Maximum principle, mean value operators and quasi boundedness in non-euclidean settings

This work deals with some classes of linear second order partial differential operators with non-negative characteristic form and underlying non- Euclidean structures. These structures are determined by families of locally Lipschitz-continuous vector fields in RN, generating metric spaces of Carnot- Carath´eodory type. The Carnot-Carath´eodory metric related to a family {Xj}j=1,...,m is the control distance obtained by minimizing the time needed to go from two points along piecewise trajectories of vector fields. We are mainly interested in the causes in which a Sobolev-type inequality holds with respect to the X-gradient, and/or the X-control distance is Doubling with respect to the Lebesgue measure in RN. This study is divided into three parts (each corresponding to a chapter), and the subject of each one is a class of operators that includes the class of the subsequent one. In the first chapter, after recalling “X-ellipticity” and related concepts introduced by Kogoj and Lanconelli in [KL00], we show a Maximum Principle for linear second order differential operators for which we only assume a Sobolev-type inequality together with a lower terms summability. Adding some crucial hypotheses on measure and on vector fields (Doubling property and Poincar´e inequality), we will be able to obtain some Liouville-type results. This chapter is based on the paper [GL03] by Guti´errez and Lanconelli. In the second chapter we treat some ultraparabolic equations on Lie groups. In this case RN is the support of a Lie group, and moreover we require that vector fields satisfy left invariance. After recalling some results of Cinti [Cin07] about this class of operators and associated potential theory, we prove a scalar convexity for mean-value operators of L-subharmonic functions, where L is our differential operator. In the third chapter we prove a necessary and sufficient condition of regularity, for boundary points, for Dirichlet problem on an open subset of RN related to sub-Laplacian. On a Carnot group we give the essential background for this type of operator, and introduce the notion of “quasi-boundedness”. Then we show the strict relationship between this notion, the fundamental solution of the given operator, and the regularity of the boundary points.

Welfare provision in Sweden and the dominant position of the Sap

There have been almost fifty years since Harry Eckstein' s classic monograph, A Theory of Stable Democracy (Princeton, 1961), where he sketched out the basic tenets of the “congruence theory”, which was to become one of the most important and innovative contributions to understanding democratic rule. His next work, Division and Cohesion in Democracy, (Princeton University Press: 1966) is designed to serve as a plausibility probe for this 'theory' (ftn.) and is a case study of a Northern democratic system, Norway. What is more, this line of his work best exemplifies the contribution Eckstein brought to the methodology of comparative politics through his seminal article, “ “Case Study and Theory in Political Science” ” (in Greenstein and Polsby, eds., Handbook of Political Science, 1975), on the importance of the case study as an approach to empirical theory. This article demonstrates the special utility of “crucial case studies” in testing theory, thereby undermining the accepted wisdom in comparative research that the larger the number of cases the better. Although not along the same lines, but shifting the case study unit of research, I intend to take up here the challenge and build upon an equally unique political system, the Swedish one. Bearing in mind the peculiarities of the Swedish political system, my unit of analysis is going to be further restricted to the Swedish Social Democratic Party, the Svenska Arbetare Partiet. However, my research stays within the methodological framework of the case study theory inasmuch as it focuses on a single political system and party. The Swedish SAP endurance in government office and its electoral success throughout half a century (ftn. As of the 1991 election, there were about 56 years - more than half century - of interrupted social democratic "reign" in Sweden.) are undeniably a performance no other Social Democrat party has yet achieved in democratic conditions. Therefore, it is legitimate to inquire about the exceptionality of this unique political power combination. Which were the different components of this dominance power position, which made possible for SAP's governmental office stamina? I will argue here that it was the end-product of a combination of multifarious factors such as a key position in the party system, strong party leadership and organization, a carefully designed strategy regarding class politics and welfare policy. My research is divided into three main parts, the historical incursion, the 'welfare' part and the 'environment' part. The first part is a historical account of the main political events and issues, which are relevant for my case study. Chapter 2 is devoted to the historical events unfolding in the 1920-1960 period: the Saltsjoebaden Agreement, the series of workers' strikes in the 1920s and SAP's inception. It exposes SAP's ascent to power in the mid 1930s and the party's ensuing strategies for winning and keeping political office, that is its economic program and key economic goals. The following chapter - chapter 3 - explores the next period, i.e. the period from 1960s to 1990s and covers the party's troubled political times, its peak and the beginnings of the decline. The 1960s are relevant for SAP's planning of a long term economic strategy - the Rehn Meidner model, a new way of macroeconomic steering, based on the Keynesian model, but adapted to the new economic realities of welfare capitalist societies. The second and third parts of this study develop several hypotheses related to SAP's 'dominant position' (endurance in politics and in office) and test them afterwards. Mainly, the twin issues of economics and environment are raised and their political relevance for the party analyzed. On one hand, globalization and its spillover effects over the Swedish welfare system are important causal factors in explaining the transformative social-economic challenges the party had to put up with. On the other hand, Europeanization and environmental change influenced to a great deal SAP's foreign policy choices and its domestic electoral strategies. The implications of globalization on the Swedish welfare system will make the subject of two chapters - chapters four and five, respectively, whereupon the Europeanization consequences will be treated at length in the third part of this work - chapters six and seven, respectively. Apparently, at first sight, the link between foreign policy and electoral strategy is difficult to prove and uncanny, in the least. However, in the SAP's case there is a bulk of literature and public opinion statistical data able to show that governmental domestic policy and party politics are in a tight dependence to foreign policy decisions and sovereignty issues. Again, these country characteristics and peculiar causal relationships are outlined in the first chapters and explained in the second and third parts. The sixth chapter explores the presupposed relationship between Europeanization and environmental policy, on one hand, and SAP's environmental policy formulation and simultaneous agenda-setting at the international level, on the other hand. This chapter describes Swedish leadership in environmental policy formulation on two simultaneous fronts and across two different time spans. The last chapter, chapter eight - while trying to develop a conclusion, explores the alternative theories plausible in explaining the outlined hypotheses and points out the reasons why these theories do not fit as valid alternative explanation to my systemic corporatism thesis as the main causal factor determining SAP's 'dominant position'. Among the alternative theories, I would consider Traedgaardh L. and Bo Rothstein's historical exceptionalism thesis and the public opinion thesis, which alone are not able to explain the half century social democratic endurance in government in the Swedish case.

