The analytic formulas of bed sparated fissures equivalent area and equivalent flow diameter are calculated both before and after initial rupture of the key stratum.

By using R and L, some equivalent conditions for adequate transversal to be a quasi-ideal are obtained.

The authors construct a semidirect product I×-σ S~0 of a left regular band I and an adequate transversal S~0 and shows that I×-σ S~0 is a lpp semigroup whose idempotents form a left regular band with an adequate transversal isomorphic to S~0.

In this paper, the concept of adequate transversals of left adequate semigroups is introduced.

After obtaining some properties of such semigroup, we prove that an abundant semigroup is a disjoint union of multiplicative adequate transversals if and only if it is isomorphic to the direct product of a rectangular band and an adequate semigroup.