Asymmetric strecker synthesis of alpha-amino acids via a crystallization-induced asymmetric transformation using (R)-phenylglycine amide as chiral auxiliary

[reaction: see text]. Diastereoselective Strecker reactions based on (R)-phenylglycine amide as chiral auxiliary are reported. The Strecker reaction is accompanied by an in situ crystallization-induced asymmetric transformation, whereby one diastereomer selectively precipitates and can be isolated in 76-93% yield and dr > 99/1. The diastereomerically pure alpha-amino nitrile obtained from pivaldehyde (R1 = t-Bu, R2 = H) was converted in three steps to (S)-tert-leucine in 73% yield and >98% ee.     

Preparation,purification, and analysis of alkylated cyclodextrins

Methods of alkylation of α-, β- and γ-cyclodextrins have been optimized with regard to the parameters of reaction, degree of alkylation and yields. The analysis of the reaction mixtures and of the isolated single species has been performed by high temperature GC and HPLC. The phase systems of the preferably applied HPLC have been carefully adjusted by variation of both the stationary and mobile phases to the very different hydrophobicities of the various alkylated CD species which have been synthesized. Several partially or fully alkylated CD species were isolated from preparative scale HPLC separations in high purity.     

Synthese,Strukturuntersuchung und Reaktionen Phosphansubstituierter Derivate von Fe3(CO)9(μ3-CF)2

Syntheses, Structure Determination and Reactions of Phosphine Substituted Derivatives of Fe₃(CO)₉(μ₃-CF)₂ Photolysis of Fe₃(CO)₉(μ₃-CF)₂ 1 in the presence of acetonitrile 2a or benzoenitrile 2b results in the substitution of a single carbonyl ligand by a nitrile ligand yielding Fe₃(CO)₈(CH₃CN)(μ₃-CF)₂ 3a and Fe₃(CO)₈(C₆H₅CN)(μ₃-CF)₂ 3b, respectively. The acetonitrile ligand in 3a can be easily replaced by trimethyl-phosphine 4a or triphenylphosphine 4b . The monosubstituted compounds Fe₃(CO)₈(PR₃)(μ₃-CF)₂5, R = CH₃ a, R = C₆H₅, b are obtained as major products besides a small amount of the disubsituted products Fe₃(CO)₇(PR₃)₂(μ₃-CF)₂ 6. The structure of 5a has been elucidated by a single crystal X-ray structure determination. Thermal ligand substitution in 1, however, results in the formation of a mixture of mono-, disubstituted, and trisubstituted products, in which 6b is the major product for diphenylphosphine. 5a reacts with ethyne 7 forming a phosphine substituted diferra-allyl-cluster Fe₃(CO)₇(PR₃)(μ₃-CF)(μ₃? CF? CH? CH) 8. The structure of one isomere of 8 has been determinated by X-ray crystallography.     

Some contributions to the model order reduction of large scale non-linear electric circuits

Model order Reduction (MOR) has become an ubiquitous technique in the simulation of large-scale dynamical systems (i.e. 10⁴ and more equations). One technique for non-linear MOR is the trajectory piecewise-linear approach (TPWL) [1]. TPWL approximates a non-linear differential system by a weighted sum of linear systems which have a significantly reduced number of equations. One open question is which weight representations provide physical meaning of the weighted sum [2]. In this article we propose two representations. (© 2010 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

No Borel Connections for the Unsplitting Relations

We prove that there is no Borel connection for non‐trivial pairs of unsplitting relations. This was conjectured in [3].     

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.

     

On the gonality sequence of an algebraic curve

For any smooth irreducible projective curve X, the gonality sequence ${\{d_r \;| \; r \in \mathbb N\}}$ is a strictly increasing sequence of positive integer invariants of X. In most known cases d _r+1 is not much bigger than d _r . In our terminology this means the numbers d _r satisfy the slope inequality. It is the aim of this paper to study cases when this is not true. We give examples for this of extremal curves in ${{\mathbb P}^r}$ , for curves on a general K3-surface in ${{\mathbb P}^r}$ and for complete intersections in ${{\mathbb P}^3}$ .