Estimates of Fourier Coefficients of Siegel Cusp Forms for Subgroups and in the Case of Small Weight

Here we develop estimates for Fourier coefficients of Siegelcusp forms. First we consider the case of Siegel modular formsfor the full modular group     

Phosphane Copper(I) Dicarboxylates: Synthesis and Their Potential Use as Precursors for the Spin‐coating Process in the Deposition of Copper

Dicopper dicarboxylates [(R₃P)_mCuXCu(PR₃)_m] ( 5a , X = O₂CCO₂, R = Ph, m = 2; 5b , X = O₂CCO₂, R = nBu, m = 3) were prepared by treatment of [Cu₂O] ( 1a ) with HO₂CCO₂H ( 2a ) in presence of PR₃ ( 4a , R = Ph; 4b , R = nBu). A further synthesis approach to mono‐ and dicopper dicarboxylates is given using an electrolysis cell equipped with Cu electrodes and charged with acids H₂X and phosphanes R₃P. Without addition of a base mononuclear [(nBu₃P)_mCuXH] ( 6a , m = 3, XH = O₂CCO₂H, 6b , m = 3, XH = O₂CCH₂CO₂H, 6c , m = 3, XH = O₂CCH₂CH₂CO₂H, 6d , m = 2, XH = O₂C‐2‐C₅H₄N‐6‐CO₂H) was formed, whereas in presence of NEt₃ ( 3 ), the dicopper systems [(R₃P)_mCuXCu(PR₃)_m] ( 5a , X = O₂CCO₂, R = Ph, m = 2; 5b , X = O₂CCO₂, R = nBu, m = 3; 5c , X = O₂CCH₂CO₂, R = nBu, m = 3; 5d , X = O₂CCH₂CH₂CO₂, R = nBu, m = 3; 5e , X = O₂C‐2‐C₅H₄N‐6‐CO₂, R = nBu, m = 3) were produced. When 6a reacted with [(tmeda)Zn(nBu)₂] ( 7 ), trimetallic [(tmeda)Zn((nBu₃P)₃CuO₂CCO₂)₂] ( 8 ) was accessible. In this heterobimetallic complex the Zn(tmeda) unit spans two CuO₂CCO₂ entities. The molecular structures of 5a , 6a and 6d in the solid state were determined by single X‐ray structure analysis. Complexes 5a and 6a are monomers, whereas 6d creates in the solid state a linear open chain coordination polymer by hydrogen bridge formation. Characteristic for 6d is the somewhat distorted trigonal bipyrimidal arrangement around the copper atom with the nBu₃P ligands in axial and the C₅H₃NCO₂H oxygen and nitrogen atoms in equatorial positions. In 5a the oxalate connectivity binds in a μ‐1,2,3,4 fashion being part of a planar Cu₂(oxalate) core. TG studies of several mono‐ and dicopper dicarboxylates were carried out. Release of the PR₃ ligands is recognized and the remaining Cu‐(di)carboxylate unit decomposes to afford elemental copper and CO₂. The deposition of copper onto pieces of PVD‐Cu oxidized silicon wafers by applying the spin‐coating process and using 5c and 5d as precursors is discussed.     

Spectroscopy vs. Electrochemistry: Catalyst Layer Thickness Effects on Operando/In Situ Measurements

In recent years, operando/in situ X-ray absorption spectroscopy (XAS) has become an important tool in the electrocatalysis community. However, the high catalyst loadings often required to acquire XA-spectra with a satisfactory signal-to-noise ratio frequently imply the use of thick catalyst layers (CLs) with large ion- and mass-transport limitations. To shed light on the impact of this variable on the spectro-electrochemical results, in this study we investigate Pd-hydride formation in carbon-supported Pd-nanoparticles (Pd/C) and an unsupported Pd-aerogel with similar Pd surface areas but drastically different morphologies and electrode packing densities. Our in situ XAS and rotating disk electrode (RDE) measurements with different loadings unveil that the CL-thickness largely determines the hydride formation trends inferred from spectro-electrochemical experiments, therewith calling for the minimization of the CL-thickness in such experiments and the use of complementary thin-film control measurements.     

Bulk and surface properties of blends with semifluorinated polymers and block copolymers

The goal of the investigation presented here is the development of extremely hydrophobic materials based on polysulfone that can be applied, for instance, as fouling-resistant membrane materials. The concept used is the addition of semifluorinated polymers to polysulfone in suitable blend compositions. The influence of molecular parameters like chain structure of the semifluorinated polymer (segmented block copolymers, random copolymers) and segment molecular weight on the state of phase separation in the bulk and its influence on the surface properties have been systematically examined. It could be shown that segmented block copolymers with semifluorinated polyester segments with intermediate segment molecular weight are more suitable in blends with polysulfone than random polysulfone copolymers having semifluorinated side chains with respect to form homogeneous thin films (coatings) with highly non-wetting properties.     

Thermolysis of Geminal Diazido Malonamides: Simple Access to Tetrazoles and Functionalization of In Situ Formed Isocyanates

In recent years, the development of synthetic methods to afford nitrogen-containing heterocycles has become increasingly popular. Among these, tetrazoles – an important class of aromatic heterocycles – are of significant interest for example, in medicinal chemistry serving as important bioisosteres. Herein, we present a method to easily access C-substituted tetrazoles via thermolysis of geminal diazido malonamides. Formation and functionalization of in situ formed isocyanates and corresponding reactions were also studied.     

Evaporation‐Driven Self‐Assembly of Colloidal Silica Dispersion: New Insights on Janus Particles

The evaporation driven self‐assembly of novel colloidal silica Janus particles was evaluated by scanning electron microscopy in comparison to unfunctionalized silica particles. The cyclodextrin‐ and azobenzene‐modified compound was obtained utilizing Pickering emulsion approach, in which the particles were immobilized on solidified wax droplets and subsequently functionalized. Silica particles were modified with 3‐aminopropyl trimethoxysilane and afterward reacted with tosyl‐β‐CD or phenylazo(benzoic acid), respectively. Mesoscopic structures of the colloidal dispersions, as dried films from aqueous solution, have been investigated by scanning electron microscopy and dynamic light scattering. Interestingly, it has been observed that the Janus particles show a significantly different evaporation‐induced assembly than the unmodified particles.     

Variational integrators for open-loop and closed-loop optimal control of mechanical systems

Mechanical systems have structural properties, e.g. symplecticity, symmetry, and a specific energy behavior, which get lost in standard integration methods. Therefore, symplectic integration methods are used in simulation and control of mechanical systems. This paper combines two methods of the class of structure-preserving control methods, namely a recently developed feedback control method and open loop optimal control based on variational integrator discretization. The combination is applied to the benchmark example of a cart pendulum system. (© 2017 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Characterization of Mixing Efficiency in Polymerization Reactors Using Competitive-Parallel Reactions

Summary: In this article particular attention is paid to processes of mixing fluids with different viscosities relevant for polymerization where the reaction is fast and mixing is the limiting factor. Apart from this, mixing fluids with different viscosities is still one of the challenging tasks in industrial chemistry. Therefore, the characterization of mixing elements is another important topic. Two different multiple chemical reactions, based on the principle of competitive-parallel reactions, were used and compared to investigate (micro)mixing efficiency in polymerization reactors. The well-known Villermaux-Dushman reaction and the third Bourne reaction were applied. The observed product distribution represents the quantity of segregation of the fluid which gives in turn information about the dependency on certain parameters like type and speed of stirrer, dosing period, feed position, and the viscosity of the fluid. The results from semibatch and continuous stirred tank reactors and two different stirrers, Rushton and INTERMIG^® impeller, are discussed.