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PSI-Potsdam
(2018)
In Brandenburg kommt der Universität Potsdam eine besondere Rolle zu: Sie ist die einzige, an der zukünftige Lehrerinnen und Lehrer die erste Phase ihres Werdegangs – das Lehramtsstudium – absolvieren können. Vor diesem Hintergrund wurde bereits kurz nach der Gründung im Jahr 1991 das „Potsdamer Modell der Lehrerbildung“ entwickelt. Dieses Modell strebt fortlaufend eine enge Verzahnung von Theorie und Praxis über das gesamte Studium hinweg an und bindet hierfür die schulpraktischen Studienanteile in besonderer Weise ein. Eine erneute Stärkung erfuhr die Lehrerbildung im Dezember 2014 mit der Gründung des Zentrums für Lehrerbildung und Bildungsforschung (ZeLB). Aus der koordinierenden Arbeit des Zentrums entstand das fakultätsübergreifende Projekt „Professionalisierung – Schulpraktische Studien – Inklusion“ (PSI-Potsdam) das im Rahmen der Qualitätsoffensive Lehrerbildung des Bundesministeriums für Bildung und Forschung erfolgreich gefördert wurde (2015–2018) und dessen Verlängerung (2019–2023) bewilligt ist.
Der vorliegende Band vermittelt in den drei großen Kapiteln „Erhebungsinstrumente“, „Seminarkonzepte“ und „Vernetzungen“ einen Überblick über einige der praxisnahen Forschungszugänge, hochschuldidaktischen Ansätze und Strategien zur Vernetzung innerhalb der Lehrerbildung, die im Rahmen von PSI-Potsdam entwickelt und umgesetzt wurden. Die Beiträge wurden mit dem Ziel verfasst, Kolleginnen und Kollegen an Universitäten und Hochschulen, Akteur_innen des Vorbereitungsdiensts sowie der Fort- und Weiterbildung von Lehrkräften möglichst konkrete Einblicke zu gewähren.
Unter der Herausgeberschaft von Prof. Dr. Andreas Borowski (Fachdidaktik Physik), Prof. Dr. Antje Ehlert (Inklusionspädagogik mit dem Förderschwerpunkt Lernen) und Prof. Dr. Helmut Prechtl (Fachdidaktik Biologie) vereinen sich Autor_innen mit breit gestreuter fachdidaktischer und bildungswissenschaftlicher Expertise.
This paper deals with the long-term behavior of positive operator semigroups on spaces of bounded functions and of signed measures, which have applications to parabolic equations with unbounded coefficients and to stochas-tic analysis. The main results are a Tauberian type theorem characterizing the convergence to equilibrium of strongly Feller semigroups and a generalization of a classical convergence theorem of Doob. None of these results requires any kind of time regularity of the semigroup.
We give a new and very short proof of a theorem of Greiner asserting that a positive and contractive -semigroup on an -space is strongly convergent in case it has a strictly positive fixed point and contains an integral operator. Our proof is a streamlined version of a much more general approach to the asymptotic theory of positive semigroups developed recently by the authors. Under the assumptions of Greiner's theorem, this approach becomes particularly elegant and simple. We also give an outlook on several generalisations of this result.
We complete the picture how the asymptotic behavior of a dynamical system is reflected by properties of the associated Perron-Frobenius operator. Our main result states that strong convergence of the powers of the Perron-Frobenius operator is equivalent to setwise convergence of the underlying dynamic in the measure algebra. This situation is furthermore characterized by uniform mixing-like properties of the system.
We present new conditions for semigroups of positive operators to converge strongly as time tends to infinity. Our proofs are based on a novel approach combining the well-known splitting theorem by Jacobs, de Leeuw, and Glicksberg with a purely algebraic result about positive group representations. Thus, we obtain convergence theorems not only for one-parameter semigroups but also for a much larger class of semigroup representations. Our results allow for a unified treatment of various theorems from the literature that, under technical assumptions, a bounded positive C-0-semigroup containing or dominating a kernel operator converges strongly as t ->infinity. We gain new insights into the structure theoretical background of those theorems and generalize them in several respects; especially we drop any kind of continuity or regularity assumption with respect to the time parameter.
For a finite measure space X, we characterize strongly continuous Markov lattice semigroups on Lp(X) by showing that their generator A acts as a derivation on the dense subspace D(A)L(X). We then use this to characterize Koopman semigroups on Lp(X) if X is a standard probability space. In addition, we show that every measurable and measure-preserving flow on a standard probability space is isomorphic to a continuous flow on a compact Borel probability space.
If (T-t) is a semigroup of Markov operators on an L-1-space that admits a nontrivial lower bound, then a well-known theorem of Lasota and Yorke asserts that the semigroup is strongly convergent as t -> infinity. In this article we generalize and improve this result in several respects. First, we give a new and very simple proof for the fact that the same conclusion also holds if the semigroup is merely assumed to be bounded instead of Markov. As a main result, we then prove a version of this theorem for semigroups which only admit certain individual lower bounds. Moreover, we generalize a theorem of Ding on semigroups of Frobenius-Perron operators. We also demonstrate how our results can be adapted to the setting of general Banach lattices and we give some counterexamples to show optimality of our results. Our methods combine some rather concrete estimates and approximation arguments with abstract functional analytical tools. One of these tools is a theorem which relates the convergence of a time-continuous operator semigroup to the convergence of embedded discrete semigroups.
We provide explicit examples of positive and power-bounded operators on c(0) and l(infinity) which are mean ergodic but not weakly almost periodic. As a consequence we prove that a countably order complete Banach lattice on which every positive and power-bounded mean ergodic operator is weakly almost periodic is necessarily a KB-space. This answers several open questions from the literature. Finally, we prove that if T is a positive mean ergodic operator with zero fixed space on an arbitrary Banach lattice, then so is every power of T .