Sierpinski curve Julia sets for quadratic rational maps

We investigate under which dynamical conditions the Julia set of a quadratic rational map is a Sierpiński curve.

Sierpinski curve Julia sets for quadratic rational maps

We investigate under which dynamical conditions the Julia set of a quadratic rational map is a Sierpiński curve.

A proposal for a new specification for a conditionally heteroskedastic variance model: the Quadratic Moving-Average Conditional Heteroskedasticity and an application to the D. Mark-U.S. dollar Exchange Rate

Ever since the appearance of the ARCH model [Engle(1982a)], an impressive array of variance specifications belonging to the same class of models has emerged [i.e. Bollerslev's (1986) GARCH; Nelson's (1990) EGARCH]. This recent domain has achieved very successful developments. Nevertheless, several empirical studies seem to show that the performance of such models is not always appropriate [Boulier(1992)]. In this paper we propose a new specification: the Quadratic Moving Average Conditional heteroskedasticity model. Its statistical properties, such as the kurtosis and the symmetry, as well as two estimators (Method of Moments and Maximum Likelihood) are studied. Two statistical tests are presented, the first one tests for homoskedasticity and the second one, discriminates between ARCH and QMACH specification. A Monte Carlo study is presented in order to illustrate some of the theoretical results. An empirical study is undertaken for the DM-US exchange rate.

Economic growth and atmospheric pollution in Spain: discussing the environmental Kuznets curve by hypothesis

The environmental Kuznets curve (EKC) hypothesis posits an inverted U relationship between environmental pressure and per capita income. Recent research has examined this hypothesis for different pollutants in different countries. Despite certain empirical evidence shows that some environmental pressures have diminished in developed countries, the hypothesis could not be generalized to the global relationship between economy and environment at all. In this article we contribute to this debate analyzing the trends of annual emission flux of six atmospheric pollutants in Spain. The study presents evidence that there is not any correlation between higher income level and smaller emissions, except for SO2 whose evolution might be compatible with the EKC hypothesis. The authors argue that the relationship between income level and diverse types of emissions depends on many factors. Thus it cannot be thought that economic growth, by itself, will solve environmental problems.

Long-run Inflation-Unemployment Dynamics: The Spanish Phillips Curve and Economic Policy

This paper takes a new look at the long-run dynamics of inflation and unemployment in response to permanent changes in the growth rate of the money supply. We examine the Phillips curve from the perspective of what we call "frictional growth", i.e. the interaction between money growth and nominal frictions. After presenting theoretical models of this phenomenon, we construct an empirical model of the Spanish economy and, in this context, we evaluate the long-run inflation-unemployment trade for Spain and examine how recent policy changes have afected it.

The third order Melnikov function of a quadratic center under quadratic perturbation

We study quadratic perturbations of the integrable system (1+x)dH; where H =(x²+y²)=2: We prove that the first three Melnikov functions associated to the perturbed system give rise at most to three limit cycles.

Quadratic perturbations of a quadratic reversible Lotka-Volterra System

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Algebraic properties of isochronous centers of polynomial quadratic-like Hamiltonian systems

Projecte de recerca elaborat a partir d’una estada a la School of Mathematics and Statistics de la University of Plymouth, United Kingdom, entre abril juliol del 2007.Aquesta investigació és encara oberta i la memòria que presento constitueix un informe de la recerca que estem duent a terme actualment. En aquesta nota estudiem els centres isòcrons dels sistemes Hamiltonians analítics, parant especial atenció en el cas polinomial. Ens centrem en els anomenats quadratic-like Hamiltonian systems. Diverses propietats dels centres isòcrons d'aquest tipus de sistemes van ser donades a [A. Cima, F. Mañosas and J. Villadelprat, Isochronicity for several classes of Hamiltonian systems, J. Di®erential Equations 157 (1999) 373{413]. Aquell article estava centrat principalment en el cas en que A; B i C fossin funcions analítiques. El nostre objectiu amb l'estudi que estem duent a terme és investigar el cas en el que aquestes funcions són polinomis. En aquesta nota formulem una conjectura concreta sobre les propietats algebraiques que venen forçades per la isocronia del centre i provem alguns resultats parcials.

