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.

Determinants of Decentralization within the Firm: Some Empirical Evidence from Spanish Small and Medium- Sized Enterprise

This paper examines empirically the determinants of decentralization of decision- making in the firm for small and medium-sized enterprises (SMEs) that tend to be highly centralized. By decentralization of decisions we mean the delegation of decision rights from the owner or manager to the plant supervisor or even to floor workers. Our findings show that the allocation of authority to basic workers or a team of workers depends on firm characteristics such as firm size, the use of internal networks or the number of workplaces, and workers characteristics, in particular, the composition of the laborforce in terms of education and seniority and whether or not workers receive pay incentives. External factors such as the intensity of competition and the firm s export intensity are also important determinants of the allocation of authority.

X-Ray systems: radiation protection program in basic research applications

Although the radiation doses involved in basic research radiology are relatively small, the increasing number of radiological procedures makes risks becoming increasingly high. Quality control techniques in radiological practice have to ensure an adequate system of protection for people exposed to radiation. These techniques belong to a quality assurance program for X-ray machines and are designed to correct problems related to equipment and radiological practices, to obtain radiological images of high quality and to reduce the unnecessary exposures.

Chaotic dynamics in credit constrained emerging economies

This paper analyzes the role of financial development as a source of endogenous instability in small open economies. By assuming that firms face credit constraints, our model displays a complex dynamic behavior for intermediate values of the parameter representing the level of financial development of the economy. The basic implication of our model is that economies experiencing a process of financial development are more unstable than both very underdeveloped and very developed economies. Our instability concept means that small shocks have a persistent effect on the long run behavior of the model and also that economies can exhibit cycles with a very high period or even chaotic dynamic patterns.

Endogeneizing know-how flows through the nature of R&D investments

In this paper we carefully link knowledge flows to and from a firms innovation process with this firms investment decisions. Three types of investments are considered: investments in applied research, investments in basic research, and investments in intellectual property protection. Only when basic research is performed, can the firm effectively access incoming knowledge flows and these incoming spillovers serve to increase the efficiency of own applied research.. The firm can at the same time influence outgoing knowledge flows, improving appropriability of its innovations, by investing in protection. Our results indicate that firms with small budgets for innovation will not invest in basic research. This occurs in the short run, when the budget for know-how creation is restricted, or in the long-run, when market opportunities are low, when legal protection is not very important, or, when the pool of accessible and relevant external know-how is limited. The ratio! of basic to applied research is non-decreasing in the size of the pool of accessible external know-how, the size and opportunity of the market, and, the effectiveness of intellectual property rights protection. This indicates the existence of economies of scale in basic research due to external market related factors. Empirical evidence from a sample of innovative manufacturing firms in Belgium confirms the economies of scale in basic research as a consequence of the firms capacity to access external knowledge flows and to protect intellectual property, as well as the complementarity between legal and strategic investments.

Implementació amb Visual Basic d'un algorisme per a encriptar i desencriptar

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 2005. La criptografia és l’art d’escriure un llenguatge convingut, amb l’ús d’unes claus i de la seva operació inversa se’n diu criptoanalitzar. Els sistemes criptogràfics han estat emprats al llarg de la història. Actualment existeixen multituds de software i de hardware destinats a analitzar el tràfic de dades en xarxes de computadores. Encara que aquestes eines constitueixen un avenç en tècniques de seguretat i protecció, el seu ús indegut es al mateix temps un greu problema i una enorme font d’atacs a la intimitat dels seus usuaris i a la integritat dels seus propis sistemes. Des d’aquest punt de vista, s’explica com s’ha dissenyat dos aplicacions informàtiques per encriptar i desencriptar.

What works best for getting the unemployed back to work: employment services or small-business assistance programs? evidence from Romania

Recent empirical evidence has found that employment services and small-business assistance programmes are often successful at getting the unemployed back to work. Â One important concern of policy makers is to decide which of these two programmes is more effective and for whom. Â Using unusually rich (for transition economies) survey data and matching methods, I evaluate the relative effectiveness of these two programmes in Romania. Â While I find that employment services (ES) are, on average, more successful than a small-business assistance programme (SBA), estimation of heterogeneity effects reveals that, compared to non-participation, ES are effective for workers with little access to informal search channels, and SBA works for less-qualified workers and those living in rural areas. Â When comparing ES to SBA, I find that ES tend to be more efficient than SBA for workers without a high-school degree, and that the opposite holds for the more educated workers.

Subgroups of small index in Aut(Fn) and Kazhdan's property (T)

We give a series of interesting subgroups of finite index in Aut(Fn). One of them has index 42 in Aut(F3) and infinite abelianization. This implies that Aut(F3) does not have Kazhdan’s property (T) (see [3] and [6] for another proofs). We proved also that every subgroup of finite index in Aut(Fn), n &= 3, which contains the subgroup of IA-automorphisms, has a finite abelianization.

Model structures on the category of small double categories

In this paper we obtain several model structures on DblCat, the category of small double categories. Our model structures have three sources. We first transfer across a categorification-nerve adjunction. Secondly, we view double categories as internal categories in Cat and take as our weak equivalences various internal equivalences defined via Grothendieck topologies. Thirdly, DblCat inherits a model structure as a category of algebras over a 2-monad. Some of these model structures coincide and the different points of view give us further results about cofibrant replacements and cofi brant objects. As part of this program we give explicit descriptions and discuss properties of free double categories, quotient double categories, colimits of double categories, and several nerves and categorifications.

Explaining High Economic Growth in Small Tourism Countries with a Dynamic General Equilibrium Model

This paper shows that tourism specialisation can help to explain the observed high growth rates of small countries. For this purpose, two models of growth and trade are constructed to represent the trade relations between two countries. One of the countries is large, rich, has an own source of sustained growth and produces a tradable capital good. The other is a small poor economy, which does not have an own engine of growth and produces tradable tourism services. The poor country exports tourism services to and imports capital goods from the rich economy. In one model tourism is a luxury good, while in the other the expenditure elasticity of tourism imports is unitary. Two main results are obtained. In the long run, the tourism country overcomes decreasing returns and permanently grows because its terms of trade continuously improve. Since the tourism sector is relatively less productive than the capital good sector, tourism services become relatively scarcer and hence more expensive than the capital good. Moreover, along the transition the growth rate of the tourism economy holds well above the one of the rich country for a long time. The growth rate differential between countries is particularly high when tourism is a luxury good. In this case, there is a faster increase in the tourism demand. As a result, investment of the small economy is boosted and its terms of trade highly improve.

A Thomason model structure on the category of small n-fold categories

We construct a cofibrantly generated Thomason model structure on the category of small n-fold categories and prove that it is Quillen equivalent to the standard model structure on the category of simplicial sets. An n-fold functor is a weak equivalence if and only if the diagonal of its n-fold nerve is a weak equivalence of simplicial sets. We introduce an n-fold Grothendieck construction for multisimplicial sets, and prove that it is a homotopy inverse to the n-fold nerve. As a consequence, the unit and counit of the adjunction between simplicial sets and n-fold categories are natural weak equivalences.

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.

A three dimensional signed small ball inequality

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

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.