Stability, Resonance and Lyapunov Inequalities for Periodic Conservative Systems

This paper is devoted to the study of Lyapunov type inequalities for periodic conservative systems. The main results are derived from a previous analysis which relates the best Lyapunov constants to some especial (constrained or unconstrained) minimization problems. We provide some new results on the existence and uniqueness of solutions of nonlinear resonant and periodic systems. Finally, we present some new conditions which guarantee the stable boundedness of linear periodic conservative systems.Comment: 19 page

Bohmian Trajectories of Airy Packets

The discovery of Berry and Balazs in 1979 that the free-particle Schr\"odinger equation allows a non-dispersive and accelerating Airy-packet solution has taken the folklore of quantum mechanics by surprise. Over the years, this intriguing class of wave packets has sparked enormous theoretical and experimental activities in related areas of optics and atom physics. Within the Bohmian mechanics framework, we present new features of Airy wave packet solutions to Schr\"odinger equation with time-dependent quadratic potentials. In particular, we provide some insights to the problem by calculating the corresponding Bohmian trajectories. It is shown that by using general space-time transformations, these trajectories can display a unique variety of cases depending upon the initial position of the individual particle in the Airy wave packet. Further, we report here a myriad of nontrivial Bohmian trajectories associated to the Airy wave packet. These new features are worth introducing to the subject's theoretical folklore in light of the fact that the evolution of a quantum mechanical Airy wave packet governed by the Schr\"odinger equation is analogous to the propagation of a finite energy Airy beam satisfying the paraxial equation. Numerous experimental configurations of optics and atom physics have shown that the dynamics of Airy beams depends significantly on initial parameters and configurations of the experimental set-up.Comment: 8 page

Dividing Line between Quantum and Classical Trajectories: Bohmian Time Constant

This work proposes an answer to a challenge posed by Bell on the lack of clarity in regards to the line between the quantum and classical regimes in a measurement problem. To this end, a generalized logarithmic nonlinear Schr\"odinger equation is proposed to describe the time evolution of a quantum dissipative system under continuous measurement. Within the Bohmian mechanics framework, a solution to this equation reveals a novel result: it displays a time constant which should represent the dividing line between the quantum and classical trajectories. It is shown that continuous measurements and damping not only disturb the particle but compel the system to converge in time to a Newtonian regime. While the width of the wave packet may reach a stationary regime, its quantum trajectories converge exponentially in time to classical trajectories. In particular, it is shown that damping tends to suppress further quantum effects on a time scale shorter than the relaxation time of the system. If the initial wave packet width is taken to be equal to 2.8 10^{-15} m (the approximate size of an electron), the Bohmian time constant is found to have an upper limit, i. e., ${\tau_{B\max}} = {10^{- 26}}s$

APPLYING CHAID TO IDENTIFY THE ACCOUNTING-FINANCIAL CHARACTERISTICS OF THE MOST PROFITABLE REAL ESTATE COMPANIES IN SPAIN

The aim of this study is the determination, from an empirical perspective, of the accounting and financial features which could condition financial profitability of real estate companies, to identify the performances that guarantee its permanency in the current marketplace, characterized by the world economic crisis, specially in Spain, whose housing sector represents an important contributor to the economic growth. Although at a theoretical level the DuPont Model establishes the relationships between a group of accounting ratios and financial profitability. This paper uses a sample of 5,484 Spanish real estate companies to quantify these relationships and to extract the most relevant ones and to obtain the patterns of the most profitable companies. We use ROE to measure profitability and we analyze various independent variables about solvency, liquidity, activity, turnover, financial equilibrium and investment structure. The main contribution is of methodological nature, as we have applied statistics tools that do not require initial hypotheses on the distribution of the variables, by using a data mining technique of classification and regression tree based on rule induction algorithms known as CHAID. The study provides quantitatively success profiles by means of a set of rules describing the patterns of the most profitable companies.CHAID; financial profitability; classification trees; accounting ratios; Spain.