A doubling measure on R(d) can charge a rectifiable curve

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A critical analysis of dimensions and curve fitting practice in economics

When dealing with sustainability we are concerned with the biophysical as well as the monetary aspects of economic and ecological interactions. This multidimensional approach requires that special attention is given to dimensional issues in relation to curve fitting practice in economics. Unfortunately, many empirical and theoretical studies in economics, as well as in ecological economics, apply dimensional numbers in exponential or logarithmic functions. We show that it is an analytical error to put a dimensional unit x into exponential functions ( a x ) and logarithmic functions ( x a log ). Secondly, we investigate the conditions of data sets under which a particular logarithmic specification is superior to the usual regression specification. This analysis shows that logarithmic specification superiority in terms of least square norm is heavily dependent on the available data set. The last section deals with economists’ “curve fitting fetishism”. We propose that a distinction be made between curve fitting over past observations and the development of a theoretical or empirical law capable of maintaining its fitting power for any future observations. Finally we conclude this paper with several epistemological issues in relation to dimensions and curve fitting practice in economics

Inflation dynamics and the New Keynesian Phillips curve in EU-4

The paper seeks to shed light on inflation dynamics of four new EU member states: the Czech Republic, Hungary, Poland and Slovakia. To this end, the New Keynesian Phillips curve augmented for open economies is estimated and additional statistical tests applied. We find the following. (1) The claim of New Keynesians that the real marginal cost is the main inflation-forcing variable is fragile. (2) Inflation seems to be driven by external factors. (3) Although inflation holds a forward-looking component, the backward-looking component is substantial. An intuitive explanation for higher inflation persistence may be rather adaptive than rational price setting of local firms.

A functional equation related to the product in a quadratic number field

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Reconsideration of dimensions and curve fitting practice in economics ellaborating on Georgescu-Roegen’s economic methodology

This paper is to examine the proper use of dimensions and curve fitting practices elaborating on Georgescu-Roegen’s economic methodology in relation to the three main concerns of his epistemological orientation. Section 2 introduces two critical issues in relation to dimensions and curve fitting practices in economics in view of Georgescu-Roegen’s economic methodology. Section 3 deals with the logarithmic function (ln z) and shows that z must be a dimensionless pure number, otherwise it is nonsensical. Several unfortunate examples of this analytical error are presented including macroeconomic data analysis conducted by a representative figure in this field. Section 4 deals with the standard Cobb-Douglas function. It is shown that the operational meaning cannot be obtained for capital or labor within the Cobb-Douglas function. Section 4 also deals with economists "curve fitting fetishism". Section 5 concludes thispaper with several epistemological issues in relation to dimensions and curve fitting practices in economics.

Predicting random level and seasonality of hotel prices. A structural equation growth curve approach

This article examines the effect on price of different characteristics of holiday hotels in the sun-and-beach segment, under the hedonic function perspective. Monthly prices of the majority of hotels in the Spanish continental Mediterranean coast are gathered from May to October 1999 from the tour operator catalogues. Hedonic functions are specified as random-effect models and parametrized as structural equation models with two latent variables, a random peak season price and a random width of seasonal fluctuations. Characteristics of the hotel and the region where they are located are used as predictors of both latent variables. Besides hotel category, region, distance to the beach, availability of parking place and room equipment have an effect on peak price and also on seasonality. 3- star hotels have the highest seasonality and hotels located in the southern regions the lowest, which could be explained by a warmer climate in autumn

Modelling the cardiovascular system for automatic interpretation of the blood pressure curve

A four compartment model of the cardiovascular system is developed. To allow for easy interpretation and to minimise the number of parameters, an effort was made to keep the model as simple as possible. A sensitivity analysis is first carried out to determine which are the most important model parameters to characterise the blood pressure signal. A four stage process is then described which accurately determines all parameter values. This process is applied to data from three patients and good agreement is shown in all cases.