Vanishing ideals over graphs and even cycles

Let X be an algebraic toric set in a projective space over a finite field. We study the vanishing ideal, I(X), of X and show some useful degree bounds for a minimal set of generators of I(X). We give an explicit description of a set of generators of I(X), when X is the algebraic toric set associated to an even cycle or to a connected bipartite graph with pairwise disjoint even cycles. In this case, a fomula for the regularity of I(X) is given. We show an upper bound for this invariant, when X is associated to a (not necessarily connected) bipartite graph. The upper bound is sharp if the graph is connected. We are able to show a formula for the length of the parameterized linear code associated with any graph, in terms of the number of bipartite and non-bipartite components

Regularity and algebraic properties of certain lattice ideals

We study the regularity and the algebraic properties of certain lattice ideals. We establish a map I --> I\~ between the family of graded lattice ideals in an N-graded polynomial ring over a field K and the family of graded lattice ideals in a polynomial ring with the standard grading. This map is shown to preserve the complete intersection property and the regularity of I but not the degree. We relate the Hilbert series and the generators of I and I\~. If dim(I)=1, we relate the degrees of I and I\~. It is shown that the regularity of certain lattice ideals is additive in a certain sense. Then, we give some applications. For finite fields, we give a formula for the regularity of the vanishing ideal of a degenerate torus in terms of the Frobenius number of a semigroup. We construct vanishing ideals, over finite fields, with prescribed regularity and degree of a certain type. Let X be a subset of a projective space over a field K. It is shown that the vanishing ideal of X is a lattice ideal of dimension 1 if and only if X is a finite subgroup of a projective torus. For finite fields, it is shown that X is a subgroup of a projective torus if and only if X is parameterized by monomials. We express the regularity of the vanishing ideal over a bipartie graph in terms of the regularities of the vanishing ideals of the blocks of the graph.Comment: Bull. Braz. Math. Soc. (N.S.), to appea

New Pact for Europe - National Report - PORTUGAL. EPC Project Report, October 2017

This is the seventh in a series of National Reports to be published as part of the new phase of the New Pact for Europe project.* According to the Portuguese NPE Reflection Group, the EU has shown a lot of resilience in the past few years when it had to deal with a multitude of crises, but it also warns of the dangers of being complacent. The EU is still facing several identity, legitimacy and institutional challenges, which are very complex and multi-dimensional

Country branding and foreign investment location : the case of Portugal

Mestrado em MarketingNation branding is not a new concept. It has been researched, discussed and applied in some cases with success. Neither the concept is a consensual issue nor its practice; however, the pressures felt by countries in today's globalized world have been pushing governments, public and private entities, and citizens to take a more active role in managing their country branding. Branding and marketing techniques usually adopted by companies are now used by countries to compete with each other in the attraction of tourists, talented people, exports and investors. The purpose of this study is to contribute to the understanding of the relevance of nation branding concept from a corporate perspective and to introduce a less researched issue: the role of national image in investment decisions. Over 500 corporate decision-makers in the largest foreign companies operating in Portugal were surveyed. To accomplish our purposes, the personification marketing tool was used through the Corporate Character Scale developed by Davies et al., as well as a 23-item list of determinants for investment location choice, derived from literature review. Findings revealed a positive relation between the country's image and the overall image of the country as an investment location. We also observed that the country image explains around 40% for the option of Portugal as an investment location. Finally, limitations of the study and suggestions for future investigations can be found in this paper.info:eu-repo/semantics/publishedVersio

Part I : Comparing derivatization methods for amino acids – one and two-step procedures using gas chromatography – flame ion detector (GC-FID) Part II: Story of an icon from its execution until its conservation

Dissertação apresentada na Faculdade de Ciências e Tecnologia da Universidade Nova de Lisboa para obtenção do grau de Mestre em Conservação e RestauroTwo derivatization methods were tested in twenty-one standard amino acids (AAs) for further identification and quantification by the analytical technique of Gas Chromatography with Flame Ion Detector (GC-FID). For the one-step derivatization reaction N-methyl-N (tert.- butyldimethylsilyl)trifluoroacetamide (MTBSTFA) was used and for the two-step reaction we used hydrochloridic acid (HCl) and trifluoroacetic anhydride (TFAA). We obtained better results with the derivatization procedure in two-steps, although it takes longer, and we concluded that the reproducibility of these reactions is difficult to achieve