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.

     

ToF-SIMS measurements with topographic information in combined images

In 2D and 3D time-of-flight secondary ion mass spectrometric (ToF-SIMS) analysis, accentuated structures on the sample surface induce distorted element distributions in the measurement. The origin of this effect is the 45° incidence angle of the analysis beam, recording planar images with distortion of the sample surface. For the generation of correct element distributions, these artifacts associated with the sample surface need to be eliminated by measuring the sample surface topography and applying suitable algorithms. For this purpose, the next generation of ToF-SIMS instruments will feature a scanning probe microscope directly implemented in the sample chamber which allows the performance of topography measurements in situ. This work presents the combination of 2D and 3D ToF-SIMS analysis with topographic measurements by ex situ techniques such as atomic force microscopy (AFM), confocal microscopy (CM), and digital holographic microscopy (DHM). The concept of the combination of topographic and ToF-SIMS measurements in a single representation was applied to organic and inorganic samples featuring surface structures in the nanometer and micrometer ranges. The correct representation of planar and distorted ToF-SIMS images was achieved by the combination of topographic data with images of 2D as well as 3D ToF-SIMS measurements, using either AFM, CM, or DHM for the recording of topographic data.     

Halide Anion Triggered Reactions of Michael Acceptors with Tropylium Ion

Tropylium bromide undergoes noncatalyzed, regioselective additions to a large variety of Michael acceptors. In this way, acrylic esters are converted into β-bromo-α-cycloheptatrienylpropionic esters. The reactions are interpreted as nucleophilic attack of bromide ions at the electron-deficient olefins and the approach of the tropylium ion to the incipient carbanion. Quantum chemical calculations were performed to elucidate the analogy to the amine- or phosphine-catalyzed Rauhut–Currier reactions. Subsequent synthetic transformations of the bromo-cycloheptatrienylated adducts are reported.     

Melt spinning of propylene carbonate‐plasticized poly(acrylonitrile)‐co‐poly(methyl acrylate)

The primary use of poly(acrylonitrile) (PAN) fibers, commonly referred to as acrylic fibers, is in textile applications like clothing, furniture, carpets, and awnings. All commercially available PAN fibers are processed by solution spinning; however, alternative, more cost‐effective processes like melt spinning are still highly desired. Here, the melt spinning of PAN‐co‐poly(methyl acrylate) (PMA) plasticized with propylene carbonate (PC) at 175°C is reported. The use of methyl acrylate (MA) as comonomer and PC as an external plasticizer renders the approach a combination of internal and external plasticization. Various mixtures of PAN and PC used in this work were examined by rheology, subjected to melt spinning, followed by discontinuous and continuous washing, respectively. The best fibers were derived from a PAN‐co‐PMA copolymer containing 8.1 mol‐% of MA having a number‐average molecular weight M _n of 34 000 g/mol, spun in the presence of 22.5 wt.‐% of PC. The resulting fibers were analyzed by scanning electron microscopy and wide‐angle X‐ray scattering (WAXS), and were subjected to mechanical testing.