On Stabilization of EkE_k Chains

We study special subgroups of infinite groups that generalize double centralizers. We analyze sufficient conditions for descending chains of such subgroups to stop after finitely many steps. We discuss whether this phenomenon can happen in the class of groups satisfying chain condition on centralizers

Essential work of fracture of poly(ϵ-caprolactone)/boehmite alumina nanocomposites: Effect of surface coating

The essential work of fracture (EWF) approach has been adopted to reveal the effect of nanofillers on the toughness of poly(ε-caprolactone)/boehmite alumina (PCL/BA) nanocomposites. Synthetic BA particles of different surface treatments were dispersed in the PCL matrix by extrusion melt compounding. The morphology of composites was studied by scanning electron microscopy. Differential scanning calorimetry and wide angle X-ray scattering were used to detect changes in the crystalline structure of PCL. Besides the mode I type EWF tests, dynamic mechanical analysis (DMA) and quasi-static tensile tests were applied to study the effect of BA nanofillers on the mechanical properties. BA was homogenously dispersed and acted as heterogeneous crystallization nucleant and non-reinforcing filler in PCL. The tensile modulus and yield strength slightly increased, whereas the yield strain decreased with increasing BA content (up to 10 wt%). Effect of the BA surface treatment with octylsilane (OS) was negligible by contrast to alkylbenzene sulphonic acid (OS2). Like the tensile mechanical data, the essential and non-essential work of fracture parameters did not change significantly, either. Improved PCL/BA adhesion in case of OS2 treatment excluded the usual EWF treatise. This was circumvented by making use of energy partitioning between yielding and necking. The yielding related essential work of fracture decreased while the non-essential one increased with BA content and with better interfacial adhesion. This was attributed to the effect of matrix/filler debonding

Finite Volume Method for the Relativistic Burgers Model on a (1+1)-Dimensional de Sitter Spacetime

Several generalizations of the relativistic models of Burgers equations have recently been established and developed on different spacetime geometries. In this work, we take into account the de Sitter spacetime geometry, introduce our relativistic model by a technique based on the vanishing pressure Euler equations of relativistic compressible fluids on a (1+1)-dimensional background and construct a second order Godunov type finite volume scheme to examine numerical experiments within an analysis of the cosmological constant. Numerical results demonstrate the efficiency of the method for solutions containing shock and rarefaction waves