A Cartan-Eilenberg approach to Homotopical Algebra

In this paper we propose an approach to homotopical algebra where the basic ingredient is a category with two classes of distinguished morphisms: strong and weak equivalences. These data determine the cofibrant objects by an extension property analogous to the classical lifting property of projective modules. We define a Cartan-Eilenberg category as a category with strong and weak equivalences such that there is an equivalence of categories between its localisation with respect to weak equivalences and the relative localisation of the subcategory of cofibrant objects with respect to strong equivalences. This equivalence of categories allows us to extend the classical theory of derived additive functors to this non additive setting. The main examples include Quillen model categories and categories of functors defined on a category endowed with a cotriple (comonad) and taking values on a category of complexes of an abelian category. In the latter case there are examples in which the class of strong equivalences is not determined by a homotopy relation. Among other applications of our theory, we establish a very general acyclic models theorem.

On the relation between tax rates and evasion in a multi-period economy

We extend the basic tax evasion model to a multi-period economy exhibiting sustained growth. When individuals conceal part of their true income from the tax authority, they face the risk of being audited and hence of paying the corresponding fine. Both taxes and fines determine individual saving and the rate of capital accumulation. In this context we show that the sign of the relation between the level of the tax rate and the amount of evaded income is the same as that obtained in static setups. Moreover, high tax rates on income are typically associated with low growth rates as occurs in standard growth models that disregard the tax evasion phenomenon.

Stable rank of leavitt path algebra

We characterize the values of the stable rank for Leavitt path algebras, by giving concrete criteria in terms of properties of the underlying graph.

On two examples by Iyama and Yoshino

In a recent paper Iyama and Yoshino consider two interesting examples of isolated singularities over which it is possible to classify the indecomposable maximal Cohen-Macaulay modules in terms of linear algebra data. In this paper we present two new approaches to these examples. In the first approach we give a relation with cluster categories. In the second approach we use Orlov's result on the graded singularity category. We obtain some new results on the singularity category of isolated singularities which may be interesting in their own right.

COMUNICAEMAT: comunicant objectius matemàtics unint nombres, càlcul, algebra, espai, mesura anglès i tecnologia

S' ha realitzat una anàlisi de processos comunicatius i didàctics en un treball de matemàtiques a Primària en llengua anglesa, emmarcat dins un projecte escolar plurilingüe. El treball s' organitza en forma de recerca-acció que analitza dos objectius principals: (a) elaboració de propostes d' activitat matemàtica i de formació de professorat, i (b) anàlisi del treball realitzat en una experiència escolar. Els resultats mostren que: (1) Les dificultats generals observades, es centren més sobre el contingut de la llengua matemàtica (anomenat L4), pel damunt de les pròpies de l’ús de la llengua anglesa L3. (2) Les decisions del professorat privilegiant l’ús de L1 i L2 (català i castellà) per a treballar L4 s’han mostrat positives i adients. La proposta elaborada, que segueix el model CLIL (Content Language Integrated Learning) ha estat positiva i reproduïble (3) Ha estat possible constatar un bon treball amb els estudiants de formació inicial de mestres de llengua estrangera futurs docents dins l'assignatura de Matemàtiques i la seva Didàctica.a la Formació de professorat. Tanmateix es reconeixen dificultats degudes al poc coneixement previ dels estudiants en L3 i L4 i el fet de ser la primera experiència d’aquest tipus que realitzen. (4) L’alumnat de l’escola és capaç de tenir una bona conversa oral en anglès al final de Primària, que creix en qualitat fins dominar estructures causals pròpies del raonament deductiu. (5) L’alumnat guanya en confiança en l’ús de les quatre llengües ,(6) el professorat incorpora relativament elements didàctics nous en la seva acció pedagògica.

A conjecture of Bavula on homomorphisms of Weyl algebra

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

When is the second local multiplier algebra of a C*-algebra equal to the first?

We discuss necessary as well as sufficient conditions for the second iterated local multiplier algebra of a separable C*-algebra to agree with the first.

Revisiting the size-R&D productivity relation: introducing the mediating role of decision-making style on the scale and quality of innovative output

We develop a mediation model in which firm size is proposed to affect the scale and quality of innovative output through the adoption of different decision styles during the R&D process. The aim of this study is to understand how the internal changes that firms undergo as they evolve from small to larger organizations affect R&D productivity. In so doing, we illuminate the underlying theoretical mechanism affecting two different dimensions of R&D productivity, namely the scale and quality of innovative output which have not received much attention in previous literature. Using longitudinal data of Spanish manufacturing firms we explore the validity of this mediation model. Our results show that as firms evolve in size, they increasingly emphasize analytical decision making, and consequently, large-sized firms aim for higher-quality innovations while small firms aim for a larger scale of innovative output.

Opening Education Beyond the Property Relation: From Commons to Communism

Open Education, and specifically the OER movement, seeks to provide universal access to knowledge, undermining the historical enclosure and the increasing privatisation of the public education system. In this paper we examine this aspiration by submitting the implicit theoretical assumptions of Open Education to the test of critical political economy. We acknowledge the Open Education movement's revolutionary potential but outline the inherent limitations of its current focus on the commons (property relations) rather than the social relations of capitalist production (wage work, the company) and because of this, argue that it will only achieve limited, rather than revolutionary, impact.

