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

On the concavity of some functions connected with the two-dimensional normal distribution

The abstracts (in two languages) can be found in the pdf file of the article.&#x0D; Original author name(s) and title in Russian and Lithuanian:&#x0D; Н. А. Бодин, В. А. Залгаллер. Вогнутость некоторых функций, связанных с двумерных нормальным распределением&#x0D; N. Bodin, V. Zalgaller. Kai kurių funkcijų, susijusių su dvimačiu normaliniu pasiskirstymu, įgaubtumas</jats:p