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Abstract

Using the characterization of the segments in the max-plus semimodule Rnmax, provided by Nitica and Singer, we find a class of metrics on the finite part of Rnmax. One of them is the Euclidean length of the max-plus segment connecting two points. This metric is not quasi-convex. There is exactly one other metric in our class that does possess this property. Each metric in our class is associated with a weighting function, which is concave and non-decreasing.

Author Bio

Uri Carl is a senior majoring in mathematics at Yeshiva University. He plans on pursuing a Ph.D. in applied mathematics. Additionally, he enjoys reading philosophy books and listening to music. This research was performed during the summer of 2012 as part of the NSF mathematics REU at the Pennsylvania State University.

Kevin O'Neill is a senior majoring in mathematics at Harvey Mudd College. Aside from thinking about abstract mathematical concepts, he is an avid runner on the track team. This research was performed during the summer of 2012 as part of the NSF mathematics REU at the Pennsylvania State University.

Nicholas Ryder is a junior majoring in mathematics at Rice University. After his undergraduate studies, he plans to pursue a PhD in mathematics. He enjoys playing music and is the manager of KTRU, the radio station at Rice University. This research was performed during the summer of 2012 as part of the NSF mathematics REU at the Pennsylvania State University.

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