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Let X be a non-singular irreducible complex projective curve of genus g ≥ 2. The concept of stability of coherent systems over X depends on a positive real parameter α, given then a (finite) family of moduli spaces of coherent systems. We use (t, ℓ)-stability to prove the existence of coherent systems over X that are α-stable for all allowed α > 0.
The fracture behavior of polypropylene (PP) and its composites was studied as a function of concentration of multiwall carbon nanotubes (MWCNT) and modified montmorillonite (m-MMT). SAXS and WAXS (Small/Wide Angle X-ray Scattering) techniques were used to monitor the morphological changes (i.e. nanocomposite structure and crystalline morphology) caused by various nanoparticle concentrations and polymer uniaxial stretching deformation. The effect of nanoparticle nature was also investigated. The mechanical analysis shows a great effect of nanoclay concentration on the PP deformation, while uniaxial stretching of the PP/MWCNT nanocomposites was less affected by carbon nanotubes concentration. The SAXS and WAXS analysis of stretched samples indicated that the pure polypropylene and nanocomposites with low nanoparticles concentrations (1 wt/wt%) developed a fracture governed by shear yielding mechanism, while PP nanocomposites with higher concentrations of carbon nanotubes and nanoclay showed a crazing and microcraking fracture mechanism. On the other hand, different chemical nature of MWCNT and m-MMT did not affect the fracture mechanism of polypropylene at low nanoparticles concentrations.
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