Hypercomplex Algebras and their application to the mathematical formulation of Quantum Theory

Quantum theory (QT), namely in terms of Schr\"odinger's 1926 wave functions in general requires complex numbers to be formulated. However, it soon turned out to even require some hypercomplex algebra. Incorporating Special Relativity leads to an equation (Dirac 1928) requiring pairwise anti-commuting coefficients, usually $4\times 4$ matrices. A unitary ring of square matrices is an associative hypercomplex algebra by definition. Since only the algebraic properties and relations of the elements matter, we replace the matrices by biquaternions. In this paper, we first consider the basics of non-relativistic and relativistic QT. Then we introduce general hypercomplex algebras and also show how a relativistic quantum equation like Dirac's one can be formulated using biquaternions. Subsequently, some algebraic preconditions for operations within hypercomplex algebras and their subalgebras will be examined. For our purpose equations akin to Schr\"odinger's should be able to be set up and solved. Functions of complementary variables should be Fourier transforms of each other. This should hold within a purely non-real subspace which must hence be a subalgebra. Furthermore, it is an ideal denoted by $\mathcal{J}$. It must be isomorphic to $\mathbb{C}$, hence containing an internal identity element. The bicomplex numbers will turn out to fulfil these preconditions, and therefore, the formalism of QT can be developed within its subalgebras. We also show that bicomplex numbers encourage the definition of several different kinds of conjugates. One of these treats the elements of $\mathcal{J}$ like the usual conjugate treats complex numbers. This defines a quantity what we call a modulus which, in contrast to the complex absolute square, remains non-real (but may be called `pseudo-real'). However, we do not conduct an explicit physical interpretation here but we leave this to future examinations.Comment: 21 pages (without titlepage), 14 without titlepage and appendi

For the win! Male politicians are more likely to represent women’s interests if their re-election is at risk

Daniel Höhmann shows that male MPs do play a distinct role in women’s representation and that many of them are willing to represent women’s interest in parliament. However, one of the key drivers of this behaviour seems to be a rational calculation of how they can enhance their re-election prospects, rather than an intrinsic motivation to stand up for gender equality: male MPs are significantly more likely to speak on behalf of women if their re-election security is low and if they are therefore forced to cater to additional (female) voters to get re-elected

Algebraic fidelity decay for local perturbations

From a reflection measurement in a rectangular microwave billiard with randomly distributed scatterers the scattering and the ordinary fidelity was studied. The position of one of the scatterers is the perturbation parameter. Such perturbations can be considered as {\em local} since wave functions are influenced only locally, in contrast to, e. g., the situation where the fidelity decay is caused by the shift of one billiard wall. Using the random-plane-wave conjecture, an analytic expression for the fidelity decay due to the shift of one scatterer has been obtained, yielding an algebraic $1/t$ decay for long times. A perfect agreement between experiment and theory has been found, including a predicted scaling behavior concerning the dependence of the fidelity decay on the shift distance. The only free parameter has been determined independently from the variance of the level velocities.Comment: 4 pages, 5 figure

Risorse linguistiche per la comunicazione nel settore del turismo

Come affrontare la complessità linguistica e comunicativa che caratterizza il settore turistico? E, contestualmente, come affrontare le difficoltà dello studio linguistico? A tal riguardo è utile richiamare l'attenzione sul fatto che la possibilità di accedere ad una grande quantità di dati e di elaborarli con strumenti informatici ha cambiato radicalmente il panorama della ricerca, dell'apprendimento e della produzione di servizi anche in ambito linguistico. Nell'ambito di una pubblicazione dedicata principalmente alla geografia, si desidera mettere in luce l'importanza delle lingue straniere in contesti turistici da un ulteriore punto di vista. Da un'indagine è risultato che ca. il 19% degli intervistati ha indicato il rammarico di non riuscire a comunicare con gli italiani, neanche in inglese o in francese, lingue normalmente studiate a scuola. Va rilevato, infine, che le difficoltà di comunicazione possono trasformarsi in un vero e proprio fattore economico nel momento in cui il turista preferisce scegliere una meta di viaggio che offra la possibilità di comunicare in modo soddisfacente sia con gli operatori turistici che con la gente del posto e esclude a priori i posti di villeggiatura che presentino problemi di carattere linguistico

