Generalized Eigenvectors for Resonances in the Friedrichs Model and Their Associated Gamov Vectors

A Gelfand triplet for the Hamiltonian H of the Friedrichs model on R with finite-dimensional multiplicity space K, is constructed such that exactly the resonances (poles of the inverse of the Livsic-matrix) are (generalized) eigenvalues of H. The corresponding eigen-antilinearforms are calculated explicitly. Using the wave matrices for the wave (Moller) operators the corresponding eigen-antilinearforms on the Schwartz space S for the unperturbed Hamiltonian are also calculated. It turns out that they are of pure Dirac type and can be characterized by their corresponding Gamov vector, which is uniquely determined by restriction of S to the intersection of S with the Hardy space of the upper half plane. Simultaneously this restriction yields a truncation of the generalized evolution to the well-known decay semigroup of the Toeplitz type for the positive half line on the Hardy space. That is: exactly those pre-Gamov vectors (eigenvectors of the decay semigroup) have an extension to a generalized eigenvector of H if the eigenvalue is a resonance and if the multiplicity parameter k is from that subspace of K which is uniquely determined by its corresponding Dirac type antilinearform.Comment: 16 page

Duality of compact groups and Hilbert C*-systems for C*-algebras with a nontrivial center

In the present paper we prove a duality theory for compact groups in the case when the C*-algebra A, the fixed point algebra of the corresponding Hilbert C*-system (F,G), has a nontrivial center Z and the relative commutant satisfies the minimality condition A.'\cap F = Z as well as a technical condition called regularity. The abstract characterization of the mentioned Hilbert C*-system is expressed by means of an inclusion of C*-categories T_\c < T, where T_\c{i}s a suitable DR-category and T a full subcategory of the category of endomorphisms of A. Both categories have the same objects and the arrows of T can be generated from the arrows of T_\c{a}nd the center Z. A crucial new element that appears in the present analysis is an abelian group C(G), which we call the chain group of G, and that can be constructed from certain equivalence relation defined on G^, the dual object of G. The chain group, which is isomorphic to the character group of the center of G, determines the action of irreducible endomorphisms of A when restricted to Z. Moreover, C(G) encodes the possibility of defining a symmetry $\epsilon$ also for the larger category T of the previous inclusion.Comment: Final version appeared in Int. J. Math. 15 (2004) 759-812. Minor changes w.r.t. to the previous versio

Rate constants for the reaction of Cl atoms with O3 at temperatures from 298 to 184 K

Using the standard, low pressure, discharge-flow technique, with resonance fluorescence in the vacuum ultraviolet to observe Cl atoms, rate constants have been determined for the reaction of Cl atoms with O$_3$ at temperatures down to 184 K. The measured rate constants for 298-184 K fit the Arrhenius expression: k(T) = (3.6 $\pm$ 0.7) $\times$ 10$^{-11}$ exp(( - 310 $\pm$ 50 K) / T) cm$^3$ molecule$^{-1}$ s$^{-1}$. The results extend the data on this key atmospheric reaction to slightly lower temperatures. The data are in fairly good agreement with those currently in the literature but suggest that the rate constant approximately 15% lower than that given by currently recommended rate expressions at the lowest temperatures found in the stratosphere

L’érable négundo (Acer negundo) au nord du Rhin supérieur : contribution à l’évaluation d’un néophyte sous l’aspect de la protection de la nature

Der Eschen-Ahorn (Acer negundo) hat in Mitteleuropa seinen Verbreitungsschwerpunkt an der Donau unterstrom von Wien sowie am Nördlichen Oberrhein, am Mittel- und Niederrhein. A. negundo zeichnet sich durch eine hohe Überflutungstoleranz aus, seine Samen weisen gegenüber den Diasporen von Weiden und Pappeln eine wesentlich längere Keimfähigkeit auf. Dadurch ist die Art in der Lage, offene Standorte in dynamischen Systemen über einen langen Zeitraum zu besiedeln und einheimische Gehölze zu verdrängen. Eine Bekämpfung der Art in Auenschutzgebieten wird empfohlen.In Central Europe, Ashleaf Maple (Acer negundo) occurs mainly in the Danube valley to the south of Vienna, in the northern Upper Rhine valley, and in the Central and Lower Rhine valley. It tolerates long-term flooding, and the germination capacity of its seeds is notably better than that of Salix or Populus. As a consequence, the Ashleaf Maple can successfully colonise open sites in the dynamic systems of river valleys, displacing native species. It is recommended that this species be eradicated in floodplain conservation areas.En Europe centrale l'espèce est particulièrement fréquente en aval du Danube après Vienne ainsi que le long du Rhin supérieur, moyen et inférieur. A. negundo se caractérise par une haute tolérance aux incidences des crues et ses graines ont une capacité de germination plus perdurables que les graines des saules et des peupliers. Grâce à ces propriétés, l’espèce est capable de peupler sur une longue période des sites ouverts dans des systèmes dynamiques et de repousser les bocages autochtones. Il est recommandé de lutter contre cette espèce dans les zones protégées des plaines alluviales

