Alkaline-Earth Metal Mediated Benzene-to-Biphenyl Coupling

Complex [(^DIPePBDI)Ca]₂(C₆H₆), with a C₆H₆²⁻ dianion bridging two Ca²⁺ ions, reacts with benzene to yield [(^DIPePBDI)Ca]₂(biphenyl) with a bridging biphenyl²⁻ dianion (^DIPePBDI=HC[C(Me)N-DIPeP]₂; DIPeP=2,6-CH(Et)₂-phenyl). The biphenyl complex was also prepared by reacting [(^DIPePBDI)Ca]₂(C₆H₆) with biphenyl or by reduction of [(^DIPePBDI)CaI]₂ with KC₈ in presence of biphenyl. Benzene-benzene coupling was also observed when the deep purple product of ball-milling [(^DIPPBDI)CaI(THF)]₂ with K/KI was extracted with benzene (DIPP=2,6-CH(Me)₂-phenyl) giving crystalline [(^DIPPBDI)Ca(THF)]₂(biphenyl) (52 % yield). Reduction of [(^DIPePBDI)SrI]₂ with KC₈ gave highly labile [(^DIPePBDI)Sr]₂(C₆H₆) as a black powder (61 % yield) which reacts rapidly and selectively with benzene to [(^DIPePBDI)Sr]₂(biphenyl). DFT calculations show that the most likely route for biphenyl formation is a pathway in which the C₆H₆²⁻ dianion attacks neutral benzene. This is facilitated by metal-benzene coordination.     

Detection of traces of oxidized and reduced sulfur compounds in small samples by combination of different high-performance liquid chromatography methods

Depending on the sulfur species, picomoles of different inorganic sulfur compounds can be detected and separated by HPLC in one arrangement in a sample volume less than 50 μl. The combination of fluorescence labelling of reduced inorganic sulfur compounds such as sulfide (S²⁻), sulfite(SO₃²⁻ and thiosulfate (S₂O₃²⁻) with monobromobimane followed by an extraction of elemental sulfur (S°) by chloroform treatment enables the detection of all mentioned sulfur compounds as well as sulfate (remaining aqueous phase) in the same sample. While the derivatized sulfur compounds could be detected by their fluorescence emission at 480 nm, elemental sulfur is identified by its UV absorption at 263 nm. Sulfate in the remaining aqueous phase is detected by HPLC with indirect UV detection at 254 nm. Detection ranges for the different sulfur compounds examined are as follows: sulfide (5 μM to 1.5 mM), sulfite (5 μM to 1.0 mM), thiosulfate (1 μM to 1.5 mM), elemental sulfur (2 μM to 32 mM) and sulfate (5 μM to >1 mM).     

Self-adjoint Analytic Operator Functions: Local Spectral Function and Inner Linearization

In this note we continue the study of spectral properties of a self-adjoint analytic operator function A(z) that was started in [5]. It is shown that if A(z) satisfies the Virozub–Matsaev condition on some interval Δ₀ and is boundedly invertible in the endpoints of Δ₀, then the ‘embedding’ of the original Hilbert space into the Hilbert space , where the linearization of A(z) acts, is in fact an isomorphism between a subspace of and . As a consequence, properties of the local spectral function of A(z) on Δ₀ and a so-called inner linearization of the operator function A(z) in the subspace are established.      

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.     

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)     

Application of a line implicit method to fully coupled system of equations for turbulent flow problems

For unstructured finite volume methods, we present a line implicit Runge–Kutta method applied as smoother in an agglomerated multigrid algorithm to significantly improve the reliability and convergence rate to approximate steady-state solutions of the Reynolds-averaged Navier–Stokes equations. To describe turbulence, we consider a one-equation Spalart–Allmaras turbulence model. The line implicit Runge–Kutta method extends a basic explicit Runge–Kutta method by a preconditioner given by an approximate derivative of the residual function. The approximate derivative is only constructed along predetermined lines which resolve anisotropies in the given grid. Therefore, the method is a canonical generalisation of point implicit methods. Numerical examples demonstrate the improvements of the line implicit Runge–Kutta when compared with explicit Runge–Kutta methods accelerated with local time stepping.     

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.     

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.     

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.

     

Investigation of solid-state reaction in Ag/Sn nanostructured thin films at room temperature

Diffusion intermixing processes in nanostructured Ag/Sn thin-film system at room temperature were investigated by means of secondary neutral mass Spectrometry depth profiling technique. As it was confirmed by X-ray diffraction too, the reaction started already in the as-deposited sample. Since the bulk diffusion was frozen at room temperature, the Ag₃Sn phase was formed along the grain boundaries (GBs), gradually consuming the interior of grains, and was grown perpendicular to the GBs. At the same time, formation and growth of a small compact reaction layer near the interface were observed and the shift of the bordering parallel interfaces was controlled by GB diffusion. From the kinetics of the diffusion process in the above two mechanisms, both the interface velocity in the diffusion-induced grain boundary motion regime as well as the coefficient of parabolic growth in the planar growth regime were determined.