Longwall coal mine operators in the U.S. are required to ventilate multipanel longwall districts, but may have little or no knowledge about what happens to the ventilation air between the inlet evaluation points (IEPs), bleeder evaluation points (BEPs) and bleeder fans. The effectiveness of bleeder performance can directly influence the ability of a ventilation system to remove and dilute coal ...

Let G be a subgroup of the additive group of real numbers and let C ⊆ G be infinite and convex in G. We show that G is definable in (R,+, ⋅, C) and that Z is definable if G has finite rank. This has a number of consequences for expansions of certain o-minimal structures on the real field by multiplicative groups of complex numbers. We answer some questions about expansions of o-minimal structur...