In this paper we define a field K of characteristic zero with valuation whose value group is (R,+), and we show that this field of generalised Puiseux series is algebraically closed and complete with respect to the norm induced by its valuation. We consider this field to be a good candidate for the base field for tropical geometry.

Unlike other primates, humans exhibit extensive inter-group tolerance and frequently build relationships with out-group members. Despite its common occurrence, little is known about the conditions leading to out-group relationship building in humans. What are the social and ecological factors promoting valuation of out-group members as potential social partners? Do they differ from those promot...

After having established elementary results on the relationship between a finite complex (pseudo-)reflection group W ⊂ GL(V ) and its reflection arrangement A, we prove that the action of W on A is canonically related with other natural representations of W , through a ‘periodic’ family of representations of its braid group. We also prove that, when W is irreducible, then the squares of definin...

Pseudo-Relevance Feedback (PRF) assumes that the topranking n documents of the initial retrieval are relevant and extracts expansion terms from them. In this work, we introduce the notion of pseudo-irrelevant documents, i.e. high-scoring documents outside of top n that are highly unlikely to be relevant. We show how pseudo-irrelevant documents can be used to extract better expansion terms from ...

The title compound, C15H14N2OS2, adopts a helix conformation. An intra-molecular N-H⋯O hydrogen bond leads to a six-membered pseudo-ring [r.m.s. deviation = 0.0212 Å, maximum deviation = 0.033 (1) Å for the N atom bearing the benzoyl group] in the central unit. The benzene and (methyl-sulfan-yl)benzene ring [r.m.s = 0.0028 Å and largest deviation of 0.067 (3) Å for the methyl-sulfanyl C atom] m...

Let G be a group acting via ring automorphisms on an integral domain R. A ring-theoretic property of R is said to G-invariant, if $$R^G$$ also has the property, where $$R^G=\{r\in \ | \sigma (r)=r \text {for all} \in G\},$$ fixed action. In this paper we prove following classes rings are invariant under operation $$R\rightarrow R^G:$$ locally pqr domains, Strong G-domains, Hilbert rings, S-stro...