Relation between temperature and mortality in thirteen Spanish cities

In this study we examined the shape of the association between temperature and mortality in 13 Spanish cities representing a wide range of climatic and socio demographic conditions. The temperature value linked with minimum mortality (MMT) and the slopes before and after the turning point (MMT) were calculated. Most cities showed a V-shaped temperature-mortality relationship. MMTs were generally higher in cities with warmer climates. Cold and heat effects also depended on climate: effects were greater in hotter cities but lesser in cities with higher variability. The effect of heat was greater than the effect of cold. The effect of cold and MMT was, in general, greater for cardio-respiratory mortality than for total mortality, while the effect of heat was, in general, greater among the elderly

Attention, memory and verbal learning and their relation to schizotypal traits in unaffected parents of schizophrenic patients

The main objective of this ex post facto study is to compare the differencesin cognitive functions and their relation to schizotypal personality traits between agroup of unaffected parents of schizophrenic patients and a control group. A total of 52unaffected biological parents of schizophrenic patients and 52 unaffected parents ofunaffected subjects were assessed in measures of attention (Continuous PerformanceTest- Identical Pairs Version, CPT-IP), memory and verbal learning (California VerbalLearning Test, CVLT) as well as schizotypal personality traits (Oxford-Liverpool Inventoryof Feelings and Experiences, O-LIFE). The parents of the patients with schizophreniadiffer from the parents of the control group in omission errors on the ContinuousPerformance Test- Identical Pairs, on a measure of recall and on two contrast measuresof the California Verbal Learning Test. The associations between neuropsychologicalvariables and schizotpyal traits are of a low magnitude. There is no defined pattern ofthe relationship between cognitive measures and schizotypal traits

Neogene antecedents of the modern human hand and its relation to bipedalism

El present projecte s'ha dut a terme a l'American Museum of Natural History (AMNH, New York) entre el 31 de Desembre de 2010 i el 30 de Desembre de 2012. L'objectiu del projecte era elucidar la història evolutiva de la mà humana: traçar els canvis evolutius en la seva forma i proporcions que van propiciar la seva estructura moderna que permet als humans manipular amb precisió. El treball realitzat ha inclòs recol•lecció de dades i anàlisis, redacció de resultats i formació en mètodes analítics específics. Durant aquest temps, l'autor a completat la seva de base de dades existent en mesures lineals de la mà a hominoides. També s'han agafat dades del peu; d'aquesta forma ara mateix es compta amb una base de dades amb més de 500 individus, amb més de 200 mesures per cada un. També s'han agafat dades en tres imensions utilitzant un làser escàner. S'han après tècniques de morfometria geomètrica 3D directament dels pioners al camp a l'AMNH. Com a resultat d'aquesta feina s'han produït 10 resums (publicats a congressos internacionals) i 9 manuscrits (molts d'ells ja publicats a revistes internacionals) amb resultats de gran rellevància: La mà humana posseeix unes proporcions relativament primitives, que són més similars a les proporciones que tenien els hominoides fòssils del Miocè que no pas a la dels grans antropomorfs actuals. Els darrers tenen unes mans allargades amb un polzes molt curts que reflexen l'ús de la mà com a eina de suspensió sota les branques. En canvi, els hominoides del Miocè tenien unes mans relativament curtes amb un polze llarg que feien servir per estabilitzar el seu pes quan caminaven per sobre de les branques. Una vegada els primers homínids van aparèixer al final del Miocè (fa uns 6 Ma) i van començar a fer servir el bipedisme com a mitjà més comú de locomoció, les seves mans van ser "alliberades" de les seves funcions locomotores. La selecció natural—ara només treballant en la manipulació—va convertir les proporcions ja existents de la mà d'aquests primats en l'òrgan manipulatori que representa la mà humana avui dia.

Definitional verbal patterns for semantic relation extraction

In this paper we present a description of the role of definitional verbal patterns for the extraction of semantic relations. Several studies show that semantic relations can be extracted from analytic definitions contained in machine-readable dictionaries (MRDs). In addition, definitions found in specialised texts are a good starting point to search for different types of definitions where other semantic relations occur. The extraction of definitional knowledge from specialised corpora represents another interesting approach for the extraction of semantic relations. Here, we present a descriptive analysis of definitional verbal patterns in Spanish and the first steps towards the development of a system for the automatic extraction of definitional knowledge.

A singular function and its relation with the number systems involved in its definition

Minkowski's ?(x) function can be seen as the confrontation of two number systems: regular continued fractions and the alternated dyadic system. This way of looking at it permits us to prove that its derivative, as it also happens for many other non-decreasing singular functions from [0,1] to [0,1], when it exists can only attain two values: zero and infinity. It is also proved that if the average of the partial quotients in the continued fraction expansion of x is greater than k* =5.31972, and ?'(x) exists then ?'(x)=0. In the same way, if the same average is less than k**=2 log2(F), where F is the golden ratio, then ?'(x)=infinity. Finally some results are presented concerning metric properties of continued fraction and alternated dyadic expansions.

The quasi-judicial role of large retailers: An efficiency hypothesis of their relation with suppliers

The paper explores an efficiency hypothesis regarding the contractual process between large retailers, such as Wal-Mart and Carrefour, and their suppliers. The empirical evidence presented supports the idea that large retailers play a quasi-judicial role, acting as "courts of first instance" in their relationships with suppliers. In this role, large retailers adjust the terms of trade to on-going changes and sanction performance failures, sometimes delaying payments. A potential abuse of their position is limited by the need for re-contracting and preserving their reputations. Suppliers renew their confidence in their retailers on a yearly basis, through writing new contracts. This renovation contradicts the alternative hypothesis that suppliers are expropriated by large retailers as a consequence of specific investments.