Fermat's treatise on quadrature: A new reading

The Treatise on Quadrature of Fermat (c. 1659), besides containing the first known proof of the computation of the area under a higher parabola, R x+m/n dx, or under a higher hyperbola, R x-m/n dx with the appropriate limits of integration in each case , has a second part which was not understood by Fermat s contemporaries. This second part of the Treatise is obscure and difficult to read and even the great Huygens described it as'published with many mistakes and it is so obscure (with proofs redolent of error) that I have been unable to make any sense of it'. Far from the confusion that Huygens attributes to it, in this paper we try to prove that Fermat, in writing the Treatise, had a very clear goal in mind and he managed to attain it by means of a simple and original method. Fermat reduced the quadrature of a great number of algebraic curves to the quadrature of known curves: the higher parabolas and hyperbolas of the first part of the paper. Others, he reduced to the quadrature of the circle. We shall see how the clever use of two procedures, quite novel at the time: the change of variables and a particular case of the formulaof integration by parts, provide Fermat with the necessary tools to square very easily curves as well-known as the folium of Descartes, the cissoid of Diocles or the witch of Agnesi.

Three Continents, one Language: Studying English in a Portuguese Landscape (Brazil, Cape Verde and Portugal)

Unlike other languages, English has spread to all continents and become a truly global language, a process observable in countries, like Brazil, Cape Verde, and Portugal, located in three different continents, and sharing a common official language: Portuguese. This relatively recent development has contributed to the wide exposure to English and the growing influence of the language in their societies, being used with lingua franca communicative purposes, which raises pedagogical issues. Our aim is to map the exposure and use of English as a Lingua Franca in these Portuguese speaking countries through a comparative study of the results from three case studies (Berto 2009, Cavalheiro 2008 and Nunes 2010). By taking into consideration the findings from questionnaires answered by students and teachers of English, it compares and contrasts the respondents’ opinions on the profile of English teachers — native vs. non-native —, the varieties of English to be taught, and the language teaching resources available. In addition, it explores the learners’ interests, motives and purposes in relation to English and the potential communicative interactions between all speakers, so as to better understand ELF in English language education, and how these factors affect or should affect pedagogical practices in a Portuguese environment.

Planeamento de experiências : modelos e desafios dos planos em blocos incompletos.

O principal objetivo de um Planeamento de Experiências reside essencialmente na procura de relações entre variáveis e na comparação de níveis de fatores, recorrendo ao tratamento estatístico dos dados recolhidos. A utilização de blocos no Planeamento de Experiências é fundamental, pois permite reduzir ou eliminar a variabilidade introduzida por fatores que podem influenciar a experiência mas que não interessam e/ou não foram explicitamente incluídos durante o planeamento. Neste trabalho apresentamos os resultados do estudo e investigação dos Planos em Blocos Incompletos Equilibrados (BIBD), Planos em Blocos Incompletos Equilibrados com repetição de blocos (BIBDR) e Planos em Blocos Incompletos com blocos de diferentes dimensões (VBBD). Exploramos algumas propriedades e métodos de construção destes planos e ilustramos, sempre que possível, com exemplos. Tendo como base o planeamento em blocos, apresentamos uma aplicação dos BIBDR na área da Educação com o objetivo de comparar cinco domínios do pensamento algébrico de uma amostra de alunos do 1º ano do ensino superior em Cabo Verde. Para a análise dos dados da amostra foi utilizado o software R, versão 2.12.1. Pudemos constatar que existem diferenças significativas entre alguns dos domínios do pensamento algébrico, nomeadamente entre os domínios da Generalização da Aritmética e Tecnicismo Algébrico com os restantes domínios. Recomendamos a escolha de uma amostra mais representativa constituída por alunos de todas as instituições superiores de Cabo Verde

Timing of seasonal sales

We present a model of timing of seasonal sales where stores chooseseveral designs at the beginning of the season without knowingwich one, if any, will be fashionable. Fashionable designs have achance to fetch high prices in fashion markets while non-fashionableones must be sold in a discount market. In the beginning of theseason, stores charge high prices in the hope of capturing theirfashion market. As the end of the season approaches with goods stillon the shelves, stores adjust downward their expectations that theyare carrying a fashionable design, and may have sales to capture thediscount market. Having a greater number of designs induces a storeto put one of them on sales earlier to test the market. Moreover,price competition in the discount market induces stores to startsales earlier because of a greater perceived first-mover advantage incapturing the discount market. More competition, perhaps due todecreases in the cost of product innovation, makes sales occur evenearlier. These results are consistent with the observation that thetrend toward earlier sales since mid-1970's coincides with increasingproduct varieties in fashion good markets and increasing storecompetition.