Pomeranian in the Brazilian State of Espírito Santo : results and perspectives from a sociolinguistic study

The present article deals with aspects of language maintenance and measurement for language revitalization of Pomeranian in the Brazilian state of Espírito Santo, based on the sociolinguistic study by Höhmann (2011). Following the introduction, in which an overview of the research situation and the socio-demographic data is provided, the text presents quantitative data on language preference and intergenerational language transmission of the studied language community. In addition, the use of the minority language in education and the resulting research desiderata are stated. The Pomeranian language revitalization project PROEPO and aspects of the latest standardization activities of the minority language are presented. Finally, perspectives for language preservation are discussed.Der vorliegende Artikel behandelt Aspekte des Spracherhalts und Maßnahmen für die Sprachrevitalisierung des Pommerischen im brasilianischen Bundesstaat Espírito Santo. Die vorgestellten Daten basieren auf der soziolinguistischen Studie von Höhmann (2011). Nach der Einleitung, in der ein Überblick über die Forschungslage und die soziodemographischen Daten der untersuchten Sprachgemeinschaft gegeben wird, werden quantitative Daten zur Sprachpräferenz und zur intergenerationalen Sprachtransmission aus der Studie vorgestellt. Desweiteren werden die Verwendung der Minderheitensprache im Schulunterricht und daraus resultierende Forschungsdesiderate dargelegt. Es wird auf das pommerische Sprachrevitalisierungsprojekt PROEPO und auf Aspekte der Standardisierungsmaßnahmen der Minderheitensprache eingegangen. Abschließend werden Perspektiven für den Spracherhalt erörtert.O presente artigo abrange aspectos da manutenção linguística e as medidas de preservação linguística do pomerano no estado brasileiro do Espírito Santo, com base no estudo sóciolinguístico de Höhmann (2011). Após a introdução, na qual é dada uma visão geral da situação de pesquisa e dos dados sóciodemográficos da respectiva comunidade linguística, são apresentados dados quantitativos sobre a preferência linguística e de transmissão intergeracional da língua. Além de comprovar o uso de línguas minoritárias nas escolas e os desideratos de pesquisa resultante. O projeto de revitalização PROEPO e aspectos da recente padronização da língua minoritária são apresentados. Finalmente, as perspectivas para a preservação da língua são discutidas

Collegial management of schools. By way of example the Laborschule Bielefeld shows the consequence for daily work

Die Autorin schildert zunächst die kollegiale Schulleitung als juristische Form, als besondere Form des Selbstverständnisses von "Leitung" und als Form der Arbeitsorganisation und charakterisiert dann die organisatorischen Rahmenbedingungen der kollegialen Schulleitung an der Laborschule Bielefeld, wobei sie betont, dass dazu auch ein gut organisiertes Lehrerkollegium gehört. Am Beispiel der Unterrichtsverteilung wird abschließend ein konkreter "Einblick in das Leitungsverständnis" an der Laborschule gegeben. (DIPF/Bi.)Even in times of officially nominated headmasters, who are perceived as managers of their schools and thus conform to the established view, collegial management of schools remains an interesting subject. Collegial management is not only a formal matter, but is also based on a different idea about the function of leadership in schools. This can be shown by considering how the school hours are allotted in the Laborschule in Bielefeld. (DIPF/Orig.

