We characterize the polynomial closure of a pseudo-convergent sequence in valuation domain V arbitrary rank, and then we use this result to show that is never topological when has rank at least 2.

The existence of valuation domains admitting non-standard uniserial modules for which certain Exts do not vanish was proved in [1] under Jensen’s Diamond Principle. In this note, the same is verified using the ZFC axioms alone. In the construction of large indecomposable divisible modules over certain valuation domainsR, the first author used the property thatR satisfied Ext1R(Q,U) 6= 0, where ...

We define an integral domain D to be anti-Archimedean if ⋂∞ n=1 a nD 6= 0 for each 0 6= a ∈ D. For example, a valuation domain or SFT Prüfer domain is anti-Archimedean if and only if it has no height-one prime ideals. A number of constructions and stability results for anti-Archimedean domains are given. We show that D is anti-Archimedean ⇔ D[[X1, . . .

We present a new approach to model edges in monochrome images. The method is divided in two parts: the localization of possible edge points and their valuation. The first part is based on the theory of minimal paths, where the selection of an energy and a set of sources determines a partition of the domain. Then, the valuation is obtained by the creation of a contrast driven hierarchy of partit...

It is shown that every dp-minimal integral domain R a local ring and for non-maximal prime ideal ℘ of R, the localization R℘ valuation ℘R℘ = ℘. Furthermore, if only its residue field infinite or finite maximal principal.

We present here IMITATOR II, a new version of IMITATOR, a tool implementing the “inverse method” for parametric timed automata: given a reference valuation of the parameters, it synthesizes a constraint such that, for any valuation satisfying this constraint, the system behaves the same as under the reference valuation in terms of traces, i.e., alternating sequences of locations and actions. IM...