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Given a basis of pseudoidentities for a pseudovariety of ordered semigroups containing the 5-element aperiodic Brandt semigroup , under the natural order, it is shown that the same basis, over the most general graph over which it can be read, defines the global. This is used to show that the global of the pseudovariety of level of Straubing-Thérien’s concatenation hierarchy has infinite vertex rank.
Given a basis of pseudoidentities for a pseudovariety of ordered
semigroups containing the 5-element aperiodic Brandt
semigroup B2, under the natural order, it is shown that the same basis,
over the most general graph over which it can be read, defines the
global. This is used to show that the global of the pseudovariety of
level 3/2 of Straubing-Thérien's concatenation hierarchy has
infinite vertex rank.
We give an approach to large deviation type asymptotic problems without evident probabilistic representation behind. An example provided by the mean field models of quantum statistical mechanics is considered.
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