dc.contributor.supervisor Momeni, Abbas dc.contributor.author Sultana, Sharmin dc.contributor.author University of Lethbridge, Faculty of Arts and Science dc.date.accessioned 2016-02-12T21:51:34Z dc.date.available 2016-02-12T21:51:34Z dc.date.issued 2015 dc.identifier.uri https://hdl.handle.net/10133/4413 dc.description.abstract The transport problem proposed by Monge in the 1780's, was to find the best way to move a pile of soil or rubble to an excavation or fill, with the least effort where the cost of a transport map or the transport plan is generally determined by the integral of some powers of the distance, such as $\vert x-y \vert ^ p$. But in many cases in real applications, the actual cost is not generally determined by a transport path. Sometimes a Y-shaped'' path is less expensive compared to a V-shaped path'', to transport items from two starting point to one destination point. Here, we will show that one can transport any Radon probability measure to another Radon probability measure through a general optimal transport path, which is given by a vector measure in our setting. Also, we define a new distance function $d_\alpha$ on the space of probability measures which indeed metrizes the weak* topology of measures. This thesis is an exposition of a paper by Qinglan Xia, Optimal paths related to transport problems'', World Scientific, $51(2): 252-289, 2002$. en_US dc.language.iso en_CA en_US dc.publisher Lethbridge, Alta : University of Lethbridge, Dept. of Mathematics and Computer Science en_US dc.relation.ispartofseries Thesis (University of Lethbridge. Faculty of Arts and Science) en_US dc.subject Radon measure en_US dc.subject optimal transport path en_US dc.title Optimal Paths Related to Discrete Transport Problems en_US dc.type Thesis en_US dc.publisher.faculty Arts and Science en_US dc.publisher.department Mathematics and Computer Science en_US dc.degree.level Masters en_US dc.proquest.subject 0405 en_US dc.proquest.subject 0984 en_US dc.proquest.subject 0501 en_US dc.proquestyes Yes en_US dc.embargo No en_US
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