Non-linear Group Actions with Polynomial Invariant Rings and a Structure Theorem for Modular Galois Extensions

Let $G$ be a finite $p$-group and $k$ a field of characteristic $p>0$. We show that $G$ has a \emph{non-linear} faithful action on a polynomial ring $U$ of dimension $n=\mathrm{log}_p(|G|)$ such that the invariant ring $U^G$ is also polynomial. This contrasts with the case of \emph{linear and graded} group actions with polynomial rings of invariants, where the classical theorem of Chevalley-Shephard-Todd and Serre requires $G$ to be generated by pseudo-reflections. Our result is part of a general theory of "trace surjective $G$-algebras", which, in the case of $p$-groups, coincide with the Galois ring-extensions in the sense of \cite{chr}. We consider the \emph{dehomogenized symmetric algebra} $D_k$, a polynomial ring with non-linear $G$-action, containing $U$ as a retract and we show that $D_k^G$ is a polynomial ring. Thus $U$ turns out to be \emph{universal} in the sense that every trace surjective $G$-algebra can be constructed from $U$ by "forming quotients and extending invariants". As a consequence we obtain a general structure theorem for Galois-extensions with given $p$-group as Galois group and any prescribed commutative $k$-algebra $R$ as invariant ring. This is a generalization of the Artin-Schreier-Witt theory of modular Galois field extensions of degree $p^s$.Comment: 20 page

Hydrodynamic limit fluctuations of super-Brownian motion with a stable catalyst

We consider the behaviour of a continuous super-Brownian motion catalysed by a random medium with infinite overall density under the hydrodynamic scaling of mass, time, and space. We show that, in supercritical dimensions, the scaled process converges to a macroscopic heat flow, and the appropriately rescaled random fluctuations around this macroscopic flow are asymptotically bounded, in the sense of log-Laplace transforms, by generalised stable Ornstein-Uhlenbeck processes. The most interesting new effect we observe is the occurrence of an index-jump from a 'Gaussian' situation to stable fluctuations of index 1+gamma, where gamma is an index associated to the medium.Comment: 40 page

The Invariant Fields of the Sylow groups of Classical Groups in the natural characteristic

Let X be any finite classical group defined over a finite field of characteristic p>0. In this paper we determine the fields of rational invariants for the Sylow p-subgroups of X, acting on the natural module. In particular we prove that these fields are generated by orbit products of variables and certain invariant polynomials which are images under Steenrod operations, applied to the respective invariant linear forms defining X.Comment: 33 page

Aerobic biodegradation of chiral phenoxyalkanoic acid derivatives during incubations with activated sludge

The aerobic biodegradation of racemic mixtures of five chiral phenoxyalkanoic acids was studied according to a biodegradation test that was complemented with enantiomer-specific analysis. Both enantiomers of (RS)-2-phenoxypropanoic acid, (RS)-2-(3-chlorophenoxy)propanoic acid, and (RS)-2-(4-chlorophenoxy)propanoic acid, were completely degraded within 25 days when aerobically incubated with activated sludge. During incubations of (RS)-2-phenoxypropanoic acid, the (R) enantiomer was degraded before the (S) enantiomer, whereas during incubations of (RS)-2-(3-chlorophenoxy)propanoic acid the (S) enantiomer was preferentially degraded. The (R) enantiomer of (RS)-2-(2-chlorophenoxy)propanoic acid was removed after 24 days while only 30% of the (S) enantiomer was degraded within 47 days of incubation. (RS)-2-(2,4,5-Trichlorophenoxy)propanoic acid was the most persistent of all the racemic mixtures tested. After 47 days, the concentration of the (S) enantiomer was nearly unchanged, and the concentration of (R)-2-(2,4,5-trichlorophenoxy)propanoic acid had decreased only by about 40%. The differences observed in the length of the lag phases and in the degradation rates of individual enantiomers can lead to accumulations of the more recalcitrant enantiomer in aquatic or terrestrial ecosystem

Estimating entropies from molecular dynamics simulations

The methods to compute the excess entropy and the entropy of solvation using liquid water as a test system were studied. The accuracy and convergence behavior of five methods based on thermodynamic integration and perturbation techniques was evaluated. Through the thermodynamic integration accurate entropy differences were obtained in which many copies of a solute were desolvated. Only two methods yield useful results, the calculation of solute-solvent entropy through thermodynamic integration and the calculation of solvation entropy through the temperature derivative of the corresponding free-energy difference, when one solute molecule is involved

Butterfly-like spectra and collective modes of antidot superlattices in magnetic fields