Übersetzen als kulturelles Handeln: zur politischen Motivation der Übersetzungsstrategien in Thomas Braschs Shakespeareübersetzung "Wie es euch gefällt"

This article analyses the different translation strategies in Thomas Brasch's German translation of Shakespeare's "As You Like It" with respect to their impulse towards adaptation. The article takes as its starting point the assumption that the cultural performance of a translation can be experienced independently of the criterion of similarity. This is the case whenever one manages to elucidate how a translation cites and at the same time dislocates its source and target (con-)texts. In this double distance between source context and the inherited context of its own target language translation is manifested as an act of cultural intervention. Brasch’s analysed translation reveals its emotional, linguistic and cultural richness as the reader recognizes how the various translation strategies are meaningfully related to his political convictions.Der folgende Artikel untersucht die sich in Thomas Braschs Übersetzung von Shakespeares "Wie es euch gefällt" manifestierenden Übersetzungsstrategien im Hinblick auf den ihnen jeweils zugrundeliegenden Bearbeitungsimpuls. Der Artikel geht dabei von der Annahme aus, dass die kulturelle Leistung einer Übersetzung als unabhängig von Ähnlichkeitskriterien erfahrbar werden kann; nämlich dann, wenn es gelingt, zu verdeutlichen, wie sie ihre beiden an Ursprungs- und Zielsprache gebundenen kulturellen (Kon-)Texte als sprachlich-ästhetisch gefasste Welten zitiert und immer zugleich variiert. In dieser doppelten Distanz zu Ursprungstext und tradiertem Kontext der eigenen Zielsprache manifestiert sich Übersetzung als kulturelle Handlung. Braschs Übersetzung enthüllt ihren emotionalen, sprachlichen, und kulturellen Reichtum, sobald der Leser erkennt, wie die politische Überzeugung des Autors seinen verschiedenen Übersetzungsstrategien zugrundeliegt

Interkulturelles Lernen und lehrbuchgestütze, individualisierende Unterrichtsformen im schulischen DaF-Unterricht

The following essay discusses the possibilities of integrating linguistic and semantic aspects of teaching German as a Foreign Language in secondary schools in Santa Catarina using an interculturally orientated approach. Drawing on the insight that 'otherness' is a relational notion, so that the image we create of 'the other' depends essentially on the understanding of one's own culture and the histories, values and social reality inscribed in it, the article proposes a didactic approach that uses the teaching of morpho-syntactic structures to instigate intercultural reflections. Moreover, to be able to fully exploit the potential of divergent notions of 'self' and 'otherness' in the language classroom, teaching activities are proposed that allow learners to respond individually to the material presented. The article proposes and discusses various didactic activities that allow the teacher to use the course book in order to create and explore interculturally significant material.Este ensaio discute as possibilidades de integrar os aspetos linguísticos e semânticos da abordagem didática intercultural para o ensino de alemão como língua estrangeira. Baseando-se na concepção de 'alteridade' como uma noção relacional, isto é, a imagem do 'outro' depende fundamentalmente da compreensão da própria cultura e das historias, valores e realidades sociais inscritas nela, o artigo propõe uma didática que use o ensino de formas morfosintáticas para instigar reflexões interculturais. Além disso, propõe-se uma didática voltada às reações individualizadas por parte dos alunos para poder aproveitar plenamente as diferenças das noções do 'próprio' e do 'outro'. Neste contexto, sugere e discute-se atividades didáticas que permitam fazer uso do livro didático para criar e explorar material interculturalmente significante