Elementary proofs of Embedding Theorems for Potential Spaces of Radial Functions

We present elementary proofs of weighted embedding theorems for radial potential spaces and some generalizations of Ni's and Strauss' inequalities in this setting.Comment: 19 page

Women and Reparations

Reparations for victims of gross human rights violations are becoming an increasingly acknowledged feature in post-authoritarian and post-conflict societies coping with the legacy of a violent past. Despite some recent progress much more work needs to be done for massive reparations programs to respond better to the needs of women. This article, resting as it does on a comprehensive conception of reparations, outlines both the procedural and substantive components of reparations programs necessary for the programs to fulfill the goal of providing (partial) justice to women

A Reformulation of Matrix Graph Grammars with Boolean Complexes

Prior publication in the Electronic Journal of Combinatorics.Graph transformation is concerned with the manipulation of graphs by means of rules. Graph grammars have been traditionally studied using techniques from category theory. In previous works, we introduced Matrix Graph Grammars (MGG) as a purely algebraic approach for the study of graph dynamics, based on the representation of simple graphs by means of their adjacency matrices. The observation that, in addition to positive information, a rule implicitly defines negative conditions for its application (edges cannot become dangling, and cannot be added twice as we work with simple digraphs) has led to a representation of graphs as two matrices encoding positive and negative information. Using this representation, we have reformulated the main concepts in MGGs, while we have introduced other new ideas. In particular, we present (i) a new formulation of productions together with an abstraction of them (so called swaps), (ii) the notion of coherence, which checks whether a production sequence can be potentially applied, (iii) the minimal graph enabling the applicability of a sequence, and (iv) the conditions for compatibility of sequences (lack of dangling edges) and G-congruence (whether two sequences have the same minimal initial graph).This work has been partially sponsored by the Spanish Ministry of Science and Innovation, project METEORIC (TIN2008-02081/TIN)