A theorem now known as Sperner’s Lemma [5] states that a largest collection of subsets of an n-element set such that no subset contains another is obtained by taking the collection of all the subsets with cardinal bn=2c. (We denote by bxc, resp. dxe, the largest integer less than or equal to x, resp. the smallest integer greater than or equal to x.) In other words, the density of a largest anti...

Saving a patients live in an emergency state especially if he is far from medical institutions, is considered to be the primary concern of the physician. With a mobile physician, patients health state may vary to be in a critical situation that requires immediate medical intervention. Having chosen the medical institution as destination, the doctor must react immediately and reach his patient a...

Given a rectangle A and a set S of n points in A, we consider the problem, called the maximum empty rectangle problem, of finding a maximum area rectangle that is fully contained in A and does not contain any point of S in its interior. An O(n’) time algorithm is presented. Furthermore, it is shown that if the points of S are drawn randomly and independently from A, the problem can be solved in...

in this paper we show that if q is a power of a prime p , then the projective special linear group psl(2, q) and the stabilizer of a point of the projective line have maximum sum element orders among all proper subgroups of projective general linear group pgl(2, q) for q odd and even respectively

A generalized pseudo effect algebra (GPEA) is a partially ordered partial algebraic structure with a smallest element 0, but not necessarily with a unit (i.e, a largest element). If a GPEA admits a so-called unitizing automorphism, then it can be embedded as an order ideal in its so-called unitization, which does have a unit. We study unitizations of GPEAs with respect to a unitizing automorphi...

‎We characterize the finite simple groups $L_2(q)$ by the group orders and the largest‎ ‎element orders‎, ‎where $q$ is a prime or $q=2^a$‎, ‎with $2^a+1$ or $2^a-1$ a prime‎.