On the Complex Dimensions of Nonlattice Fractal Strings in Connection with Dirichlet Polynomials

In this paper we give a new characterization of the closure of the set of the real parts of the zeros of a particular class of Dirichlet polynomials that is associated with the set of dimensions of fractality of certain fractal strings. We show, for some representative cases of nonlattice Dirichlet polynomials, that the real parts of their zeros are dense in their associated critical intervals, confirming the conjecture and the numerical experiments made by M. Lapidus and M. van Frankenhuysen in several papers.

Teaching as a fractal: from experience to model

The aim of this work is to improve students’ learning by designing a teaching model that seeks to increase student motivation to acquire new knowledge. To design the model, the methodology is based on the study of the students’ opinion on several aspects we think importantly affect the quality of teaching (such as the overcrowded classrooms, time intended for the subject or type of classroom where classes are taught), and on our experience when performing several experimental activities in the classroom (for instance, peer reviews and oral presentations). Besides the feedback from the students, it is essential to rely on the experience and reflections of lecturers who have been teaching the subject several years. This way we could detect several key aspects that, in our opinion, must be considered when designing a teaching proposal: motivation, assessment, progressiveness and autonomy. As a result we have obtained a teaching model based on instructional design as well as on the principles of fractal geometry, in the sense that different levels of abstraction for the various training activities are presented and the activities are self-similar, that is, they are decomposed again and again. At each level, an activity decomposes into a lower level tasks and their corresponding evaluation. With this model the immediate feedback and the student motivation are encouraged. We are convinced that a greater motivation will suppose an increase in the student’s working time and in their performance. Although the study has been done on a subject, the results are fully generalizable to other subjects.

Estudio del comportamiento fractal espacial de la superficie del terreno, considerando factores del relieve climáticos, estructurales y litológicos

El presente estudio parte de la hipótesis de que hay una relación numérica entre la forma de la superficie geomórfica y los factores de modelado del relieve. La metodología utilizada es el análisis multifractal de las curvas de nivel de Modelos Digitales del Terreno de toda España. Para ello hemos utilizado software libre en todos los pasos. Los resultados obtenidos hacen pensar que esta correlación existe, en el factor climático (gradiente de precipitación máxima anual) y estructural (peligrosidad sísmica). El factor litológico no ha dado ajuste algo, probablemente debido a la falta de datos precisos.

The Proactive International Dimension and the Breakdown of Authoritarian Regimes

There is international consensus among scholars that democratic transitions are multicausal processes in which both internal and international variables are involved (Pridham 1991, 1995; Whitehead 1996; Schmitter 1996; Linz and Stepan 1996; Carothers 1999; Morlino and Magen 2008; Grilli di Cortona 2009). This chapter is limited, on the one hand, to the dependent variable consisting solely of the crisis/breakdown/transformation of non-democratic regimes in the Third Wave of democratization, and, on the other hand, to an independent variable identified solely with the international dimension of democratic transition. This factor, which can be termed the Proactive International Dimension (PID), specifically concerns that combination of actions or processes, produced by one or more international actors, that, intentionally or not, cause or contribute to the crisis/breakdown/transformation of a non-democratic regime.

The Europeanisation of Criminal Law and the Criminal Law Dimension of European Integration. Research Papers in Law, 3/2005

From the Introduction. In the academic year 1991-1992, Utrecht University, on my initiative, started to offer courses in European criminal law. This initiative came at a symbolic moment, just prior to the entry into force of the EU Treaty of Maastricht1 and the outlining of European policy in the areas of Justice and Home Affairs (JHA). The Director of the Legal Department, Paul DEMARET, was aware of the significance of this development and I have been given the opportunity to teach this subject at the College of Europe since 1995. Since then, JHA has evolved into one of the main areas of EU legislation. Now we are again on the threshold of an important historical feat. In June 2003, the European Convention reached agreement concerning a draft Treaty establishing a Constitution for Europe.2 The use of the term “Constitution” for the future EU Treaty is not simply cosmetic. The realisation has dawned that EU integration must be embedded in a treaty document which also regulates the rights and duties of citizens, not just with respect to European citizenship, but also with respect to, for example, Justice. Where JHA is concerned, this result acknowledges that the harmonisation of criminal law and criminal procedure and transnational cooperation cannot preclude the harmonisation of principles of due law and fair trial. Despite the substantial Europeanisation of criminal law, many criminal lawyers are defending the achievements and typicalities of their national criminal law like never before. EU initiatives are assessed from the perspective of the national agenda and national achievements. We are still too far removed from a European criminal law policy that is both European and enjoys national support. The core issue is therefore not how to keep our criminal (procedural) law national and free from European influences, but rather how to ensure democratic decision making, the quality of the constitutional state and the guarantees of criminal law in a national administrative model which has to operate increasingly interactively within a European and international context. In this contribution, the contours of the Europeanisation of criminal law are outlined and analysed. First, attention will be paid to the EC and, second, to the JHA. Following this, an evaluation and a look ahead at the current IGC are indicated.