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

A defence of Hart's semantics as nonambitious conceptual analysis

Two methodological claims in Hart's The Concept of Law have produced perplexity: that it is a book on “analytic jurisprudence” 1 and that it may also be regarded as an essay in “descriptive sociology.” 2 Are these two ideas reconcilable? We know that mere analysis of our legal concepts cannot tell us much about their properties, that is, about the empirical aspect of law. We have learned this from philosophical criticisms of conceptual analysis; yet Hart informs us that analytic jurisprudence can be reconciled with descriptive sociology. The answer to this puzzle lies in the notion of nonambitious conceptual analysis. The theorist analyzes concepts but accepts the limitations of conceptual analysis and therefore uses empirical knowledge and substantive arguments to explain, refine, or perhaps refute initial insights provided by intuitions. This is the conclusion that this paper arrives at as an argumentative strategy to defend Hart's legal theory from the criticisms of Stavropoulos and Dworkin. The latter argues that Hart's legal theory cannot explain theoretical disagreements in law because he relies on a shared criterial semantics. Stavropoulos aims to show that Hart's semantics is committed to ambitious conceptual analysis and relies on the usage of our words as a standard of correctness. Both attacks aim to show that the semantic sting stings Hart's legal theory. This essay refines both challenges and concludes that not even in the light of the most charitable interpretation of these criticisms is Hart's legal theory stung by the semantic sting. This study defends the view that Hart's methodological claims were modest and that he was aware of the limits of conceptual analysis as a philosophical method. He was, this study claims, far ahead of his time. 1 H.L.A Hart, THE CONCEPT OF LAW (1994). 2 Id

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