The Brezis-Nirenberg type problem involving the square root of the Laplacian

We establish existence and non-existence results to the Brezis-Nirenberg type problem involving the square root of the Laplacian in a bounded domain with zero Dirichlet boundary condition.

Vigilance behavior of Pyrenean chamois (Rupicapra pyrenaica pyrenaica): Effect of sex and position in the herd

The Pyrenean chamois (Rupicapra pyrenaica pyrenaica) is a mountain-dwelling ungulate with an extensive presence in open areas. Optimal group size results from the trade off between advantages (a reduction in the risk of predation) and disadvantages (competition between members of the herd) of group living. In addition, advantages and disadvantages of group living may vary depending on the position of each individual within the herd. Our objective was to study the effect of central vs. peripheral position in the herd on feeding and vigilance behavior in male and female Pyrenean chamois and to ascertain if a group size effect existed. We used focal animal sampling and recorded social interactions when a focal animal was involved. With males, vigilance rate was higher in the central part of the group than at the periphery, probably due to a higher density of animals in the central part of the herd and a higher probability of being disturbed by conspecifics. With females, vigilance rate did not differ according to position in the herd. Females spent more time feeding than males, and males showed a higher frequency of the vigilance behavior than females. We did not observe a clear relationship between group size and vigilance behavior. The differences in vigilance behavior might be due to social interactions.

The Division problem with voluntary participation

The division problem consists of allocating a given amount of an homogeneous and perfectly divisible good among a group of agents with single-peaked preferences on the set of their potential shares. A rule proposes a vector of shares for each division problem. The literature has implicitly assumed that agents will find acceptable any share they are assigned to. In this paper we consider the division problem when agents' participation is voluntary. Each agent has an idiosyncratic interval of acceptable shares where his preferences are single-peaked. A rule has to propose to each agent either to not participate or an acceptable share because otherwise he would opt out and this would require to reassign some of the remaining agents' shares. We study a subclass of efficient and consistent rules and characterize extensions of the uniform rule that deal explicitly with agents' voluntary participation.

Behavior study of pipes after forming, coating and bending

A study of the main types of coatings and its processes that modern industry commonly apply to prevent to the corrosion due to the environmental effects to energetic market pipelines have been done. Extracting main time and temperature range values, coating heat treatment recreation have been applied to x65 pipelines steel grade samples obtained from a pipe which was formed using UOE forming process. Experimental tensile tests and Charpy V‐Notch Impact test have been carried out for a deeply knowledge of the influence on the steel once this recreations are applied. The Yield Strength and toughness have been improved despite lower values in rupture strain and ductile‐brittle temperature transition have been obtained. Finite Element Method have been applied to simulate the entirely pipe cold bending process to predict the mechanical properties and behaviour of the pipe made from x65 steel grade under different conditions.

Discontinuous Galerkin methods for the Multi-dimensional Vlasov-Poisson problem

We introduce and analyze two new semi-discrete numerical methods for the multi-dimensional Vlasov-Poisson system. The schemes are constructed by combing a discontinuous Galerkin approximation to the Vlasov equation together with a mixed finite element method for the Poisson problem. We show optimal error estimates in the case of smooth compactly supported initial data. We propose a scheme that preserves the total energy of the system.

Repeated Interaction and the Revelation of the Monitor's Type: A Principal-Monitor-Agent Problem

This paper studies a dynamic principal-monitor-agent relation where a strategic principal delegates the task of monitoring the effort of a strategic agent to a third party. The latter we call the monitor, whose type is initially unknown. Through repeated interaction the agent might learn his type. We show that this process damages the principal's payoffs. Compensation is assumed exogenous, limiting to a great extent the provision of incentives. We go around this difficulty by introducing costly replacement strategies, i.e. the principal replaces the monitor, thus disrupting the agent's learning. We found that even when replacement costs are null, if the revealed monitor is strictly preferred by both parties, there is a loss in efficiency due to the impossibility of bene…tting from it. Nonetheless, these strategies can partially recover the principal's losses. Additionally, we establish upper and lower bounds on the payoffs that the principal and the agent can achieve. Finally we characterize the equilibrium strategies under public and private monitoring (with communication) for different cost and impatience levels.

