Quasilocal density functional theory and its application within the extended Thomas-Fermi approximation

In this paper we propose a generalization of the density functional theory. The theory leads to single-particle equations of motion with a quasilocal mean-field operator, which contains a quasiparticle position-dependent effective mass and a spin-orbit potential. The energy density functional is constructed using the extended Thomas-Fermi approximation and the ground-state properties of doubly magic nuclei are considered within the framework of this approach. Calculations were performed using the finite-range Gogny D1S forces and the results are compared with the exact Hartree-Fock calculations

Contractive probability metrics and asymptotic behavior of dissipative kinetic equations

The present notes are intended to present a detailed review of the existing results in dissipative kinetic theory which make use of the contraction properties of two main families of probability metrics: optimal mass transport and Fourier-based metrics. The first part of the notes is devoted to a self-consistent summary and presentation of the properties of both probability metrics, including new aspects on the relationships between them and other metrics of wide use in probability theory. These results are of independent interest with potential use in other contexts in Partial Differential Equations and Probability Theory. The second part of the notes makes a different presentation of the asymptotic behavior of Inelastic Maxwell Models than the one presented in the literature and it shows a new example of application: particle's bath heating. We show how starting from the contraction properties in probability metrics, one can deduce the existence, uniqueness and asymptotic stability in classical spaces. A global strategy with this aim is set up and applied in two dissipative models.

The optimum quantity of money: Theory and evidence

In this paper we propose a simple and general model for computing the Ramsey optimal inflation tax, which includes several models from the previous literature as special cases. We show that it cannot be claimed that the Friedman rule is always optimal (or always non--optimal) on theoretical grounds. The Friedman rule is optimal or not, depending on conditions related to the shape of various relevant functions. One contribution of this paper is to relate these conditions to {\it measurable} variables such as the interest rate or the consumption elasticity of money demand. We find that it tends to be optimal to tax money when there are economies of scale in the demand for money (the scale elasticity is smaller than one) and/or when money is required for the payment of consumption or wage taxes. We find that it tends to be optimal to tax money more heavily when the interest elasticity of money demand is small. We present empirical evidence on the parameters that determine the optimal inflation tax. Calibrating the model to a variety of empirical studies yields a optimal nominal interest rate of less than 1\%/year, although that finding is sensitive to the calibration.

Self-dynamic structure factor of dense liquids: Theory and simulation

The self-intermediate dynamic structure factor Fs(k,t) of liquid lithium near the melting temperature is calculated by molecular dynamics. The results are compared with the predictions of several theoretical approaches, paying special attention to the Lovesey model and the Wahnstrm and Sjgren mode-coupling theory. To this end the results for the Fs(k,t) second memory function predicted by both models are compared with the ones calculated from the simulations.

Stability and asymptotic analysis of a fluid-particle interaction model

We are interested in coupled microscopic/macroscopic models describing the evolution of particles dispersed in a fluid. The system consists in a Vlasov-Fokker-Planck equation to describe the microscopic motion of the particles coupled to the Euler equations for a compressible fluid. We investigate dissipative quantities, equilibria and their stability properties and the role of external forces. We also study some asymptotic problems, their equilibria and stability and the derivation of macroscopic two-phase models.

Convergence across countries and regions: theory and empirics

This paper surveys the recent literature on convergence across countries and regions. I discuss the main convergence and divergence mechanisms identified in the literature and develop a simple model that illustrates their implications for income dynamics. I then review the existing empirical evidence and discuss its theoretical implications. Early optimism concerning the ability of a human capital-augmented neoclassical model to explain productivity differences across economies has been questioned on the basis of more recent contributions that make use of panel data techniques and obtain theoretically implausible results. Some recent research in this area tries to reconcile these findings with sensible theoretical models by exploring the role of alternative convergence mechanisms and the possible shortcomings of panel data techniques for convergence analysis.

Political autonomy and independence: theory and experimental evidence

We study the process by which subordinated regions of a country can obtain a more favourable political status. In our theoretical model a dominant and a dominated region first interact through a voting process that can lead to different degrees of autonomy. If this process fails then both regions engage in a costly political conflict which can only lead to the maintenance of the initial subordination of the region in question or to its complete independence. In the subgame-perfect equilibrium the voting process always leads to an intermediate arrangement acceptable for both parts. Hence, the costly political struggle never occurs. In contrast, in our experiments we observe a large amount of fighting involving high material losses, even in a case in which the possibilities for an arrangement without conflict are very salient. In our experimental environment intermediate solutions are feasible and stable, but purely emotional elements prevent them from being reached.

