On the lattice structure of kernel operators

Consider the lattice of bounded linear operators on the space of Borel measures on a Polish space. We prove that the operators which are continuous with respect to the weak topology induced by the bounded measurable functions form a sublattice that is lattice isomorphic to the space of transition kernels. As an application we present a purely analytic proof of Doob's theorem concerning stability of transition semigroups.     

High-pressure in situ 129Xe NMR spectroscopy and computer simulations of breathing transitions in the metal-organic framework Ni2(2,6-ndc)2(dabco) (DUT-8(Ni))

Recently, we have described the metal-organic framework Ni(2)(2,6-ndc)(2)(dabco), denoted as DUT-8(Ni) (1) (DUT = Dresden University of Technology, 2,6-ndc = 2,6-naphthalenedicarboxylate, dabco = 1,4-diazabicyclo[2.2.2]octane). Upon adsorption of molecules such as nitrogen and xenon, this material exhibits a pronounced gate-pressure effect which is accompanied by a large change of the specific volume. Here, we describe the use of high-pressure in situ (129)Xe NMR spectroscopy, i.e., the NMR spectroscopic measurements of xenon adsorption/desorption isotherms and isobars, to characterize this effect. It appears that the pore system of DUT-8(Ni) takes up xenon until a liquid-like state is reached. Deeper insight into the interactions between the host DUT-8(Ni) and the guest atom xenon is gained from ab initio molecular dynamics (MD) simulations. van der Waals interactions are included for the first time in these calculations on a metal-organic framework compound. MD simulations allow the identification of preferred adsorption sites for xenon as well as insight into the breathing effect at a molecular scale. Grand canonical Monte Carlo (GCMC) simulations have been performed in order to simulate adsorption isotherms. Furthermore, the favorable influence of a sample pretreatment using solvent exchange and drying with supercritical CO(2) as well as the influence of repeated pore opening/closure processes, i.e., the "aging behavior" of the compound, can be visualized by (129)Xe NMR spectroscopy.     

Polymorphism in ferroic functional elements

The present study describes an approach for the scale-bridging modeling of ferroic materials as functional elements in micro- and nanoelectronic devices. Ferroic materials are characterized by temperature-dependent complex ordering phenomena of the internal magnetic, electronic, and structural degrees of freedom with several involved length and time scales. Hence, the modelling of such compounds is not straightforward, but relies on a combination of electronic-structure-based methods like ab-initio and density-functional schemes with classical particle-based approaches given by Monte-Carlo simulations with Ising, lattice-gas, or Heisenberg Hamiltonians, which incorporate material-specific parameters both from theory and experiment. The interplay of those methods is demonstrated for device concepts based on electroceramic materials like ferroelectrics and multiferroics, whose functionality is closely related with their propensity towards structural and magnetic polymorphism. In the present case, such scale-bridging techniques are employed to aid the development of an organic field effect transistor on a ferroelectric substrate generated by the self-assembly of field-sensitive molecules on the surfaces of ferroic oxides. Electronic-structure-based methods yield the microscopic properties of the oxide, the surface, the molecules, and the respective interactions. They are combined with classical particle-based methods on a scale-hopping basis. This combination allows to study the morphology evolution during the self-assembly of larger adsorbate arrays on the (defective) oxide surface and to investigate the interplay of low-temperature magnetic ordering phenomena with the ferroelectric functionality at higher temperatures in multiferroic oxides like the hexagonal manganites. The combination of density-functional data with classical continuum modelling also yielded a model Hamiltonian for the quick determination of the properties of a gate structure based on bio-functionalized carbon nanotubes.     

Zur Optimierung der emissionsspektrometrischen Mineralienanalyse

Zusammenfassung Nach der Diskussion verschiedener Methoden zur schnellen Analyse mineralischer Stoffe mit der Emissionsspektrometrie im lichtoptischen Bereich wird über Verbesserungen an einem Verfahren mit Aufschlu\ und nachfolgendem Herstellen einer Pastille berichtet. Die Wahl geeigneter Bezugs- und Analysenlinien wird diskutiert und ein Verfahren zur Eichung des Gerätes mit synthetischen Substanzgemischen geschildert. Der Zeitbedarf für eine Einzelbestimmung mit Probenaufbereitung, Aufschlu\, Vermahlen mit Graphit, Herstellen eines Pre\lings und zweimaliger spektrometrischer Untersuchung liegt bei etwa 6 min.

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Summary Different methods for the rapid analysis of mineral substances by emission spectrometry in the visible region are discussed and improvements are reported for a method employing decomposition and subsequent preparation of a pellet. The selection of suitable reference and analysis lines is discussed and a procedure is described for the calibration of the apparatus by means of synthetic mixtures of substances. The time required for a single determination inclusive of sample preparation, decomposition, grinding together with graphite, preparation of a pellet and two spectrometric examinations is about 6 min.

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Den Herren A. Bellmann, H. Brück und L. Krämer danke ich für Anregungen und sorgfältige Ausführung von Versuchen.     

Theoretical investigation of amplitudes and phases in exciton reflection spectra

The phase difference Δ between the p and s component of light reflected from a semiconductor in the spectral region of the 1-S exciton is theoretically investigated. The exciton polariton theory used leads to a very good agreement with experimental spectra. No additional assumptions, such as ABC (additional boundary condition) or dead layer are necessary.