It is shown that if a planar straight line graph (PSLG) with n vertices in general position in the plane can be augmented to a 3-edge-connected PSLG, then 2n−2 new edges are enough for the augmentation. This bound is tight: there are PSLGs with n ≥ 4 vertices such that any augmentation to a 3-edge-connected PSLG requires 2n− 2 new edges.

It is shown that every connected planar straight line graph with n ≥ 3 vertices has an embedding preserving augmentation to a 2-edge connected planar straight line graph with at most b(2n − 2)/3c new edges. It is also shown that every planar straight line tree with n ≥ 3 vertices has an embedding preserving augmentation to a 2-edge connected planar topological graph by adding at most bn/2c edge...

Familial prevalence of mitral valve prolapse in a Chinese population was determined in 22 propositi of whom 10 had straight back (group A), three had abnormally high metacarpal index (group B), and nine had neither (group C). Of 71 (32 male and 39 female subjects) first degree relatives screened, mitral valve prolapse was found in 19 (seven male and 12 female subjects) (26.8%). The familial pre...

prediction of mechanical properties of carbon nanotube-based composite is one of the important issues which should be addressed reasonably. a proper modeling approach is a multi-scale technique starting from nano scale and lasting to macro scale passing in-between scales of micro and meso. the main goal of this research is to develop a multi-scale modeling approach to extract mechanical propert...