A balanced pair in an ordered set P = (V,6) is a pair (x, y) of elements of V such that the proportion of linear extensions of P that put x before y is in the real interval [1/3, 2/3]. We prove that every finite N -free ordered set which is not totally ordered has a balanced pair.

Let B and R be point sets (of blue and red points, respectively) in the plane, such that P := B ∪R is in general position, and |P | is even. A line l is balanced if it spans one blue and one red point, and on each open halfplane of l, the number of blue points minus the number of red points is the same. We prove that P has at least min{|B|, |R|} balanced lines. This refines a result by Pach and...

The purpose of this research is to evaluate the effectiveness of implementation Quality Management System (ISO 9001:2000) in gas processing plants of National Iranian Gas Company using balanced scorecard approach. More specifically, we chose the balanced scorecard framework to examine five well-known gas processing plants in National Iranian Gas Company from four different perspectives in order...