Characterization of instrumental and sensory quality of papaya ‘Solo' and 'Local' produced in Santiago - Cape Verde and critical analysis on the importation of papaya

O estudo teve por objectivo fazer a caracterização dos atributos de qualidade de duas variedades (Solo e Local) de papaia produzida em Santiago, Cabo Verde, e definir os atributos que os distribuidores procuram. Foram realizadas avaliações físico-químicas, sensorial e um estudo de mercado. Os parâmetros avaliados foram o peso, cor interior e exterior, textura, espessura da polpa, pH, acidez titulável, SST, fez-se avaliação sensorial a aplicação de um questionário aos importadores de papaia. Os parâmetros SST, Acidez, pH e peso variam significativamente com as variedades, sendo as papaias da variedade Local mais pesadas. A textura varia em função dos graus de maturação, a firmeza apresenta uma diminuição ao longo do amadurecimento, na deformação percebe-se um decréscimo com avançar da maturação, nos parâmetros de cor interna e externa as diferenças encontram-se na interacção entre Variedade e Estado de maturação. A variedade Solo foi mais valorizada na avaliação sensorial assim como no preço, certificação/selo qualidade e doçura pelos distribuidores.

Natural parasitism of Diaphorina citri Kuwayama (Hemiptera, Psyllidae) nymphs by Tamarixia radiata Waterston (Hymenoptera, Eulophidae) in São Paulo orange groves

The psyllid Diaphorina citri Kuwayama 1908 has become the main citrus pest species in the state of São Paulo, Brazil, after the introduction of the huanglongbing or citrus greening. This study evaluated the parasitism of 3rd, 4th and 5th instar D. citri nymphs by Tamarixia radiata (Waterston, 1922) in citrus groves under a regimen of regular insecticide applications in ten producing regions: Araraquara, Barretos, Bauru, Botucatu, Franca, Itapetininga, Jaú, Limeira, Lins and São João da Boa Vista. Sixty-nine samples of new branches infested with nymphs of D. citri were collected from 2005 to 2008 in orange groves ranging from 1 to 20 years old, of the varieties Hamlin, Pera, Valencia and Natal. The parasitoid T. radiata is widely distributed in São Paulo orange groves, and was identified in 50 (72%) of the samples, showing a mean parasitism rate of 12.4%. The highest parasitism rate was observed in the "summer" (from January through March), with a mean of 25.7%. Nymphal parasitism was above 90% in two samples. The probable causes of the variations in parasitism of D. citri by T. radiata are discussed.

Teoremas de isomorfía en grupos diedros

En este art\'\ı culo discutimos los resultados principalesalcanzados en mi trabajo de grado, el cual fue dirigido por elprofesor Jairo Charris Casta\~neda. La discusi\'on la limitaremos alos llamados $(p, q)$ grupos, en particular a los grupos diedros.

Unified formalism for non-autonomous mechanical systems

We present a unified geometric framework for describing both the Lagrangian and Hamiltonian formalisms of regular and non-regular time-dependent mechanical systems, which is based on the approach of Skinner and Rusk (1983). The dynamical equations of motion and their compatibility and consistency are carefully studied, making clear that all the characteristics of the Lagrangian and the Hamiltonian formalisms are recovered in this formulation. As an example, it is studied a semidiscretization of the nonlinear wave equation proving the applicability of the proposed formalism.

