One of the most classical results in extremal set theory is Sperner's theorem, which says that largest antichain Boolean lattice 2[n] has size Θ(2nn). Motivated by an old problem Erdős on growth infinite Sidon sequences, this note we study rate maximum antichains. Using well known Kraft's inequality for prefix codes, it not difficult to show antichains should be “thinner” than corresponding fin...

The Turán number of a graph H, denoted ex(n,H), is the maximum number of edges in an n-vertex graph with no subgraph isomorphic to H. Solymosi [17] conjectured that if H is any graph and ex(n,H) = O(n) where α > 1, then any n-vertex graph with the property that each edge lies in exactly one copy of H has o(n) edges. This can be viewed as conjecturing a possible extension of the removal lemma to...

This study examines the correlates of forced sexual intercourse among pregnant refugee women attending an antenatal clinic in Sidon, Lebanon. A total of 349 pregnant women were interviewed during a clinic visit for a prenatal check-up during the months of June and July 2005. The Abuse Assessment Screen was used to identify cases of abuse. The outcome variable was whether the woman was forced to...

A graph G = (V, E) is said to be magic if there exists an integer labeling f : V ∪ E −→ [1, |V ∪ E|] such that f(x) + f(y) + f(xy) is constant for all edges xy ∈ E. Enomoto, Masuda and Nakamigawa proved that there are magic graphs of order at most 3n + o(n) which contain a complete graph of order n. Bounds on Sidon sets show that the order of such a graph is at least n + o(n). We close the gap ...

The present work is associated with dietary reconstruction using δ13C and δ15N analysis of humans from the site of Sidon, a Middle Bronze Age (2000BC-1550BC) settlement in Lebanon. The main objective of this research is to focus on collagen extraction of 23 individual bones, discovered in a cemetery, College site (season 2001-2002) in ancient Sidon. Collagen could only be extracted from the 8 a...

The Bohnenblust–Hille inequality says that the l 2m m+1 -norm of the coefficients of an m-homogeneous polynomial P on C is bounded by ‖P‖∞ times a constant independent of n, where ‖ · ‖∞ denotes the supremum norm on the polydisc D. The main result of this paper is that this inequality is hypercontractive, i.e., the constant can be taken to be C for some C > 1. Combining this improved version of...