyclic Chemistry - The intercalation reactions betweenn-alkylamines and α-titanium phosphate in aqueous media have been investigated. The compounds with...     

Thermal degradation of polymer-fire retardant mixtures: Part IV—Mechanism of fire retardancy in polypropylene-chlorinated paraffin mixtures

From oxygen and nitrous oxide indices of polypropylene-chlorinated paraffin mixtures it can be deduced that, in addition to the flame poisoning effect of HCl eliminated by the chloroparaffin, the lower flammability of the volatile products formed by thermal degradation of polypropylene heated in the presence of this additive seems to contribute to its fire retardance activity.     

Determination of the Composition of Cyclopolymers in Terms of Structural Units

A method based on the analytical evaluation of residual unsaturations and on the knowledge of the cyclization ratios is presented for the determination of the cyclopolymer composition in terms of structural units. The application of this method to the products of the free radical polymerization of vinyl-transcrotonate and of divinyl ether is described.