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.

On moments and tail behaviors of storage processes

We study the existence of moments and the tail behaviour of the densitiesof storage processes. We give sufficient conditions for existence andnon-existence of moments using the integrability conditions ofsubmultiplicative functions with respect to Lévy measures. Then, we studythe asymptotical behavior of the tails of these processes using the concaveor convex envelope of the release rate function.

Minimum distance estimation of stationary and non-stationary ARFIMA processes

A new parametric minimum distance time-domain estimator for ARFIMA processes is introduced in this paper. The proposed estimator minimizes the sum of squared correlations of residuals obtained after filtering a series through ARFIMA parameters. The estimator iseasy to compute and is consistent and asymptotically normally distributed for fractionallyintegrated (FI) processes with an integration order d strictly greater than -0.75. Therefore, it can be applied to both stationary and non-stationary processes. Deterministic components are also allowed in the DGP. Furthermore, as a by-product, the estimation procedure provides an immediate check on the adequacy of the specified model. This is so because the criterion function, when evaluated at the estimated values, coincides with the Box-Pierce goodness of fit statistic. Empirical applications and Monte-Carlo simulations supporting the analytical results and showing the good performance of the estimator in finite samples are also provided.

Processes and consequences in business ethical dilemmas: The oil industry and climate changes

This paper proposes a framework to examine business ethical dilemmas andbusiness attitudes towards such dilemmas. Business ethical dilemmas canbe understood as reflecting a contradiction between a socially detrimentalprocess and a self-interested profitable consequence. This representationallows us to distinguish two forms of behavior differing by whetherpriority is put on consequences or on processes. We argue that theseforms imply very different business attitudes towards society:controversial or competitive for the former and aligned or cooperativefor the latter. These attitudes are then analyzed at the discursive level in order to address the question of good faith in businessargumentation, i.e. to which extent are these attitudes consistent withactual business behaviors. We argue that consequential attitudes mostlyinvolve communication and lobbying actions aiming at eluding the dilemma.Therefore, the question of good faith for consequential attitudes liesin the consistency between beliefs and discourse. On the other hand,procedural attitudes acknowledge the dilemma and claim a change of theprocess of behavior. They thus raise the question of the consistencybetween discourses and actual behavior. We apply this processes/consequencesframework to the case of the oil industry s climate change ethical dilemmawhich comes forth as a dilemma between emitting greenhouse gases and making more profits . And we examine the different attitudes of two oilcorporations-BP Amoco and ExxonMobil-towards the dilemma.

Logistics integration processes in the food industry

This paper analyses the integration process that firms follow toimplement Supply Chain Management (SCM). This study has beeninspired in the integration model proposed by Stevens (1989). Hesuggests that companies internally integrate first and then extendintegration to other supply chain members, such as customers andsuppliers.To analyse the integration process a survey was conducted amongSpanish food manufacturers. The results show that there are companiesin three different integration stages. In stage I, companies are notintegrated. In stage II, companies have a medium-high level of internalintegration in the Logistics-Production interface, a low level ofinternal integration in the Logistics-Marketing interface, and a mediumlevel of external integration. And, in stage III, companies have highlevels of integration in both internal interfaces and in some of theirsupply chain relationships.

A comparison of the processes of institutionalisation of political economy in Spain and Italy (1860-1900)

[spa] El estudio de los procesos a través de los cuales la economía política se ha transformado en una disciplina académica es un área de creciente interés en la historia del pensamiento económico. Dicho estudio se ha abordado a través del análisis de la importancia de la economía política en un conjunto de instituciones, consideradas clave en la expansión de la economía en las sociedades occidentales en la segunda mitad del siglo XIX y primeras décadas del XX: universidades, sociedades económicas, publicaciones periódicas de contenido económico y los parlamentos nacionales. Este papel presenta una comparación entre los desarrollos del proceso de institutionalización de la economía política en España e Italia, a través del estudio de la presencia de esta disciplina en las instituciones mencionadas para el periodo 1860-1900. El objetivo es medir la posible existencia de una vía común en la institucionalización de la economía política en ambos países, como un primer paso hacia la elaboración de un modelo supranacional de institucionalización de la economía en este periodo.

Why Italy and not Spain?: comparing two industrialization processes from a dissagregate time-series perspective

This study presents new evidence concerning the uneven processes of industrialization innineteenth century Spain and Italy based on a disaggregate analysis of the productivesectors from which the behaviour of the aggregate indices is comprised. The use of multivariate time-series analysis techniques can aid our understanding and characterization of these two processes of industrialization. The identification of those sectors with key rolesin leading industrial growth provides new evidence concerning the factors that governed thebehaviour of the aggregates in the two economies. In addition, the analysis of the existenceof interindustry linkages reveals the scale of the industrialization process, and wheresignificant differences exist, accounts for many of the divergences recorded in the historiography for the period 1850-1913.

