Open Alexandrov spaces of nonnegative curvature

Let $X$ be an open (i.e. complete, non-compact and without boundary) Alexandrov $n$-space of nonnegative curvature with a soul $S$. In this paper, we will establish several structural results on $X$ that can be viewed as counterparts of structural results on an open Riemannian manifold with nonnegative sectional curvature.Comment: 39page

Bio-inspired Design and Fabrication of Super-Strong and Multifunctional Carbon Nanotube Composites

Carbon nanotubes (CNTs) are ideal scaffolds to design and architect high-performance composites at high CNT volume fractions. In these composites, the CNT alignment determines the level of aggregation and the structure morphology, and thus the load transfer efficiency between neighboring CNTs. Here, we discuss two major solutions to produce high-volume fraction CNT composites, namely the layer-by-layer stacking of aligned CNT sheets and the stretching of entangled CNT webs (networks). As inspired by the growth procedure of natural composites, the aggregation of CNTs can be well controlled during the assembling process. As a result, the CNTs can be highly packed, aligned, and importantly unaggregated, with the impregnated polymers acting as interfacial adhesion or mortars to build up the composite structure. The CNT/bismaleimide composites can yield a super-high tensile strength up to 6.27–6.94 GPa and a modulus up to 315 GPa