Highly edge‐connected detachments of graphs and digraphs

Let G = (V,E) be a graph or digraph and r : V → Z₊. An r‐detachment of G is a graph H obtained by ‘splitting’ each vertex ν ∈ V into r(ν) vertices. The vertices ν₁,…,ν_r(ν) obtained by splitting ν are called the pieces of ν in H. Every edge uν ∈ E corresponds to an edge of H connecting some piece of u to some piece of ν. Crispin Nash‐Williams 9 gave necessary and sufficient conditions for a graph to have a k‐edge‐connected r‐detachment. He also solved the version where the degrees of all the pieces are specified. In this paper, we solve the same problems for directed graphs. We also give a simple and self‐contained new proof for the undirected result. © 2003 Wiley Periodicals, Inc. J Graph Theory 43: 67–77, 2003     

Local chain‐configuration dependence of the mechanisms of the chemical reaction of poly(vinyl chloride). IX. Novel results on stereoselectivity of chlorination reaction

A poly(vinyl chloride) (PVC) sample was chlorinated in solution in the presence of 2,2′‐azobisisobutyronitrile and by the fluid‐bed method. The aim was to evaluate the scope of the stereoselectivity of the chlorination reaction. The quantitative microstructural analysis of the residual PVC with a degree of chlorination was followed by ¹³C NMR spectroscopy. From the evolution of the content of isotactic (mm), heterotactic (mr), and syndiotactic (rr) triads and of mmmm, mmmr, and rmmr isotactic pentads in the unchlorinated parts of the polymer, it was unambiguously inferred that the chlorination reaction proceeds by a stereoselective mechanism in that the mr heterotactic triads are the most reactive structures followed by the isotactic triad at mmmr and rmmr pentads. This conclusion was confirmed on the basis of the Fourier transform infrared results. The results provide valuable information regarding the effect of tacticity and related local conformations in the chemical reactions of PVC. © 2003 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 41: 508–519, 2003     

Determination of the rheological behavior of epoxy–amine thermosets by dynamic mechanical analysis: Isothermal methods versus nonisothermal methods

The reticulation process of an epoxy resin using an amine as a cure agent was studied at different temperatures and concentrations of the cure agent with dynamic mechanical thermal analysis. The study was performed under both isothermal and nonisothermal conditions, and a temperature–time–transformation diagram was obtained. The measurements from the two modes gave similar results, although the nonisothermal mode required fewer experiments. © 2003 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 41: 1965–1977, 2003     

Effects of alcohols on micellization and on the reaction methyl 4‐nitrobenzenesulfonate + Br− in cetyltrimethylammonium bromide aqueous micellar solutions

The effects of n‐hexanol, n‐pentanol, and n‐butanol on the critical micelle concentration (cmc), on the micellar ionization degree (α), and on the rate of the reaction methyl 4‐nitrobenzenesulfonate + Br^? have been investigated in cetyltrimethylammonium bromide (CTAB) aqueous solutions. An increase in the alcohol concentration present in the solution produces a decrease in the cmc and an increase in the micellar ionization degree. Kinetic data show that the observed rate constant decreases as alcohol concentration increases. This result was rationalized by considering variations in the equilibrium binding constant of the methyl 4‐nitrobenzenesulfonate molecules to the micelles, variations in the interfacial bromide ion concentration, and variations in the characteristics of the water–alcohol bulk phase provoked by the presence of alcohols. When these operative factors are considered, kinetic data in this and other works show that the second‐order rate constants in the micellar pseudophases of water–alcohol micellar solutions are quite similar to those estimated in the absence of alcohols. © 2004 Wiley Periodicals, Inc. Int J Chem Kinet 36: 634–641, 2004     

Analysis and finite element simulations of a second‐order fluid model in a bounded domain

This article is concerned with the equations governing the steady motion of a viscoelastic incompressible second‐order fluid in a bounded domain. A new proof of existence and uniqueness of strong solutions is given. In addition, using appropriate finite element methods to approximate a coupled equivalent problem, sharp error estimates are obtained using a fixed point argument. The method is applied to the two‐dimensional lid‐driven cavity problem, at low Reynolds number and in a certain range of values of the viscoelastic parameters, to analyze the combined effects of inertia and viscoelasticity on the flow. © 2007 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2007