The problem of the competitiveness of nuclear energy: a biophysical explanation

In this study I try to explain the systemic problem of the low economic competitiveness of nuclear energy for the production of electricity by carrying out a biophysical analysis of its production process. Given the fact that neither econometric approaches nor onedimensional methods of energy analyses are effective, I introduce the concept of biophysical explanation as a quantitative analysis capable of handling the inherent ambiguity associated with the concept of energy. In particular, the quantities of energy, considered as relevant for the assessment, can only be measured and aggregated after having agreed on a pre-analytical definition of a grammar characterizing a given set of finite transformations. Using this grammar it becomes possible to provide a biophysical explanation for the low economic competitiveness of nuclear energy in the production of electricity. When comparing the various unit operations of the process of production of electricity with nuclear energy to the analogous unit operations of the process of production of fossil energy, we see that the various phases of the process are the same. The only difference is related to characteristics of the process associated with the generation of heat which are completely different in the two systems. Since the cost of production of fossil energy provides the base line of economic competitiveness of electricity, the (lack of) economic competitiveness of the production of electricity from nuclear energy can be studied, by comparing the biophysical costs associated with the different unit operations taking place in nuclear and fossil power plants when generating process heat or net electricity. In particular, the analysis focuses on fossil-fuel requirements and labor requirements for those phases that both nuclear plants and fossil energy plants have in common: (i) mining; (ii) refining/enriching; (iii) generating heat/electricity; (iv) handling the pollution/radioactive wastes. By adopting this approach, it becomes possible to explain the systemic low economic competitiveness of nuclear energy in the production of electricity, because of: (i) its dependence on oil, limiting its possible role as a carbon-free alternative; (ii) the choices made in relation to its fuel cycle, especially whether it includes reprocessing operations or not; (iii) the unavoidable uncertainty in the definition of the characteristics of its process; (iv) its large inertia (lack of flexibility) due to issues of time scale; and (v) its low power level.

Mètodes algebraics i de teoria de la prova per a la formalització del raonament vague

Projecte de recerca elaborat a partir d’una estada a la Università degli studi di Siena, Italy , entre 2007 i 2009. El projecte ha consistit en un estudi de la formalització lògica del raonament en presència de vaguetat amb els mètodes de la Lògica Algebraica i de la Teoria de la Prova. S'ha treballat fonamental en quatre direccions complementàries. En primer lloc, s'ha proposat un nou plantejament, més abstracte que el paradigma dominant fins ara, per l'estudi dels sistemes de lògica borrosa. Fins ara en l'estudi d'aquests sistemes l'atenció havia recaigut essencialment en l'obtenció de semàntiques basades en tnormes contínues (o almenys contínues per l'esquerra). En primer nivell de major abstracció hem estudiat les propietats de completesa de les lògiques borroses (tant proposicionals com de primer ordre) respecte de semàntiques definides sobre qualsevol cadena de valors de veritat, no necessàriament només sobre l'interval unitat dels nombres reals. A continuació, en un nivell encara més abstracte, s’ha pres l'anomenada jerarquia de Leibniz de la Lògica Algebraica Abstracta que classifica tots els sistemes lògics amb un bon comportament algebraic i s'ha expandit a una nova jerarquia (que anomenem implicacional) que permet definir noves classes de lògiques borroses que contenen quasi totes les conegudes fins ara. En segon lloc, s’ha continuat una línia d'investigació iniciada els darrers anys consistent en l'estudi de la veritat parcial com a noció sintàctica (és a dir, com a constants de veritat explícites en els sistemes de prova de les lògiques borroses). Per primer cop, s’ha considerat la semàntica racional per les lògiques proposicionals i la semàntica real i racional per les lògiques de primer ordre expandides amb constants. En tercer lloc, s’ha tractat el problema més fonamental del significat i la utilitat de les lògiques borroses com a modelitzadores de (part de) els fenòmens de la vaguetat en un darrer article de caràcter més filosòfic i divulgatiu, i en un altre més tècnic en què defensem la necessitat i presentem l'estat de l'art de l'estudi de les estructures algèbriques associades a les lògiques borroses. Finalment, s’ha dedicat la darrera part del projecte a l'estudi de la complexitat aritmètica de les lògiques borroses de primer ordre.

The generator problem for Z-stable C*-algebras

The generator problem was posed by Kadison in 1967, and it remains open until today. We provide a solution for the class of C*-algebras absorbing the Jiang-Su algebra Z tensorially. More precisely, we show that every unital, separable, Z-stable C*-algebra A is singly generated, which means that there exists an element x є A that is not contained in any proper sub-C*- algebra of A. To give applications of our result, we observe that Z can be embedded into the reduced group C*-algebra of a discrete group that contains a non-cyclic, free subgroup. It follows that certain tensor products with reduced group C*-algebras are singly generated. In particular, C*r (F ∞) ⨂ C*r (F ∞) is singly generated.