Conflict prevention and decentralized governance: some remarks about the state of the art in theory and practice

Is there a link between decentralized governance and conflict prevention? This article tries to answer the question by presenting the state of the art of the intersection of both concepts. Provided that social conflict is inevitable and given the appearance of new threats and types of violence, as well as new demands for security based on people (human security), our societies should focus on promoting peaceful changes. Through an extensive analysis of the existing literature and the study of several cases, this paper suggests that decentralized governance can contribute to these efforts by transforming conflicts, bringing about power-sharing and inclusion incentives of minority groups. Albeit the complexity of assessing its impact on conflict prevention, it can be contended that decentralized governance might have very positive effects on the reduction of causes that bring about conflicts due to its ability to foster the creation of war/violence preventors. More specifically, this paper argues that decentralization can have a positive impact on the so-called triggers and accelerators (short- and medium-term causes).

Generalized descriptive set theory and classification theory

Descriptive set theory is mainly concerned with studying subsets of the space of all countable binary sequences. In this paper we study the generalization where countable is replaced by uncountable. We explore properties of generalized Baire and Cantor spaces, equivalence relations and their Borel reducibility. The study shows that the descriptive set theory looks very different in this generalized setting compared to the classical, countable case. We also draw the connection between the stability theoretic complexity of first-order theories and the descriptive set theoretic complexity of their isomorphism relations. Our results suggest that Borel reducibility on uncountable structures is a model theoretically natural way to compare the complexity of isomorphism relations.

Moduli of smoothness and growth properties of Fourier transforms: two-sided estimates

We prove two-sided inequalities between the integral moduli of smoothness of a function on R d[superscript] / T d[superscript] and the weighted tail-type integrals of its Fourier transform/series. Sharpness of obtained results in particular is given by the equivalence results for functions satisfying certain regular conditions. Applications include a quantitative form of the Riemann-Lebesgue lemma as well as several other questions in approximation theory and the theory of function spaces.

Using problem-based learning for introducing producer theory and market structure in intermediate microeconomics

This paper shows how instructors can use the problem‐based learning method to introduce producer theory and market structure in intermediate microeconomics courses. The paper proposes a framework where different decision problems are presented to students, who are asked to imagine that they are the managers of a firm who need to solve a problem in a particular business setting. In this setting, the instructors’ role isto provide both guidance to facilitate student learning and content knowledge on a just‐in‐time basis

Fuzzy set Theory and Quantum Chemistry

Es discuteixen breument algunes consideracions sobre l'aplicació de la Teoria delsConjunts difusos a la Química quàntica. Es demostra aqui que molts conceptes químics associats a la teoria són adequats per ésser connectats amb l'estructura dels Conjunts difusos. També s'explica com algunes descripcions teoriques dels observables quàntics espotencien tractant-les amb les eines associades als esmentats Conjunts difusos. La funciódensitat es pren com a exemple de l'ús de distribucions de possibilitat al mateix temps queles distribucions de probabilitat quàntiques

Conditional compositional biplots: theory and application

The biplot has proved to be a powerful descriptive and analytical tool in many areasof applications of statistics. For compositional data the necessary theoreticaladaptation has been provided, with illustrative applications, by Aitchison (1990) andAitchison and Greenacre (2002). These papers were restricted to the interpretation ofsimple compositional data sets. In many situations the problem has to be described insome form of conditional modelling. For example, in a clinical trial where interest isin how patients’ steroid metabolite compositions may change as a result of differenttreatment regimes, interest is in relating the compositions after treatment to thecompositions before treatment and the nature of the treatments applied. To study thisthrough a biplot technique requires the development of some form of conditionalcompositional biplot. This is the purpose of this paper. We choose as a motivatingapplication an analysis of the 1992 US President ial Election, where interest may be inhow the three-part composition, the percentage division among the three candidates -Bush, Clinton and Perot - of the presidential vote in each state, depends on the ethniccomposition and on the urban-rural composition of the state. The methodology ofconditional compositional biplots is first developed and a detailed interpretation of the1992 US Presidential Election provided. We use a second application involving theconditional variability of tektite mineral compositions with respect to major oxidecompositions to demonstrate some hazards of simplistic interpretation of biplots.Finally we conjecture on further possible applications of conditional compositionalbiplots