Vol. 4 No. 1 (2012)

Following work of Palasinska and Pigozzi on partially ordered varieties and quasi-varieties of universal algebras, the author recently introduced partially ordered systems (posystems) and partially ordered functors (pofunctors) to cover the case of the algebraic systems arising in categorical abstract algebraic logic. Analogs of the ordered homomorphism theorems of universal algebra were shown to hold in the context of pofunctors. In the present work, operators on classes of pofunctors are introduced and it is shown that classes of pofunctors are closed under the HSP and the SPPU operators, forming analogs of the well-known variety and quasi-variety operators, respectively, of universal algebra.

In current work we discuss the issue of the analytic continuation of a power series along a logarithmic spiral outside of the convergence disc. A necessary and sufficient condition in terms of the interpolating entire function is obtained. Moreover, the relation in between the possibility of analytic continuation and the density of the lacunas of a power series is studied.

In this paper, we characterize the relationship between the fuzzy ideals (fuzzy filters) and the characteristic mappings of fuzzy ideals (fuzzy filters) in $\Gamma$-Semigroups.