We prove that the endomorphism semiring of a nontrivial semilattice is always subdirectly irreducible and describe its monolith. The endomorphism semiring is congruence simple if and only if the semilattice has both a least and a largest element.

We introduce and study the notion of a completely regular ternary semiring. Necessary and sufficient conditions for a ternary semiring to be completely regular are furnished. AMS Mathematics Subject Classification (2010): 16Y30, 16Y99

We have used dynamic interfacial tension measurements to understand the structure of the ordered monolayer at the hexadecane/water interface induced by the presence of surfactant molecules. No abrupt changes in the interfacial tension (gamma) are observed during the expansion and contraction cycle below the interfacial ordering temperature (Ti) as observed for alkanes in contact with air. The l...

In this lecture, we summarize the interprocedural-dataflow-analysis method of Esparza et al., which generalizes Newton’s method from a numerical-analysis algorithm for finding roots of real-valued functions to a method for finding fixed-points of systems of equations over semirings. As in its real-valued counterpart, each iteration of the method of Esparza et al. solves a simpler “linearized” p...

problems concrete problems P α γ α γ( (P)) α α (P) = P Fig. 3. The on rete and the abstra t problem. In Figure 3, P is the starting SCSP problem. Then with the mapping we get ~ P = (P ), whi h is an abstra tion of P . By applying the mapping to ~ P , we get the problem ( (P )). Let us rst noti e that these two problems (P and ( (P ))) are related by a pre ise property, as stated by the followin...

In 1996 Zhou and Hansen proposed a first-order interval logic called Neighbourhood Logic (NL) for specifying liveness and fairness of computing systems and also defining notions of real analysis in terms of expanding modalities. After that, Roy and Zhou presented a sound and relatively complete Duration Calculus as an extension of NL. We present an embedding of NL into an idempotent semiring of...

The concepts of tropical semiring and tropical hypersurface, are extended to the case of an arbitrary ordered group. Then, we define the tropicalization of a polynomial with coefficients in a Krull-valued field. After a close study of the properties of the operator “tropicalization” we conclude with an extension of Kapranov’s theorem to algebraically closed fields together with a valuation over...