Nucleophilic Aromatic Substitution at Benzene with Powerful Strontium Hydride and Alkyl Complexes

Key to the isolation of the first alkyl strontium complex was the synthesis of a strontium hydride complex that is stable towards ligand exchange reactions. This goal was achieved by using the super bulky β‐diketiminate ligand ^DIPePBDI (CH[C(Me)N‐DIPeP]₂, DIPeP=2,6‐diisopentylphenyl). Reaction of ^DIPePBDI‐H with Sr[N(SiMe₃)₂]₂ gave (^DIPePBDI)SrN(SiMe₃)₂, which was converted with PhSiH₃ into [(^DIPePBDI)SrH]₂. Dissolved in C₆D₆, the strontium hydride complex is stable up to 70 °C. At 60 °C, H–D isotope exchange gave full conversion into [(^DIPePBDI)SrD]₂ and C₆D₅H. Since H–D exchange with D₂ is facile, the strontium hydride complex served as a catalyst for the deuteration of C₆H₆ by D₂. Reaction of [(^DIPePBDI)SrH]₂ with ethylene gave [(^DIPePBDI)SrEt]₂. The high reactivity of this alkyl strontium complex is demonstrated by facile ethylene polymerization and nucleophilic aromatic substitution with C₆D₆, giving alkylated aromatic products and [(^DIPePBDI)SrD]₂.     

Chemo-, regio-, and stereoselective cyclizations of 1,3-bis(trimethylsilyloxy)-1,3-butadienes with alpha-chloroacetic acid chlorides and alpha-chloroacetic acetals

Treatment of 1,3-bis(trimethylsilyloxy)-1,3-butadienes with alpha-chlorocarboxylic acid chlorides resulted in chemo- and regioselective formation of 6-chloro3,5-dioxo esters, which were regioselectively converted into functionalised 3(2H)furanones. Chemo- and regioselective condensation of 1,3-bis(trimethylsilyloxy)-1,3-butadienes with alpha-chloroacetic dimethyl acetal afforded 6-chloro-5-methoxy-3-oxo esters, which could be regio- and stereoselectively transformed into 2-alkylidene-4-methoxytetrahydrofurans.     

Regio- and stereoselective synthesis of Nor-nonactinic acid derivatives--kinetic reaction control in the Lewis acid mediated domino reaction of 1,3-dicarbonyl dianions with 1-bromo-2,3-epoxypropanes

Reaction of 1,3-dicarbonyl dianions with epibromohydrin derivatives results in formation of functionalized 2-alkylidene-5-hydroxymethyltetrahydrofurans. These reactions proceed by chemoselective attack of the dianion onto the carbon attached to the bromine atom and subsequent nucleophilic attack of the resultant monoanion onto the epoxide. The cyclization products, which were formed with very good regio- and stereoselectivities, are of pharmacological relevance and represent versatile building blocks for the synthesis of natural products.     

Ortho effect in the mass spectrometric behaviour of N(pyrimidin-4-yl)aminobenzoic acids and their methyl esters

Ortho-. meta- and para-isomers of N-(pyrimidin-4-yl)aminobenzoic acid and their methyl esters were investigated by electron impact mass Spectrometry. Their fragmentation was found to be strongly dependent on the position of the substituent in the aminobenzoic moiety. Two different kinds of ortho effect were studied and confirmed with the aid of deuterium-labelled derivatives.     

Two-level hierarchically preconditioned conjugate gradient methods for solving linear elasticity finite element equations

In this paper we study and compare some preconditioned conjugate gradient methods for solving large-scale higher-order finite element schemes approximating two- and three-dimensional linear elasticity boundary value problems. The preconditioners discussed in this paper are derived from hierarchical splitting of the finite element space first proposed by O. Axelsson and I. Gustafsson. We especially focus our attention to the implicit construction of preconditioning operators by means of some fixpoint iteration process including multigrid techniques. Many numerical experiments confirm the efficiency of these preconditioners in comparison with classical direct methods most frequently used in practice up to now.     

On the Loewner problem in the class

Loewner's theorem on boundary interpolation of functions is proved under rather general conditions. In particular, the hypothesis of Alpay and Rovnyak (1999) that the function , which is to be extended to an function, is defined and continuously differentiable on a nonempty open subset of the real line, is replaced by the hypothesis that the set on which is defined contains an accumulation point at which satisfies some kind of differentiability condition. The proof of the theorem in this note uses the representation of functions in terms of selfadjoint relations in Pontryagin spaces and the extension theory of symmetric relations in Pontryagin spaces.

     

Dual-primal isogeometric tearing and interconnecting solvers for multipatch continuous and discontinuous Galerkin IgA equations

We present results regarding fast and robust solvers for equations arising from continuous and discontinuous Galerkin discretization of heterogeneous diffusion problems in the context of Isogeometric Analysis. The solvers considered belong to the class of non-overlapping domain decomposition methods which use tearing and interconnection strategies. (© 2016 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Functional A Posteriori Error Estimates for Time-Periodic Parabolic Optimal Control Problems

This article is devoted to the a posteriori error analysis of multiharmonic finite element approximations to distributed optimal control problems with time-periodic state equations of parabolic type. We derive a posteriori estimates of the functional type, which are easily computable and provide guaranteed upper bounds for the state and co-state errors as well as for the cost functional. These theoretical results are confirmed by several numerical tests that show high efficiency of the a posteriori error bounds.     

Adjoint Linear Systems on Normal Log Surfaces

We prove a Reider type theorem for separating any cluster by an adjoint system to a pseudoeffective divisor on a normal surface. As a corollary we get a Reider type theorem for adjoint linear systems (to a nef Q-divisor) on normal log surfaces. This theorem is new even for smooth surfaces.