A spanning tree of an unweighted graph is a minimum average stretch spanning tree if it minimizes the ratio of sum of the distances in the tree between the end vertices of the graph edges and the number of graph edges. We consider the problem of computing a minimum average stretch spanning tree in polygonal 2-trees, a super class of 2-connected outerplanar graphs. For a polygonal 2-tree on n ve...

ß We develop an application to identify and characterize polygonal features in SAR images, based on a watershed algorithm, modified for a good robustness to radar noise. ß Our system performs a multi-scale analysis of the image. Oversegmentation is prevented by a selection of outstanding contours; regions with less prominent contours are merged ß This analysis is applied to Venus images from th...

In 2000 A. Bezdek asked which plane convex bodies have the property that whenever an annulus, consisting of the body less a sufficiently small scaled copy of itself, is covered by strips, the sum of the widths of the strips must still be at least the minimal width of the body. We characterise the polygons for which this is so. In this note we will give a complete answer for convex polygons to t...

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...

The paper presents numerical modelling and an operational experiment to forge a slab ingot P40N from 55NiCrMoV7 tool steel the procedure for optimization of its production. aim simulation forging was verify existing plate conventional polygonal 8K with shape surfaces. effect on achievement required reduction strain after cross section plate, final dimensions approximately 1010 mm width × 310 th...