We calculate the energy band structure for electrons in an external periodic potential combined with a perpendicular magnetic field. Electron-electron interactions are included within a Hartree approximation. The calculated energy spectra display a considerable degree of self-similarity, just as the ``Hofstadter butterfly.'' However, screening affects the butterfly, most importantly the bandwidths oscillate with magnetic field in a characteristic way. We also investigate the dynamic response of the electron system in the far-infrared (FIR) regime. Some of the peaks in the FIR absorption spectra can be interpreted mainly in semiclassical terms, while others originate from inter(sub)band transitions.Comment: 4 pages with 2 embeded eps figures. Uses revtex, multicol and graphicx styles. Accepted for publication in PRB Brief Report

Major flaws in conflict prevention policies towards Africa : the conceptual deficits of international actors’ approaches and how to overcome them

Current thinking on African conflicts suffers from misinterpretations oversimplification, lack of focus, lack of conceptual clarity, state-centrism and lack of vision). The paper analyses a variety of the dominant explanations of major international actors and donors, showing how these frequently do not distinguish with sufficient clarity between the ‘root causes’ of a conflict, its aggravating factors and its triggers. Specifically, a correct assessment of conflict prolonging (or sustaining) factors is of vital importance in Africa’s lingering confrontations. Broader approaches (e.g. “structural stability”) offer a better analytical framework than familiar one-dimensional explanations. Moreover, for explaining and dealing with violent conflicts a shift of attention from the nation-state towards the local and sub-regional level is needed.Aktuelle Analysen afrikanischer Gewaltkonflikte sind häufig voller Fehlinterpretationen (Mangel an Differenzierung, Genauigkeit und konzeptioneller Klarheit, Staatszentriertheit, fehlende mittelfristige Zielvorstellungen). Breitere Ansätze (z. B. das Modell der Strukturellen Stabilität) könnten die Grundlage für bessere Analyseraster und Politiken sein als eindimensionale Erklärungen. häufig differenzieren Erklärungsansätze nicht mit ausreichender Klarheit zwischen Ursachen, verschärfenden und auslösenden Faktoren. Insbesondere die richtige Einordnung konfliktverlängernder Faktoren ist in den jahrzehntelangen gewaltsamen Auseinandersetzungen in Afrika von zentraler Bedeutung. Das Diskussionspapier stellt die große Variationsbreite dominanter Erklärungsmuster der wichtigsten internationalen Geber und Akteure gegenüber und fordert einen Perspektivenwechsel zum Einbezug der lokalen und der subregionalen Ebene für die Erklärung und Bearbeitung gewaltsamer Konflikte

The invariant fields of the Sylow groups of classical groups in the natural characteristic

Let X be any finite classical group defined over a finite field of characteristic p > 0. In this article, we determine the fields of rational invariants for the Sylow p-subgroups of X, acting on the natural module. In particular, we prove that these fields are generated by orbit products of variables and certain invariant polynomials which are images under Steenrod operations, applied to the respective invariant linear forms defining X.info:eu-repo/semantics/publishedVersio

The invariant rings of the Sylow groups of GU(3,q2), GU(4,q2), Sp(4,q) and O+(4,q) in the natural characteristic

Let G be a Sylow p-subgroup of the unitary groups GU(3, q2), GU(4, q2), the symplectic group Sp(4, q) and, for q odd, the orthogonal group O +(4, q). In this paper we construct a presenta tion for the invariant ring of G acting on the natural module. In particular we prove that these rings are generated by orbit products of variables and certain invariant polynomials which are images under Steenrod operations, applied to the respective invariant form defining the corresponding classical group. We also show that these generators form a SAGBI basis and the invariant ring for G is a complete intersection.info:eu-repo/semantics/publishedVersio

Acceptance of Speech-to-Text Technology: Exploring Language Proficiency and Psychological Safety in Global Virtual Teams

Natural Language Processing, such as speech-to-text technology, is increasingly implemented in collaboration software that is used by global virtual teams (GVT). GVT collaboration has become ubiquitous and has additionally accelerated during the COVID-19 pandemic. The main issues of global virtual teams are technology difficulties, language and time zone differences, and lower levels of psychological safety. Advances in collaboration technology aim at improving collaboration for GVT. But we know little about the acceptance of these technologies. Therefore, the objective of this study is to explore how Millennial and Gen Z members of GVT accept speech-to-text technology; namely, automated captions in virtual conferences and automated meetings transcripts. Particularly, we are comparing antecedents of acceptance across levels of language proficiency and psychological safety. We surveyed 530 users of speech-to-text technology in GVT both before and after they used the technology. The pre-survey was administered before the COVID-19 pandemic hit; when participants completed the post-survey all were under some degree of lockdown. Results suggest that use of the technology reduces anxiety and effort, but decreases performance expectation and hedonic motivation. Non-native speakers rate the technology more positively. The impact of psychological safety is limited to self-efficacy and anxiety