Qinglan Xia
The Exchange Value Embedded In A Transport System.
Fri, 01/29/2010 - 16:01 — SomNambulAuthors: Qinglan Xia, Shaofeng Xu
Subjects: Optimization and Control
AbstractThis paper shows that a well designed transport system has an embedded
exchange value by serving as a market for potential exchange between consumers.
Under suitable conditions, one can improve the welfare of consumers in the
system simply by allowing some exchange of goods between consumers during
transportation without incurring additional transportation costs. We propose an
explicit valuation formula to measure this exchange value for a given
compatible transport system. This value is always nonnegative and bounded from
above.On the transport dimension of measures.
Thu, 09/03/2009 - 17:38 — SomNambulAuthors: Qinglan Xia, Anna Vershynina
Subjects: Optimization and Control
AbstractIn this article, we define the transport dimension of probability measures on
$\mathbb{R}^m$ using ramified optimal transportation theory. We show that the
transport dimension of a probability measure is bounded above by the Minkowski
dimension and below by the Hausdorff dimension of the measure. Moreover, we
introduce a metric, called "the dimensional distance", on the space of
probability measures on $\mathbb{R}^m$.On the transport dimension of measures.
Thu, 09/03/2009 - 17:38 — SomNambulAuthors: Qinglan Xia, Anna Vershynina
Subjects: Optimization and Control
AbstractIn this article, we define the transport dimension of probability measures on
$\mathbb{R}^m$ using ramified optimal transportation theory. We show that the
transport dimension of a probability measure is bounded above by the Minkowski
dimension and below by the Hausdorff dimension of the measure. Moreover, we
introduce a metric, called "the dimensional distance", on the space of
probability measures on $\mathbb{R}^m$.
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