Supports of Weighted Equilibrium Measures: Complete Characterization

In this paper, we prove that a compact set K???? ⁿ is the support of a weighted equilibrium measure if and only it is not pluripolar at each of its points, extending a result of Saff and Totik to higher dimensions. Thus, we characterize the supports of weighted equilibrium measures completely. Our proof is a new proof even in one dimension.     

Local and global -regularity

A bounded domain is called -regular if the plurisubharmonic envelope of every continuous function on extends continuously to . We show using Gauthier's Fusion Lemma that a domain is locally -regular if and only if it is -regular.

     

Nanomorphology and fire behavior of polystyrene/organoclay nanocomposites containing brominated epoxy and antimony oxide

Organoclay nanocomposites were prepared by ultrasound‐assisted solution intercalation technique based on polystyrene containing brominated epoxy and a combination of brominated epoxy and antimony oxide. Aspects of nanomorphology and nanodispersion were investigated by X‐ray diffraction and transmission electron microscopy whereas flammability and reaction to fire were evaluated using limiting oxygen index, UL‐94, and mass loss calorimeter tests. Polystyrene/brominated‐epoxy‐blend‐based nanocomposites showed mixed intercalated–exfoliated nanomorphology where polymer‐intercalated crystallites predominantly exist in polystyrene matrix and exfoliated silicate layers reside on polystyrene/brominated epoxy phase boundaries and within brominated epoxy domains. Organoclay was found to impart a compatibilization effect on polystyrene and dispersed brominated epoxy, which facilitates uniform distribution of a fine flame‐retarding phase within the matrix. With the reduction of the rate at which decomposition products evolve into the gas phase, organoclay nanocomposites showed notable reductions in peak heat release rate and increases in limiting oxygen index. The gas‐phase hot radical entrapment by halogenated flame‐retardant system was coupled with the condensed‐phase physical action of nanodispersed organoclay, which increased the overall fire‐retardant effectiveness. Fire‐retardant mechanisms of nanocomposites based on polystyrene/brominated epoxy blends were attributed to nanoconfinement and tortuous pathway effects of organoclay rather than to carbonaceous char formation proposed earlier for polystyrene/organoclay systems without conventional flame retardants. Copyright © 2011 John Wiley & Sons, Ltd.     

The critical speed of a moving time-harmonic load acting on a system consisting a pre-stressed orthotropic covering layer and a pre-stressed half-plane

The dynamic response of a system consisting of an initially stressed covering layer and an initially stressed half-plane to a moving time-harmonic load is investigated within the scope of the piecewise-homogeneous body model utilizing three-dimensional linearized wave propagation theory in the initially stressed body. It is assumed that the material of the layer and half-plane is orthotropic. It is also assumed that the velocity of the line-located time harmonic moving load which acts on the covering layer is constant. The investigations were carried out were for the plane-strain state under subsonic velocity of the moving load for two types of contact conditions, namely: complete and incomplete. An algorithm is developed for the determination of the values of the moving load’s critical velocity. For various values of the problem parameters the numerical results were presented and discussed.