In this paper, we propose a pair of shape features for shape-similarity search of 3D polygonal-mesh models. The shape features are extension of the D2 shape functions proposed by Osada et al. [Osada01, Osada02]. Our proposed shape features are tolerant of topological variations and geometrical degeneracies. Our shape feature is also invariant to similarity transformation. Experiments showed tha...

In this paper, an ultra low carbon High Strength Low Alloy Grade Steel was subjected to a two-step forging process and this was followed by different post cooling methods. The highest strength was obtained at a faster cooling rate due to the highly dislocated acicular ferrite structure with the fine precipitation of microalloying carbides and carbonitrides. At a slow cooling rate, the strength ...

In the article the formal characterization of triangular numbers (famous from [15] and words “EYPHKA! num = ∆ + ∆ + ∆”) [17] is given. Our primary aim was to formalize one of the items (#42) from Wiedijk’s Top 100 Mathematical Theorems list [33], namely that the sequence of sums of reciprocals of triangular numbers converges to 2. This Mizar representation was written in 2007. As the Mizar lang...