Introducing a Romanian Frequency List and the Romanian Vocabulary Levels Test

Vocabulary is considered essential to language learning, thus English word lists and tests based on frequency information have become the centre of attention for researchers, teachers and learners alike. As a result, it is argued hereby that frequency based word lists and tests should be adapted and regarded as key elements for teaching and learning Romanian as an additional language as well. Since there are currently no reliable frequency lists and lexical tests in Romanian, this paper aims to bridge this gap by introducing the first Romanian Word List and the Romanian Vocabulary Levels Test. The list contains the 10,000 most frequent Romanian words and is based on the Romanian Balanced Annotated Corpus (ROMBAC, Ion, Irimia, Ștefănescu, Tufiș 2012). The primary objective of the paper is to elaborate on the compilation criteria, the challenges involved and the benefits of such a list in the case of teaching, learning and curriculum design for Romanian as an additional language. The secondary objective is to present a practical application of the word list by introducing an exemplary Romanian lexical test, the Romanian Vocabulary Levels Test and examine its reliability and validity

Minimal Reversible Nonsymmetric Rings

Marks showed that $\mathbb{F}_2Q_8$, the $\mathbb{F}_2$ group algebra over the quaternion group, is a reversible nonsymmetric ring, then questioned whether or not this ring is minimal with respect to cardinality. In this work, it is shown that the cardinality of a minimal reversible nonsymmetric ring is indeed 256. Furthermore, it is shown that although $\mathbb{F}_2Q_8$ is a duo ring, there are also examples of minimal reversible nonsymmetric rings which are nonduo

The Rokhlin dimension of topological Z^m-actions

We study the topological variant of Rokhlin dimension for topological dynamical systems (X,{\alpha},Z^m) in the case where X is assumed to have finite covering dimension. Finite Rokhlin dimension in this sense is a property that implies finite Rokhlin dimension of the induced action on C*-algebraic level, as was discussed in a recent paper by Ilan Hirshberg, Wilhelm Winter and Joachim Zacharias. In particular, it implies under these conditions that the transformation group C*-algebra has finite nuclear dimension. Generalizing a result of Yonatan Gutman, we show that free Z^m-actions on finite dimensional spaces satisfy a strengthened version of the so-called marker property, which yields finite Rokhlin dimension for said actions.Comment: 27 pages; with minor corrections in some proof

A short note on the continuous Rokhlin property and the universal coefficient theorem

Let $G$ be a metrizable compact group, $A$ a separable C*-algebra and $\alpha$ a strongly continuous action of $G$ on $A$. Provided that $\alpha$ satisfies the continuous Rokhlin property, we show that the property of satisfying the UCT in E-theory passes from $A$ to the crossed product C*-algebra $A\rtimes_\alpha G$ and the fixed point algebra $A^\alpha$. This extends a result by Gardella in the case that $G$ is the circle and $A$ is nuclear. For circle actions on separable, unital C*-algebras with the continuous Rokhlin property, we establish a connection between the $E$-theory equivalence class of the coefficient algebra $A$ and the fixed point algebra $A^\alpha$.Comment: 7 page

Equivariant Kirchberg-Phillips-type absorption for amenable group actions

We show an equivariant Kirchberg-Phillips-type absorption theorem for pointwise outer actions of discrete amenable groups on Kirchberg algebras with respect to natural model actions on the Cuntz algebras $\mathcal{O}_\infty$ and $\mathcal{O}_2$. This generalizes results known for finite groups and poly-$\mathbb{Z}$ groups. The model actions are shown to be determined, up to strong cocycle conjugacy, by natural abstract properties, which are verified for some examples of actions arising from tensorial shifts. We also show the following homotopy rigidity result, which may be understood as a precursor to a general Kirchberg-Phillips-type classification theory: If two outer actions of an amenable group on a unital Kirchberg algebra are equivariantly homotopy equivalent, then they are conjugate. This marks the first C*-dynamical classification result up to cocycle conjugacy that is applicable to actions of all amenable groups.Comment: v3 42 pages; this version has been accepted for publication in Communications in Mathematical Physic