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.

     

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.     

Double Pancake Versus Long Chalcogen–Chalcogen Bonds in Six‐Membered C,N,S‐Heterocycles

The double “pancake” bonding in the dimers of the six‐membered heterocycles 1,3‐dithia‐2,4,6‐triazine ( 4 ) and 1,3‐dithia‐2,4‐diazine ( 16 ) were investigated by means of high‐level quantum chemical calculations (B3LYP and CCSD(T)). It was found that the S–S dimers, 20 a and 27 , are not the most stable isomers, but the dimers showing short S?N ( 21 a ) and S?C ( 25 , 28 ) bonds. An investigation of the 5‐phenyl‐1,3‐dithia‐2,4,6‐triazine ( 4 b ) yields that the syn dimer with two S?S bonds (2.57 Å) is the most stable one. In this dimer, the phenyl groups are placed on top of each other. The additional dispersion energy of the phenyl rings causes a stabilization of the syn‐S–S (C_2v‐like) isomer. As a result, two weak albeit relevant single S?S bonds (2.57 Å) are predicted. These findings contradict the recently published concept of double “pancake” bonding in the dimer 4 b ₂.     

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.     

Pushing the Upper Limit of Nucleophilicity Scales by Mesoionic N-Heterocyclic Olefins

A series of mesoionic, 1,2,3-triazole-derived N-heterocyclic olefins (mNHOs), which have an extraordinarily electron-rich exocyclic CC-double bond, was synthesized and spectroscopically characterized, in selected cases by X-ray crystallography. The kinetics of their reactions with arylidene malonates, ArCH=C(CO₂Et)₂, which gave zwitterionic adducts, were investigated photometrically in THF at 20 °C. The resulting second-order rate constants k₂(20 °C) correlate linearly with the reported electrophilicity parameters E of the arylidene malonates (reference electrophiles), thus providing the nucleophile-specific N and s_N parameters of the mNHOs according to the correlation lg k₂(20 °C)=s_N(N+E). With 21<N<32, the mNHOs are much stronger nucleophiles than conventional NHOs. Some mNHOs even excel the reactivity of mono- and diacceptor-substituted carbanions. It is exemplarily shown that the reactivity parameters thus obtained allow to calculate the rate constants for mNHO reactions with further Michael acceptors and predict the scope of reactions with other electrophilic reaction partners including carbon dioxide, which gives zwitterionic mNHO-carboxylates. The nucleophilicity parameters N correlate linearly with a linear combination of the quantum-chemically calculated methyl cation affinities and buried volumes of mNHOs, which offers a valuable tool to tailor the reactivities of strong carbon nucleophiles.