On a conjecture about the Randi? index

A conjecture of Delorme, Favaron and Rautenbach [On the Randi? index, Discrete Math. 257 (2002) 29-38] about the Randi? index of a graph, in relation to its order and minimum degree, is refuted by the AutoGraphiX 2 system. Moreover, a modified conjecture is derived from presumably extremal graphs obtained with that system.     

NMR and DSC investigations of the miscibility of blends of cis-1,4-polyisoprene with polybutadienes of different microstructures

Differential scanning calorimetry and torsional braid analysis investigations of the phase diagram of cis-1,4-polyisoprene/polybutadiene blends as a function of the polybutadiene microstructure were reported by several authors. Polybutadienes containing a high vinyl content were shown to be miscible with cis-1,4-polyisoprene on the DSC spatial scale, whereas polybutadienes containing a low vinyl content were immiscible. In this article, we used variable-temperature determinations of ¹H NMR free induction decays and low-temperature, high-resolution solid-state ¹³C NMR measurements of proton spin-lattice relaxation times in the rotating frame to probe the phase behavior of the cis-1,4-polyisoprene/polybutadiene blends at the smaller spatial scale of the NMR technique. Blends of cis-1,4-polyisoprene with a polybutadiene having a large number of vinyl 1,2 linkages appeared to be miscible on the molecular scale, in spite of small regions in which the polybutadiene component is not uniformily dispersed in the other polymer. On the contrary, blends in which the polybutadiene has a low content of vinyl 1,2 sequences were phase separated over the whole temperature range considered and no intermixed regions could be detected. The limiting case was observed with the polybutadiene containing 33 wt % vinyl 1,2 units, for which miscibility on a molecular scale is highly dependent on the blend composition. © 1995 John Wiley & Sons, Inc.     

Aromatization of cyclohexadienes by TEMPO electro-mediated oxidation: Kinetic and structural aspects

Cyclohexadienes are easily converted into the corresponding aromatics in excellent yield (>90%) in the presence of 2,2,6,6-tetramethyl-1-oxopiperidinium ion (TEMPO⁺). The TEMPO radical was used in catalytic amount and was electrochemically regenerated in the presence of 2,6-lutidine as a base in hydro-organic medium (AcCN/H₂O 95/5). This work has been focused on the kinetic aspects. We have demonstrated that the reactivity of different cyclohexadienes is strongly dependent on the configuration of the double bonds and on the nature of the substituents. Competition between allylic functionalization and aromatization has been observed during the oxidation of 1,2-dihydro-4-phenylnaphthalene.     

Sweeping process with right uniformly lower semicontinuous mappings

Positivity - In this paper, we establish, in the setting of infinite dimensional Hilbert space, a new existence result for nonconvex sweeping process with right uniformly lower semicontinuous sets....     

Polymerization-induced Phase Separation: Phase Behavior Developments and Hydrodynamic Interaction

The process of polymer synthesis based on polymerization-induced phase separation (PIPS) is revisited from the theoretical point of view. Cahn–Hilliard–Cook theories for spinodal decomposition are adapted to describe the kinetics of phase separation and deduce the time-resolved scattering function, while the double reaction model is used to describe the kinetics of polymerization. Coupling of these two kinetics is provided by the Carother's equation relating the fraction of reacted monomers to the degree of polymerization at time t, denoted N(t). It is argued that the approach to criticality is governed by a critical parameter, χ_c, that is different from the usual parameter for spinodal decomposition, χ_s, deduced from the second derivative of the free energy. While the latter parameter depends on the reciprocal degree of polymerization N^?1(t), the former one depends on its time integral. This leads to significant consequences on the phase behavior developments during the PIPS process. Hydrodynamic interactions are found to speed up the emergence of instability modes. Although the qualitative trends remain similar to those of the Rouse dynamics, important quantitative changes are found due to the long-range viscous flow effects.     

Asymptotic analysis of contact problems between an elastic material and thin-rigid plates

We consider an elastic material in contact with a three-dimensional rigid plate of varying thickness. We suppose that a perfect adhesion occurs along thin zones disposed in a self-similar way on the interface between the two materials. We suppose that the elasticity coefficients in the plate depend on its thickness and tend to infinity as this thickness tends to zero. We derive the effective material properties using Γ-convergence methods.     

Transmissions of quantum entangled states in anisotropic depolarizing channels

We investigate the effect of an anisotropic depolarizing channel on the classical transmission of quantum entangled states. We calculate numerically mutual information between honest parts as a function of the degree of anisotropy of the depolarizing channel. In contrast to the case of isotropic channels, we found that the mutual information depends on both the degree of anisotropy and the degree of entanglement. It increases with increase in the degree of entanglement for a quantum channel with sufficiently large depolarizing anisotropy and decreases with increase in the entanglement.     

Sous ellipticite dans le cadre du calcul S(m,g)

Abstract

We study the regularity of the free boundary in the two membranes problem. We prove that around any point the free boundary is either a C ^{1, α} surface or a cusp, as in the obstacle problem. We also prove C ^{1, 1} regularity for the pair of functions solving the problem.     

Design,synthesis, characterization and catechol oxidase activity of novel class of multi-tripodal pyrazole and triazole-based derivatives

Research on Chemical Intermediates - A class of novel multi-tripodal ligands has been prepared via condensation reaction between pyrazole or triazole moieties and...