Linearizable 3-webs and the Gronwall conjecture

In the article "On the linearizability of 3-webs" (Nonlinear analysis 47, (2001) pp.2643-2654), published in 2001, we studied the linearizability problem for 3-webs on a 2-dimensional manifold. Four years after the publication of our article, V.V.Goldberg and V.V.Lychagin in the paper "On linearization of planar three-webs and Blaschke's conjecture" (C.R.Acad. Sci. Paris, Ser. I. vol. 341. num 3 (2005)) obtained similar results by a different method and criticized our article by qualifying the proofs incomplete. However, they obtained false result on the linearizability of a certain web. We present here the complete version of our work with computations and explicit formulas, because we deem that their opinion concerning our work is unjustified.Comment: 14 page

The inverse problem for Lagrangian systems with certain non-conservative forces

We discuss two generalizations of the inverse problem of the calculus of variations, one in which a given mechanical system can be brought into the form of Lagrangian equations with non-conservative forces of a generalized Rayleigh dissipation type, the other leading to Lagrangian equations with so-called gyroscopic forces. Our approach focusses primarily on obtaining coordinate-free conditions for the existence of a suitable non-singular multiplier matrix, which will lead to an equivalent representation of a given system of second-order equations as one of these Lagrangian systems with non-conservative forces.Comment: 28 page

Silicon-carbide transistors for class-D audio amplifiers

Der Klang von Musik hat die Menschen seit jeher fasziniert. Im Vergleich zu Aristoteles´ Zeit, ist ein Konzertbesuch heute nicht mehr nur eine willkommene Abwechslung, sondern ein Klangerlebnis, welches durch die Unterstützung von Licht-, Ton- und Videotechnik zu einem emotionalen Moment wird. Folglich müssen die in der Tontechnik eingesetzten Audioverstärker höchsten Anforderungen bezüglich Audioqualität und Wirkungsgrad genügen. Zum Erreichen der benötigten Gesamtleistung kann eine Beschallungsanlage aus über 100 einzelnen Audioverstärkern bestehen. Mit steigender Geräteanzahl nimmt der Aufwand der Verkabelung sowie die physische Anstrengung zum Auf- und Abbauen der Beschallungsanlage zu. Obwohl die Komplexität einer Beschallungsanlage durch schaltende Verstärker der Klasse D reduziert würde, werden meist Verstärker bevorzugt, deren Leistungstransistoren linear arbeiten (Klasse H). Die linearen Verstärker werden u.a. wegen der geringen harmonischen Verzerrungen geschätzt, da dies zu einer höherwertigen Audioqualität führt. In einem Klasse-D-Verstärker hingegen entstehen vermehrt harmonische Verzerrungen, welche u.a. durch die Transistoren in der Schaltstufe verursacht werden. Zur Zeit werden diese Verzerrungen durch komplexe Rückkopplungs-Topologien mit einem erheblichen Aufwand in der Entwicklung lediglich reduziert. Ziel dieser Dissertation ist es, das Potential von Transistoren aus Siliziumkarbid (SiC) für die Klasse-D-Technik zu ergründen, um bei der Ursache der harmonischen Verzerrungen anzusetzen. Das schnelle Schaltverhalten der SiC-Transistoren könnte genutzt werden, um die Entstehung der harmonischen Verzerrungen in der Leistungsstufe vom Grunde her zu reduzieren und so die Audioqualität in dieser Hinsicht zu verbessern. Darüber hinaus ergeben sich weitere viel versprechende Vorteile, beispielsweise im Zusammenhang mit Ausgangsleistung und Wirkungsgrad. In dieser Arbeit werden vier Endstufen eines Klasse-D-Verstärkers entwickelt und charakterisiert. Die fundierte Analyse der Audioqualität deckt interessante Aspekte bezüglich der etablierten Theorie eines D-Verstärkers auf. Insbesondere die Erkenntnisse im Kontext von Leistung und Wirkungsgrad sind auch auf andere schaltende Anwendungen in der Leistungselektronik übertragbar. Darüber hinaus wird der Zusammenhang zwischen den Halbleitereigenschaften des Transistors und der Entstehung von harmonischen Verzerrungen erstmalig ausführlich ergründet. Die Analyse-Ergebnisse sind jeweils im Kapitel ’Einfluss der Transistor-Charakteristika auf..’ zusammengestellt. Der Einsatz von Siliziumkarbid-Transistoren würde in vielen Aspekten der Klasse-D-Technik neue Perspektiven eröffnen. Die vorliegende Dissertation widmet sich der Untersuchung von Audioqualität, Leistung und Wirkungsgrad.The sound of music has always fascinated mankind. In contrast Aristotels’ time, visiting a concert is more than mere entertainment in the normal course of life – nowadays, it is a splendid performance, turned into an emotional moment by light and audio engineering. To meet the arising demands, the audio engineering must utilise a so-called public address system (PA system) consisting of an array of single amplifiers, to drive loudspeakers. Each amplifier requires high performance in terms of energy efficiency and audio quality. In order to achieve the desired power level, a PA system may consist of over 100 single amplifiers. The intricacy of wiring as well as the physical effort to build up a PA system increase rapidly with the number of amplifiers. Although the complexity of a PA system could be reduced using switch-mode class D amplifiers, in the majority of cases linear class H amplifiers are used. These linear amplifiers are less efficient but provide excellent audio quality due to low harmonic distortion. A switch-mode class D amplifier works efficiently but generates harmonic distortion to a greater extent. Currently, this harmonic distortion is generally reduced by complex feedback topologies requiring major time and effort during the designing process of the amplifier. This thesis investigates the benefit of silicon carbide (SiC) transistors for the power stage of a class-D amplifier, since harmonic distortion is also caused by the power stage devices. The fast-switching SiC-transistors may partially resolve the root of the poorer sound quality by minimising the harmonic distortion of the power stage. Further advantages also arise; e.g. concerning output power and efficiency. In this work, four class D power stages are developed and characterised. Detailed analysis of the audio quality reveals interesting aspects relating to existing class D amplifier theory. The outcome, particularly with regard to output power and efficiency, may be transferred to other switch-mode applications in power electronics. Beyond that, the relationship between the transistor’s semiconductor-characteristics and the source of harmonic distortion is investigated in detail for the first time. The results are outlined in each chapter beginning with ’Einfluss der Transistor-Charakteristika auf..’. The use of silicon carbide power devices would open new prospects in many aspects of class D amplifier performance. This work examines these aspects with respect to audio quality, output power and efficiency

