Spirocyclic Boraamidinate Complexes of Lanthanide(III) Metals

The reaction of Li₂[Phbam^Dipp] (Phbam^Dipp = PhB(NDipp)₂; Dipp = 2,6‐iPr₂C₆H₃) with lanthanum(III) triiodides LnI₃(THF)_3.5 (Ln = La, Sm) in THF produces complexes of the type [Li(THF)₄]₂[(Phbam^Dipp)₂LnI], which were characterized in solution by multinuclear NMR spectroscopy and in the solid state by single‐crystal X‐ray structural determinations. The ion‐separated complexes are comprised of a spirocyclic anion in which two Phbam^Dipp ligands and an iodide ion are linked to the five‐coordinate metal atom; charge balance is provided by two tetrasolvated lithium ions [Li(THF)₄]⁺.     

Lipschitz Continuous and Compact Composition Operators in Hyperbolic Classes

Natural metrics in the hyperbolic α-Bloch-, weighted Dirichlet- and Q _p -classes are introduced, and these classes are shown to be complete metric spaces with respect to the corresponding metrics. Then Lipschitz continuous and compact composition operators C _φ (f) = f ◦ φ acting from the hyperbolic α-Bloch-class to the hyperbolic weighted Dirichlet- or Q _p -class are characterized by conditions depending on the symbol φ only.     

Layer-by-layer deposition of Ti-4,4′-oxydianiline hybrid thin films

Features of the two thin-film techniques, atomic layer deposition (ALD) and molecular layer deposition (MLD), are combined to build up a stable novel inorganic-organic hybrid material of the (-Ti-N-C₆H₄-O-C₆H₄-N-)_n type, deposited from successive pulses of TiCl₄ and 4,4′-oxydianiline precursors. Depositions in the temperature range of 160-230 °C resulted in unstable films, while the films obtained in the temperature range of 250-490 °C were found stable in atmospheric air. The growth rate increased with increasing temperature, from 0.3 Å per cycle at 160 °C to 1.1 Å per cycle at 490 °C.     

Bond stretching and redox behavior in coinage metal complexes of the dichalcogenide dianions [(SPh2P)2CEEC(PPh2S)2]2- (E=S, Se): diradical character of the dinuclear copper(I) complex (E=S)

The metathetical reactions of a) [Li(tmeda)]₂[(S)C(PPh₂S)₂] (Li₂? 3 c ) with CuCl₂ and b) [Li(tmeda)]₂[(SPh₂P)₂CSSC(PPh₂S)₂] (Li₂? 4 c ) with two equivalents of CuCl both afford the binuclear Cu^I complex {Cu₂[(SPh₂P)₂CSSC(PPh₂S)₂]} ( 5 c ). The elongated (C)S? S(C) bond (ca. 2.54 and 2.72 Å) of the dianionic ligand observed in the solid‐state structure of 5 c indicate the presence of diradical character as supported by theoretical analyses. The treatment of [Li(tmeda)]₂[(SPh₂P)₂CSeSeC(PPh₂S)₂] (Li₂? 4 b ) and Li₂? 4 c with AgOSO₂CF₃ produce the analogous Ag^I derivatives, {Ag₂[(SPh₂P)₂CEEC(PPh₂S)₂]} ( 6 b , E=Se; 6 c , E=S), respectively. The diselenide complex 6 b exhibits notably weaker Ag? Se(C) bonds than the corresponding contacts in the Cu^I congeners, and the ³¹P NMR data suggest a possible isomerization in solution. In contrast to the metathesis observed for Cu^I and Ag^I reagents, the reactions of Li₂? 4 b and Li₂? 4 c with Au(CO)Cl involve a redox process in which the dimeric dichalcogenide ligands are reduced to the corresponding monomeric dianions, [(E)C(PPh₂S)₂]^2? ( 3 b , E=Se; 3 c , E=S), and one of the gold centers is oxidized to generate the mixed‐valent Au^I/Au^III complexes, {Au[(E)C(PPh₂S)₂]}₂ ( 7 b , E=Se; 7 c , E=S), with relatively strong aurophilic Au^I???Au^III interactions. The new compounds 5 c , 6 b , c and 7 b , c are characterized in solution by NMR spectroscopy and in the solid state by X‐ray crystallography ( 5 c , 6 b , 7 b and 7 c ) and by Raman spectroscopy ( 5 c and 6 c ). The UV‐visible spectra of coinage metal complexes of the type 5 , 6 and 7 are discussed in the light of results from theoretical analyses using time‐dependent density functional theory.     

Anthranilamides with quinoline and β-carboline scaffolds: design,synthesis, and biological activity

Molecular Diversity - In the present study, we report the design and synthesis of novel amide-type hybrid molecules based on anthranilic acid and quinoline or β-carboline heterocyclic...     

Phenomenological and numerical modelling of short fibre reinforced cementitious composites

In this paper, a constitutive model for short fibre reinforced cementitious composites will be presented. This model is based on the St. Venant–Kirchhoff model, which is a special case of a hyperelastic material. This model is refined to include the fibre orientation distribution. Numerical FEM simulations with the developed constitutive model and fracture simulations using the discrete element method are presented. The outcomes of these numerical methods demonstrate how important it is to monitor and further to control the fibre orientation distribution during the manufacturing process. As the manufacturing process might involve casting, as, e.g., in the case of steel fibre reinforced concrete, an outlook on simulations of the manufacturing process in order to predict and to control the fibre orientation distribution is given.     

Characterization of dynamical systems under noise using recurrence networks: Application to simulated and EEG data

In this letter, we study the influence of observational noise on recurrence network (RN) measures, the global clustering coefficient (C) and average path length (L  ) using the Rössler system and propose the application of RN measures to analyze the structural properties of electroencephalographic (EEG) data. We find that for an appropriate recurrence rate (RR>0.02$RR>0.02$) the influence of noise on C can be minimized while L is independent of RR for increasing levels of noise. Indications of structural complexity were found for healthy EEG, but to a lesser extent than epileptic EEG. Furthermore, C performed better than L in case of epileptic EEG. Our results show that RN measures can provide insights into the structural properties of EEG in normal and pathological states.     

Causal coupling inference from multivariate time series based on ordinal partition transition networks

Nonlinear Dynamics - Identifying causal relationships is a challenging yet crucial problem in many fields of science like epidemiology, climatology, ecology, genomics, economics and neuroscience,...     

A fast Fourier transform based direct solver for the Helmholtz problem

This article is devoted to the efficient numerical solution of the Helmholtz equation in a two‐ or three‐dimensional (2D or 3D) rectangular domain with an absorbing boundary condition (ABC). The Helmholtz problem is discretized by standard bilinear and trilinear finite elements on an orthogonal mesh yielding a separable system of linear equations. The main key to high performance is to employ the fast Fourier transform (FFT) within a fast direct solver to solve the large separable systems. The computational complexity of the proposed FFT‐based direct solver is $\mathrm{??}(N\log N)$ operations. Numerical results for both 2D and 3D problems are presented confirming the efficiency of the method discussed.     

Toeplitz operators on the space of analytic functions with logarithmic growth

Continuous and compact Toeplitz operators for positive symbols are characterized on the space of analytic functions with logarithmic growth on the open unit disc of the complex plane. The characterizations are in terms of the behaviour of the Berezin transform of the symbol. The space was introduced and studied by Taskinen. The Bergman projection is continuous on this space in a natural way, which permits to define Toeplitz operators. Sufficient conditions for general symbols are also presented.