Biocatalytic deuterium- and hydrogen-transfer using over-expressed ADH-'A': enhanced stereoselectivity and 2H-labeled chiral alcohols

Employing the over-expressed highly organic solvent tolerant alcohol dehydrogenase ADH-'A' from Rhodococcus ruber DSM 44541, versatile building blocks, which were not accessible by the wild type catalyst, were obtained in > 99% e.e.; furthermore, employing d8-2-propanol as deuterium source, stereoselective biocatalytic deuterium transfer was made feasible to furnish enantiopure deuterium labeled sec-alcohols on a preparative scale employing a single enzyme.     

Rank one transformations with singular spectral type

We show that a certain class of measures arising from generalized Riesz products is singular. In particular, cutting and stacking (i.e. rank one) transformations whose cuts do not grow too rapidly, have singular maximal spectral type. The precise condition is , wherew _h is the number of cuts at stagen. Supported by a Canada NSERC grant. Supported by an NSF grant.     

Anwendungen des Kationenaustausches in der Analyse

Zusammenfassung Die unterschiedlichen Affinitäten der Kationen zu dem Austauscherharz Wofatit KS werden untersucht und relative Zahlen dafür angegeben. Die dabei festgestellten größeren Unterschiede zwischen Lithium, Natrium und Kalium sowie zwischen Cadmium und Zink werden benutzt, um durch Eluieren derartiger gemischter Belegungen aus einer Austauschersäule mit verdünnter Säure diese Kationen voneinander zu trennen. Eine hierfür entwickelte Leitfähigkeitsmeßapparatur gestattet es, derartige Trenndiagramme registrierend aufzunehmen, die nach voraufgegangener Eichung einer quantitativen Auswertung zugänglich sind.I. M. Mitteilung diese Z. 132, 241 (1951); II. Mitteilung diese Z. 132, 321 (1951).Herrn Dr. Krüger, dem Leiter des Untersuchungslaboratoriums der Chemischen Werke Hüls, G. m. b. H., bin ich für seine wertvollen Anregungen und Ratschläge, durch die die vorliegende Arbeit stark gefördert wurde, zu großem Dank verpflichtet.     

Adaptive eigenvalue computation: complexity estimates

This paper is concerned with the design and analysis of a fully adaptive eigenvalue solver for linear symmetric operators. After transforming the original problem into an equivalent one formulated on ℓ ₂, the space of square summable sequences, the problem becomes sufficiently well conditioned so that a gradient type iteration can be shown to reduce the error by some fixed factor per step. It then remains to realize these (ideal) iterations within suitable dynamically updated error tolerances. It is shown under which circumstances the adaptive scheme exhibits in some sense asymptotically optimal complexity. This research was supported in part by the Leibniz Programme of the DFG, by the SFB 401 funded by DFG, the DFG Priority Program SPP1145 and by the EU NEST project BigDFT.     

A Germylene Stabilized by Homoconjugation

The synthesis of a bicyclic germylene from the reaction of a germole dianion with hafnocene dichloride is reported. This germylene is stabilized by a homoconjugative interaction of the dicoordinated germanium atom with a remote C=C double bond. First reactivity studies revealed its nucleophilic character and resulted in the synthesis of bimetallic hafnium/iron and hafnium/tungsten complexes with a germylene group linker.     

Tensor Networks and Hierarchical Tensors for the Solution of High-Dimensional Partial Differential Equations

Hierarchical tensors can be regarded as a generalisation, preserving many crucial features, of the singular value decomposition to higher-order tensors. For a given tensor product space, a recursive decomposition of the set of coordinates into a dimension tree gives a hierarchy of nested subspaces and corresponding nested bases. The dimensions of these subspaces yield a notion of multilinear rank. This rank tuple, as well as quasi-optimal low-rank approximations by rank truncation, can be obtained by a hierarchical singular value decomposition. For fixed multilinear ranks, the storage and operation complexity of these hierarchical representations scale only linearly in the order of the tensor. As in the matrix case, the set of hierarchical tensors of a given multilinear rank is not a convex set, but forms an open smooth manifold. A number of techniques for the computation of hierarchical low-rank approximations have been developed, including local optimisation techniques on Riemannian manifolds as well as truncated iteration methods, which can be applied for solving high-dimensional partial differential equations. This article gives a survey of these developments. We also discuss applications to problems in uncertainty quantification, to the solution of the electronic Schrödinger equation in the strongly correlated regime, and to the computation of metastable states in molecular dynamics.