  The first step when forming the polynomial hierarchies of languages is to
consider languages of the form KaL where K and L are over a finite alphabet A
and from a given variety V of languages, a being a letter from A. All such
KaL's generate the variety of languages BPol1(V).
  We estimate the numerical parameters of the language KaL in terms of their
values for K and L. These parameters include the state complexity of the
minimal complete DFA and the size of the syntactic monoids. We also estimate
the cardinality of the image of A* in the Schuetzenberger product of the
syntactic monoids of K and L. In these three cases we obtain the optimal
bounds.
  Finally, we also consider estimates for the cardinalities of free monoids in
the variety of monoids corresponding to BPol1(V) in terms of sizes of the free
monoids in the variety of monoids corresponding to V.