Flank stability and processes off the western Canary Islands: a review from El Hierro and La Palma

The morphological characterisation of the western submarine island flanks of El Hierro and La Palma differentiates four type-zones that may give new insights into the evolution of oceanic island slopes. The different type-zones result from the interplay between constructive volcanic processes, hemipelagic settling and volcano collapses. The latter results in massive debris avalanche deposits, which form large volcaniclastic aprons. In most cases, the headwall scarps are clearly exposed on the emerged part of the islands. The events that occurred in the youngest and westernmost islands of El Hierro and La Palma have vertical runouts exceeding 6,000 m and volumes that can reach several hundred km3. The landslide frequency for the entire Canaries is one major event per 90 ka. Triggering mechanisms are closely related to magmatic processes. The increase in the shear stress is directly linked with the forceful intrusion of magma along ridge-rift systems, while in the western Canary Islands it seems that the main process reducing shear resistance may be related to the rise in pore pressure due to hydrothermal circulation.

Relaxation times of non-Markovian processes

We consider a general class of non-Markovian processes defined by stochastic differential equations with Ornstein-Uhlenbeck noise. We present a general formalism to evaluate relaxation times associated with correlation functions in the steady state. This formalism is a generalization of a previous approach for Markovian processes. The theoretical results are shown to be in satisfactory agreement both with experimental data for a cubic bistable system and also with a computer simulation of the Stratonovich model. We comment on the dynamical role of the non-Markovianicity in different situations.

Relaxation time of processes driven by multiplicative noise

We consider systems described by nonlinear stochastic differential equations with multiplicative noise. We study the relaxation time of the steady-state correlation function as a function of noise parameters. We consider the white- and nonwhite-noise case for a prototype model for which numerical data are available. We discuss the validity of analytical approximation schemes. For the white-noise case we discuss the results of a projector-operator technique. This discussion allows us to give a generalization of the method to the non-white-noise case. Within this generalization, we account for the growth of the relaxation time as a function of the correlation time of the noise. This behavior is traced back to the existence of a non-Markovian term in the equation for the correlation function.

Mean first-passage time of continuous non-Markovian processes driven by colored noise

An equation for mean first-passage times of non-Markovian processes driven by colored noise is derived through an appropriate backward integro-differential equation. The equation is solved in a Bourret-like approximation. In a weak-noise bistable situation, non-Markovian effects are taken into account by an effective diffusion coefficient. In this situation, our results compare satisfactorily with other approaches and experimental data.

Stochastic processes induced by dichotomous markov noise: Some exact dynamical results

Stochastic processes defined by a general Langevin equation of motion where the noise is the non-Gaussian dichotomous Markov noise are studied. A non-FokkerPlanck master differential equation is deduced for the probability density of these processes. Two different models are exactly solved. In the second one, a nonequilibrium bimodal distribution induced by the noise is observed for a critical value of its correlation time. Critical slowing down does not appear in this point but in another one.

Theory for correlation functions of processes driven by external colored noise

We study steady-state correlation functions of nonlinear stochastic processes driven by external colored noise. We present a methodology that provides explicit expressions of correlation functions approximating simultaneously short- and long-time regimes. The non-Markov nature is reduced to an effective Markovian formulation, and the nonlinearities are treated systematically by means of double expansions in high and low frequencies. We also derive some exact expressions for the coefficients of these expansions for arbitrary noise by means of a generalization of projection-operator techniques.

Some critical reflections on Michel Foucault's reading of Plutarch's Eroticus (Amatorius)

This aim of this article is to reflect on Michel Foucault's reading of Plutarch's Eroticus in his Histoire de la sexualité, putting emphasis on the fact that, against what it is affirmed by the French thinker, the real debate is not, in the author's opinion, about true pleasure, that obtained by the erastés from his erómenos or that obtained by husbands from their wives, but the need to assign also love and friendship (éros kaì philia) to the conjugal love.

Leaving the cave in search of life (A Platonic reading of R. Sirera's La caverna (The Cave)

The aim of this article is to show how a contemporary playwright thinks once more of the Platonic image of the cave in order to reflect on the necessary existential journey of men and women as in the case of a Bildungsroman. Sooner or later men and women must abandon the protection that any sort of cavern such as home, the family garden or family itself can offer. In spite of writing from a by no means idealistic or metaphysical point of view, thanks to R. Sirera and to the very applicability of Platonic images, Plato becomes once again a classical reference which is both useful and even unavoidable if one bears in mind the Platonic origin of all the literary caverns.