Irreducible numerical semigroups with multiplicity three and four

In this paper we analyze the irreducibility of numerical semigroups with multiplicity up to four. Our approach uses the notion of Kunz-coordinates vector of a numerical semigroup recently introduced in (Blanco-Puerto, 2011). With this tool we also completely describe the whole family of minimal decompositions into irreducible numerical semigroups with the same multiplicity for this set of numerical semigroups. We give detailed examples to show the applicability of the methodology and conditions for the irreducibility of well-known families of numerical semigroups as those that are generated by a generalized arithmetic progression.Comment: 18 page

A Social-ecological Approach to Voluntary Environmental Initiatives: The Case of Nature-based Tourism

This paper addresses the role of voluntary environmental initiatives by the tourism industry to alleviate social dilemmas for the management of natural resources

Of the use of the “English sector” in trigonometry: what amount of mathematical training was necessary in the 18th century?

In 1723 Edmund Stone published The construction and principal uses of mathematical instruments, which was essentially a translation from the French of Bion’s Traité de la construction et des principaux usages des instrumens de mathématique (1709). As the title of the book indicated, Stone annexed a number of instruments that had been omitted by Bion, in particular, those invented or improved by the English. Hence, after the translation of Book II, on the construction and uses of the “French sector”, Stone added a chapter on the “English sector”. In the 17th century there had been a number of debates concerning the amount of mathematical training required for the study of mathematical instruments. In the context of the study of mathematical instruments in the 18th century, it is worth exploring the link theory-practice in the books on instruments. The aim of this contribution is to explore the mathematical knowledge involved in the use and applications of the “English sector” in trigonometry in a number of 18th-century books on mathematical instruments.Peer ReviewedPostprint (published version

Campaniforme o no Campaniforme: una perspectiva sobre las cerámicas ‘pellizcadas’ en vasos con perfil en ‘s’ del Calcolítico en la Península Ibérica

The Bell Beaker phenomenon is the sum of several regional answers. Those are diluted into a reality with several shared characteristics. Nevertheless, and although being one of the most studied expressions of the European Recent Prehistory, more specific adaptations are still to be understood. This is the case of the paired fingernail imprints, or pinched motifs, that due to their scarceness are mostly unnoticed in Iberia. However, one was able to highpoint a scarceness of these standardised motifs in funerary contexts and a concentration in contexts dated from the last quarter of the IIIrd millennium BC, in the precise period of transition in the way of life of the peninsular human groups. Also, the regression in the communicative ability of the vessels, but at the same time dear links with other European Bell Beaker contexts seems to strengthen the hypothesis that this large-scale style must be understood as another agent in the ongoing identarian and social processes acting, as such, in the transition to the beginning of the Peninsular Bronze Age.info:eu-repo/semantics/publishedVersio