On the trace of an endofunctor of a small category

The trace of a square matrix can be defined by a universal property which, appropriately generalized yields the concept of "trace of an endofunctor of a small category". We review the basic definitions of this general concept and give a new construction, the "pretrace category", which allows us to obtain the trace of an endofunctor of a small category as the set of connected components of its pretrace. We show that this pretrace construction determines a finite-product preserving endofunctor of the category of small categories, and we deduce from this that the trace inherits any finite-product algebraic structure that the original category may have. We apply our results to several examples from Representation Theory obtaining a new (indirect) proof of the fact that two finite dimensional linear representations of a finite group are isomorphic if and only if they have the same character.

Congested hubs

Hub congestion is a major problem and a relevant policy issue because it causes delays and many organizational problems at airports that end up implying unpleasant consequences both for air travelers and airlines. In a competitive framework in which carriers choose aircraft size, this paper suggests that airlines schedule too many flights using overly small aircraft, which constitutes a major contributor to congestion. Two- part congestion tolls, accounting for the congestion imposed on other carriers and the congestion imposed on all passengers, are needed to recover e¢ ciency. Finally, we analyze the validity of the results by studying the effects of network size, airport capacity, competition in layover time, and the formation of airline alliances. Keywords: congestion; hub-and-spoke networks; overprovision of frequency; con- gestion internalization; congestion tolls JEL Classiffication Numbers: L13; L2; L93

Small firms, growth and financial constraints

This paper analyses the impact of different sources of finance on the growth of firms. Using panel data from Spanish manufacturing firms for the period 2000-2006, we investigate the effects of internal and external finances on firm growth. In particular, we examine three dimensions of these financial sources: a) the performance of the firms’ capital structure in accordance with firm size; b) the effects of internal and external financial sources on growth performance; c) the combined effect of equity, external debt and cash flow on firm growth. We find that low-growth firms are sensitive to cash flow and short-term bank debt, while high-growth firms are more sensitive to long-term debt. Furthermore, equity capital seems to reduce barriers to external finance. Our main conclusion is that during the start-up phase, firms are unable to increase their financial leverage and so their capital structure fails to promote correct investment strategies. However, as their equity capital increases, alternative financial mechanisms, in particular long-term debt, become available, which have a positive impact on firm growth.

System GMM estimation with a small sample

Properties of GMM estimators for panel data, which have become very popular in the empirical economic growth literature, are not well known when the number of individuals is small. This paper analyses through Monte Carlo simulations the properties of various GMM and other estimators when the number of individuals is the one typically available in country growth studies. It is found that, provided that some persistency is present in the series, the system GMM estimator has a lower bias and higher efficiency than all the other estimators analysed, including the standard first-differences GMM estimator.

(Optimal) Spatial Aggregation in the Determinants of Industrial Location

Empirical studies on the determinants of industrial location typically use variables measured at the available administrative level (municipalities, counties, etc.). However, this amounts to assuming that the effects these determinants may have on the location process do not extent beyond the geographical limits of the selected site. We address the validity of this assumption by comparing results from standard count data models with those obtained by calculating the geographical scope of the spatially varying explanatory variables using a wide range of distances and alternative spatial autocorrelation measures. Our results reject the usual practice of using administrative records as covariates without making some kind of spatial correction. Keywords: industrial location, count data models, spatial statistics JEL classification: C25, C52, R11, R30

Estudi per la implantació d'un ERP en una empresa d'aplicació de pintura industrial i decorativa

La implantació d'un sistema ERP no és senzilla, requereix grans esforços i una bona administració a més de considerar molts altres aspectes per arribar a tenir èxit. Per aquest motiu, la presa de requeriments en aquest tipus de projectes esdevé pedra angular. A Estudi per la implantació d'un ERP en una empresa d'aplicació de pintura industrial i decorativa es realitza un estudi detallat de l'organització de l'empresa amb la finalitat de trobar els requeriments d'aquesta, seguidament es realitza un estudi de tres sistemes ERP per acabar trobant la solució que millor encaixa en les necessitats de l'empresa.

A three dimensional signed small ball inequality

"Vegeu el resum a l'inici del document del fitxer adjunt."

Casolà o industrial?: estudi organolèptic i microbiològic de la vida útil del pernil cuit

Treball de recerca realitzat per un alumne d'ensenyament secundari i guardonat amb un Premi CIRIT per fomentar l'esperit científic del Jovent l'any 2009. Aquest treball tracta sobre el temps de garantia o de vida útil d’un producte alimentari i està basat en esbrinar quin és el millor mètode o envàs per conservar el pernil cuit llescat durant la seva vida útil, per tal que es mantinguin les propietats organolèptiques i microbiològiques inicials de l’aliment durant el màxim de temps possible. Per comparar envasos he utilitzat els industrials (envàs al buit i envàs en atmosfera) i els envasos que podem trobar quan comprem un producte llescat en el mostrador d’una botiga o supermercat. Per a fer l’estudi doncs s’ha utilitzat el pernil cuit, conegut com a pernil dolç, un dels productes més consumits per la societat actual. El pernil ha estat tractat en tres situacions diferents: llescat en una màquina de carnisseria i envasat en mètodes de conservació domèstics, llescat en màquines industrials i envasat en diferents envasos (al buit i en atmosfera modificada) utilitzats per les grans empreses i llescat en màquines industrials i envasat al buit sotmès a un tractament amb altes pressions. Després d’aquests processos s’ha realitzat un estudi de vida útil, és a dir, s’ha analitzat el producte al laboratori, amb l’objectiu de trobar quin és el millor envàs per a la conservació del pernil cuit.

