On Cooperative solutions of a generalized assignment game: limit theorems to the set of competitive equilibria

We study two cooperative solutions of a market with indivisible goods modeled as a generalized assignment game: Set-wise stability and Core. We first establish that the Set-wise stable set is contained in the Core and it contains the non-empty set of competitive equilibrium payoffs. We then state and prove three limit results for replicated markets. First, the sequence of Cores of replicated markets converges to the set of competitive equilibrium payoffs when the number of replicas tends to infinity. Second, the Set-wise stable set of a two-fold replicated market already coincides with the set of competitive equilibrium payoffs. Third, for any number of replicas there is a market with a Core payoff that is not a competitive equilibrium payoff.

On stability of solutions to systems of convex inequalities

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

Existence and uniqueness of viscosity solution for Hamilton-Jacobi equation with discontinuous coefficients dependent on time

The main result is a proof of the existence of a unique viscosity solution for Hamilton-Jacobi equation, where the hamiltonian is discontinuous with respect to variable, usually interpreted as the spatial one. Obtained generalized solution is continuous, but not necessarily differentiable.

Compositional data analysis of archaeological glass: problems and possible solutions

Presentation in CODAWORK'03, session 4: Applications to archeometry

Decentralization in Croatia: problems and possible solutions

El 2001 Croàcia va posar en marxa la iniciativa destinada a afluixar un alt grau de centralització mitjançant l'ampliació dels mandats de les unitats locals i el canvi de les fonts de finançament de les funcions públiques. No obstant això, els passos inicials en el procés de descentralització no ha estat seguida per altres mesures de descentralització fiscal, i en conseqüència, el seu nivell s'ha mantingut pràcticament sense canvis. El treball es proposa elaborar els principals problemes i obstacles en relació amb l'aplicació efectiva del procés de descentralització i donar tres grups de propostes per a la descentralització: (i) la divisió dels poders obligatoris entre les diferents unitats locals, (ii) el canvi en el finançament i (Iii) modificar la divisió territorial del país.

Speed of wave-front solutions to hyperbolic reaction-diffusion equations

The asymptotic speed problem of front solutions to hyperbolic reaction-diffusion (HRD) equations is studied in detail. We perform linear and variational analyses to obtain bounds for the speed. In contrast to what has been done in previous work, here we derive upper bounds in addition to lower ones in such a way that we can obtain improved bounds. For some functions it is possible to determine the speed without any uncertainty. This is also achieved for some systems of HRD (i.e., time-delayed Lotka-Volterra) equations that take into account the interaction among different species. An analytical analysis is performed for several systems of biological interest, and we find good agreement with the results of numerical simulations as well as with available observations for a system discussed recently

From bargaining solutions to claims rules: a proportional approach

Is it important to negotiate on proportions rather than on numbers? To answer this question, we analyze the behavior of well-known bargaining solutions and the claims rules they induce when they are applied to a "proportionally transformed" bargaining set SP -so-called bargaining-in-proportions set. The idea of applying bargaining solutions to claims problems was already developed in Dagan and Volij (1993). They apply the bargaining solutions over a bargaining set that is the one de ned by the claims and the endowment. A comparison among our results and theirs is provided. Keywords: Bargaining problem, Claims problem, Proportional, Constrained Equal Awards, Constrained Equal Losses, Nash bargaining solution. JEL classi fication: C71, D63, D71.

LdShake: learning design solutions sharing and co-edition

Two important challenges that teachers are currently facing are the sharing and the collaborative authoring of their learning design solutions, such as didactical units and learning materials. On the one hand, there are tools that can be used for the creation of design solutions and only some of them facilitate the co-edition. However, they do not incorporate mechanisms that support the sharing of the designs between teachers. On the other hand, there are tools that serve as repositories of educational resources but they do not enable the authoring of the designs. In this paper we present LdShake, a web tool whose novelty is focused on the combined support for the social sharing and co-edition of learning design solutions within communities of teachers. Teachers can create and share learning designs with other teachers using different access rights so that they can read, comment or co-edit the designs. Therefore, each design solution is associated to a group of teachers able to work on its definition, and another group that can only see the design. The tool is generic in that it allows the creation of designs based on any pedagogical approach. However, it can be particularized in instances providing pre-formatted designs structured according to a specific didactic method (such as Problem-Based Learning, PBL). A particularized LdShake instance has been used in the context of Human Biology studies where teams of teachers are required to work together in the design of PBL solutions. A controlled user study, that compares the use of a generic LdShake and a Moodle system, configured to enable the creation and sharing of designs, has been also carried out. The combined results of the real and controlled studies show that the social structure, and the commenting, co-edition and publishing features of LdShake provide a useful, effective and usable approach for facilitating teachers' teamwork.

Consistent solutions in exchange economies: A characterization of the price mechanism

We characterize the Walrasian allocations correspondence by means offour axioms: consistency, replica invariance, individual rationality andPareto optimality. It is shown that for any given class of exchange economiesany solution that satisfies the axioms is a selection from the Walrasianallocations with slack. Preferences are assumed to be smooth, but may besatiated and non--convex. A class of economies is defined as all economieswhose agents' preferences belong to an arbitrary family (finite or infinite)of types. The result can be modified to characterize equal budget Walrasianallocations with slack by replacing individual rationality with individualrationality from equal division. The results are valid also for classes ofeconomies in which core--Walras equivalence does not hold.

Periodic Solutions in Low-Dimensional Climatic Models

Classic climatic models use constitutive laws without any response time. A more realistic approach to the natural processes governing climate dynamics must introduce response time for heat and radiation fluxes. Extended irreversible thermodynamics (EIT) is a good thermodynamical framework for introducing nonclassical constitutive laws. In the present study EIT has been used to analyze a Budyko–Sellers one-dimensional energybalance model developed by G. R. North. The results present self-sustained periodic oscillations when the response time is greater than a critical value. The high-frequency (few kiloyears) damped and nondamped oscillations obtained can be related to abrupt climatic changes without any variation in the external forcing of the system

Evaluating solutions to process, view and listen mathematical formula within an accessible context

Proves de conversió de fòrmules matemàtiques des d'editors de text ofimàtics i des de Làtex. Visionat en HTML i MathML. El millor resultat s'aconsegueix amb MSWord+MathType i IE+MathPlayer.

Single-valued solutions for the Böhm-Bawerk horse market game

Single-valued solutions for the case of two-sided market games without product differentiation, also known as Böhm-Bawerk horse market games, are analyzed. The nucleolus is proved to coincide with the tau-value, and is thus the midpoint of the core. Moreover a characterization of this setof games in terms of the assignment matrix is provided.