Trisections of a 3-rotationally symmetric planar convex body minimizing the maximum relative diameter

In this work we study the fencing problem consisting of finnding a trisection of a 3-rotationally symmetric planar convex body which minimizes the maximum relative diameter. We prove that an optimal solution is given by the so-called standard trisection. We also determine the optimal set giving the minimum value for this functional and study the corresponding universal lower bound.Comment: Preliminary version, 20 pages, 15 figure

El carlismo aragonés en armas. La revuelta de 1855

In 1855, taking advantage of the reforms of the progressive government, the carlists organized a revolt in which they expected to attract the most conservative sectors of the Moderantism. But this didn´t happen and the popular support was much lesser than expected. Besides that, in Aragon the plot was discovered by the authorities, which accelerated its beginning and made its failure easier. In the end, after 19 days of marches and pursuits, the Aragonese carlists were totally defeated. The failure of the revolt showed that the Carlism had lost the support of much of the Aragonese population, in part because the improvement of the economy, but also because the bad memory they had of the last war and the preference of the conservative for moderate Liberalism.En 1855, aprovechando la llegada al poder de los progresistas, los carlistas organizaron una revuelta, a la que esperaban atraerse a los sectores más conservadores del moderantismo. Pero esto no sólo no se produjo, sino que el respaldo popular de la rebelión fue mucho menor del esperado. Además, en Aragón la conjura fue descubierta por las autoridades, lo que precipitó su inicio y facilitó su rápido final. Al final, tras 19 días de correrías y de persecuciones, los carlistas aragoneses fueron totalmente derrotados. El fracaso de la revuelta mostró que el carlismo había perdido el apoyo de gran parte de la población aragonesa, en parte por la mejora de la economía, pero también por el mal recuerdo que tenían de la última guerra y por la preferencia de los sectores conservadores por el liberalismo moderado

Ideas lingüísticas de Antonio de Torquemada

En este ensayo sobre "Las ideas lingüísticas de Antonio Torquemada" intento mostrar la gran preocupación sobre este asunto en su "Manual de Escribientes". No debemos olvidar que este trabajo no es realmente un tratado gramatical, sino que tiene otros objetivos esenciales. Por lo tanto, es imposible buscar un análisis coherente y sistemático de los problemas gramaticales. Sin embargo, es una labor fundamental para la historiografía lingüística de la Edad de Oro. Pueden encontrarse algunos detalles útiles para comprobar la evolución y el cambio lingüístico, esencialmente fonológicos, que se están produciendo en ese momento. Torquemada es un testimonio excepcional ya que, en general, sigue los principios tradicionales de la ortografía, pero permite analizar los cambios y vacilaciones de ese momento en casi todos los casos. Del mismo modo, podemos encontrar interesantes problemas sociolingüisticos, tales como las diferencias según el discurso de la corte y el de las zonas rurales o en el mantenimiento de arcaísmos y la introducción de neologismos.In this essay on «Antonio Torquemada's Linguistic Ideas» I try to evince the great concern about this subject existing in his Manual de Escribientes. We must not forget that this work is not realy a grammatical treatise, but that it has other essential aims. Therefore, it is impossible to Iook for a coherent and systematic analysis of the grammar problems. It is, however, a fundamental work for the Iinguistical historiography of the Golden Ages. There can be found sorne details useful to verify the evolution and the linguistical shift, essentially phonological, which is taking place nowadays. Torquemada is an exceptional witness because he generally follows the traditional spelling principies, but he examines the changes and the hesitations of that moment in nearly ali the cases. Likewise, we can find interesting sociolinguistical problems, such as the differences be- tween court speech and rural speech or the maintenance of archaisms and the entering of neologisms

La adecuación entre grafía y fonema en los ortógrafos del Siglo de Oro

Una de las notas que aparecen como dominantes en la historia de la Ortografía española del Siglo de Oro, es la opinión sobre la acomodación entre escritura y pronunciación en una lengua. Gran parte de los planteamientos ortográficos de la época tienen su punto de partida, precisamente, en este problema, por lo que es de interesante analizar las diversas corrientes sobre el tema.One of the dominant notes in the spelling Spanish history in the Golden Century is the opinion about accommodation between writing and pronunciation in the language. Most of the spelling approaches of this time have their starting point, precisely in this problem, so it is interesting to analyze the various currents on the subject