Mesopotamia, the land that is today part of Iraq, Syria, and Turkey, is home to one of the oldest civilizations to have ever been discovered. It is here that the civilizations of Sumer, Babylon, and Assyria existed. This land is noteworthy in the Bible because it was here that the exiles were taken captive after the destruction of Jerusalem. It was also here that Abraham had lived before he set...

In this paper, we generalize a result by Rubin and Ungar on Hamiltonian systems with a strong constraining potential to thermally embedded systems, i.e. to Langevin dynamics. Such highly oscillatory systems arise, for example, in the context of molecular dynamics. We derive averaged equations of motion for the slowly varying solution components. This includes in particular the derivation of a c...

Erdős, Purdy, and Straus conjectured that the number of distinct (nonzero) areas of the triangles determined by n noncollinear points in the plane is at least b 2 c, which is attained for dn/2e and respectively bn/2c equally spaced points lying on two parallel lines. We show that this number is at least 17 38 n − O(1) ≈ 0.4473n. The best previous bound, ( √ 2 − 1)n − O(1) ≈ 0.4142n, which dates...

In [Comput. Math. Appl. 41 (2001), 135–147], A.A. Ungar employs the Möbius gyrovector spaces for the introduction of the hyperbolic trigonometry. This Ungar’s work plays a major role in translating some theorems from Euclidean geometry to corresponding theorems in hyperbolic geometry. In this paper we explore the theorems of Stewart and Steiner in the Poincaré disc model of hyperbolic geometry.

Given a set of points in Euclidean space, we say that two linear functionals diier on that set if they give rise to diierent linear orderings of the points. We investigate what the largest and smallest number of diierent linear functionals can be as a function of the number of points and the dimension of the space. 1. Introduction The purpose of this paper is to investigate the number of diiere...

This study attempted to elucidate the controversy surrounding the experiments of Ungar examining the effects of scotophobin on dark preference in mice. The behavior of 45 noninjected mice in the type of maze described by Ungar was examined. Seven subsequent tests were conducted for dark box time (DBT) and motor activity. In general, the results indicated that DBT in all subpopulations of mice s...