33 research outputs found
Lower Bound for Convex Hull Area and Universal Cover Problems
In this paper, we provide a lower bound for an area of the convex hull of
points and a rectangle in a plane. We then apply this estimate to establish a
lower bound for a universal cover problem. We showed that a convex universal
cover for a unit length curve has area at least 0.232239. In addition, we show
that a convex universal cover for a unit closed curve has area at least
0.0879873.Comment: 12 pages, 9 figure
The Necessary and Sufficient Conditions for Representing Lipschitz Bivariate Functions as a Difference of Two Convex Functions
In the article the necessary and sufficient conditions for a representation
of Lipschitz function of two variables as a difference of two convex functions
are formulated. An algorithm of this representation is given. The outcome of
this algorithm is a sequence of pairs of convex functions that converge
uniformly to a pair of convex functions if the conditions of the formulated
theorems are satisfied. A geometric interpretation is also given