La traduction des textes de théatre. Analyse comparée des réalités contemporaines française et italienne

The aim of the present study is to address contemporary drama translation by comparing two different scenarios, namely France and Italy. For each country, the following areas are described: publications of translated drama texts, their promotion and dissemination, the legal framework concerning copyright in publication and performance contracts. Moreover, the analysis highlights that the translation process of drama texts is part of a working cycle networking different professional figures, such as dramatic authors, directors, actors and publishers. Within this cycle, the translator is in a middle and central position at the same time, a sort of border zone between different contexts, i.e. the source language and culture and the target language and culture. As regards translation-related issues, on the basis of theoretical approaches that can be applied to drama translation, a number of translators’ opinions, statements, positions and practices are compared, thus highlighting an idea of drama translation wavering between translation and adaptation. Drama translators seem to follow these two orientations simultaneously, in compliance with translation ethics and the functional needs of target texts. Such ambivalence is due to the desire and difficulty of translating the specific nature of drama texts, i.e. translating textual elements that are linked, eventually, to stage performance. Indeed, the notion of text or form fidelity is replaced by the notion of fidelity to the theatrical value of a text, in terms of fidelity to its theatrical nature and rhythmical tension. The analysis reveals that drama translators work together with theatre operators, and that in many cases translators are authors, directors or actors themselves. These drama skills enable translators to apply relevant strategies when translating elements that generate rhythm, thus choosing from deleting, reproducing or recreating.

What are the components that contribute to variability in echocardiographic measurements in aortic stenosis?

INTRODUCTION Echocardiography is the standard clinical approach for quantification of the severity of aortic stenosis (AS). A comprehensive examination of its overall reproducibility and the simultaneous estimation of its variance components by multiple operators, readers, probe applications, and beats have not been undertaken. METHOD AND RESULTS Twenty-seven subjects with AS were scanned over 7 months in the echo-department by a median of 3 different operators. From each patient and each operator multiple runs of beats from multiple probe positions were stored for later analysis by multiple readers. The coefficient of variation was 13.3%, 15.9%, 17.6%, and 20.2% for the aortic peak velocity (Vmax), and velocity time integral (VTI), and left ventricular outflow tract (LVOT) Vmax and VTI respectively. The largest individual contributors to the overall variability were the beat-to-beat variability (9.0%, 9.3%, 9.5%, 9.4% respectively) and that of inability of an individual operator to precisely apply the probe to the same position twice (8.3%, 9.4%, 12.9%, 10.7% respectively). The tracing (inter-reader) and reader (inter-reader), and operator (inter-operator) contribution were less important. CONCLUSIONS Reproducibility of measurements in AS is poorer than often reported in the literature. The source of this variability does not appear, as traditionally believed, to result from a lack of training or operator and reader specific factors. Rather the unavoidable beat-to-beat biological variability, and the inherent impossibility of applying the ultrasound probe in exactly the same position each time are the largest contributors. Consequently, guidelines suggesting greater standardisation of procedures and further training for sonographers are unlikely to result in an improvement in precision. Clinicians themselves should be wary of relying on even three-beat averages as their expected coefficient of variance is 10.3% for the peak velocity at the aortic valve.