Planar Manhattan local minimal and critical networksстатья
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Дата последнего поиска статьи во внешних источниках: 18 июля 2013 г.
Аннотация:In the present paper we investigate the functional of Manhattan length whose
lagrangian equals the sum of absolute values of projections of velociy
vector onto coordinate axis. Such functionals are useful for solving
problems appearing in Electronics, Robotics, chip design, etc.
It turns out that for such functional the local minimality does not imply
the extremality (however, each extreme network is local minimal). In the
case of Manhattan plane we shall present a ctriterion of extremality of a
local minimal network. This criterion demonstrates that the extremality
with respect to Manhattan length functional is a global topological
property of networks.