Navigating the European space: physical and virtual forms of cross-border mobility among EU citizens

Drawing on earlier works in the EUCROSS series, this working paper proposes a comprehensive picture of physical and virtual mobility practices. Physical mobilities are characterised with regards to the time factor, thus distinguishing between high and low permanence practices (or ‘migrationlike’ and ‘tourism-like’ mobilities). Virtual mobilities may have personal or impersonal character (taking a ‘facebook-like’ or an ‘eBay-like’ form). A short discussion of each mobility type is additionally described with existing sources (mainly from Eurostat). This range of cross-border practices is then mapped within the European countries in which the EUCROSS survey was carried out (Germany, the UK, Denmark, Italy, Spain and Romania). Quite against conventional wisdom which suggests that EU citizens make modest use of their free movement rights and are rather immobile, we found that one in six Europeans of the EUCROSS sample has spent at least three months in another EU country in their lifetime. Furthermore, 51 per cent have visited another EU member state, even if for a short vacation, in the last two years. Europeans cross borders in a nonphysical sense as well (almost three quarters of our sample), when they connect online or on the phone with significant others who migrated or with friends they met during their physical trips. Finally, Europeans increasingly engage in cross-border transactions (almost one third of EUCROSS sample), shopping online but also transferring money abroad. All these practices are socially structured, their likelihood depending significantly on education, socioeconomic status, gender and age in differing degrees, as multivariate analyses detail. National contexts matter as well. Danes are most mobile when it comes to low permanence physical mobility and impersonal virtual moves. In turn, Britons and Romanians – possibly with different purposes – have definitely higher odds of having migrated, even in the wider sense of migration as ‘long-permanence mobility’ that we used. This reverberates on being more strongly networked with other persons abroad than any other nationality examined

Persone, contesti e istituzioni. Una riflessione sulla sociologia della cittadinanza

Un dialogo con Lorenzo Grifone Baglioni sulla sociologia della cittadinanza. La sfida che le pressioni migratorie pongono alla sociologia della cittadinanza in Europa: comprendere il rapporto fra cittadini e democrazia in Europa triangolando tre questioni weberiane: (a) la questione dell’agire di comunità, a livello terri- toriale, con (b) i problemi di selezione e di cooptazione dell’élite (a livello locale, nazionale, europeo), con (c) le s de di political economy di oggi (sostanzialmente legate alla creazione di occupazione di qualità e integrazione progressiva degli immigrati)