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We consider the solution of matching problems with a
convex cost function via a network flow algorithm. We review the general
mapping between matching problems and flow problems on skew symmetric networks
and revisit several results on optimality of network flows. We use these results to
derive a balanced capacity scaling algorithm for matching problems with
a linear cost function. The latter is later generalized to a balanced capacity
scaling algorithm also for a convex cost function. We prove the correctness and
discuss the complexity of our solution.
We analyse the
proximity effect in hybrid nanoscale junctions involving superconducting leads.
We develop a general framework for the analysis of the proximity effect using
the same theoretical methods typically employed for the analysis of conductance
properties. We apply our method to a normal-superconductor tunnel contact and
compare our results to previous results.