The set of directions from a finite area quadratic differential on Riemann surface type that diverge average under Teichmüller geodesic flow has Hausdorff dimension exactly equal to one-half.

The Steiner k -eccentricity of a vertex v graph G is the maximum distance over all -subsets V ( ) which contain . In this paper 3-eccentricity studied on trees. Some general properties trees are given. A tree transformation does not increase average As its application, several lower and upper bounds for derived.

Abstract Fujii obtained a formula for the average number of Goldbach representations with lower-order terms expressed as sum over zeros Riemann zeta function and smaller error term. This assumed Hypothesis. We obtain an unconditional version this result applications conditional on various conjectures function.

when any extraordinary sacrifice or expenditure is intentionally and reasonably made or incurred for the common safety for the purpose of preserving from peril, the property (ship and cargoes) involved in a common maritime adventure, the interests saved , are required to make contributions in general average to the owner of lost or damaged property . general average rules originates from ancien...