Homotopy Batalin-Vilkovisky algebras

This paper provides an explicit cofibrant resolution of the operad encoding Batalin-Vilkovisky algebras. Thus it defines the notion of homotopy Batalin-Vilkovisky algebras with the required homotopy properties. To define this resolution we extend the theory of Koszul duality to operads and properads that are defind by quadratic and linear relations. The operad encoding Batalin-Vilkovisky algebras is shown to be Koszul in this sense. This allows us to prove a Poincare-Birkhoff-Witt Theorem for such an operad and to give an explicit small quasi-free resolution for it. This particular resolution enables us to describe the deformation theory and homotopy theory of BV-algebras and of homotopy BV-algebras. We show that any topological conformal field theory carries a homotopy BV-algebra structure which lifts the BV-algebra structure on homology. The same result is proved for the singular chain complex of the double loop space of a topological space endowed with an action of the circle. We also prove the cyclic Deligne conjecture with this cofibrant resolution of the operad BV. We develop the general obstruction theory for algebras over the Koszul resolution of a properad and apply it to extend a conjecture of Lian-Zuckerman, showing that certain vertex algebras have an explicit homotopy BV-algebra structure.

Projecte de legalització d'una activitat dedicada a l'explotació ramadera i a la formatgeria artesanal

La integració en una mateixa activitat d'una explotació ramadera ecològica basada en el bestiar cabrú de llet i d'una formatgeria artesanal basada en varietats autòctones de formatge de cabra, permet ocupar un nínxol de mercat encara poc explotat actualment a Catalunya. D'igual manera, la dificultat que tenen actualment molts dels formatgers artesans del país per trobar llet de cabra en quantitats suficients i amb unes mínimes garanties higiènico-sanitàries dificulten l'avanç d'un sector amb molt bones perspectives de futur com és el de la formatgeria artesanal i justifica la necessitat de crear noves explotacions (o reconvertir-ne de ja existents) orientant-les de ple vers l'aprofitament lleter del bestiar cabrú, que és actualment molt reduït en l'àmbit Català. A més d'això, les actuals exigències en el camp del benestar animal així com en el camp de la qualitat i de la seguretat alimentaria, exigeixen a les explotacions ramaderes i a les indústries alimentàries el compliment d'una sèrie de requisits, tan de disseny dels locals i de les instal•lacions, com de control de les activitats i dels productes elaborats, que garanteixin en tot moment la seva correcte gestió i funcionament en aquestes matèries. L'objectiu d'aquest projecte, doncs, és la legalització d'una activitat, que anomenarem “Mas Peirot, S.L.”, dedicada a l'explotació ramadera ecològica de bestiar cabrú de llet i a la formatgeria artesanal de formatge de cabra. És important mencionar que tot i tractar-se d'un projecte de legalització d'una activitat,, també s'hi han contemplat aspectes i detalls relacionats amb l'execució de la mateixa, al tractar-se d'unes obres d'una certa complexitat i considerant que així es tracten amb més detall i rigorositat les actuacions projectades. En concret, en aquest projecte es planifiquen les operacions de rehabilitació de dues naus ramaderes actualment en desús, per tal que puguin destinar-se a l'explotació ramadera de bestiar cabrú i a la formatgeria artesanal, projectant-se així mateix totes les instal•lacions necessàries per tal que a les mencionades naus s'hi puguin desenvolupar les activitats citades. Com a conclusions més importants d'aquest projecte podem dir que amb un cens de 100 caps de bestiar cabrú és possible obtenir una producció mitjana de llet de 32.500 litres anuals, que es corresponen a un volum total de 3.823 quilograms de formatge a l'any (de les tipologies Formatge Garrotxa i Formatge de cabra amb oli, ambdues varietats tradicionals catalanes) obtenint un benefici de 21.389,47 Euros/any durant els primers 15 anys i un benefici de 33.386,39 Euros/any a partir del 16è any, cosa que permetrà recuperar la inversió inicial de 172.716,76 Euros que valen les naus i instal•lacions projectades, en un termini de 8 anys i permetrà, com s'ha dit, ocupar un nínxol de mercat encara poc explotat per la indústria agroalimentària a Catalunya.

Macaulay style formulas for sparse resultants

We present formulas for computing the resultant of sparse polyno- mials as a quotient of two determinants, the denominator being a minor of the numerator. These formulas extend the original formulation given by Macaulay for homogeneous polynomials.

Generating functions for the numbers of Abelian extensions of a local field

The aim of this paper is to give an explicit formula for the num- bers of abelian extensions of a p-adic number field and to study the generating function of these numbers. More precisely, we give the number of abelian ex- tensions with given degree and ramification index, and the number of abelian extensions with given degree of any local field of characteristic zero. Moreover, we give a concrete expression of a generating function for these last numbers