Russia and Germany in Europe: recent trends of political and economic relations

'Die Beziehungen zwischen Deutschland und Rußland bilden ein wichtiges und unverzichtbares Element gesamteuropäischer Zusammenarbeit. Sowohl Bundeskanzler Kohl als auch Präsident Jelzin charakterisierten das jeweils andere Land wiederholt als 'wichtigsten Partner in Europa'. Dies trifft in unterschiedlicher Weise sicher zu. So ist Deutschland für Rußland der weltweit stärkste Handelspartner, während umgekehrt Rußland für Deutschland (und den Westen insgesamt) unverzichtbar ist, wenn es um die Neuordnung in Ostmitteleuropa geht. Dennoch gibt es in den deutsch-russischen Beziehungen auch Probleme, wozu kriegsbedingte Altlasten ebenso gehören wie unterschiedliche Vorstellungen über eine neue europäische Sicherheitsordnung und unzureichende Rahmenbedingungen in Rußland für ausländische Wirtschaftsaktivitäten. Der vorliegende Bericht befaßt sich mit Chancen und Problemen der Beziehungen Deutschland - Rußland in ihrer bi- und multilateralen Dimension. Dabei stützt er sich auf Originalquellen, wissenschaftliche Literatur und Beiträge aus der Publizistik beider Länder.' (Autorenreferat)'Relations between Germany and Russia constitute an important and indispensable element of European co-operation. Both Chancellor Kohl and President Yeltsin have on a number of occasions described each other's country as their 'most important partner in Europe'. This is certainly true, albeit in different ways for each country. Whereas Germany is Russia's most important world-wide trading partner, Russia is essential for Germany (and indeed for the West as a whole) in the establishment of a new order in East Central Europe. Nevertheless, the relationship is also a troubled one that is burdened both by unresolved issues outstanding from World War II as well as by differing ideas about the new European security arrangements and by the unsatisfactory conditions for foreign economic activity in Russia. The present report examines the problems of and prospects for German-Russian relations in both their bi- and multilateral dimensions. It draws on original sources, scholarly literature and press materials from both countries.' (author's abstract

Die struktur-funktionalistische Theorie sozialer Probleme: eine Korrektur liebgewordener Fehldeutungen des Beitrages von Robert K. Merton

'Die deutsche theoretische Diskussion zur Soziologie sozialer Probleme hat sich in einer Reihe von Beiträgen mit der Frage befaßt, ob es so etwas wie eine 'Theorie sozialer Probleme' geben kann. Dabei hat sich der Streit insbesondere an der Frage entzündet, ob die Beiträge Mertons oder die der interaktionistischen Tradition (Blumer, Kitsuse, Spector etc.) die geeignetere Grundlage für ein solches Bemühen darstellen. Der vorliegende Aufsatz soll zeigen, daß zum einen der Versuch zur Entwicklung einer 'Theorie sozialer Probleme' aus epistemologischen und inhaltlichen Gründen scheitern muß, zum anderen die spezifischen Absichten und Vorschläge Mertons in dieser Debatte meist mißverstanden oder unvollständig rezipiert werden. Insbesondere wird postuliert, daß sich die Position Mertons dann sinnvoll nutzen läßt, wenn man 'soziale Probleme als Modell' konzipiert.' (Autorenreferat)'A lot of German contributions to the sociology of social problems has debated the question whether something like a 'theory of social problems' is possible. One of the central issues in this discussions is the topic whether the contributions of Robert K. Merton or the ideas of the interactionist paradigm (Blumer, Kitsuse, Spector etc.) offer the stronger foundations for such a theory. The objetive of this essay is to show that all efforts towards such a 'theory of social problems' have to fail because of epistemological and substiantial reasons. Furthermore the paper tries to demonstrate that many German authors do not really comprehend and realize Merton's very specific ideas and propositions. We suggest that Merton's position will be very productive if we conceptualize his approach as 'social problems as a model.' (author's abstract)

Die Komparativ- und Superlativformen besser/am besten/das Beste als Varianten in modalen Vergleichskonstruktionen: Eine Pilotstudie zu Sprach- und Ausdrucksvarianten im Deutschen und Italienischen

It is well known that linguistic variants play a key role in the acquisition of language skills in the first, second or foreign language as well as in writing and translation processes and in general in communicative interactions. Thus, a major research goal is the systematic investigation of intra- and interlinguistic variation. Due to its complexity, its qualitative-quantitative analysis continues to be a challenging issue, but it seems to become more and more feasible thanks to both the possibility of compiling very large corpora and the availability of high-performing corpus-linguistic tools. The paper discusses a corpus-linguistic pilot study concerning the use of besser, am besten and das Beste as pragmatic markers in a cross-linguistic perspective. In particular, the analysis focusses on selected superlative and comparative constructions on the left periphery used for expressing advice. The data basis consists mainly of German and Italian comparable very large web corpora and, to a lesser extent, of bilingual sentence pairs drawn from parallel corpora. As will be shown, even restricting the analysis to a very small segment of microvariation, in both languages the modal constructions appear to be characterized by the combination of numerous overlapping and interplaying variants and by different tendencies in language use