El bosc dels fartets o la història d'una depuradora ecològica

Treball de recerca realitzat per una alumna d'ensenyament secundari i guardonat amb un Premi CIRIT per fomentar l'esperit científic del Jovent l'any 2009. Aquest treball té per objectiu plantejar el disseny d’una depuradora ecològica i un petit bosc de ribera amb la finalitat de divulgar i reivindicar el paper crucial que juguen les zones humides en el gran ecosistema de la Terra. Davant l’imminent esgotament de les principals energies fòssils i la manca de recursos tant bàsics com l’aigua, es pretén insistir en els molts avantatges d’importar la capacitat depuradora de les zones humides com a tecnologia alternativa per tractar aigües residuals industrials, agrícoles i urbanes, amb una despesa energètica pràcticament nul•la i uns beneficis ecològics, econòmics i de cost de la oportunitat més que evidents. El reciclatge d’aigües residuals es presenta com un dels reptes més importants de les societats actuals. La denominada fitodepuració aprofita el poder refinador de la vegetació present en les zones humides per reduir o eliminar contaminants de l’aigua mitjançant una sèrie de complexos processos biològics i fisicoquímics que la natura, en la seva dinàmica perfecte, ha dissenyat durant 4500 milions d anys. I és en base a aquestes qualitats depuradores d’aquests ecosistemes aquàtics que sorgeix la figura de l’aiguamoll artificial.

Relationship between technological progress, capital elasticity and emissions of industrial pollutants for the production sectors in Catalonia

As is known, the Kyoto Protocol proposes to reinforce national policies for emission reduction and, furthermore, to cooperate with other contracting parties. In this context, it would be necessary to assess these emissions, both in general and specifically, by pollutants and/or among productive sectors. The object of this paper is precisely to estimate the polluting emissions of industrial origin in Catalonia in the year 2001, in a multivariate context which explicitly allows a distinction to be made between the polluter and/or the productive sector causing this emission. Six pollutants considered, four directly related to greenhouse effect. A multi-level model, with two levels, pollutants and productive sectors, was specified. Both technological progress and elasticity of capital were introduced as random effects. Hence, it has been permitted that these coefficients vary according to one or other level. The most important finding in this paper is that elasticity of capital has been estimated as very non-elastic, with a range which varies between 0.162 (the paper industry) and 0.556 (commerce). In fact, and generally speaking, the greater capital the sector has, the less elasticity of capital has been estimated. Key words: Kyoto protocol, multilevel model, technological progress

Exponentially small splitting of separatrices in the perturbed McMillan map

The McMillan map is a one-parameter family of integrable symplectic maps of the plane, for which the origin is a hyperbolic fixed point with a homoclinic loop, with small Lyapunov exponent when the parameter is small. We consider a perturbation of the McMillan map for which we show that the loop breaks in two invariant curves which are exponentially close one to the other and which intersect transversely along two primary homoclinic orbits. We compute the asymptotic expansion of several quantities related to the splitting, namely the Lazutkin invariant and the area of the lobe between two consecutive primary homoclinic points. Complex matching techniques are in the core of this work. The coefficients involved in the expansion have a resurgent origin, as shown in [MSS08].

Generic Nekhoroshev theory without small divisors

In this article, we present a new approach of Nekhoroshev theory for a generic unperturbed Hamiltonian which completely avoids small divisors problems. The proof is an extension of a method introduced by P. Lochak which combines averaging along periodic orbits with simultaneous Diophantine approximation and uses geometric arguments designed by the second author to handle generic integrable Hamiltonians. This method allows to deal with generic non-analytic Hamiltonians and to obtain new results of generic stability around linearly stable tori.

Industrial district effects and innovation in the Tuscan shipbuilding industry

The aim of the present work is to investigate innovative processes within a geographical cluster, and thus contribute to the debate on the effects of industrial clusters on innovation capacity. In particular, we would like to ascertain whether the advantages of industrial districts in promoting innovation, as already revealed by literature (diffusion of knowledge, social capital and trust, efficient networking), are also keys to success in the Tuscan shipbuilding industry of pleasure and sporting boats. First, we verify the existence of clusters of shipbuilding in Tuscany, using a specific methodology. Next, in the identified clusters, we analyse three innovative networks financed in a policy to support innovation, and examine whether the typical features of a cluster for promoting innovation are at work, using a questionnaire administered to 71 actors. Finally, we develop a performance analysis of the cluster firms and ascertain whether their different behaviours also lead to different performances. The analysis results show that our case records effects of industrial clustering on innovation capacity, such as the important role given to trust and social capital, the significant worth put in interfirm relations and in each partner’s specific competencies, or even the distinctive performance of firms belonging to a cluster.