The first purpose of this paper is to propose a formulation of general area-preserving motion of polygonal curves by using a system of ODEs. Solution polygonal curves belong to a prescribed polygonal class, which is similar to admissible class used in the so-called crystalline curvature flow. Actually, if the initial curve is a convex polygon, then our polygonal flow is nothing but the crystall...

in this paper, an ultra low carbon high strength low alloy grade steel was subjected to a two-step forging processand this was followed by different post cooling methods. the highest strength was obtained at a faster coolingrate due to the highly dislocated acicular ferrite structure with the fine precipitation of microalloying carbides andcarbonitrides. at a slow cooling rate, the strength fel...

Consider a planar linkage, consisting of disjoint polygonal arcs and cycles of rigid bars joined at incident endpoints (polygonal chains), with the property that no cycle surrounds another arc or cycle. We prove that the linkage can be continuously moved so that the arcs become straight, the cycles become convex, and no bars cross while preserving the bar lengths. Furthermore, our motion is pie...

Consider a planar linkage, consisting of disjoint polygonal arcs and cycles of rigid bars joined at incident endpoints (polygonal chains), with the property that no cycle surrounds another arc or cycle. We prove that the linkage can be continuously moved so that the arcs become straight, the cycles become convex, and no bars cross while preserving the bar lengths. Furthermore, our motion is pie...

We will prove that a closed connected set S in ET whose points of local nonconvexity can be decomposed into a finite number of convex parts also possesses a simple type of polygonal connectedness. Furthermore, if S has a finite number of points of local nonconvexity, we obtain another result. In order to describe this situation easily we use the notation of Ln set used by Horn and Valentine [l ...