Abelian varieties with finite abelian group action

An automorphism of an abelian variety induces a decomposition of the variety up to isogeny. There are two such results, namely the isotypical decomposition and Roan’s decomposition theorem. We show that they are essentially the same. Moreover, we generalize in a sense this result to abelian varieties with action of an arbitrary finite abelian group. An early version of this article was inadvertently published before all the revisions had been completed and then retracted [https://doi.org/10.1007/s00013-018-1244-3]. This article is the final peer reviewed version.

     

Correction to: Two-Dimensional Culture Systems to Enable Mechanics-Based Assays for Stem Cell-Derived Cardiomyocytes

Experimental Mechanics - The authors would like to correct the sentence “The mass ratio……” in the subsection on Engineered Substrate System in MATERIALS AND METHODS, to read:     

Microstructure morphology transitions at mesoscopic epitaxial surfaces

Spiral surface growth is well understood in the limit where motion of the spiral ridge is controlled by the local supersaturation of adatoms in its surrounding. In liquid epitaxial growth, however, spirals can form governed by both, transport of heat as well as solute. We propose for the first time a two-scale model of epitaxial growth which takes into account all of these transport processes. This new model assumes a separation of length scales for the transport of heat compared to that of the solutal field. It allows for the first time numerical simulations of extended surface regions by at the same time taking into account microstructure evolution and microstructure interaction. We apply this model successfully to extend the scaling relation for the step spacing given by the BCF theory [Phil. Trans. R. Soc. London, Ser. A 243, 299 (1951)] to microstructure evolution governed by heat and solute diffusion. Further applications to understand the mechanisms and consequences of spiral interaction at epitaxial surfaces, in particular the resulting morphology transitions, are discussed.     

Monte Carlo Simulations of Observation Time-Dependent Self-Diffusion in Porous Media Models

Observation time-dependent self-diffusion coefficients can be used to obtain microstructural information of porous media. This paper presents two different kinds of Monte Carlo simulations of the self diffusion process of fluids like water in porous systems, a lattice-free method and a lattice-based method. The results for simple porous media model geometries agree well with each other and with published analytical as well as semi-analytical equations. The use of these equations, which are important for the interpretation of Pulsed Field Gradient-Nuclear Magnetic Resonance (PFG-NMR) time-dependent diffusion data with respect to properties of porous media, is discussed.     

Experiences with the Application of QSAR in the Routine of the Notification Procedure

Abstract

On behalf of the Umweltbundesamt the Fraunhofer Gesellschaft has developed a software system (SAR-system) comprising more than 90 estimation models for endpoints relevant in environmental risk assessment. These estimation models are based on the approach of quantitative structure-activity relationships (QSAR). All models were checked for their validity and application range. In the last months the Umweltbundesamt started to test the applicability of some models concerning the endpoints fish acute toxicity, daphnia acute toxicity and ready (i.e., ultimate) biodegradability in the daily routine of the notification procedure. For testing these models the corresponding confidential data given in the dossiers of substances notified 1993 in Germany, were used. We were able to make calculations for 36% of the notified substances. For the remaining 64% of the chemicals it was impossible to accomplish SAR estimations due to several reasons, e.g., ionic structure of the compounds. Different results for the applicability of the mentioned endpoints are obtained. The predictions of the fish and Daphnia toxicity are in sufficient agreement with the experimental results, in case of the fish toxicity we receive 58% agreement, for the Daphnia toxicity 56% The corresponding values which were obtained in the US EPA/E.C. Joint Project on the evaluation of (quantitative) structure activity relationships were 82.3% and 70.9% About 300 different models were used for the calculations of these endpoints within the framework of the EPA/EC project. The SAR-system presented here contains 8 models for estimating the fish toxicity and 6 models for the Daphnia toxicity. For the prediction of the biodegradability the results obtained with the SAR-system are rather poor and have to be improved. Meanwhile the SAR-system is commercially available and can be ordered at the Fraunhofer Institute for Environmental Chemistry and Ecotoxicology, Schmallenberg (Germany).     

On the theory of the Buckingham effect

We apply general arguments (based on spatial transformation properties, intrinsic symmetry and dimensional analysis) to the theory of the Buckingham effect (electric-field–gradient-induced birefringence in a gas). These yield, in a simple manner, the temperature-dependent and temperature-independent terms in the birefringence (each to within a numerical factor), and also the expression, derived by Buckingham and Longuet-Higgins, for the effective quadrupole centre of a molecule. We show in addition how the calculation of the two numerical factors can be simplified in our approach.