Exponential decay towards equilibrium and global classical solutions for nonlinear reaction–diffusion systems

We consider a system of reaction–diffusion equations describing the reversible reaction of two species \({\mathcal{U}}\), \({\mathcal{V}}\) forming a third species \({\mathcal{W}}\) and vice versa according to mass action law kinetics with arbitrary stoichiometric coefficients (equal or larger than one). Firstly, we prove existence of global classical solutions via improved duality estimates under the assumption that one of the diffusion coefficients of \({\mathcal{U}}\) or \({\mathcal{V}}\) is sufficiently close to the diffusion coefficient of \({\mathcal{W}}\). Secondly, we derive an entropy entropy-dissipation estimate, that is a functional inequality, which applied to global solutions of these reaction–diffusion systems proves exponential convergence to equilibrium with explicit rates and constants.     

Synthesis of 1,1-Diacetyl-2-arylhydrazines

The reaction of arylhydrazines 1 with acetic anhydride in the presence of a catalytic amount of 4-(dimethylamino)pyridine leads to 1,1-diacetyl-2-arylhydrazines 4.     

Development of an ICP-HRIDMS method for accurate determination of traces of silicon in biological and clinical samples

An inductively coupled plasma-high resolution isotope dilution mass spectrometric (ICP-HRIDMS) method in combination with a microwave-assisted decomposition technique has been developed for the determination of traces of silicon in biological and clinical samples. A 30Si-enriched spike solution was used for the isotope dilution step. Decomposition of the samples was achieved by use either of HNO3 or a mixture of HNO3 and HF. By application of both methods of digestion to the same sample it was possible to differentiate between a poorly soluble silicate fraction and an HNO3-soluble silicon species. Traces of silicon were determined in different reference materials, which are not certified for this element, and in other biological and clinical samples. A concentration range of 1-600 microgram g(-1) was covered by the different samples. For homogeneous samples relative standard deviations of 2-4% were obtained. The detection limit was strongly affected by the blank. In this connection purification of water, used in the analytical procedure, was especially critical. The blank contribution of the ICP-MS instrument could be minimized by applying a nebulizer and a spray chamber made of PFA, a sapphire injection tube, and a silicon nitride torch. Under these conditions detection limits of 0.15 microgram g(-1) and 0.2 microgram g(-1) were obtained for the HNO3 and HNO3-HF digestion methods, respectively, when a sample weight of 0.5 g was used. With regard to expected silicon content this enables determination in almost all biological and clinical samples. The ICP-HRIDMS results were compared with those recently obtained in an interlaboratory study. This isotope-dilution method is an potential option for certification of silicon in reference materials, a method for which is still required.     

Stability of stationary states of non-local equations with singular interaction potentials

We study the large-time behaviour of a non-local evolution equation for the density of particles or individuals subject to an external and an interaction potential. In particular, we consider interaction potentials which are singular in the sense that their first derivative is discontinuous at the origin.For locally attractive singular interaction potentials we prove under a linear stability condition local non-linear stability of stationary states consisting of a finite sum of Dirac masses. For singular repulsive interaction potentials we show the stability of stationary states of uniformly bounded solutions under a convexity condition.Finally, we present numerical simulations to illustrate our results.     

Long-range 1H-15N heteronuclear shift correlation across wide F1 spectral windows

Long‐range ¹H? ¹⁵N heteronuclear shift correlation experiments at natural abundance are becoming more routinely utilized in the characterization of unknown chemical structures from a diverse range of sources including natural products and pharmaceuticals. Apart from the inherent challenges of the low gyromagnetic ratio and natural abundance of ¹⁵N, investigators are also occasionally hampered by having to deal with the wide spectral range inherent to various nitrogen functional groups, which can exceed 500 ppm. Earlier triple resonance cryoprobe designs typically provided 90° ¹⁵N pulses in the range of 35–40 µs, which did not allow the uniform excitation of wide F₁ spectral ranges for ¹H? ¹⁵N GHMBC spectra. We report the results obtained with a newly designed Bruker 600 MHz triple resonance TCI Micro CryoProbe? using methyl orange as a model compound, in which the ¹⁵N resonances are separated by > 450 ppm. Copyright © 2010 John Wiley & Sons, Ltd.     

Unimodular completion and direct flat representation in the context of differential flatness

Despite its significance in nonlinear controller design, the verification of the property of differential flatness and the identification of so-called flat outputs is a continuing research topic. However, the difficulty of both verification and identification heavily depends on the representation of the system. This contribution shows that flatness may be a far less complicated matter, depending on the choice of coordinates. (© 2016 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

High-energy gamma-rays accompanying the spontaneous fission of252Cf

Theγ-ray spectrum of²⁵²Cf(sf) was measured in the Darmstadt-Heidelberg Crystal Ball spectrometer, with a double ionization chamber mounted inside to detect the fission fragments. The measurement was aimed at a better understanding of an unusual component found in the high-energy region between 3 and 8 MeV, with fragment mass splits near symmetry. This component was proved to be predominantly emitted by the heavier fragment, to reach its highest intensity at a fragment mass split of 132:120, and to have an almost isotropic angular distribution. Calculations with the statistical code CASCADE could reproduce the main features.